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... Paper ID #37483 A Path to Computational Thinking and Computer Programming through Physics Problems Robert H Mason (Professor) I graduated with a B.S. in physics (1995) and an M.S. in physics (1997) from Southern Illinois University, Edwardsville. I taught as an adjunct instructor at various schools around Edwardsville for the 1997-1998 academic year before accepting a full-time position at Moberly Area Community College in Moberly, MO. After a year in Missouri I took my current position at Olney Central College in Olney, IL (1999). Over the last 23 years I have taught a wide range of courses; mathematics, physics, physical science, and pre-engineering. I found the pre-engineering courses to be especially rewarding due to the diversity and the rigor of the material. In 2016 I completed an M.A. in math education at Eastern Illinois University because of a keen interest in math as well as the need for a program that was flexible enough to accommodate my teaching schedule. This was a good decision as the focus on pedagogy was invaluable in the classroom, even with my experience. around that same time I became aware of a group called Partnership for Integration of Computation into Undergraduate Physics (PICUP) and started attending workshops. My experiences motivated me to pursue my doctorate in applied physics at Southern Illinois University, Carbondale, beginning in 2020. It is my work at SIUC that has introduced me to the ASEE. Hansika Sirikumara Hansika Sirikumara, Ph.D., is an Assistant professor of Physics and Engineering at E. S. Witchger School of Engineering, Marian University Indianapolis. She completed her MS and PhD degrees from Southern Illinois University Carbondale. Her research expertise/interests are in engineering material properties for semiconductor device applications using computational methods. American Society for Engineering Education, 2022 Powered by www.slayte.com A Path to Computational Thinking and Computer Programming through Disciplinary-Based Problems Robert H Mason Olney Central College, Olney, IL and Schools of Physics and Applied Physics, Southern Illinois University Carbondale, Carbondale, IL Dr. Hansika I Sirikumara E.S. Witchger School of Engineering, Marian University, Indianapolis, IN Dr. Thushari Jayasekera School of Physics and Applied Physics, Southern Illinois University Carbondale, Carbondale, IL Abstract We propose a novel approach to improve computational thinking (CT) and computer programming (CP) via a disciplinary-based problem solving approach. We hypothesize that the syntax needed for writing a computer code can be introduced through support programs in problem solving. This article demonstrates this approach through the problem of non-linear pendulum, a familiar problem solved in most engineering and physics classes. It is basically focused on implementing numerical techniques for solving ordinary differential equations (ODEs). Instead of using a syntax-based teaching approach, support programs can be used to identify the required coding elements. We envision that this approach can be transferable to many problems in STEM classes to motivate students towards computer programming. 1 Introduction The proliferation of computer science into STEM fields has resulted in a high demand for STEM jobs in computing. Thus, it is crucial that students majoring in STEM subjects other than Computer Science (non-CS) should have easily accessible resources to develop CT and practice CP, which is a skill they should develop like reading, writing, and solving algebraic equations. 1,2,3,4. We hypothesize that the use of support programs through the problem solving instead of traditional syntax-based approach for teaching computer programming for those who have no prior-knowledge of computer programming. 2 Explanation of the Problem and Computational Details The dynamics of the simple pendulum consisting of a mass, m attached to the end of a massless string of length L is given by 5: d2 g = sin dt2 L Notice that we use t as the time, which is measured in seconds. By the conversion, t t , above equation changes to: l/g d2 = sin dt2 (1) Figure 1: (a)Schematic diagram of a simple pendulum. (b) (blue) and (red) as a function of time (c) the phase space diagram, i. e. angular velocity vs . Now t is measured in terms of p l/g ,i.e. t in the above equation is dimensionless. This is a non-linear second order ordinary differential equation, which is hard to be solved analytically. In the small angle approximation, for which, sin d2 = dt2 , which has a solution of the form, = 0 sin(t + ), where 0 and are determined using the boundary conditions. If the pendulum bob is released at an angle 0 with a zero velocity, 0 is the initial angle and is zero. Here, is a periodic function of t. We can clearly visualize the periodic nature in vs t graph. Additionally, we can plot the phase space diagram, which also shows the periodic nature of the motion as shown in Fig. 1. The phase space diagram shown in the Fig. 1 shows that the pendulum bob passes the same position with same speed, which assures the periodic motion. At time t = 0, pendulum bob is released from rest at an angle 0 = 10o . This starting position is marked by A in the plots. Position B is the central position (where = 0), when the pendulum bob passes with the highest speed and reach the maximum angle (i.e. 0 ) at position C. The speed of the pendulum bob reaches zero at position C and changes the direction of motion. It will reach the original position A via the central point D. The dynamics of the simple pendulum for large angles described by eq. 1 is a non-linear second order ODE, which can be solved using numerical approaches. Here, students can be guided to numerically solve the first order ODEs and second order ODEs using support programs. Students will be guided to improve CT through applying the numerical techniques to solve non-linear pendulum. 3 Numerical Solutions to First Order ODEs Support Program Solve the following equation numerically with the boundary condition at t=0, N=3000. Take = 5s. dN N = (2) dt Write a computer code to plot N as a function of t, using different numerical algorithms, and compare the solution with the analytic solution. This equation has an analytic solution 7 , N (t) = N0 e(t/ ) where the constant, N0 is determined using the boundary condition of the physical problem, and is a characteristic time constant of the system. Even though this equation has an analytic solution, students can be guided to learn numerical solutions to first order ODEs using this problem. First the independent axis t will be descretized for the time axis tinitial to tf inal with a step size t. Figure 2: The axis of independent variable is discretized in steps of t. The goal of a numerical algorithm is to evaluate N (t + t) for all grid points. There are different algorithms to do this task. Here We will use two numerical algorithms without their mathematical derivation, which can be found elsewhere 6 . Euler Algorithm N (t + t) relates to N (t)) as N (t + t) = N (t) + tf (N (t), t), Fourth Order Runge-Kutta (RK4) Method finds, N (t + t) = N (t) + where, 1 (k1 + 2k2 + 2k3 + k4 ) , 6 k1 = tf (N, t) 1 1 k2 = tf (N + k1 , t + t) 2 2 1 1 k3 = tf (N + k2 , t + t) 2 2 k4 = tf (N + k3 , t + t) where f (N, t) = (N (t))/ for this problem defined by eq. 2. Implementation of the algorithm The numerical algorithms can be implements in python as: # Input Parameters tau=1 # Known for the given problem N=3000 # given - the N at time t=0 tinitial=0.0 tfinal=3.0 # Notice this t is now given in deltat=0.05 # Defined by the programmer, which must assure the convergence of the results. import numpy as np tlist=np.arange(tinitial,tfinal,deltat) # Numerical Solutions -Euler Algorithm Nlist=[] # creating a list for storing the data def fxn(N,t): return -N/tau for t in tlist: Nlist.append(N) N+=deltat*exp(-t/tau) # Plotting Data import matplotlib.pyplot as plt plt.plot(tlist,Nlist) plt.show() The results for eq. 2 , displayed in Fig. 3, show the increase in the accuracy for different algorithms. Figure 3: Analytical and Numerical solutions for the eq. 2 In a similar way, RK4 algorithm can be implemented in 4 steps as follows. # RK4 Algorithm: for t in tlist: Nlist.append(N) k1 = t fxn(N,t) k2 = t fxn(N+ 12 k1, t + 12 t) k3 = t fxn(N+ 12 k2, t + 12 t) k4 = t fxn(N+k3, t+t) N + = 16 (k1 + 2k2 + 2k3 + k4) 4 Numerical Solutions to Coupled First Order ODEs Support Program (Numerical solutions to coupled first order ODEs.) Consider the following two coupled ODEs. dx = 0.3x + 0.8y dt and dy = 0.5x 0.25y dt (3) which can be written in the matrix form:      x 0.3 0.8 x d = AX = which can be written as dtd X dt y 0.5 0.25 y This set of equation has a solution: x(t)= a11 e1 t + a21 e2 t and y(t) = a12 e1 t + a22 e2 t where 1 and 2 are the eigenvalues of the matrix A and the coefficients (aij ) are its eigenvectors. The constants and are determined by the boundary conditions. Write a program to numerically solve the above two ODEs. Plot the solutions along with the analytic solution for few selected initial conditions. Figure 4: Solution to the coupled differential equation (eq.3 ) with 4 different sets of boundary conditions. The solid lines are the analytic solution and the dotted lines are the numerical solutions Figure 4 shows the results of eq.3, which were numerically solved for different boundary conditions: (a) x=-7,y=7 (red), (b) x=7,y=-6.5 (blue), (c) x=-7,y=4 (green) and (d) x=8,y=-4 (orange). The implementation of the algorithm (Euler) is shown below. import numpy as np # Input Parameters: x,y=-7,7 tinitial,tfinal=0,10.0 deltat=0.01 # Diescretization of time axis tlist=np.arange(tinitial,tfinal,deltat) def fxnxy(x,y): fxnx=-0.3x+0.8y fxny=0.50x-0.25y return fxnx,fxny # Euler Algorithm xlist=[] ylist=[] for t in tlist: xlist.append(x) ylist.append(y) x+=t * fxnxy[0] y+=t * fxnxy[1] # Euler Algorithm from matplotlib import pylab as pl pl.plot(xlist,ylist) pl.show() 5 Numerical Solutions to Non-Linear Simple Pendulum Dynamics of the non-linear pendulum is described by a second order ODE given in eq. 1. A common approach to numerically solve a second order ODE is to consider it as two coupled first order ODEs. The eq. 1 can be considered as: d d = and = sin (4) dt dt These two first order ODEs are coupled through time. We can solve coupled first order ODEs using any algorithm discussed in the previous section. The assignment of applying the numerical solutions to solve eq. 1 will improve students Computational Thinking. The angular displacement () vs. time (t) and the phase space diagram for the results obtained for pendulum with initial angle = 100 using t = 0.01 and t = 0.001 plotted with analytic solutions are shown in Fig. 5. It appears that (Fig.6) when we use a time step, t = 0.01, numerical results generated with RK4 algorithm agree with the analytic solution for small angles. However, Euler method does not seem to converge with t = 0.01. Figure 5: Numerical and Analytical solutions to nonlinear simple pendulum with initial angle 0 = 100 . Upper and lower panels show the results obtained with two time steps t = 0.01 and t = 0.001. Figure 6: Numerical and Analytical solutions to non-linear simple pendulum with initial angle 0 = 100 using t = 0.01 Numerical Instability: When we analyze the solution for the longer time period (Fig. 6), we note that the solutions with Euler method becomes highly unstable. This numerical instability is a result from accumulation of error through the computation, which has been discussed. We can conclude that the Euler method is not suitable for solving the nonlinear simple pendulum. Previous studies have used a improved Euler-Cromer algorithm which fixes that numerical instability. However, we did not include that in this discussion. This exercise clearly demonstrate the importance of checking the convergence of all calculation parameters before we produce realistic results. Now we will move on with RK4 algorithm. The results of nonlinear simple pendulum for large angles is shown in Fig. 7. Unlike in the small angle approximation, the time period strongly depends on the maximum angle of oscillations. The variation of time period follows the data reported in the literature 8 . Figure 7: Angular displacement vs. time (left) and the angular velocity (right) as a function of time for nonlinear simple pendulum. Results with maximum angle 0 = 100 and 0 = 1750 are shown in upper and lower panels. 6 Conclusion We provided a novel approach with support programs to identify required coding elements to teach computer programming for non-CS STEM majors We demonstrated this approach with the problem of simple pendulum, a routinely taught problem in upper level engineering and physics classes. We envision that similar exercises can be developed to improve CT and CP among non-CS STEM major students in upper division undergraduate students or starting graduate students. References [1] Li, Y., Schoenfeld A. H., diSessa A. A., Graesser A. C., Benson L. C., English L. D., Duschl R. H., On Computational Thinking and STEM Education, Journal of STEM Education Research, 3, 147, (2020). [2] Lyon J. A., Magana, A. J., Computational Thinking in Higher Education: A Review of the Literature, Computer Applications in Engineering Education, 28, 1174, (2020). [3] Swaid, S.I, Bringing Computational Thinking to STEM Education, Procedia Manufacturing, 3, 3657, ( 2015 ). [4] Wang J. M., Computational Thinking,Commun. ACM., 49, 33-35, (2014). [5] Thornton, S. T., Marion J. B., Classical Dynamics of Paticles and Systems, Thomson Learning (2003). [6] Newman,M., Computational Physics, (2012). [7] Giordano, N. J., Nakanishi H., Computational Physics, Pearson Education Inc. (2006). [8] Kidd R. B., Fogg S. L., A Simple Formula for the Large Angle Pendulum Period, Physics Teacher, 40, 81, (2002).  ...

... Paper ID #36710 Development and Assessment of an Introductory Undergraduate Course in Biophysics Tanja Greene Tanja Greene, MSBME, received a Bachelor of Science in Biomedical Engineering in 2013 and a Master of Science in Biomedical Engineering in 2015, both from the Purdue School of Engineering at Indiana University Purdue University of Indianapolis (IUPUI), Indiana. During her master studies, she investigated the influence of microenvironments on cell fate processes through the encapsulation of cells within chemically modified, biomimetic hydrogels. After graduating, she continued her research through working in a tissue engineering/ biomaterials laboratory until 2017. She then became an Instructor of Physics and Engineering at Marian University of Indianapolis, Indiana, where she currently teaches Physics I, Physics II, Biophysics, and will soon be developing courses related to biomaterials for the launch of the new ES Witchger School of Engineering at Marian University. American Society for Engineering Education, 2022 Powered by www.slayte.com Development and Assessment of an Introductory Undergraduate Course in Biophysics Abstract In the pursuit of deepening ones understanding of physics and its implications on biological functions, Biophysics presents itself as the forerunner in useful courses serving in this capacity. As a modern, interdisciplinary field of science weaving concepts of Physics, Biology, Math, and Chemistry, Biophysics provides the space for novel approaches and discoveries answering the questions of many scientists and engineers. Due to the broad reach of its purposes, Biophysics requires a multidisciplinary education. Students working towards degrees in any science, technology, engineering, and mathematics (STEM) degree can benefit from taking a Biophysics course. In this paper, course design and types of instruction are presented and discussed, as well as student outcomes and feedback for the first iteration of this biophysics course. This course will offer undergraduate students a look into a multitude of techniques, based on physical principles and laws, which are used to explore biological functions. In addition, students will be challenged to improve their understanding of molecular structures in biological contexts and will explore the thermodynamic and kinetic regulation of biological systems as well as the bioenergetics of molecular and environmental interactions. Due to the level of coursework expected, students will have the opportunity to participate in active and passive learning activities, will be given learning assessments utilizing all levels of Blooms Taxonomy, and will be assigned a project involving Research as Inquiry. Check points will be built into the course to monitor students progress on projects, at which time feedback and guidance will be offered. Upon completion of this course, STEM students will be able to clearly express their scientific thinking in both written and verbal form while successfully connecting concepts across their undergraduate curriculum. Students will be required to sharpen their skills as researchers as they learn how to focus their questions of inquiry and will then present their findings. Through developing an undergraduate course in Biophysics, a roadmap is presented helping STEM students to make necessary connections among their foundational undergraduate education. Introduction As the focus on STEM gains momentum, a degree in physics has become more desirable among students, especially among those in the Dual Degree Engineering Program (DDEP) at Marian University in Indianapolis, Indiana. DDEP is a 5-year program where students earn a Bachelor of Science of their choice from the university and a Bachelor of Science in an engineering discipline from a partnering university, Purdue University. To offer students within the DDEP a new degree option from Marian University, a program in Applied Physics was adopted and approved in May 2020, soon to be renamed Engineering Physics. Within this program, PHY 350 Biophysics is included as a required upper-level undergraduate course. The increase in Engineering Physics interest allowed the opportunity to develop the already proposed and approved PHY 350. The course description as provided by the Marian Universitys course catalog is an Introduction to the physical principles of biological systems. Molecular structures in biological contexts, bioenergetics, environmental interactions, thermodynamic and kinetic regulation of biological systems. Biophysics is an interesting subject that has appeal to many disciplines. Not only is it modern in its approach utilizing a multitude of technologies based on physical principles, but Biophysics also requires the synergy of many disciplines to understand its concepts. Subjects such as Physics, Biology, Mathematics, and Chemistry intertwine offering new approaches and discoveries and thus allowing the inquiries of researchers of science and engineering to be investigated.[1] It has been my experience as a trained biomedical engineer teaching algebra-based physics to students pursuing biology, chemistry, pre-med, etc., that in general, students struggle to identify overlapping concepts among subjects. Their learning is compartmentalized, meaning students only study each subject as its own entity and fail to see how one subject may affect or even dictate another. Being able to synthesize the information from one individual course and apply it to another course is important in developing critical thinking and problem-solving skills. Because biophysics is a subject of great breadth, students pursuing degrees in STEM will find biophysics beneficial as it inspires them to create these connections amongst their foundational core subjects. Course Overview As described in the course syllabus, PHY 350 Biophysics is a one semester introduction to the physical principles of biological systems. Molecular structures in biological contexts, bioenergetics, environmental interactions, thermodynamic and kinetic regulation of biological systems will be investigated. Emphasis will be given to underlying physical principles as well as understanding the techniques and instrumentation used to investigate biological systems at the nanoscale. Ideally students will be able to discuss physical laws and their implications quantitatively and qualitatively on the above-mentioned topics. More specifically, PHY 350 Biophysics is a ~15-week course designed to meet two times a week for a period of one hour and fifteen minutes each session. Pre-requisites include algebra-based general physics II, or calculus-based University Physics II, and Calculus II. However, to include more STEM majors such as those on the pre-med track and to help DDEP students who are off rotation in Math courses, the course has been developed so that the with the completion of Calculus I, students can take the course with instructor permission. Two textbooks provide the groundwork for this first iteration of Marian Universitys PHY 350, Biological Physics Student Edition: Energy, Information, Life by Philip Nelson and Physical Biology of the Cell by Rob Phillips and others. A wide variety of instructional activities including lectures, hands-on activities, demonstrations, discussions, worksheets, and videos are utilized. The entire course is graded using three main areas: class participation (10%), quizzes (30%), and a semester-long project (60%). There are many deliverables due for the project including the submission of: (1) topic of interest (2) primary research articles of interest (x3) (3) proposed experiments (x2) As well as the presentation of: (1) literature review and proposed hypothesis (midterm presentation) (2) completed final project (final presentation) Course Development An instrumental document in helping to develop PHY 350 is the resource published in recent months by the American Journal of Physics entitled Resource Letter BP-1: Biological physics. As stated in the abstract of this resource letter, it provides an overview of the literature in biological physics, a vast, active, and expanding field that links the phenomena of the living world to the tools and perspectives of physics. [2] This compilation aided in building resource pages for students in PHY 350 by providing guidance to seminars, videos, and recent peerreviewed publications on specific biophysical topics as well the technologies used to investigate those topics. In addition, Blooms taxonomy is an important guide in structuring the course and its activities. As depicted in Figure 1, Blooms taxonomy contains six levels of proficiencies ranging from lower-order skills that require less critical thinking to higher-order skills that require a greater degree of critical thought processes. Utilizing all levels of Blooms Taxonomy is an important tool helping students to make the necessary connections among different Figure 1: Blooms Taxonomy - A system of classification for teaching, learning, and assessment. Adapted from Blooms Taxonomy website.[3] disciplines. Students struggle with essential higher-order skills such as their application of knowledge and critical thinking and thus benefit from a course organized in this manner. [4-6] As described in the article Blooms Taxonomy of Cognitive Learning Objectives, Blooms taxonomy is beneficial in two ways. As an instructor developing a course, its use promotes aligning courses learning outcomes with what the students can and will achieve; and most importantly, the use of Blooms taxonomy shines light on learning outcomes that require higherorder thought processes. This promotes more meaningful learning and application of knowledge from the students throughout the course. [7] Another crucial aspect considered when developing Biophysics is the use of active and passive learning techniques. Passive learning occurs when students receive information from their learning environment without receiving feedback from the instructor. It is influential in producing low-order thinking skills. [5, 6, 8, 9] Examples of passive learning techniques include lectures, videos, simulations without reflection or interaction with instructor or the material directly. Whereas active learning is necessary to produce higher-order thinking skills and occurs through engagement. [5, 6, 8, 9] Examples of active learning techniques include any activity where students are participating through reflection and interaction with the instructor or the material. Low-order thinking utilizes the lower levels of Blooms taxonomy and high-order thinking utilizes the upper levels of Blooms taxonomy; therefore, each learning style has its benefits, and as such, it is important that both are incorporated into this course. Participation Biophysics is very much a modern subject and as such the course is developed to encourage students to openly talk about topics of interest while learning how physical ideas are at play. Participation consists of contributing to discussions while being present in-class thus forcing students to be involved in active learning while utilizing many of the proficiencies defined in Figure 1. Quizzes The quizzes constructed for the course offer combinations of questions utilizing multiple levels in Blooms Taxonomy. Students are expected to answer a variety of questions that may come in the form of true/false, multiple choice, filling in blanks, creating lists, or even matching. All of which fall into the lowest level of taxonomy, Remember. In addition, students are asked to describe/discuss/explain their answers thus utilizing the level of Understand. Sometimes, students are asked to solve for an unknown or to interpretate the meaning of an idea. These items fall into the middle level Apply. Students are also asked to Analyze items and must distinguish differences or make comparing/contrasting statements. Finally, students are asked to support their claims thus using the taxonomy level Evaluate. As evidence, a quiz administered to students over lecture parts 5 and 6 is included in Appendix A. Project The semester-long project not only includes components that fall into the lower levels in Blooms taxonomy, but it also forces students to utilize the uppermost level, Create. Essentially students are forced to work their way through each level as they move into the different parts of their semester-long project beginning with choosing a topic of interest and finishing with presenting a full project. Using Research as Inquiry students are to investigate a complex issue, compiling information from a wide variety of sources to develop their own answer to a question or to provide a solution to a problem that they have identified through their own research.[10] Checkpoints are in place to monitor students progress and to provide feedback. A topic of interest will be chosen and then research conducted looking into what others have done with that topic of interest. Through that research, a hypothesis will be formulated, and then different methods, or experiments, will be planned to test that hypothesis. This project will involve reading research/scientific articles, and then applying their knowledge of physics, skills, and imagination, students build on these items and then propose something worth exploring further. The purpose of the Articles is to sharpen the students skills as a thinker through applying "Research as Inquiry". Using the topic of interest identified, students will work to narrow their focus and to develop a research question or hypothesis through investigating the research of others. The Midterm Presentations serve as a chance to show others what direction each students inquiry has taken and how much they understand about physical ideas in their biological topic of choice. Proposing Experiments allows students to further develop their understanding of physical ideas as they apply these ideas to explain their own methods. In addition, the methods developed must work to investigate and answer the research question in which they are interested. Finally, the Final Presentations is the students final opportunity to create a well-organized project anchored in critical thinking and a deeper understanding of the physical principles at play in biological systems. Course Content The course schedule of deliverables/assessments, lectures, and activities is shown in Table 1 below. As indicated by the course schedule, students are expected to be either preparing for a quiz or working on a portion of their semester long project. This is different than most of their courses as students are not assigned traditional homework assignments each week. Table 1: Fall 2021 Schedule of Course Deliverables/Assessments, Lectures, and Activities Week 1 Monday Session Wednesday Session Course Introduction 2 Lecture(s) Covered Part 1 Quiz 1 Part 1 continued, Part 2 Topic of Interest due Part 2 4 Research Article 1 due Part 2 continued, Part 3 5 Quiz 2 Research Article 2 due Part 3 continued, Part 4 Research Article 3 due Part 4 continued, Part 5 Quiz 3 Part 5 continued, Part 6 3 6 Labor Day Diffusion vs Directed Processes Hands-on Activity/Demo 7 8 Midterm Presentations Midterm Presentations Part 6 9 Fall Break Quiz 4 Non-Newtonian Hands-On Activity/Demo Part 7 10 11 Part 7 continued All Campus Mass No lecture Disorder as Info Hands-on Activity/Demo Quiz 5 Part 8 Experiment 1 Due Part 8 continued 13 Quiz 6 Part 8 continued, Part 9 14 Experiment 2 Due Part 9 continued 15 Quiz 7 Part 9 continued 12 16 Final Presentations Final Presentations As noted in the right-hand column of Table 1, the expected lecture material to be covered is listed. To provide a better understanding of the course content within these lectures, the lecture titles as well as brief descriptions are listed below. Overview of lectures Part 1: What is Biophysics o An introduction/preview of energy transformations in biological systems including a look at thermodynamics, free energy transductions, and disorder as information. Part 2: Whats Inside a Cell o A review of cell components including cell physiology function and structures both internal/external and a review of the chemical world atoms to molecules to macromolecules to assemblies, molecular devices, and motors as well as physical models of representation (structural hierarchy). Part 3: Equilibrium in a Cell o A look at transformations in matter and energy to understand chemical and mechanical equilibrium in biological components. Part 4: Structural Beams are Everywhere o Understanding how cooperativity, or favorable energetic reactions, aides in the assembly of proteins into their structural hierarchy and assist with environmental interactions. Part 5: Random Walks, Friction, and Diffusion o An introduction to the randomness of predictable, organized behavior/mechanics of biological entities and how dissipative processes affect their behavior. Part 6: Biological Applications of Diffusion o Investigating the role of diffusion across membranes and how diffusion affects cellular processes like absorption, transport, establishing membrane potentials, and determining charge states of cells. Part 7: The Low Reynolds Number World o A guide to the mechanics of nanoscale biological entities living in a viscous world dominated by friction. Part 8: Entropy, Temperature, and Free Energy o Diving deeper into disorder as information while also exploring the specifics of the effects heat has on disorder and probing the competition between entropy and energy reflected as free energy. Part 9: Enzymes and Molecular Machines o A journey into how living organisms transduce free energy through the application of chemical concepts including enzyme kinetics and how certain molecular machines interact with their environments. Nearly all lectures include a look at biophysical techniques pertinent to the topics covered such as the use of optical traps or tweezers to understand the cooperativity in proteins and macromolecules, electrophoresis to exploit the charge state of polymers when assessing protein samples, and centrifugation which exploits the gravitational effects on sedimentation to ensure molecule separation by size and density to name a few. Course Assessment Student Performance The first iteration of PHY 350 Biophysics had an enrollment of 8 male students and no female students. Five of those students are of Senior class standing, 1 of Junior class standing, and two of Sophomore class standing. All students are in the DDEP also majoring in either Applied Physics (5 students), Chemistry (2 students), or Mathematics (1 student) at their primary university. At the end of the course, students outcomes should include a better understanding of how different disciplines come together to explain physical laws. In addition, students should be able to discuss and explain the implications physical laws have quantitatively and qualitatively on molecular structures in biological contexts, bioenergetics, environmental interactions, thermodynamic regulation of biological systems, and the kinetic regulation of biological systems. One of the primary methods of assessing students knowledge in the course is the use of quizzes. Table 2 offers a view of what information was covered in each quiz. Table 2: Average Scores of Learning Assessments and Lecture Material Covered Quiz Lectures Covered Average Score (%) 1 Part 1: What is biophysics 37.9 2 Part 2: Whats inside a cell 88.0 3 Part 3: Equilibrium in a cell Part 4: Structural Beams are Everywhere 78.5 4 Part 5: Random Walks, Friction, and Diffusion Part 6: Biological Applications of Diffusion 48.8 5 Part 7: The Low Reynolds Number World 60.6 6 Part 8: Entropy, Temperature, and Free Energy 93.3 7 Allowed students an opportunity to freely express their likes and dislikes about the course. n/a Quizzes Overall Average Score (%) 67.8 Overall, students performed just below average on their quizzes. Shown in Table 3, mapping quizzes to student outcomes, without investigating each question individually, it appears that students struggled with a few of the topics. However, for a few outcomes, students showed some improvement as specifics were learned indicating that students were in fact gaining a better understanding of the concepts covered by biophysics. Table 3: Average Scores of Learning Assessments Mapped to Course Outcomes Quiz Scores of Topics Covered (%) Quiz 1 2 3 4 5 6 Topic Average Molecular Structures 88.0 78.5 Bioenergetics 37.9 78.5 93.3 83.3 69.9 Environmental Interactions 88.0 78.5 60.6 75.7 Thermodynamic Regulation 37.9 Kinetic Regulation 48.8 93.3 48.8 60.6 93.3 60.0 67.5 Table 4 offers a look at the average scores obtained by students during their semester-long projects. With instructor feedback and guidance, projects improved upon as each stage progressed. Table 4: Average Scores of Project Deliverables Average Scores (%) 1 Articles 2 3 Midterm Presentation 1 Experiments 2 Final Presentation 86.7 89.1 91.9 94.8 67.5 78.5 89.3 Overall Project 88.4 For the project deliverable Articles, students were required to write/type 3 brief 12 page reviews of 3 different yet related primary research articles. In their review they were to include answers to following questions (1) What is the question and the biophysics explored in the article; (2) Explain any methods/techniques, computations, or modeling utilized (be sure to include any physical principles at play and be able to explain how you know this); (3) Summarize important findings of the paper AND identify a gap (item 4 may help in identifying a gap); (4) Provide 2-3 Pros and 2-3 Cons of each paper. (Think to yourself: What did you like and what didnt you like? What would change? Why? How would you change something? Do you question the validity of methods? Or maybe its the application of methods in question?) Students were assessed on the completion of the above instructions and the application and discussion of the underlying physical principles at play. The project deliverable Midterm Presentation required students to create a 910 minute PowerPoint presentation that was delivered in-person to the entire class. Specifically, students were asked to provide each papers significance, experiments, and results, as well as their proposed pros and cons. In addition, they were asked to identify a cohesive gap in the methods/findings of the 3 reviewed articles and to explain the significance of this gap. From this significance, a new, testable question was to be proposed and a hypothesis provided. Midterm presentations were assessed using the rubric found in Appendix B. For the project deliverable Experiments students were encouraged to first gain inspiration from one of the many biophysical techniques or methods covered in class or beyond. They then were required to write/type a 1-page detailed overview for each of their own proposed experimental methods. Each detailed overview was to include the following (1) Explain in detail the proposed experimental method. (2) How will the experiment help you to answer your hypothesis? (3) What are the physical principles at play, what is their effect, and how do you know this? Students could explore the physics through a multitude of methods. Examples include quantitative methods such as mathematical derivations or computational modeling, or through the application of qualitative such as proofs of concepts/laws and explicit descriptions. Students were assessed on the completion of the above instructions and their application and discussion of the underlying physical principles at play. The final project deliverable Final Presentation required students to create a 1415 minute PowerPoint presentation that was delivered in-person to the entire class. Specifically, students were asked to provide the following information (1) Background - Give a general background to the topic, and explain key concepts (2) Problem statement - What gap did you identify? (3) Purpose or Significance - Why is the gap important? What was unknown in the studies you read, and why should we care? (4) Research Question or Hypothesis - How will the gap be closed? Make sure it is testable. (5) Experimental Methods - How does the technique work? Be sure to explain governing physical laws behind the technique. Possibly useful questions: what instruments are needed? What is the sensitivity or resolution? How is raw data analyzed? (6) Future directions - How would you extend this work? Whats an interesting or important experiment to be done, and how (roughly) could you do it? (Be brief.) (7) References - Use APA format and include on a slide at the end. Final presentations were assessed using the rubric found in Appendix C. Ultimately, after all deliverables and assessments were graded, students finished the course with an overall class average of 84.8%. Student Feedback As a Marian University initiative to aide in improving student experiences, students are asked to provide evaluations of their courses and instruction each semester through Watermark, formerly EvaluationKIT. Instructors receive mean scores of their course, their department, their college, and the university using a scale of 0 to 5, with 0 being the lowest rating and 5 being the highest rating. Table 5 displays these mean scores with 100% response rate. Table 5: Means in Student Responses to Course Evaluations Means Question The syllabus clearly communicated the learning outcomes of the course. The readings, discussions, lectures, labs, and/or projects helped me attain the stated learning outcomes of this course. Multiple instructional methods were used in the course (e.g. lectures, problem solving, case studies, hands-on-activities, experiments, discussions, etc.). The activities and assignments challenged me to think more deeply/critically about the course subject matter. I would recommend this course to another student. Biophysics Department College University 4.50 4.56 4.50 4.53 4.50 4.43 4.39 4.43 4.50 4.32 4.32 4.37 4.25 4.41 4.40 4.43 4.50 4.33 4.26 4.31 As evidenced by the data in the Table 5, students were satisfied with the course. Many of the categories for the course score on par or even better than the department, college, and university. When polled about their experience in the first iteration of PHY 350 Biophysics, dual degree engineering students also majoring in Math, Chemistry, or Applied Physics recognized the crossover of disciplines within the biophysics course. The students appreciated the opportunity to think more critically about a subject and responded with the following comments I enjoyed how physics was applied throughout the course. Although there are parts that were mainly biology, the aha moments were very satisfying when I was able to relate it to the topics that we have covered in our engineering courses. I think the experiments and research we had to do helped us apply the things we were learning to better understand our own research. Although biology is not the most interesting field of study for me, I found that this course gave me a better understanding of how things work. The first and most important thing I like about biophysics was the relationship to all the material I have seen through my engineering student career. Looking at stresses, thermodynamics, fluids, etc. I really enjoyed the idea of having a project-based course as it allowed me to choose a topic I am really interested in and dig deeper into the biophysics behind it. Even though it was different material I enjoyed the change of pace from all the math and physics-based classes. In addition to the comments above, students also mentioned wanting more in the way of homework, and that they felt the material was rather difficult at times. I would have liked little assignments to set us up better for quizzes whether or not this includes a mini assignment each week or a review assignment. This will help to push us to learn the concepts a little better. The class was a bit too advanced for the previous classes that were completed in the major. Some of the quizzes were pretty tough. I would improve upon the lack of homework by adding more homework, not super hard or long, but to help process what information we should be learning for quizzes. Quizzes covered too many topics. I would like to see more homework. Although it sounds weird, having more homework forces the student to learn some of the concepts firsthand. Reflection After reviewing the information provided above, students who participated in PHY 350 found the course to be interesting although difficult. Based on students responses to course evaluations and their comments, it is crucial that another element of assessment is incorporated to assist students with learning the more difficult material. The additional assessment may come in the form of small homework assignments or short reflections following each lecture. Regardless, this course in biophysics allowed students to make the necessary connections among their undergrad curricula through the implementation of a semester-long project accompanied with periodic quizzes. In addition, improvements in the development of the course are apparent as well. Student learning outcomes need to be reassessed and better-defined utilizing Blooms taxonomy. Although active and passive learning techniques were used to ensure all levels of proficiencies were covered in course activities, more time and attention should be spent better structuring the student outcomes and aligning the specific course activity to expected outcome. Finally, the next iteration of this course will require some reorganization of course content. The restructuring will assist in creating a better flow of information and should assist students in developing their understanding of different topics. Figure 2 provides some insight into how the topics may be rearranged. Figure 2: Reorganization of course topics to better improve course flow. Summary Biophysics is a modern, interdisciplinary field of science where concepts of Physics, Biology, Math, and Chemistry collide. A course in this field of study acts as a roadmap helping STEM students to become masters of higher-order thinking. Biophysics encourages students to apply concepts, theories, and knowledge from many of their STEM courses into the study of a single cohesive topic. Using active and passive learning techniques allows all levels of Blooms taxonomy to be employed thus creating students with deeper critical thinking, or higher-order skills. As critical thinking develops, connections across disciplines are easier made. The course assignments expected of the students required participation in active and passive learning activities, assessments utilizing all levels of Bloom's Taxonomy, and the completion of a Research as Inquiry project. Through the students involvement in these items students admitted to making connections across their undergraduate coursework. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] "What is Biophysics?" https://www.biophysics.org/what-is-biophysics (accessed November 2021. R. Parthasarathy, "Resource Letter BP-1: Biological physics," American Journal of Physics, vol. 89, pp. 1071-1078, December 01, 2021 2021, doi: 10.1119/5.0060279. "Bloom's Taxonomy." https://www.bloomstaxonomy.net (accessed November, 2021). A. Crowe, C. Dirks, and M. P. Wenderoth, "Biology in bloom: implementing Bloom's Taxonomy to enhance student learning in biology," (in eng), CBE Life Sci Educ, vol. 7, no. 4, pp. 368-81, 2008, doi: 10.1187/cbe.08-05-0024. U. Zoller, "Are lecture and learning compatible? Maybe for LOCS: Unlikely for HOCS," Journal of Chemical Education, vol. 70, no. 3, p. 195, 1993/03/01 1993, doi: 10.1021/ed070p195. J. D. Bransford, A. L. Brown, and R. R. Cocking, How people learn. Washington, DC: National academy press, 2000. N. E. Adams, "Bloom's taxonomy of cognitive learning objectives," (in eng), J Med Libr Assoc, vol. 103, no. 3, pp. 152-3, Jul 2015, doi: 10.3163/1536-5050.103.3.010. S. S. Paul, "Active and passive learning: A comparison," Global Res. Develop. J. Eng, vol. 2, no. 9, pp. 27-29, 2017. M. Prince, "Does Active Learning Work? A Review of the Research," Journal of Engineering Education, vol. 93, no. 3, pp. 223-231, 2004/07/01 2004, doi: https://doi.org/10.1002/j.2168-9830.2004.tb00809.x. A. J. Head and M. B. Eisenberg, "Assigning inquiry: How handouts for research assignments guide todays college students.," Project Information Literacy Progress Report, pp. 1-41, 2010. Appendix A Quiz 4 covering lecture Parts 5 & 6: Random Walks, Friction, and Diffusion 1. Resistance reflects frictional dissipation of energy T 2. Brownian Motion is indicative of a cells activities T 3. Excitable cells selectively tune their own membrane potentials T 4. Current is an entropic force T 5. Diffusion tends to decrease entropy T 6. Charge states influence the electric potential of membranes T 7. Nernst relation sets scale for membrane potentials T 8. Diffusive motion is always present at molecular length scales T 9. Electric Potential is an energy carrier T 10. Only electrical signaling is required for the proper functioning of cells T 11. Random walks predict the motion of a collection of many molecules T 12. Fluctuations in position are linked to the dissipation to which it is subjected T 13. In lecture we learned that we could study diffusive dynamics through two major d d or or or or or or or or or or or or F F F F F F F F F F F F d2 equations, = d and d = d 2 , Ficks 1st and 2nd Laws of Diffusion, respectively. Explain the differences between Ficks 1st Law of Diffusion and Ficks 2nd Law of Diffusion providing which equation would be preferred and why it is preferred. 14. Diffusion has one major limitation which is why directed processes are sometimes necessary. a. What is this major limitation of diffusion? b. What is the main difference between diffusion and directed processes? c. Provide an example of an object undergoing diffusion AND provide an example of THE SAME object undergoing a directed process. 15. In class we mentioned that Einstein used info from the ideal gas law, = 2 2 2 , and ideas about diffusion, 2 , and the viscous coefficient, = , and realized that there were 3 statements and 2 unknowns. We said that this means the unknowns are overdetermined and thus these statements can only hold true if & together satisfy a particular relation, the Einstein Relation, = . a. Using the definition that , = and the three statements above, prove that Einsteins Relation is true. b. What does Einsteins relation, = , say about i. A large particles drag and diffusion ii. A small particles drag and diffusion 16. (5pts) Fill in the blanks. Diffusion of ions ___________ their concentration gradient is the response to a driving force tending to _____________ the entropy of the system. What is this driving force? The ______________ in the total free energy! As ions flow, there will exist an increasing ______________ imbalance, and an associated ____________ in the electric energy of the system, . Appendix B Midterm Presentation Rubric for Assessment Appendix C Final Presentation Rubric for Assessment  ...

... Paper ID #37202 Benefits, Drawbacks, and Effects on Retention Rates to a 5 Year, Inclusive, Dual Degree Engineering Program Jeffrey David Carvell (Assistant Professor of Physics and Engineering) PhD. Physics, Purdue University Tanja Greene Tanja Greene, MSBME, received a Bachelor of Science in Biomedical Engineering in 2013 and a Master of Science in Biomedical Engineering in 2015, both from the Purdue School of Engineering at Indiana University Purdue University of Indianapolis (IUPUI), Indiana. During her master studies, she investigated the influence of microenvironments on cell fate processes through the encapsulation of cells within chemically modified, biomimetic hydrogels. After graduating, she continued her research through working in a tissue engineering/ biomaterials laboratory until 2017. She then became an Instructor of Physics and Engineering at Marian University of Indianapolis, Indiana, where she currently teaches Physics I, Physics II, Biophysics, and will soon be developing courses related to biomaterials for the launch of the new ES Witchger School of Engineering at Marian University. American Society for Engineering Education, 2022 Powered by www.slayte.com Benefits, Drawbacks, and Effects on Retention Rates to a 5 Year, Inclusive, Dual Degree Engineering Program Abstract: This paper is an evidence based practice paper. Across the United States, many universities, especially smaller, liberal arts universities, do not have the facilities to offer engineering degrees. One thing that has become very common in these schools that cant or dont offer engineering is the 3 + 2 program, where students receive a degree from one university in three years, then transfer to a partner engineering university after graduation to complete the engineering degree in the final two years. Students in these programs earn two bachelors degrees, one typically in math or science, and one in engineering. There are benefits and drawbacks to this type or arrangement and partnership, but they can be successful. Recently, we have been running a similar program but with a very important modification. Our program is still a five year program, and students still earn two bachelors degrees, one from a liberal arts school (primary university), and one from a world renowned engineering school (secondary university). The difference is that students in our program earn the degree from both schools at the same time and are enrolled students at both schools simultaneously for the full five years, and no transferring is required. Having run the program for ten years, we have noticed several benefits and drawbacks to this kind of program over the traditional 3 + 2 version. The biggest benefit is that all students are members of the home institution for the full five years, making financial aid much easier for students to deal with. All scholarships, including athletic, are valid for the full five years of the program, and the students deal only with the business side of one university. All bills and fees from the engineering institution are paid by the home university, and students never see those. By being at the home university for the full five years, students can settle and perform better knowing they dont have to up and move after three years. There are many other benefits we see, but there are also drawbacks. Communication between the business offices at both universities, getting the bills paid and keeping track of students, can be difficult. Since students are getting degrees from both schools, all degree requirements must be met, and all classes must be clearly linked at the two schools so that no requirements are missing. Also, students have to register at two schools at the same time, and pre-requisites can be issues. Overall, although there are drawbacks, the benefits can outweigh them and make a program like this successful. This engineering program has retained 94% or its students from first year to second year from graduating classes, and 97% from current students. Of the students entering the program, 83% complete it and graduate with an engineering degree, and 89% have completed any degree at the primary institution. Finally, 100% of the students who have graduated from this program have either placed into graduate school or accepted a position within the engineering industry. Keywords: Dual degree, Engineering program, Engineering program creation Introduction: This paper is an evidence based practice paper. In todays world, STEM fields, especially engineering, are very popular majors for universities, and are attracting students due to the job prospects and graduation placement rates. Across the United States, three hundred ninety-three institutions offered engineering degrees as of 2018 [1]. But for many schools, offering an engineering major is not possible due to lack of resources or facilities. Many of these are smaller, liberal arts institutions. These institutions started offering new programs in which students would major in a liberal arts and science major for three years, then transfer to an institution with an engineering major and complete the engineering major in two additional years. These programs are typically referred to as 3 + 2 programs. Recently, some schools have even started trying to work 2 + 2 programs. The benefit of these programs to the smaller institutions is that they still are able to get these engineering students to attend for the first three years, then students can transfer and get a second degree in engineering. Downsides to these programs include that acceptance to the second, transfer university isnt always guaranteed. Other issues arise in tuition and financial aid. Students obtain financial aid and pay tuition at one institution for three years but have to reapply and attempt to get financial aid a second time after transferring. Due to the transfer, tuition often isnt the same or guaranteed either. Bigger problems arise as the transfer institutions often cap the time at two years, and minus extenuating circumstances, students do not have extra time, even if some classes dont transfer properly. Other downsides to this type of program is that the first institution generally awards BA degrees, not BS degrees. Also, the transfer between schools could be anywhere, and students may end up moving across multiple states to get to the transfer institution. Ten years ago, Marian University started a new type of dual degree program. This program was originally developed through another local liberal arts university, and our school was given a similar opportunity. This new type of program is unique to these schools, and is not yet common across the US. This program operates very similar to the 3 + 2 programs mentioned earlier, with one important modification. The difference is that instead of having three years at a liberal arts school, then two years at an engineering school, students are enrolled at both the liberal arts institution, Marian University, from here called the primary institution, and the engineering school, Indiana University Purdue University Indianapolis (IUPUI), from here called the secondary institution, at the same time for all five years. In the process of the program, students earn two bachelors degrees: the first from Marian in any liberal arts or science major, and a second bachelors degree in engineering from Purdue University through the Indianapolis campus. In this case, Marian University is a private, liberal arts institution in a major metropolitan area, Indianapolis, Indiana. Marian University has approximately three thousand five hundred undergraduate students, and approximately five thousand total students. The size of classes are typically in the range of twenty to twenty-five students in all classes: engineering, science and math, or general education. IUPUI is a large, state school with a world renowned engineering program through Purdue University. IUPUI has approximately twenty-eight thousand students across undergraduate and graduate programs. At the Marian, there are approximately sixty students in this dual degree program. At IUPUI, there are approximately three thousand total engineering students. Freshman level science, math, and engineering courses at IUPUI, as well as general education courses, can regularly approach two hundred students. Sophomore and junior level engineering courses can be as large as one hundred, and upper-level engineering courses are typically twenty to forty students. Many students who enter this dual degree program state they do so due the possibility of getting the engineering degree while maintaining many classes with small class sizes. As mentioned later in the discussion, a high percentage of students in this dual degree program also participate in university athletics, and this is another draw for this program. Students enrolled in this program can enroll at both schools from the beginning of freshman year. The key to being able to run a program like this is location. The primary and secondary institutions are only two and a half miles apart, and students can commute between the two schools in under ten minutes. This allows students to take classes at both of the universities at the same time. So rather than needing to wait until year four to transfer to a new school and start the engineering degree, students can start from day one. Many students end up taking most classes at the primary institution over the first two years, but then take about half at each starting in year three. There is a lot that goes on with this program, and like the 3 + 2 programs, there are both advantages and drawbacks to this style. Program Advantages and Drawbacks: We can start by looking at the advantages of a program of this type. While analyzing the advantages and drawbacks, it is important to look at each from multiple angles: are these advantages or drawbacks to the students, the primary/secondary institutions, or both. The biggest benefit to students is that they are members of Marian University for all five years. This makes the financial aid and tuition issues seen in 3 + 2 programs much easier to deal with. Instead of getting financial aid for three years, then needing to reapply when transferring, students are awarded financial aid and scholarships that cover all five years during the initial admission process. All aid, including athletic scholarships, are valid for five years of the program. This allows students and parents to know exactly what they are getting from the beginning, with no surprises. This can also be an advantage to both universities. Marian University can plan for students, enrollment, and financial aid for the full five years, while IUPUI does not have to manage any aid or scholarships for these students. Another downside to students in 3 + 2 programs is the tuition difference. Students in this dual degree engineering program do not have to worry about that, as the tuition is paid only to the primary institution. This is another major advantage, as students never have to worry about billing, fees, or anything related to the business office at the secondary institution. Any fees or tuition costs are billed by IUPUI to the Marian directly, and the bills are paid between the schools, cutting the students out of the process entirely. This can be a disadvantage to the universities, as mentioned below. Students also have an easier time adjusting in this program, as the thought of transferring is not something they have to worry about. This allows students to settle in and perform better in the classroom. Unlike the 3 + 2 programs, where students may transfer hours and states away, students in this dual degree engineering program are students at Marian University for five years. If they choose, they can live on campus in dorms or on campus housing for all five years, never needing to move even across a street, much less across multiple states. As mentioned above, 3 + 2 programs have a problem in that students arent always guaranteed acceptance into the engineering schools. In this dual degree program, students are analyzed by Marian University for admission standards at both schools, and students arent admitted into the program unless they meet the IUPUI admission requirements. IUPUI has admission standards of five hundred seventy SAT math scores for admission. Post COVID-19, as schools are going more test-blind, the standards are now based on high school math courses taken. Students who have a B or higher in pre-calculus or above are admitted to the program, and students with a C or above in pre-calculus or calculus are then considered further. Marian University has lower admission standards for general students. These standards are similar to other engineering schools across the country. In this process, students first apply to Marian with an interest in the dual degree program, and are either accepted or denied admission to the university. Any students accepted to the university are then forwarded to a dual degree program admissions committee. That committee, typically two or three dual degree program faculty members, reviews student test scores or transcripts, depending on what is available. Anyone meeting admission standards for IUPUI is admitted to the dual degree program. Anyone not meeting the IUPUI standards are admitted Marian as an engineering physics or exploratory major. After review, the committee notifies students or their standing with admission. Students can appeal the decision and speak to the committee if they feel there is an error or extenuating circumstances, but it is rare for students to take this option. In the end, students may still not be accepted to the engineering school, but in that case, they know early on, and are not admitted as part of the dual degree program overall. Another major advantage to this type of program is the resources available to students. Since they are students at both schools from day one, they have access to all student services at both schools from day one as well. This includes all tutoring centers, writing and speaking centers, and even career centers. Students can use job posting sites from both schools when looking for internships and jobs, giving them a broader view and a better chance of finding something that fits for them. Although there are many advantages to this dual degree program, there are still some drawbacks as well. The major drawback is from an institutional side and is related to one of the student advantages. Students never see bills from the secondary university. Everything is sent through the business offices between the two schools. The communication between these offices can be difficult at times, and sometimes students will get lost in the shuffle. Those bills end up not being paid and billed separately later, making costs difficult to track. Since IUPUI is a state school, the tuition rates are different for in-state and out-of-state students, while the private Marian University has a single tuition rate. From the perspective of Marian, tuition and fees can be estimated and planned out for a typical freshman class of fifteen to twenty students, but the exact amount cant be predicted until the background and homes of students are known. This means the tuition fees Marian pays can vary semester-to-semester based on the student population. Additionally, since students are graduating with degrees from two separate schools, all graduation requirements for both universities must be met. Classes between the two schools must be tracked and properly listed in the systems and software of each university. This can cause issues with pre-requisites, as sometimes they dont properly come in. For example, Calculus I may be taken at Marian, and it is set to register at IUPUI during degree audits. During the audits, the class appears as complete. However, it doesnt always appear as a completed pre-requisite, and these have to be manually overridden, delaying class registration. Since students are enrolled from day one at both schools, it could sometimes occur that students are inactive and un-enrolled from the secondary institution. Occasionally, students take all their classes at the primary university. When this happens, they end up showing as taking no classes at the secondary university, and are labeled as inactive, and a hold is put on future registration. The secondary institution has created a zero-credit hour course for cases like this so students can register for something, but that requires students to enroll, and since it is zero credits, it doesnt effect their schedule and is easy to forget. This can be corrected by the admins of the two schools, but it once again can cause delays to registration, causing students to miss classes that fill up. Although there are both advantages and drawbacks to the dual degree program when compared to traditional 2 + 2 or 3 + 2 programs, the advantages tend to outweigh the drawbacks. The advantages of the program can be seen in the data on program analysis. Data and Discussion: This dual degree engineering program has now been running for ten years. The tenth freshman class started classes in the fall of 2021. Over the ten years, there have been six graduating classes, with the sixth class recently graduating in May of 2022. Data analyzed will include overall retention rate for first-time, full-time freshmen (FTFTF), graduation rate where applicable, six-year graduation rate at the institution whether in the engineering program or not, and post-graduation placement rate in industry or graduate school. Of the classes to have graduated, there are a total of thirty graduates that completed the full dual degree program. One of the benefits of the dual degree program being inclusive for five years is the variety of major combinations possible. Of the thirty graduates, nineteen have graduated as mechanical engineers, eight as biomedical engineers, two computer engineers, and one as construction technology (an engineering technology major). The major from the Marian University has a wide range, with sixteen math majors, six chemistry majors, four biology majors, and one major each from business, computer science, theology, and Spanish. Other than the variety in majors, the retention, graduation, six year graduation, and job placement rates are all very high. Table 1 shows the rates and data for each of the five graduated classes, and the anticipated May 2022 graduating class. Graduating class 2017 2018 2019 2020 2021 2022 # FTFTF # Engineering program graduates # of transfers # of # of graduates at engineering the primary program institution graduates outside the with job/grad engineering school program 2 2 0 0 2 2 2 0 0 2 7 5 1 1 5 7 6 1 0 6 11 10 1 0 9* 7 5 1 1 5 Table 1: Retention and graduate numbers of all programs graduates. The placement rate for the class of 2021 in the table above has an asterisk next to it. Of the ten graduates, nine have either a job or have started grad school. The final student has a standing job offer in engineering but has chosen to turn professional in athletics first. The student has worked for the company, and they understand the desire to attempt to participate in the professional sport and have offered a job once the professional career is over. The data gathered in Table 1 is rewritten in Table 2 as retention, graduation, and placement rates. Graduating class 2017 2018 2019 2020 2021 2022 # FTFTF Freshmen- Overall Graduation 6 year Posttoretention Rate of graduation graduation sophomore rate in FTFTF in rate of placement retention engineering engineering FTFTF at rate for rate at (%) program primary engineering university (%) institution program (%) (%) (%) 2 100 100 100 100 100 2 100 100 100 100 100 7 100 71 71 86 100 7 83 83 83 83 100 10 100 80 80 90 100* 8 88 75 75 88 100 Table 2: Program retention rates and graduation rates for past graduates Overall, in the six years the engineering program has been producing graduates, thirty-six students have started as FTFTF. Of those thirty-six, only four have transferred out of the university entirely, and two have changed majors within the university. Of the six to not complete the engineering program, only two have made the change after their freshmen year, and both of those have been students who transferred, one of whom transferred directly to IUPUI. These equate to an engineering program graduation rate of 83%, and a six year graduation rate at the university without regard to major of 89%. These numbers are significantly above other engineering program graduation and six-year graduation rates. [2],[3] The job/grad school placement rate for the engineering program is 100%. The FTFTF retention rate of the engineering program at the university is 94%. The rate that persisted to second year, 94%, is above the benchmark rates of 82% [4]. The graduation rate in the program of 83% is much higher than the reported rates, which typically remain around 50% [5],[6],[7],[8],[9],[10],[11],[12]. A job/grad school placement rate of 100% cannot get any better. Digging deeper into the placement rates post-graduation, eight students have gone directly into graduate school. Of those eight, three have gone into aerospace engineering, four have chosen to pursue mechanical engineering, and one has gone into computer engineering. In addition to these eight, four graduates have obtained jobs in industry, and gone to grad school part time with funding provided by their employer. Two of these four are studying mechanical engineering, a third is studying environmental engineering, and the fourth is studying public affairs with a concentration in environmental policy. The other twenty graduates have placed directly into industry. After accounting for the six graduated classes, there are four remaining groups of classes. Table 3 shows the breakdown of these classes based on retention rates in the engineering program and at the university. Projected graduation year # FTFTF 2023 2024 2025 2026 10 12 18 21 Freshmen-tosophomore retention rate Still at primary Freshmen institution retention rate in engineering program 10 10 100 12 11 100 17 16 94 20 21 95 Table 3: Current students retention rates University retention rate 100 92 89 100 Overall, the retention rate at Marian University, regardless of major, is 95%, and the freshmen-to-sophomore retention rate is 97%. Like the numbers for the graduating classes, these rates are well above the average across the US. In the current group of students, we have also seen a broader choice in majors. In addition to the engineering majors mentioned in the graduates section, students are also majoring now in electrical engineering, energy engineering, and motorsports engineering. At Marian, additional major choices include engineering physics (introduced with the class of 2023), environmental science, history, and graphic design. The dual degree program also shows advantages in some of the data within the student population. One of these areas is the percentage of students that are women. Typically, the rate of women in engineering hovers around 20% of the student population [13],[14],[15]. Over the ten years of the program, twenty-six of the ninety-one total FTFTF have been women, a rate of 29%. Of the students who stayed in the engineering program, twenty-four out of eighty-eight students in the program, or 27%, have been women, well above the 20% national average. The other area that we see large increases in student rates is student athletes. The percentage of student-athletes who are engineers across the US is hard to find, but schools typically self-report numbers in the 18% - 22% range. Of the eighty-eight students mentioned above that are still in or have completed the engineering program, sixty-five have competed on university sponsored athletic teams (not intramural). This is a rate of 74%! Over the life of the program, while completing two degrees, one in engineering, across two universities, 74% of the students have competed in intercollegiate athletics for three or more years (this includes three students forced to withdraw from athletics due to career ending injuries). This may come from students being able to be at the university for the full five years, so all athletic scholarships are handled by one university and can run the entire length of the program. This, along with the ability to compete at the NAIA level, may be attractive and could help explain this number. Conclusions: Having an engineering program across two universities, while keeping students enrolled at both at the same time, earning two separate degrees, certainly comes with its drawbacks. Some of these have to do administratively with multiple offices needing to communicate. Others are student tracking and records related, in terms of pre-requisites and meeting graduation requirements. Despite the drawbacks, the advantages to the university and students outweigh the challenges. These advantages can be seen in the numbers on the program. 27% of the students either in or graduating from the program are women, and 74% have competed in intercollegiate athletics. Even in graduation and retention rates, the differences can be seen. This engineering program has retained 94% or its students from first year to second year from graduating classes, and 97% from current students. Of the students entering the program, 83% complete it and graduate with an engineering degree, and 89% have completed any degree at the primary institution. Finally, 100% of the students who have graduated from this program have either placed into graduate school or accepted a position within the engineering industry. Overall, this program has been a success. Sources: 1 J. Roy, Engineering by the Numbers, ASEE Engineering Statistics, Washington D.C., July 2019. 2 Z. Alavi, K. Meehan, K. Buffardi, W. R. Johnson, and J. Greene, Assessing a Summer Engineering Math and Projects Bootcamp to Improve Retention and Graduation Rates in Engineering and Computer Science, Paper presented at 2020 American Society for Engineering Education Virtual Annual Conference, June 2020. 3 M. Shadaram, T. B. Morrow, and C. M. Agarwal, A Comprehensive Plan to Improve Retention and Graduation Rates in Engineering Fields, American Society for Engineering Education, San Antonio, TX, 2012. 4 B. L . Yoder, Engineering by the Numbers: ASEE Retention and Time-to-Graduation Benchmarks for Undergraduate Engineering Schools, Departments, and Programs, American Society for Engineering Education, Washington D.C., 2016. 5 S. S. Steinberg, The relations of secondary mathematics to engineering education, Mathematics teacher, Vol. 42, No. 8, 1949. 6 C. Adelman, Women and men of the engineering path: A model for the analysis of undergraduate careers, U.S. Department of Education, Washington, DC, 1998. 7 M. Besterfield-Sacre, C. J. Atman and L. J. Shuman, Characteristics of freshman engineering students: Models for determining student attrition in engineering, Journal of Engineering Education, Vol. 86, No. 2, pp. 139149, 1997. 8 S. G. Brainard and L. Carlin, A six-year longitudinal study of undergraduate women in engineering and science, Journal of Engineering Education, Vol. 87, No. 4, pp. 369375, 1998. 9 E. C. Kokkelenberg and E. Sinha, Who succeeds in STEM studies? An analysis of Binghamton University undergraduate students, Economics of Education Review, 29, pp. 935946, 2010. 10 B. Geisinger and D. R. Raman, Why They Leave: Understanding Student Attrition from Engineering Majors, International Journal of Engineering Education, Vol. 29, No. 4, pp. 914925, 2013. 11 L. Y. Yang and B. Grauer, Examining the Effectiveness of Scholars Assisting Scholars Program Among Undergraduate Engineering Students," American Society for Engineering Education, Salt Lake City, UT, 2018. 12 M. I. Abid and Z. H. Khan, Towards a Holistic Approach to Improve the Retention Rate of Freshman in Engineering, 2018 IEEE Conference on Teaching, Assessment, and Learning for Engineers (TALE), pp. 662 667, 2018. 13 Women, Minorities, and Persons with Disabilities in Science and Engineering, NSF National Center for Science and Engineering Statistics, Arlington, VA, 2017. 14 M. Diederich Ott, Retention of Men and Women Engineering Students, Research in Higher Education, Vol. 9, No. 2, pp. 137-150, 1978. 15 M. Brown, M. Hitt, A. Stephens and E. Dickman, Rocky Mountain Scholars Program: Impact on Female Undergraduate Engineering Students, International Journal of Engineering Pedagogy, Vol. 10, No. 4, pp. 9 24, 2020.  ...

... Paper ID #36713 Implementing Project Based System Analysis in Introductory Engineering Thermodynamics Jeffrey David Carvell (Assistant Professor of Physics and Engineering) PhD. Physics, Purdue University American Society for Engineering Education, 2022 Powered by www.slayte.com Implementing Project Based System Analysis in Introductory Engineering Thermodynamics Abstract: The following paper is an evidence-based practice paper. When first teaching introductory engineering thermodynamics, it was seen that the lowest scores in the semester occurred on questions regarding full thermodynamic system applications, such as power plants, internal combustion engines, and other similar systems. Typically, grades up to that point on homework assignments and exams were good, but dropped sharply with the system analysis. Even if the grades on individual component pieces were good, when combining them together, something was happening with the understanding or application. After several years of seeing this trend, a new method of teaching and learning for these systems was implemented. Instead of assigning homework problems, and making students solve different versions of systems, a team based project was used to apply the concepts of thermodynamic system analysis. During class periods, base systems of power plants and internal combustion engines were introduced. Students and faculty worked together and solved example problems for the base systems, so students had a beginning point and a basic solution to work from. The student groups then chose their project. The project consisted of choosing a basic system, and making at least two changes to the overall functioning of the system. Changes could be as simple as adding components, such as reheat cycles, to a power plant, or adding a nitrous boost to an internal combustion engine. Some changes students made were more complicated, for example changing the working fluid in a power plant to liquid salt instead of water. Students were asked to make the two changes, then perform full thermodynamic analysis, including first law, second law, and efficiency or coefficient of performance calculations, including for a range of input conditions. The groups then had to submit a full written report with results, and present their work either in class or at the annual university research symposium. The project has been implemented and part of the course for 4 years now, as much time as the course was taught without the project. On average, the students now score 15% higher on the same exam questions as they did without the project using traditional homework assignments. Keywords: Thermodynamics, Project based learning, Project implementation Introduction: The following paper is an evidence-based practice paper. Eight years ago, the institution I teach at, Marian University in Indianapolis, Indiana, introduced a new course into the curriculum for engineering students. I was assigned to teach this new course, Engineering Thermodynamics. As I was preparing to teach this course, one thing I saw was the difficulties others had documented both in teaching and learning the subject matter [1],[2],[3],[4],[5]. I went into the course looking to see where any problems would occur. For this thermodynamics course, the topics covered started with heat transfer and transfer mechanisms, then moved to the First and Second Laws of Thermodynamics, introducing steam tables along the way. Next, the class covered entropy and isentropic processes. While covering these topics, methods used included traditional lectures, in-class examples, homework assignments assigned from the textbook, and in-class group problem solving sessions. Three exams were given, and the class had a relatively high average for grades. After the last in semester exam, the final topics covered vapor power plants, the Rankine Cycle, and internal combustion engines. The topics were taught using the same methods as previous topics, and the practice problems on homework assignments and group sessions was similar. In regards to vapor power plants, the standard base Rankine Cycle system, shown in Figure 1, was the first model introduced, and one example was done to solve this system in class. Next, we would cover the changes that could be made to this basic system, such as reheat, superheat, etc. For each change, we would solve one example problem for the system in class, and they would have one or two on a homework assignment. Figure 1: Standard Rankine Cycle Power Plant used in examples for class [6] On the internal combustion engine, I would introduce the basic engine system, as shown in Figure 2. We covered the different methods of solving engine systems, including Otto, Diesel, and Dual cycles, and we would solve one example of each in class, with at least 1 on each being assigned on the homework. Figure 2: Standard piston cylinder engine and Otto Cycle diagram [7] At this point, students were solving problems as groups, turning in homework assignments, and there was no sense of anything wrong. The final exam for this thermodynamics course was a cumulative final consisting of six questions. Four of the questions were review, from the earlier material and earlier exams. Two questions were based off the vapor power plants and internal combustion engines. On the final, one problem on each, using the basic systems, was given to the students. These problems are shown in Figure 3. Figure 3: Final exam questions on engines and Rankine cycle power plants During grading of the final exam, it was clear that two problems on the test were scoring low, the problems on power plant systems and internal combustion engines. The grades on the final exam were lower on average than the rest of the semester. Since there were noticeable differences, I looked at the average scores on the review questions as a whole, and the average score on the power plant and engine questions. The class average on the four review questions was an 86%. The average on the two other questions was a 57%. It was clear something was wrong, or the students didnt completely connect to these topics as well as they did the others. As I reviewed the course and looked at what other teachers had to say, I could see that this topic was one that typically was harder to teach and harder to grasp [8],[9],[10],[11],[12],[13]. Moving into the next year, and the second attempt at teaching this class, I came in with the knowledge of where the difficulty would lie. The beginning of the course proceeded in a similar manner to the year before, and the grades were good. When we got to power plants and engines, I decided to add more examples on the base systems, thinking students needed to see more. Since the previous years exam was not returned, the same problems were used in the following years. After the final exam, it didnt seem to do much, as the scores were still very different, and the two questions on the base systems were still in the low 60% range. At the conclusion of the course, I again reviewed other sources looking for ways to improve, but I also noticed something on student evaluations. Many of the students in this class stated that they felt the textbook and problems didnt do a good job on the final few topics. So for the third year of teaching the course, I changed the textbook. Over the next two years, with a new book and more examples on power plants and engines, I still did not see a change in the scores on those problems on the final exam. After four years, the overall average on the four review questions on the final was 81%, and the four year average on the power plant and engine problems was 63%. After again reviewing the course, it was clear that I needed to try something new when teaching the power plant and engine topics. For the fifth year of the course, I cut back on the homework problems on the basic systems, assigning only two problems on basic power plants, and two problems on basic internal combustion engines. In place of the extra homework problems, students were assigned a project based on one of the two topics. Students worked in groups on the project and presented it at the end of the semester. The course has now been taught with the project for four years, and the average on the two questions on the final has increased 15%. Methods: The only difference for this class between the first four years and the following four years was the project. During the later four-year period, as mentioned above, the basic power plant and engine systems were the only ones extensively taught during class. The subsystems and changes were discussed, but no example problems were done in class. Instead, three or four examples on each of the basic systems were done. The homework assignments for this section consisted of only basic systems. Instead of covering extensively the different types of systems, students were asked to do this in a project. Over the course of the eight years this course was taught, the student demographics in the class varied. This course is taken by all engineering majors at Marian University, so the majors vary as well. Of eighty-one total students in the class, fifty-one (63%) have been mechanical engineering majors, thirteen (16%) have been biomedical engineers, five (6%) have been electrical engineers, four (5%) each in computer engineering and engineering physics, and two (2.5%) each in motorsports engineering and energy engineering. Additionally, twenty-four students (29%) have been female. Sixty students (74%) have been scholarship student-athletes. The percentages held between the group without the project and group with the project, within 3%. For the project, students are allowed to work in groups up to three students. They can choose the groups, and are asked to design a thermodynamic system using any components they want to use, and perform analysis on each component and the system in general to evaluate performance. The system has be something different from the base systems explained in class. They must change AT LEAST two components to one of the systems but can add as many as they would like. Changes to the basic system suggested include adding constant-pressure contraction to a diesel engine or adding a superheat system to the basic Rankine Cycle. Students could also choose to change the working fluid in the system or change basic parameters such as boiler pressure. The project requires students to fully analyze the system they design. They are asked to pick reasonable values for the states of the system. For example, they are asked to not use the pressure of intake air for an engine as six atm; use standard one atm pressure, so that these are reasonable systems for analysis. Students are required to show all calculations and assumptions for the system, and define the pressure, temperature, specific enthalpy, specific internal energy, and specific volume at each state. They are asked to calculate the heat added, heat removed, power developed, and power input for each stage, and find the efficiency of their system. They are also required to prove that the system is thermodynamically possible using the First and Second Laws of Thermodynamics. As part of the project, each group needs to create plots showing the efficiency of their system for varying input states, such as variable air temperature. Finally each group is asked to submit a full written report with a diagram of the system, as well as any calculations and plots as described above. They must also explain all the steps involved in the calculations, and detailed explanations of every step of their system, including changes they made. At the end of the semester, each group must present their system to their classmates as a group oral presentation. During the presentation, each group is required to present the information, calculations, and results of their project. During this portion of the project, students are essentially teaching each other the material. Rather than working on their own on a homework problem with similar changes made to the base system, they are listening to detailed reports from fellow students of how the changes effect each system. Each group is required to walk through the steps and calculations, and all students end up seeing multiple systems explained to them by each other. Each group is also given a chance to obtain extra credit for their project. In addition to the oral presentation on the project they give to the class, students are given the option to present the project as a poster at Marians Undergraduate Research Symposium. This poster presentation is open not just to engineering students and faculty, but to all majors across all schools at the university. Students have given feedback that this interaction is helpful, as they often have to explain their systems and their projects to faculty from liberal arts departments who dont have much knowledge on the topic. The groups are teaching not only each other, but they are teaching people outside their area of study who have never been in this class or studied this material. The students have given feedback that this only helps more as it makes them learn the system more and requires them to be able to explain the details on what they have done, Results: Over the four years that the project has been a part of the course, the projects and changes made have been interesting and very different. Each year, the groups try to do something new, and something that interests them or relates to other work they are doing. One of the first projects submitted was a Rankine cycle that added a reheat element to it. The diagram of the system created by the students is shown in Figure 4. The second change to the base system the group made was to change the working fluid from water to lithium nitrate. At the time, two chemistry students were taking the course, and they were doing independent research with chemistry faculty using lithium nitrate, so they used the same material here. An interesting result they found was that they system didnt work well except for a small range of values, so they only got a single efficiency of their system at 42%, an increase from the standard system using their values with water, which had an efficiency of 23%. Figure 4: Designed system with ideal Rankine cycle with Reheat used as a model to evaluate using molten lithium nitrate as medium fluid In the years since the first project, several groups have followed the same method of changing the working fluid, and each time they have chosen different fluids. One group followed a very similar model, adding reheat, but using potassium instead of water. The diagram for this system is seen in Figure 5. This group programmed code into MatLab to process their data and changes, and they found that the system is impossible. No matter the initial conditions, the group found potassium wouldnt work as the fluid in a Rankine cycle. Figure 5: Rakine cycle with reheat using potassium as the working fluid Another group changed the Rankine cycle fluid to ammonia and added a second pump to the system. Their diagram, along with a graph of the effects on the efficiency of the system is shown in Figure 6. Figure 6: Rankine cycle using ammonia as working fluid with second pump Other groups decided to make changes to the standard Otto cycle engine system. One group added an intercooling system and increased the compression ratio of the engine to 10, and saw an increase from 21% efficiency to 70% efficiency. Another group took the standard engine, and added a turbo system, while increasing the compression ratio, and analyzed using different fuels. Their hand drawn diagram, along with a graph of efficiency of the engine with different pressures and different fuels is shown in Figure 7. Figure 7: Engine with turbocharger and graph of efficiency changes. Other groups have asked for permission to venture outside the standard systems we used in class. One group worked with a jet engine, and found the output work and output speed of the jet engine as the input velocity of air varied. Another group used a Brayton cycle refrigerator, using R134-a and varying condenser temperatures. They obtained a graph of the coefficient of performance based on the condenser temperature, and that is shown in Figure 8. COP COP vs. Temp 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 y = 794589x-3.649 0 20 40 60 80 100 120 Temprature Figure 8: Graph of Coefficient of performance as a function of condenser temperature for a Brayton refrigeration cycle. These projects are just some of the examples that students have turned in over the last four years. The key to the project was the effect it had on the final exam scores. The first year the project was introduced, the exact same two questions were used on the final exam. The average on these two questions jumped from a 63% the prior four years, to a 73% with the project. For one year, this could have been an outlier, but the trend continued, and actually got even better. The project has now been used the same number of years it has not been used, and Table 1 shows the data for these sets. Number of Years Number of Students Average Percent Score on Review Questions Average Percent Score on Rankine Cycle and Engine Questions Without Project 4 37 81 63 With Project 4 44 82 78 Table 1: Average scores on Final Exam questions based on project inclusion in course As you can see in the Table 1, the average score on the Rankine cycle and Engine problems increased from 63% in the four years without the project, to a 78% in the four years with the project, a 15% increase in overall score. The yearly scores have also showed a steady increase year-over-year. As I can provide students example projects and they see what has been done, they can then apply that to their own project, and the projects become more in depth. The more detailed and complicated the projects, the better they seem to do. Figure 9 shows a graph of the average scores on the Rankine cycle and engine problems year-to-year, and the increase while using the project can be clearly seen. Also in Figure 9 is the average scores over the four years without the project, and the scores jump around and there is not a set pattern. Average Score on Rankine Cycle and Engine Problems, Yearto-year 90 85 Average Score 80 75 70 65 With Project 60 Without Project 55 50 45 40 0 1 2 3 4 5 Reference Year Number Figure 9: Year-to-year comparison graph of average scores on Rankine cycle and engine problems Discussion and Conclusions: After teaching Introduction to Engineering thermodynamics for four years, it was clear that students struggled on the final exam on two questions, one on the Rankine cycle, and the other on internal combustion engines. A project was introduced in which students had to design and present their own power plant or engine system. Since the introduction of the project, the average score on these two questions on the final has increased from 63% to 78%, a 15% overall increase. I believe that this is a significant result. Although the numbers of students are not large, eighty-one students over ten years is an average of around ten students per class. At Marian University, that is a typical size class for upper-level math, physics, and engineering classes, so this would seem to be statistically relevant results. There is a chance the problems have started to leak, but this is a large increase in these specific problems, and no change in the rest of the final exam. If this was related to a leaked exam, I would expect all problems to increase. Since the final exams are not returned, the problems would only leak if a student was able to memorize the problem. All students have been told, for the entire eight years, that these topics would be covered on the final. When I designed this project, I did so with the intent that a more hands-on, design based approach would be more popular with students, and a project they chose would keep their interest better than standard homework problems. As they work now with the project, the students are learning the method multiple times as they redo and re-calculate all the terms and take all the proper steps. As they apply these steps, they think through the problems more than if they are just trying to solve a textbook homework problem. Many engineering educators believe that implementing design into courses is useful as it better prepares students for future work. These results show agreement with that belief and show that students can learn topics better using the design aspect over homework problems. In addition, in having to present the project, they are required to understand the topic even more. I have thought for as long as Ive taught physics and engineering that if students are able to present work and teach each other, it makes them have a better understanding of the topics. Students were asked in final course evaluations to comment on the project for the past four years and asked for their opinions on the project and if they thought it helped them for the final. Although student evaluations are not always the most accurate, in this case, thirty-eight of the forty-four students have responded to this question, and all have had positive things to say about it. Some examples include The project did help me in preparing for the final exam. and I feel that the project helped advance my learning. I felt that the design project gave me a reason to think about these problems, and the real-world applications helped. One comment that stood out seemed negative at first, but turned positive in the end when the student said I did not like having to present the project. I would have liked to just prepare a report. But, as much as I didnt like this, I think it did help me understand the topics better, as I had to go over it all many times to feel comfortable to present. An increase of 15% is very good for these problems. In the future, I would continue to watch the scores for these two problems and see if they continue to increase. Over time, as the project is fine-tuned and used more, I would hope to see the average percent on the Rankine and engine problems become higher than the review questions students see on other exams during the semester. Future work on this project would include a more robust analysis of the grades within the demographics mentioned in the methods. It is an interesting thought to analyze the performance based on type of engineering major, male/female performance, ethnicity, foreign students, and other similar demographics. Works Cited: 1 C. R. Martin, J. Ranalli and J. P. Moore, Problem-based learning module for teaching thermodynamic cycle analysis Using PYroMat, American Society of Engineering Education Annual Conference and Exposition, June 2017. 2 N. Dukham and M. Schumack, Understanding the Continued Poor Performance in Thermodynamics as a First Step toward an Instructional Strategy, American Society of Engineering Education Annual Conference and Exposition, June 2013. 3 N. Dukham, Framing Students Learning Problems of Thermodynamics, American Society of Engineering Education Annual Conference and Exposition, June 2016. 4 D. Meltzer, Investigating and Addressing Learning Difficulties in Thermodynamics, American Society of Engineering Education Annual Conference and Exposition, June 2008. 5 J. P. OConnell, Challenges to Teaching and Learning Thermodynamics, Chemical Engineering Education, Vol. 53, No. 1, pp. 1 9, Winter, 2019. 6 J. R. Reisel, Principles of Engineering Thermodynamics, 1st Edition, Boston, MA, USA: Cengage Learning, 2016. 7 M.J. Moran, H. N. Shapiro, D. D. Boettner and M. B. Bailey, Fundamentals of Engineering Thermodynamics, 8th Edition, New York, NY, USA: Wiley, 2014. 8 W. Yeadon and M. Quinn, Thermodynamics Education for Energy Transformation: a Stirling Engine Experiment, Physics Education, Vol. 56, pp. 055033, 2021. 9 N. Mulop, K. M. Yusof, and Z. Tasir, A Review on Enhancing the Teaching and Learning of Thermodynamics, Procidia Social and Behavioral Sciences, Vol. 56, pp. 703-712, 2012. 10 J. P. Abulencia, M. A. Vigeant and D. L. Silverstein, Using Video Media to Enhance Conceptual Learning in an Undergraduate Thermodynamics Course, American Society of Engineering Education Annual Conference & Exposition, June 2012. 11 C. G. Deacon, R. Goulding, C. Haridass and B. de Young, Demonstration Experiments with a Stirling Engine, Physics Education, Vol. 29, pp. 180183, 1994. 12 A. Abuelyamen and R. Ben-Mansour, Energy Efficiency Comparison of Stirling Engine Types (, and ) Using Detailed CFD Modeling, International Journal of Thermal Sciences, Vol. 132, pp. 411423, 2018. 13 J. A. Caton, Maximum Efficiencies for Internal Combustion Engines: Thermodynamic Limitations, International Journal of Engine Research, Vol. 19, pp. 10051023, 2018.  ...

... LODAY CONSTRUCTIONS ON TWISTED PRODUCTS AND ON TORI arXiv:2002.00715v1 [math.AT] 3 Feb 2020 ALICE HEDENLUND, SARAH KLANDERMAN, AYELET LINDENSTRAUSS, BIRGIT RICHTER, AND FOLING ZOU Abstract. We develop a spectral sequence for the homotopy groups of Loday constructions with respect to twisted products in the case where the group involved is a constant simplicial group. We show that for commutative Hopf algebra spectra Loday constructions are stable, generalizing a result by Berest, Ramadoss and Yeung. We prove that several truncated polynomial rings are not multiplicatively stable by investigating their torus homology. Introduction When one studies commutative rings or ring spectra, important homology theories are topological Hochschild or its higher versions. These are specific examples of the Loday construction, whose definition relies on the fact that commutative ring spectra are enriched in simplicial sets: for a simplicial set X and a commutative ring spectrum R one can define the tensor X R as a simplicial spectrum whose n-simplices are ^ R. xXn By slight abuse of notation X R also denotes the commutative ring spectrum that is the geometric realization of this simplicial spectrum. This recovers topological Hochschild homology of R, THH(R), when X = S 1 , and higher topological Hochschild homology, THH[n] (R), for higher dimensional spheres S n . Tensoring satisfies several properties [8, VII, 2, 3], two of which are: If X is a homotopy pushout, X = X1 hX0 X2 , then the tensor product of R with X splits as a homotopy pushout in the category of commutative ring spectra which is the derived smash product: (X1 hX0 X2 ) R (X1 R) L (X0 R) (X2 R). A product of simplicial sets X Y gives rise to an iterated tensor product: (X Y ) R X (Y R). This last expression does not, however, imply that calculating the homotopy groups of (XY )R is easy. In particular, if one iterates the trace map from algebraic K-theory to topological Hochschild homology n times, one obtains a map K (n) (R) = K(K(. . . (K (R)) . . .)) (S 1 . . . S 1 ) R. | {z } | {z } n n Since iterated K-theory is of interest in the context of chromatic red-shift, one would like to know as much about (S 1 . . . S 1 ) R as possible. Date: February 4, 2020. 2000 Mathematics Subject Classification. Primary 18G60; Secondary 55P43. Key words and phrases. torus homology, (higher) Hochschild homology, (higher) topological Hochschild homology, stability, twisted Cartesian products. 1 In some good cases, the homotopy type of X R only depends on the suspension of X in the sense that if X Y , then one has X R Y R. This property is called stability. Stability for instance holds for Thom spectra R that arise from an infinite loop map to the classifying space BGL1 (S) (see Theorem 1.1 of [25]), or for R = KU or R = KO [14, 4]. One can also work relative to a fixed commutative ring spectrum R and consider commutative R-algebra spectra A and ask whether X R A only depends on the homotopy type of X. In this paper, we will often work with coefficients: we look at pointed simplicial sets X and place a commutative A-algebra spectrum C at the basepoint of X. In other words, when X is pointed then the inclusion of the basepoint makes X R A into a commutative A-algebra and we can look at LR X (A; C) = (X R A) A C, the Loday construction with respect to X of A over R with coefficients in C. We call the pair (A; C) stable if the homotopy type of LR X (A; C) only depends on the homotopy type of X. Note that the ring R is not part the notation when we say that (A; C) is stable although the question depends on the choice of R, so the context should specify the R we are working over. We call the commutative R-algebra A multiplicatively stable as in [14, R Definition 2.3] if X Y implies that LR X (A) LY (A) as commutative A-algebra spectra. If A is multiplicatively stable, then for any cofibrant commutative A-algebra C, the pair (A; C) is stable (see [14, Remark 2.5]). We investigate several algebraic examples, i.e., commutative ring spectra that are Eilenberg Mac Lane spectra of commutative rings. For instance we show that the pairs (HQ[t]/tm ; HQ) are not stable for all m > 2, extending a result by Dundas and Tenti [7]. We also prove integral and mod-p versions of this result. Work of Berest, Ramadoss and Yeung implies that the homotopy types of LHk X (HA; Hk) and Hk LX (HA) only depend on the homotopy type of X if k is a field and if A is a commutative Hopf algebra over k. We generalize this result to commutative Hopf algebra spectra. Moore introduced twisted cartesian products as simplicial models for fiber bundles. We develop a Serre type spectral sequence for Loday constructions of twisted cartesian products where the twisting is governed by a constant simplicial group. As a concrete example we compute the Loday construction with respect to the Klein bottle for a polynomial algebra over a field with characteristic not equal to 2. Content. In Section 1 we recall the definition of the Loday construction and fix notation. Section 2 contains the construction of a spectral sequence for the homotopy groups of Loday constructions with respect to twisted cartesian products. Our results on commutative Hopf algebra spectra can be found in Section 3. In Section 4 we prove that truncated polynomial algebras of the form Q[t]/tm and Z[t]/tm for m > 2 are not multiplicatively stable by comparing the Loday construction of tori to the Loday construction of a bouquet of spheres corresponding to the cells of the tori. We also show that for 2 6 m < p the Fp -algebra Fp [t]/tm is not stable. Acknowledgements. We thank the organizers of the third Women in Topology workshop, Julie Bergner, Angelica Osorno, and Sarah Whitehouse, and also the Hausdorff Institute of Mathematics for their hospitality during the week of the workshop. We thank the Hausdorff Research Institute for Mathematics, grants nsf-dms 1901795 and nsf-hrd 1500481AWM ADVANCE, and the Foundation Compositio Mathematica for their support of the workshop. We thank Maximilien Peroux for help with coalgebras in spectra, Inbar Klang for a helpful remark about norms, Mike Mandell for a helpful discussion on En -spaces, Jelena Grbic for pointing out [23] to us, and Thomas Nikolaus for -category support. AL was supported by Simons Collaboration Grant 359565. The last two authors thank the Department of Mathematics at Indiana University for its hospitality and BR thanks the Department of Mathematics at Indiana University for support as a short-term research visitor in 2019. 2 1. The Loday construction: basic features We recall some definitions concerning the Loday construction and we fix notation. For our work we can use any good symmetric monoidal category of spectra whose category of commutative monoids is Quillen equivalent to the category of E -ring spectra, such as symmetric spectra [12], orthogonal spectra [17] or S-modules [8]. As parts of the paper require us to work with a specific model category we chose to work with the category of S-modules. Let X be a finite pointed simplicial set and let R A C be a sequence of maps of commutative ring spectra. Definition 1.1. The Loday construction with respect to X of A over R with coefficients in C is the simplicial commutative augmented C-algebra spectrum LR X (A; C) given by ^ LR (A; C) = C A n X xXn \ where the smash products are taken over R. Here, denotes the basepoint of X and we place a copy of C at the basepoint. The simplicial structure of LR X (A; C) is straightforward: Face maps di on X induce multiplication in A or the A-action on C if the basepoint is involved. Degeneracies si on X correspond to the insertion of the unit maps A : R A over all n-simplices which are not hit by si : Xn1 Xn . As defined above, LR X (A; C) is a simplicial commutative augmented C-algebra spectrum. In the following we will always assume that R is a cofibrant commutative S-algebra, A is a cofibrant commutative R-algebra and C is a cofibrant commutative A-algebra. This ensures that the homotopy type of LR X (A; C) is well-defined and depends only on the homotopy type of X. Remark 1.2. When R A C is a sequence of maps of commutative rings, we can of course use the above definition for HR HA HC. The original construction by Loday [15, Proposition 6.4.4] used O C A xXn \ instead with the tensors taken over R as the n-simplices in LR X (A; C). This algebraic definition also makes sense if R is a commutative ring and A C is a map of commutative simplicial R-algebras. It continues to work if R is a commutative ring and A C is a map of graded-commutative R-algebras, with the n-simplices defined as above, but the maps between them require a sign correction as terms are pulled past each othersee [21, Equation (1.7.2)]. An important case is X = S n . In this case we write THH[n],R (A; C) for LR S n (A; C); this is the higher order topological Hochschild homology of order n of A over R with coefficients in C. Let k be a commutative ring, A be a commutative k-algebra, and M be an A-module. Then we define THH[n],k (A; M ) := LHk S n (HA; HM ). If A is flat over k, then THHk (A; M ) = HHk (A; M ) [8, Theorem IX.1.7] and this also holds for [n],k higher order Hochschild homology in the sense of Pirashvili [21]: THH[n],k (A; M ) = HH (A; M ) if A is k-flat [4, Proposition 7.2]. Given a commutative ring A and an element a A, we write A/a instead of A/(a). 3 2. A spectral sequence for twisted cartesian products We will start by letting R A be a map of commutative rings and we study Loday constructions LR B (A ) over a finite simplicial set B, where indicates a twisting by a discrete group G that acts on A via ring isomorphisms. This construction can be adapted as in Definition 1.1 and Remark 1.2 to allow coefficients in an A-algebra C if B is pointed, and to the case where R A is a map of commutative ring spectra, or R is a commutative ring and A is a graded-commutative R-algebra or a simplicial commutative R-algebra. If we have a twisted cartesian product (TCP) in the sense of [18, Chapter IV] E( ) = F B where the fiber F is a simplicial R-algebra and the simplicial structure group G acts on F by simplicial R-algebra isomorphisms, it is possible to generalize this definition of the Loday construction to allow twisting by a simplicial structure group, as expained in Definition 2.1 below. We show an example where such a TCP arises: if we start with a TCP of simplicial sets E( ) = F B with twisting in a simplicial structure group G acting on F simplicially on the left and with a map of commutative rings R A, we can use that twisting to construct a TCP with fiber equal R to the simplicial commutative R-algebra LR F (A) and with the structure group G acting on LF (A) by R-algebra isomorphisms. In that situation, we get that LR (A) = LR (LR (A) ), B E( ) F R R which generalizes the fact that for a product, LR F B (A) = LB (LF (A)). If the structure group G is discrete, i.e., if G is a constant simplicial group, LR E( ) (A) can be written as a bisimplicial set and we get a spectral sequence for calculating its homotopy groups. Definition 2.1. Let B be a finite simplicial set, R be a commutative ring, and A be a commutative R-algebra (or a graded-commutative R-algebra, or a simplicial commutative R-algebra). Let G be a discrete group acting on A from the left via isomorphisms of R-algebras, and let be a function from the positive-dimensional simplices of B to G so that (2.2) (b) (di b) (si b) (s0 b) = = = = [ (d0 b)]1 (d1 b) (b) (b) eG for for for for q > 1, b Bq , i > 2, q > 1, b Bq , i > 1, q > 0, b Bq , and q > 0, b Bq . The twisted Loday construction with respect to B of A over R twisted by is the simplicial com mutative (resp., graded-commutative, or bisimplicial commutative) R-algebra LR B (A ) given by O R LR A B (A )n = LBn (A) = bBn where the tensor products are taken over R, with O O Y d0 fb = gc with gc = (b)(fb ), cBn1 bBn di O bBn si O bBn fb = fb = O b:d0 b=c gc with gc = cBn1 O Y fb for 1 i n, and b:di b=c hd with hd = dBn+1 Y fb for 0 i n. b:si b=d We should think of the copy of A sitting over a simplex b Bn as sitting over its 0th vertex, and of (b) as translating between the A over bs 0th vertex and the A over bs 1st vertex. 4  Lemma 2.3. The definition above makes LR B (A ) into a simplicial set. Proof. To check this we need only check the relations involving d0 , since the ones that do not involve work in the same way that they do in the usual Loday construction. For j > 1, we get d0 dj = dj1 d0 because in both terms, for any c Bn2 we get the product over all b Bn with d0 dj b = dj1 d0 b = c of terms that are either (b)(fb ) or (dj b)(fb ). These are the same by the condition in Equation (2.2) above. For j = 1, we get the product over all b Bn with d0 d1 b = d0 d0 b = c of terms that are either (d1 b)(fb ) or (d0 b) (b)(fb ), which again agree by Equation (2.2). We get d0 s0 = id since (s0 b) = eG , and d0 si = si1 do for i > 0 since for those i, (si b) = (b).  Following Moore, May considers the following simplicial version of a fiber bundle [18, Definition 18.3]: Definition 2.4. Let F and B be simplicial sets and let G be a simplicial group which acts on F from the left. Let : Bq Gq1 for all q > 0 be functions so that d0 (b) (di+1 b) (si+1 b) (s0 b) = = = = [ (d0 b)]1 (d1 b) di (b) si (b) eq for for for for q > 1, b Bq , i 1, q > 1, b Bq , i 0, q > 0, b Bq , and q > 0, b Bq . The twisted Cartesian product (TCP) E( ) = F B is the simplicial set whose n-simplices are given by E( )n = Fn Bn , with simplicial structure maps (i) d0 (f, b) = ( (b) d0 f, d0 b), (ii) di (f, b) = (di f, di b) i > 0, and (iii) si (f, b) = (si f, si b) i 0. These structure maps satisfy the necessary relations to be a simplicial set because of the conditions that satisfies. Definition 2.5. If R is a commutative ring and E( ) = C B is a TCP as in Definition 2.4 where C is a commutative simplicial R-algebra and the simplicial group G acts on C by R-algebra isomorphisms (that is, for every q 0, the group Gq acts on the commutative R-algebra Cq by R-algebra isomorphisms) then we can use the twisting to define the twisted Loday construction with respect to B of C over R, twisted by , O R Cn LR B (C )n = LBn (Cn ) = bBn N with twisted structure maps given on monomials bBn fb , with fb Cn for all b Bn , by O Y O (b)(d0 fb ), gc with gc = d0 fb = cBn1 bBn (2.6) di O bBn si O bBn fb = fb = O b:d0 b=c gc with gc = cBn1 O Y di fb for 1 i n, and b:di b=c hd with hd = dBn+1 Y b:si b=d 5 si fb for 0 i n. Note that there are two sets of simplicial structure maps being used, those of C inside and those of B outside. This looks like the diagonal of a bisimplicial set, but since our twisting : Bq+1 Gq explains only how to twist elements in Cq , this is not the case unless the structure group G is a discrete group, viewed as a constant simplicial group. If the structure group G is discrete, there is overlap between Definition 2.1 and Definition 2.5. The simplicial commutative R-algebra case of Definition 2.1 actually gives a bisimplicial set: we use only the simplicial structure of B in the definition and if A also has simplicial structure, that remains untouched. The diagonal of that bisimplicial set agrees with the constant simplicial group case of Definition 2.5. Given any TCP of simplicial sets E( ) = F B as in Definition 2.4 and a map R A of commutative rings, we can construct LR F (A) B which is a TCP of commutative simplicial algebras R-algebras as in Definition 2.5 using the same structure group G and twisting function : Bq Gq1 . We use the simplicial left action of Gn on Fn which we denote by (g, f ) 7 gf to obtain a left action by simplicial R-algebra isomorphisms R Gn LR Fn (A) LFn (A) O O (g, af ) 7 ag1 f . (2.7) f Fn f Fn Since the original action of Gn on Fn was a left action, this is a left action. In the original monomial, the f th coordinate is af . After g Gn acts on it, the f th coordinate is bf = ag1 f . After h Gn acts on the result of the action of g, the f th coordinate is bh1 f = ag1 h1 f , which is the same as the result of acting by hg on the monomial. Proposition 2.8. If E( ) = F B is a TCP and R A is a map of commutative rings, and we use the simplicial set twisting function to construct a simplicial R-algebra twisting function to obtain a TCP LR F (A) B as above, we get that LR (A) = LR (LR (A) ). B E( ) F This uses the definition of the Loday construction of a simplicial algebra twisted by a simplicial group in Definition 2.5. Proposition 2.8 generalizes the well-known fact that for a product of simplicial sets, LR (A) = LR (LR (A)). F B B F R R Proof. Both LR E( ) (A) and LB (LF (A) ) have the same set of n-simplices for every n > 0: O O O O A= A ( A). = eE( )n bBn (f,b)Fn Bn f Fn We have to show that the simplicial structure maps agree with respect to this identification. For 1 6 i 6 n, for any choice of elements x(f,b) A, O O y(g,c) di x(f,b) = (g,c)Fn1 Bn1 (f,b)Fn Bn where y(g,c) = Y x(f,b) = Y b:di b=c (f,b):(di f,di b)=(g,c) Y f :di f =g x(f,b) . The internal product on the right-hand side is what we get from di on LR F (A) and the external product is what we get from di of LR , so this agrees with the definition in Equation (2.6). B 6 The proof that the si , 0 6 i 6 n agree is very similar. The interesting case is that of d0 . For any choice of elements x(f,b) A, the boundary d0 associated to LR E( ) (A) satisfies O O (2.9) d0 x(f,b) = y(g,c), (f,b)Fn Bn (g,c)Fn1 Bn1 where y(g,c) = Y x(f,b) = Y b:d0 b=c (f,b):d0 (f,b)=(g,c) Y f : (b)d0 f =g x(f,b) . R From the LR B (LF (A)) point of view, by Equation (2.6). O O O Y O d0 ( x(f,b) ) = (b)d0 x(f,b) bBn f Fn f Fn cBn1 b:d0 b=c = O Y O Y cBn1 b:d0 b=c = cBn1 b:d0 b=c = O (b) O Y gFn1 f :d0 f =g O Y x(f,b) gFn1 f :d0 f = (b)1 g Y (g,c)Fn1 Bn1 b:d0 b=c which is exactly what we got in (2.9). Y x(f,b) f :d0 f = (b)1 g x(f,b) ,  If G is a discrete group and E( ) is constructed using G, then for every q > 0 there is a function : Bq G satisfying the conditions listed in Equation (2.2) and G acts simplicially on F on the left. Theorem 2.10. If E( ) = F B is a TCP where the twisting is by a constant simplicial group G and if R A is a map of commutative rings so that (LR F (A)) is flat over R, then there is a spectral sequence (2.11) 2 R R Ep,q = p ((LR B ( LF (A) ))q ) p+q (LE( ) (A)). Here, LR F (A) is a graded commutative R-algebra. For any fixed p and q, we consider the degree R R R q part of LR Bp ( LF (A) ), (LBp ( LF (A) ))q . This forms a simplicial abelian group which in degree R p is (LR Bp ( LF (A)))q , with simplicial structure maps induced by those of B with the twisting by R , and p ((LR B ( LF (A) ))q ) denotes its pth homotopy group. The flatness assumption above is for instance satisfied if R is a field. Proof. Since the twisting is by a constant simplicial group G, we are able to form a bisimplicial R-algebra O O (2.12) (m, n) 7 A. bBm f Fn In the n-direction, the simplicial structure maps dFi and sFi will simply be the simplicial structure R maps of the Loday construction LR F (A) applied simultaneously to all the copies of LF (A) over all 7 B the b Bn . In the m direction, dB i and si are the simplicial structure maps of the twisted Loday construction, as in Equation (2.2) in Definition 2.1. These commute exactly because the simplicial structure maps in G are all equal to the identity. For any choice of xb LR F (A)n for all b Bm , O O O Y F xb = dB dFi (xb ) = (b)dFi (xb ) dB 0 di 0 bBm while dFi dB 0( O bBm cBm1 b:d0 b=c bBm xb ) = dFi which is the same since O Y cBm1 b:d0 b=c (b) xb = O Y dFi ( (b) xb ), cBm1 b:d0 b=c dFi ( (b) xb ) = di ( (b)) dFi (xb ) = (b) dFi (xb ). R R Note that since the twisting is by a constant simplicial group, LR E( ) (A) = LB (LF (A) ) is exactly the diagonal of the bisimplicial R-algebra in Equation (2.12). We use the standard result (see for instance [9, Theorem 2.4 of Section IV.2.2]) that the total complex of a bisimplicial abelian group with the alternating sums of the vertical and the horizontal face maps is chain homotopy equivalent to the usual chain complex associated to the diagonal of that bisimplicial abelian group. Since we know that the realization of the diagonal is homeomorphic to the double realization of the bisimplicial abelian group, in order to know the homotopy groups of the double realization of a bisimplicial abelian group, we can calculate the homology of its total complex with respect to the alternating sums of the vertical and the horizontal face maps. Filtering by columns gives an E 2 spectral sequence calculating the homology of the total complex associated to a bisimplicial abelian group consisting of what we get by first taking vertical homology and then taking horizontal homology. In the case of the bisimplicial abelian group we have in Equation (2.12), Pn the vertical qth homology of the columns will be the qth homology with respect to i=0 (1)i dFi of the complex O LR F (A) and this is isomorphic to q obtain N bBm q bBm
R LF (A) . Since O bBm LR =( F (A) we assumed that (LR F (A)) is flat over R, we O (LR F (A)))q . bBm N Here, the subscript q denotes the degree q part of the graded abelian group bBm (LR F (A)). N R Moreover, the effect of the horizontal boundary map on bBm (LF (A)) is the boundary of the twisted Loday construction, with the action of G on the graded-commutative R-algebra (LR F (A)) R induced by that of G on the commutative simplicial R-algebra LF (A). As the boundary map preserves internal degree, we get the desired spectral sequence.  2.1. Norms and finite coverings of S 1 . The connected n-fold cover of S 1 given by the degree n map can be made into a TCP as follows. Let B = S 1 be the standard simplicial circle and Cn = hi be the cyclic group of order n with generator . The twisting function : Sq1 Cn sends the non-degenerate simplex in S11 to and is then determined by Equation (2.2). Let F = Cn , viewed as a constant simplicial set, and let Cn act on F from the left. Then E( ) = F B is in fact another simplicial model of S 1 with n non-degenerate 1-simplices. Therefore, LR (A) LR1 (A) and (LR (A)) = HHR (A) E( ) E( ) S 8 R n is the constant commutative for every commutative R-algebra A. In this case, LR FA = A simplicial R-algebra, with the Cn -action given by (a1 an ) = an a1 an1 . As LR F (A) is a constant simplicial object, we obtain that ( AR n , = 0, L R (A) = F 0, > 0. If A is flat over R, the spectral sequence of Equation (2.11) is 2 R n R Ep,q = p (LR ) )q p+q LR E( ) (A) = HHp+q (A). S 1 (A But here, the spectral sequence is concentrated in q-degree zero, and hence it collapses, yielding p (LR1 (AR n ) ) = HHR (A). p S LSE( ) (A) With Proposition 2.8 we can identify if A is a commutative ring spectrum and we recover the known result (see for instance [2, p. 2150]) that THHCn (NeCn A) THH(A). (2.13) 1 Here, THHCn (A) = NCSn (A) is the Cn -relative THH defined in [2, Definition 8.2], where NeCn A is the Hill-Hopkins-Ravanel norm. See also [1, Definition 2.0.1]. The identification in (2.13) is an 1 1 instance of the transitivity of the norm: NCSn NeCn A NeS A. 2.2. The case of the Klein bottle. For the Klein bottle we compute the homotopy groups of the Loday construction of the polynomial algebra k[x] for a field k using our TCP spectral sequence and we confirm our answer using the following pushout argument. We assume that the characteristic of k is not 2, so 2 is invertible in k. Note that the Klein bottle can be represented as a homotopy pushout K (S 1 S 1 ) hS 1 D 2 . Since the Loday construction converts homotopy pushouts of simplicial sets into homotopy pushouts of commutative algebra spectra, we obtain LkK (k[x]) LkS 1 S 1 (k[x]) L Lk S1 (k[x]) LkD2 (k[x]). Homotopy invariance of the Loday construction yields that LkD2 (k[x]) = k[x], and as LkS 1 (k[x]) = HHk (k[x]) is well known to be isomorphic to k[x] (x) as a graded commutative k-algebra, we get that LkS 1 S 1 (k[x]) = LkS 1 (k[x]) k[x] LkS 1 (k[x]) = k[x] (xa , xb ) where the indices a and b allow us to distinguish between the generators emerging from each of the circles Sa1 Sb1 . Let Sc1 represent the circle along which we glue the disk, and call the corresponding generator in dimension one for the Loday construction over it xc . Let Sa1 denote the circle that Sc1 will go twice around in the same direction and Sb1 denote the circle that it will go around in opposite directions. So we have a projection K Sb1 . We can calculate LkK (k[x]) with a Tor spectral sequence whose E 2 -page is (2.14) 2 E, = Lk (k[x]) Tor, S 1   LkS 1 S 1 (k[x]), LkD2 (k[x]) k[x](xc ) (k[x] (xa , xb ), k[x]). = Tor, We need to understand the LkS 1 (k[x])-module structure on k[x] (xa , xb ), so we need to understand the map k[x] (xc ) k[x] (xa , xb ). 9 Since k[x] in both cases is the image of the Loday construction on a point, we know that x on the left maps to x on the right. If we map Sc1 to Sa1 Sb1 and then collapse Sa1 to a point, we end up with a map Sc1 Sb1 that is contractible, so if we only look at the xb part of the image of xc in (xa , xb ) (that is, if we augment xa to zero) we get zero. We deduce that k[x](xc ) Tor, (k[x] (xa , xb ), k[x]) (x ) k[x] = Tor, (k[x], k[x]) Tor, c ((xa ), k) Tork, ((xb ), k) (x ) = k[x] Tor, c ((xa ), k) (xb ). (x ) In order to calculate Tor, c ((xa ), k), we map Sc1 to Sa1 Sb1 and then collapse Sb1 to a point. This gives a map Sc1 Sa1 that is homotopic to the double cover of the circle as depicted below. We consider elements of LSc1 (k[x]), which we think of as built on the top circle, and of LSa1 (k[x]), which we think of as built on the bottom circle, and write them as sums of tensor monomials of ring elements with subscripts indicating the simplex each ring element lies over. Under this map, we have 1 vr1 x0 := 1s0 v0 1s0 v1 x0 11 7 1s0 v x x1 := 1s0 v0 1s0 v1 10 x1 7 1s0 v x Then d0 d1 maps these elements to the following: 0 r x0 7 1v0 xv1 xv0 1v1 x1 7 xv0 1v1 1v0 xv1 v0 Note that the sum of the images under d0 d1 is zero, and so x0 + x1 is a cycle with one copy of x in simplicial degree 1, which is what xc should be. Monomials that put the copy of x over s0 vi are the image under d0 d1 +d2 of monomials that put one copy of x over s20 vi , so do not contribute to the homology, and all cycles not involving those and involving only one copy of x are multiples of x0 + x1 , and so x0 + x1 represents xc . But we r v know that xa is represented by 1s0 v x , so we get that that xc 7 2xa . We take the standard resolution of k as a (xc )-module: ... xc // (xc ) xc // (xc ) Since we saw above that xc 7 2xa , tensoring () (xc ) (xa ) yields 2xa ... // (xa ) 2xa // (xa ) (x ) Since we assume that 2 is invertible in k, we get that Tor c ((xa ), k) = k, and so when 2 is invertible in k, the spectral sequence in Equation (2.14) has the form E2 = k[x] k (xb ) = k[x] (xb ), , and therefore also collapses for degree reasons, yielding Lk (k[x]) = k[x] (x). K Remark 2.15. In fact we have shown that LkK (k[x]) = LkS 1 (k[x]) and that the projection K Sb1 induces this isomorphism. 10 Now we want to get the same result using our TCP spectral sequence for A = k[x]. We will use the following simplicial model for the Klein bottle: K = (I S 1 )/(0, t) (1, flip(t)) where flip is the reflection of the circle about the y-axis. If we use the same model of the circle with two vertices and two edges that we used in the double cover picture above but we reverse the orientation on 0 so that both edges go top to bottom, this is a simplicial map preserving v0 and v1 and exchanging the i . The flip map induces a map on (LkS 1 (k[x]) = k[x] (x) sending x 7 x and x 7 x. The fact that x 7 x comes from the fact that it is the image of the Loday construction over a point. Using the same notation and argument as before, with the different orientation on 0 , x can be represented by x0 x1 , so exchanging the i sends x to x. The nontrivial twist : S 1 C2 = hi maps the non-degenerate 1-cell S11 to and is then determined by Equation (2.2), yielding (2.16) d0 (a0 a1 . . . an ) = a0 a1 a2 . . . an . The TCP spectral sequence (2.11) in this case takes the form  !   2 k k = p+q LkK (k[x]) Ep,q = p LS 1 (LS 1 (k[x])) q and since LkS 1 (k[x]) = k[x] (x), 2 Ep,q = p  LkS 1  k[x] (x)  ! , q which is the pth homotopy group of the simplicial k-vector space whose p-simplices are   LkSp1 (k[x] (x) ) . q For each p, LkS 1 (k[x](x)) LkS 1 (k[x])k LkS 1 ((x)), and so LkS 1 (k[x](x) ) LkS 1 (k[x])k p p p LkS 1 ((x) ). We can think of this tensor product of simplicial k-algebras as the diagonal of a bisimplicial abelian group, and again by [9, Theorem 2.4 of Section IV.2.2] the total complex of a bisimplicial abelian group with the alternating sums of the vertical and the horizontal face maps is chain homotopy equivalent to the usual chain complex associated to the diagonal of that bisimplicial abelian group. But in this case of a tensor product, the total complex was obtained by tensoring together two complexes, and since we are working over a field its homology is the tensor product of the homology of the two complexes, so           k LS 1 k[x] (x) LkS 1 ((x) ) . = LkS 1 (k[x]) The first factor is just the Hochschild homology of k[x]. It sits in the 0th row of the E 2 term since x has internal degree zero, and gives us (LkS 1 (k[x]) = k[x] (x)) concentrated in positions (0, 0) and (1, 0). All spectral sequence differentials vanish on it for degree reasons, and so it will just contribute k[x] (x) to the E term. The second factor in the E 2 term is the twisted Hochschild homology for (x). To calculate it, we can use the normalized chain complex and therefore we only have to consider non-degenerate elements, which means that we only have two elements to take into account in any given simplicial degree: 11 p-degree 0 1 2 ... 1 1 x 1 x x . . . x x x x x x . . . Elements of the form x . . . x will map to zero under the Hochschild boundary map. We need to consider the odd and even cases of differentials on elements of the form 1 x . . . x. The di maps in the twisted and untwisted Hochschild complex are all the same except d0 , which incorporates the twisting action of . Therefore we have d(1 (x)2k ) = x2k + (1)2k (1)x2k = 2x2k d(1 (x)2k+1 ) = x2k+1 + (1)2k+1 (1)x2k+1 = 2x2k+1 . Here, the first 1 comes from the action on x as in (2.16) and the extra 1 in brackets come from passing the one-dimensional x past an odd or an even number of copies of itself. Since we are assuming that 2 is invertible in k, we get that the second part of the E 2 term has only k left in degree 0. So, if 2 is invertible in k, then the entire E 2 term is just k[x] (x) in the 0th row, and the TCP spectral sequence collapses and confirms that Lk (k[x]) = k[x] (x). K 3. Hopf algebras in spectra We start by describing what we mean by the notion of a commutative Hopf algebra in the -category of spectra, Sp. We consider the -category CAlg of E -ring spectra. Definition 3.1. A commutative Hopf algebra spectrum is a cogroup object in CAlg. Hopf algebra spectra are fairly rare, so let us list some important examples. Example 3.2. If G is a topological abelian group, then the spherical group ring S[G] = +G equipped with the product induced by the product in G, the coproduct induced by the diagonal map G G G, and the antipodal map induced by the inverse map from G to G is a commutative Hopf algebra spectrum. This follows from the fact that the suspension spectrum functor + : S Sp is a strong symmetric monoidal functor. Here S denotes the -category of spaces. Example 3.3. If A is an ordinary commutative Hopf algebra over a commutative ring k and A is flat as a k-module then the Eilenberg-Mac Lane spectrum HA is a commutative Hopf algebra spectrum over Hk because the canonical map HA Hk HA H(A k A) is an equivalence. We use the fact that the category of commutative ring spectra is tensored over unpointed topological spaces and simplicial sets in a compatible way [8, VII, 2, 3]. If U denotes the category of unbased (compactly generated weak Hausdorff) spaces and X U , then for every pair of commutative ring spectra A and B there is a homeomorphism of mapping spaces ([8, VII, Theorem 2.9]) (3.4) CS (X A, B) = U (X, CS (A, B)). Here, CS denotes the (ordinary) category of commutative ring spectra in the sense of [8]. By [16, Corollary 4.4.4.9], (3.4) corresponds to an equivalence of mapping spaces of -categories (3.5) CAlg(X A, B) S(X, CAlg(A, B)). See also [22, 2] for a detailed account on tensors in -categories. 12 If we consider a commutative Hopf algebra spectrum H, then the space of maps CS (H, B) has a basepoint: the composition of the counit map H S followed by the unit map S B is a map of commutative ring spectra. The functor that takes an unbased space X to the topological sum of X with a point + is left adjoint to the forgetful functor the category of pointed spaces, Top , to spaces, so we obtain a homeomorphism (3.6) U (X, CS (H, B)) = Top (X+ , CS (H, B)) and correspondingly, an equivalence in the context of -categories (3.7) S(X, CAlg(H, B)) S (X+ , CAlg(H, B)). For path-connected spaces Z, May showed that the free En -space on Z, Cn (Z), is equivalent to n n Z [19, Theorem 6.1]. Segal extended this result to spaces that are not necessarily connected. He showed that for well-based spaces Z there is a model of the free E1 -space, C1 (Z), as follows: The spaces C1 (Z) and C1 (Z) are homotopy equivalent, C1 (Z) is a monoid, its classifying space BC1 (Z) is equivalent to (Z) [24, Theorem 2], and thus, C1 (Z) BC1 (Z) is a group completion. We can apply this result to Z = X+ because X+ is well-based, thus BC1 (X+ ) (X+ ). Note that BC1 (X+ ) (X+ ). Nikolaus gives an overview about group completions in the context of -categories [20]. He shows that for every E1 -monoid M , the map M BM gives rise to a localization functor of cateories in the sense of [16, Definition 5.2.7.2], such that the local objects are grouplike E1 -spaces. In particular, there is a homotopy equivalence of mapping spaces [16, Proposition 5.2.7.4] MapE1 (BC1 (X+ ), Y ) MapE1 (C1 (X+ ), Y ) if Y is a grouplike E1 -space. Here, E1 denotes the -category of E1 -spaces. If H is a commutative Hopf-algebra, then the space CAlg(H, B) is a grouplike E1 -space. Therefore, by using Equations (3.5) and (3.7), we obtain a chain of homotopy equivalences CAlg(X H, B) S(X, CAlg(H, B)) S (X+ , CAlg(H, B)) MapE1 (C1 (X+ ), CAlg(H, B)) MapE1 (BC1 (X+ ), CAlg(H, B)) MapE1 ((X+ ), CAlg(H, B)). If (X+ ) (Y+ ) is an equivalence of pointed spaces, then (X+ ) (Y+ ) as grouplike E1 -spaces and therefore we get a homotopy equivalence CAlg(X H, B) CAlg(Y H, B). Applying the Yoneda Embedding to the above equivalence yields the following result: Theorem 3.8. If H is a commutative Hopf algebra spectrum and if (X+ ) (Y+ ) is an equivalence of pointed spaces, then there is an equivalence X H Y H in CAlg. Remark 3.9. If X is a pointed simplicial set, then the suspension (X+ ) is equivalent to (X) S 1 . Therefore, if X and Y are pointed simplicial sets, such that (X) (Y ) as pointed simplicial sets, then we also obtain an equivalence between (X+ ) and (Y+ ). Segals result also works for larger n than 1. If two spaces are equivalent after an n-fold suspension, then an En -coalgebra structure on a Hopf algebra is needed for the Loday construction to be equivalent on these two spaces. There are indeed interesting spaces that are not equivalent after just one suspension, but that need iterated suspensions to become equivalent: 13  Christoph Schaper [23, Theorem 3] shows that for affine arrangements A one needs at least a (A + 2)-fold suspension in order to get a homotopy type that only depends on the poset structure of the arrangement. Here, A is a number that depends on the poset data of the arrangement, namely the intersection poset and the dimension function. For homology spheres, the double suspension theorem of James W. Cannon and Robert D. Edwards [6, Theorem in 11] states that the double suspension 2 M of any n-dimensional homology sphere M is homeomorphic to S n+2 . Here, a single suspension does not suffice unless M is an actual sphere. 4. Truncated polynomial algebras One way of showing that a commutative R-algebra spectrum A is not multiplicatively or linearly stable is to prove that the homotopy groups of the Loday construction LR T n (A) differ from those of
W n R k W W L n (A), as in [7]. Here, we write (n) S for the k -fold -sum of S k . Indeed, there is a Sk k=1 k (nk) homotopy equivalence n _ _ (T n ) ( S k ). k=1 (n) k If A is augmented over R, then for proving that R A is not multiplicatively or additively stable, it suffices to show that R W W LR k (A; R). T n (A; R) 6 L n k=1 (n) S k See [14, 2] for details and background on different notions of stability. In the following we restrict our attention to Eilenberg-Mac Lane spectra of commutative rings and we will use this strategy to show that none of the commutative Q-algebras Q[t]/tm for m > 2 can be multiplicatively stable. We later generalize this to quotients of the form Q[t]/q(t) where q(t) is a polynomial without constant term and to integral and mod-p results. Pirashvili determined higher order Hochschild homology of truncated polynomial algebras of the form k[x]/xr+1 additively when k is a field of characteristic zero [21, Section 5.4] in the case of odd spheres. A direct adaptation of the methods of [4, Theorem 8.8] together with the flowchart from [5, Proposition 2.1] yields the higher order Hochschild homology with reduced coefficients for all spheres. See also [7, Lemma 3.4]. Proposition 4.1. For all m > 2 and n > 1 ( Q (xn ) Q[yn+1 ], [n],Q HH (Q[t]/tm ; Q) = Q[xn ] Q (yn+1 ), if n is odd, if n is even. In both cases Hochschild homology of order n is a free graded commutative Q-algebra on two generators in degrees n and n + 1, respectively, and the result does not depend on m. We will determine for which m and n we get a decomposition of the form Q m m W W (4.2) L Q k (Q[t]/t ; Q). T n (Q[t]/t ; Q) = L n k=1 (nk) S Note that the right-hand side is isomorphic to n O O L Q (Q[t]/tm ; Q) Sk k=1 (n) k where all unadorned tensor products are formed over Q. Thus, if we have a decomposition as in m (4.2), then we can read off the homotopy groups of LQ T n (Q[t]/t ; Q) with the help of Proposition 4.1. 14 Expressing Q[t]/tm as the pushout of the diagram t7tm Q[t] // Q[t] t70  Q allows us to express the Loday construction for Q[t]/tm , now viewed as a commutative HQ-algebra spectrum, as the homotopy pushout of the diagram LHQ T n (HQ[t]; HQ) t7tm // LHQ T n (HQ[t]; HQ) t70  HQ and so HQ m L LHQ T n (HQ[t]/t ; HQ) LT n (HQ[t]; HQ) LHQ (HQ[t];HQ) HQ. Tn As Q[t] is smooth over Q, LHQ T n (HQ[t]; HQ) is stable [7, Example 2.6]. So we can write HQ W LHQ T n (HQ[t]; HQ) L n k=1 W (nk) Sk (HQ[t]; HQ). Again, we obtain an isomorphism Wn L Q k=1 W n k ( ) (Q[t]; Q) = Sk n O O k=1 [k],Q HH (Q[t]; Q) n k ( ) and with the help of [5, Proposition 2.1] we can identify the terms as follows: ( Q[xk ], if k is even , [k],Q HH (Q[t]; Q) = Q (xk ), if k is odd. Lemma 4.3. There is an isomorphism of graded commutative Q-algebras Wn L Q k=1 W LQ T n (Q[t];Q) (nk) Sk Q (Q[t]/tm ; Q) = LT n (Q[t]; Q) Tor (Q, Q). Proof. We already know that (4.4) Wn L Q k=1 W (nk) (Q[t]/tm ; Q) = Sk n O O k=1 [k],Q HH (Q[t]/tm ; Q) = n k n O O k=1 ( ) gFQ (xk , yk+1 ) n k ( ) where gFQ (xk ) denotes the free graded commutative Q-algebra generated by an element xk in degree k and gFQ (xk , yk+1 ) denotes the free graded commutative Q-algebra generated by an element xk in degree k and an element yk+1 in degree k + 1. Nn N n gFQ (xk ), we obtain that As LQ k=1 T n (Q[t]; Q) = ( ) k LQ (Q[t];Q) (Q, Q) Tor T n = n+1 O O =2 ( gFQ (y ) n 1 ) and hence the tensor product of the two gives a graded commutative Q-algebra isomorphic to (4.4)  15 Q Let A denote the graded commutative Q-algebra LQ T n (Q[t]; Q) and B denote LT n (Q[t]; Q) viewed as an A -module via a morphism of graded commutative Q-algebras f : A B . Lemma 4.5. Let f1 : A B be the morphism f1 = B A where A : A Q is the augmentation that sends all elements of positive degree to zero and where B : Q B is the unit map of B . Let f2 : A B be any map of graded commutative algebras such that there is ,fi an element x An with n > 0 such that f2 (x) = w 6= 0. Let TorA , (B , Q) denote the graded Tor-groups calculated with respect to the A -module structure on B given by fi . Then A ,f2 ,f1 dimQ (Tor, (B , Q))n < dimQ (TorA , (B , Q))n L ,fi A ,fi where (TorA , (B , Q))n = r+s=n Torr,s (B , Q). Proof. Let P Q be an A -free resolution of Q. We want to choose P efficiently, in the following sense: since QLis concentrated in degree zero and A0 = Q, we can choose P0 to be A . Then we nj choose P1 = jI1 A with the minimal possible number of copies of A in each suspension degree, beginning from the bottom (that is, the only reason we add a new n A is if there is a class in P1 that has not yet been L hit bynjthe suspensions of A in lower dimensions that we already have) to guarantee that d1 : jI A0 P0 is injective, and moreover M M ker(d1 : nj A0 P0 ) nj ker(A ). jI1 jI1 And of course we need Im(d1 : P1 P0 ) = ker(A : A Q) and similarly for higher . For every > 0 we choose P with M P = nj A jI so that d : L nj jI A0 P1 is injective and moreover M M ker(d : nj A0 P1 ) nj ker(A ). jI Then we get jI M Im(d : P P1 ) = ker(d1 : P1 P2 ) nj ker(A ). jI1 The Tor groups we want are the homology groups of M M B A P = B A nj A n j B = jI jI with respect to the differential id d for either A -module structure. As f1 : A B factors through the augmentation, we claim that the differentials in the chain complex B A P with the A -module structure given by f1 L are trivial: they are of the form L id d where d is the differential of P . As d sends every nj 1 jI nj A to something in jI1 nj ker(A ), M (id d)(b A nj 1) Q{b} A nj ker(A ) = 0 jI1 for all b B . Hence A ,f1 Tor,s (B , Q) = ( M nj B )s = jI M jI 16 nj Bs .  ,f1 In particular, we have of course TorA 0,s (B , Q) = Bs for all s. For the A -module structure on B given by f2 we obtain that ,f2 TorA 0, (B , Q) = B A Q but here, the tensor product results in a nontrivial quotient of B . Recall that we assumed that f2 (x) = w 6= 0. The element w 1 B A Q is trivial because the degree of x is positive and hence A (x) = 0: w 1 = f2 (x) 1 = 1 A (x) = 1 0 = 0. Therefore, A ,f1 ,f2 dimQ TorA 0,n (B , Q) < dimQ Tor0,n (B , Q). ,f2 The other Tor-terms in total degree n of the form TorA r,s (B , Q) with r + s = n are subquotients of M nj Bs jIr and hence for all (r, s) with r + s = n and r > 0 we obtain A ,f1 ,f2 dimQ TorA r,s (B , Q) 6 dimQ Torr,s (B , Q).  Note that if f : A B factors through the augmentation A Q then A TorA (B , Q) = B Tor (Q, Q). We use Lemma 4.5 to prove the following result. Theorem 4.6. Let n > 2. Then Q n W dimQ n LQ T n (Q[t]/t ; Q) < dimQ n L n k=1 W n k ( ) Sk (Q[t]/tn ; Q). In particular, for all n > 2 the pair (Q[t]/tn ; Q) is not stable and Q Q[t]/tn is not multiplicatively stable. The n = 2 case of Theorem 4.6 was obtained earlier by Dundas and Tenti [7]. Before we prove the theorem, we state the following integral version of it: Corollary 4.7. For all n > 2 the pair (Z[t]/tn ; Z) is not stable and Z Z[t]/tn is not multiplicatively stable. Proof of Corollary 4.7. If for some n > 2 the pair (Z[t]/tn ; Z) were stable, then in particular LZT n (Z[t]/tn ; Z) = LZWn k=1 W (nk) S k (Z[t]/tn ; Z). Localizing at Z \ {0} would then imply Q n W L Q T n (Q[t]/t ; Q) = L n k=1 in contradiction to Theorem 4.6. W (nk) S k (Q[t]/tn ; Q)  17 4.1. Proof of Theorem 4.6. We prove Theorem 4.6 by identifying an element in A of positive degree that is sent to a nontrivial element of B . More precisely, we will show that the map that sends t to tn sends the indecomposable element in n LQ S n (Q[t]; Q) up to a unit to the element dt1 . . . dtn n LQ (Q[t]; Q). S 1 ...S 1 We consider both elements as elements of n LQ T n (Q[t]; Q) via the inclusions of summands Q n L Q (Q[t]; Q) n LQ T n (Q[t]; Q) n LS n (Q[t]; Q). S 1 ...S 1 In the following we consider T n as the diagonal of an n-fold simplicial set where every ([p1 ], . . . , [pn ]) ()n is mapped to Sp11 . . . Sp1n . Then LQ T n (Q[t]; Q) can also be interpreted as the diagonal of an n-fold simplicial Q-vector space with an associated n-chain complex. By abuse of notation we still denote this n-chain complex by LQ T n (Q[t]; Q). We use the following notation concerning the n-chain complex LQ T n (Q[t]; Q): 0m = (0, 0, . . . , 0) and 1m = (1, 1, . . . , 1) are the vectors containing only 0 or 1, respectively, repeated m times. A vector V Nn is viewed as a multi-degree of an element in the n-chain complex. A vector v Nn for which 0n 6 v 6 V in every entry can be thought of as specifying a coordinate in the multi-matrix of an element in multi-degree V. We call the ith entry of a vector v Nn the ith place in v. It is always assumed that V = 1n if not otherwise specified. Each element of LQ T n (Q[t]; Q) in degree V = (v1 , . . . , vn ) is a multi-matrix of dimension (v1 + 1, . . . , vn + 1) with entries in Q[t] at coordinates v 6= 0n and an entry in Q at coordinate 0n . xv for x Q[t] and v Nn is the multi-matrix with term x at coordinate v and 1 at other coordinates. We say a term is trivial if it is 1 in all its coordinates. Therefore xv yw for x, y Q[t] and v, w Nn is the product of xv and yw in degree V of LQ T n (Q[t], Q) regarded as an n-simplicial ring. Explicitly, if v 6= w, it is the multi-matrix with x at coordinate v, y at coordinate w, and 1 elsewhere; if v = w, it is the multi-matrix with xy at coordiante v and 1 elsewhere. Suppose that C is an n-chain complex with differentials d1 , . . . , dn in the n different directions, then the total chain complex Tot(C ) has differential in component (v1 , . . . , vn ) given by d= n X (1)v1 +...+vi1 di . i=1 Pvi In our case we will have each di = j=0 (1)j di,j where di,j : Cv1 ,...,vn Cv1 ,...,vi 1,...vn is the face map. We are interested in low degrees, especially in 1n . Any vi = 1 will imply di = 0 since the di are cyclic differentials and Q[t] is commutative. This allows us to eliminate the di from d. We have the following three lemmas about homologous classes and tori of different dimensions: Lemma 4.8 (Split Moving Lemma). Let a, b be coordinates in degree 1n1 (that is, in 22. . .2dimensional matrices). Then x(a,1) y(b,1) x(a,0) y(b,1) + x(a,1) y(b,0) . Proof. Their difference is a boundary of an element of degree (1n1 , 2): d(x(a,1) y(b,2) ) = (1)n1 dn (x(a,1) y(b,2) ) = x(a,0) y(b,1) x(a,1) y(b,1) + x(a,1) y(b,0) .  18 For example, when n = 2, a = 0, b = 1, the    1 x 1 x d = 1 1 y 1 difference is      1 1 x 1 x + . y 1 y y 1 Let b be a coordinate of a multi-matrix of an element in degree 1nm such that b 6= 0nm . For any multi-matrix c in degree W Nm , we can form the following multi-matrix in degree (W, 1nm ) Nn : at coordinate (a, 0nm ); ca c(,0) y(0,b) has terms yb at coordinate (0m , b); 1 elsewhere. Lemma 4.9. The following is a chain map: Q Tot(LQ T m (Q[t], Q)) Tot(LT n (Q[t], Q)); c 7 c(,0) y(0,b) . Proof. Clearly di (c(,0) y(0,b) ) = di c(,0) y(0,b) for 0 6 i 6 m. But since the multi-degree of c(,0) y(0,b) is V = (W, 1nm ) Nn and whenever vi = 1, di = di,0 di,1 = 0, we also get di (c(,0) y(0,b) ) = 0, for m < i 6 n.  This lemma also applies when y(0,b) is replaced by another multi-matrix that has more than one nontrivial term, as long as the nontrivial terms are all in coordinates of the form (0m , b) for b in degree 1nm and b 6= 0nm . It has the following immediate corollary: Lemma 4.10 (Orthogonal Moving Lemma). Let b be a coordinate in degree 1nm such that b 6= 0nm . Let c, c be elements in multi-degree W Nm . If c c in multi-degree W, then c(,0nm ) y(0m ,b) c(,0nm ) y(0m ,b) in multi-degree (W, 1nm ) Conceptually, the moving lemmas tell us how to move the nontrivial elements x, y in certain multi-matrices to lower coordinates. They are stated for a special case for simplicity, but of course they work for any permulation of copies of Nn in the statement. The split moving lemma says that if we have xv and yw where the coordinates share a 1 in a particular place, the 1s can be moved to coordinate 0 separately. The orthogonal moving lemma says that the x in xv and the y in yw can be moved separately if they are supported in orthogonal tori (that is, have their nontrivial entries in different coordinates). Proposition 4.11. Let v and w be two coordinates of degree 1n . (1) If v and w are both 0 in the ith place for some 1 6 i 6 n, then xv yw 0. In particular, if v 6= 1n , then xv 0. (2) In general, xv y w X xv y w , v 6v,w 6w, v +w =1n where the sum is taken over all coordinates v and w such that They are place-wise no greater than v and w respectively; They take 1 in complementary places. 19 (3) For k > 1 and n > 1, we have the following homologous relation: X k (t )1n k Y tw i w1 ,...,wk 6=0n , i=1 w1 +...+wk =1n In particular, if k = n and we let ei denote the coordinate that has 1 at the ith place and 0 at other places, we get n (4.12) (t )1n n! n Y tei . i=1 Also, if k > n, this gives us (tk )1n 0 Proof. The class in (1) is a cycle because everything is in multi-degree 1n is a cycle; it is nullhomologous because it is in the image of the degeneracy si,0 in the ith place. For (2) we write |v| for the sum of the places of the vector v. We induct on |v| + |w|. Notice that a coordinate v of degree 1n is just a sequence of length n of 0s and 1s and |v| is just the number of 1s in it. For |v| + |w| 6 n, there are two cases: One is that v and w are both 0 in one place. Then the claim holds because the right-hand side is the empty sum and the left-hand side is 0 by part (1). The other case is that v + w = 1n . Then the claim also holds because the right-hand side has only one copy that is exactly the left-hand side. Assume that the claim is true for |v| + |w| 6 m where m > n and suppose now |v| + |w| = m + 1. Since m + 1 > n + 1, v and w have to be both 1 in some place. Without loss of generality, we assume that v = (v0 , 1), w = (w0 , 1) where v0 , w0 6 1n1 . By the Split Moving Lemma (Lemma 4.8), xv yw x(v0 ,0) yw + xv y(w0 ,0) . Since |(v0 , 0)| + |w| = |v| + |(w0 , 0)| = m, by inductive hypothesis we have that X X xv y w x(v0 ,0) yw + xv y(w0 ,0) v0 6v0 ,w 6w, (v0 ,0)+w =1n = X v 6v,w0 6w0 , v +(w0 ,0)=1n xv y w . v 6v,w 6w, v +w =1n For (3) we order the pair (k, n) by the lexicographical ordering. We induct on (k, n). When k = 1, the claim is trivially true. Suppose the claim is true for all pairs less than (k, n) where k > 2. Taking v = w = 1n , x = t and y = tk1 in part (2), we get that X X (4.13) (tk )1n tw1 (tk1 )v = tw1 (tk1 )v . w1 6=0n w1 +v =1n w1 +v =1n 20 The second step above uses that t0n = 0 because t is 0 in the Q[t]-module Q. Let m = |v |. By the inductive hypothesis, we have (4.14) (t k1 )1m k Y X twi w2 ,...,wk 6=0m , i=2 w2 +...+wk =1m For each wi which is a coordinate of degree 1m , we add in 0 in places where v is 0 to make it a coordinate of degree 1n . Denote it by wi . Then the Orthogonal Moving Lemma (Lemma 4.10), (4.13) and (4.14) combine to k X Y k (t )1n tw i . w1 ,...,wk 6=0n , i=1 w1 +...+wk =1n  Qn For any n > 2, we call t1n the diagonal class and denote it by n . We call i=1 tei the volume form and denote it by voln . If we include S 1 T n as the ith coordinate and identify the first Hochschild homology group with the Kahler differentials, the generator dt of HHQ 1 (Q[t]; Q) maps to the generator we call dti in the Loday construction of the torus. In this sense voln corresponds to the degree-n class dt1 . . . dtn . Proof of Theorem 4.6. By Equation (4.12) we know that the map t 7 tn induces a map on L Q T n (Q[t]; Q), that sends the diagonal class, n , to n!voln . Hence, by Lemma 4.5 we know that Q n n W W dimQ n (LQ k (Q[t]/t ; Q)). T n (Q[t]/t ; Q)) < dimQ n (L n n S k=1 (k) In particular, Q n n W W (LQ k (Q[t]/t ; Q)). T n (Q[t]/t ; Q)) (L n n S k=1 (k)  Remark 4.15. For the non-reduced Loday construction LQ T n (Q[t]), parts (1) and (2) of Proposition 4.11 are still true. Part (3) will become k (t )1n k Y X tw i w1 +...+wk =1n i=1 and Equation (4.12) is no longer true. 4.2. Q[t]/tm on T n for 2 6 m < n. We know that for Q[t]/tn we get a discrepancy between n of the Loday construction on the n-torus and that of the bouquet of spheres that correspond to the cells of the n-torus. We use this to first show that Q[t]/tm causes a similar discrepancy for 2 6 m < n. Proposition 4.16. Let 2 6 m 6 n. Then Q m W m L Q T n (Q[t]/t ; Q) m L n k=1 W n k ( ) Sk (Q[t]/tm ; Q). Proof. We consider the Tor-spectral sequence LQ (Q[t];Q) Tn Tor, Q m ( LQ T n (Q[t]; Q), Q) LT n (Q[t]/t ; Q) 21 Q m where the LQ T n (Q[t]; Q)-module structure on LT n (Q[t]; Q) is induced by t 7 t . The m-chain (m) complex C := LQ T m (Q[t]; Q) can be considered as an n-chain complex whose m + 1, . . . , ncoordinates are trivial. Then (m) C (n) = LQ T m (Q[t]; Q) C := LQ T n (Q[t]; Q) (n) is a sub-n-complex of C . We know that m 7 m!volm in the homology of the total complex of (m) (n) C and hence the same is true in C . Therefore the map Q m L Q T n (Q[t]; Q) m LT n (Q[t]; Q) m that is induced by t 7 tm is nontrivial and by Lemma 4.5 the dimension of m LQ T n (Q[t]/t ; Q) is strictly smaller than the dimension of Wn m L Q k=1 W n k ( ) Sk (Q[t]/tm ; Q).  4.3. Quotients by polynomials without constant term. Let q(t) = am tm + . . . + a1 t Q[t]. Then we can still write Q[t]/q(t) as a pushout Q[t] t7q(t) // Q[t] t70  // Q[t]/q(t)  Q hence the above methods carry over. Proposition 4.17. Let m0 be the smallest natural number with 1 6 m0 6 m with am0 6= 0. Then Q W m0 LQ T m0 (Q[t]/q(t); Q) m0 L m0 k=1 W (mk0 ) S k (Q[t]/q(t); Q). Q Proof. If m0 = 1, then t HHQ 1 (Q[t]; Q) maps to (q(t)) HH1 (Q[t]; Q) under the map t 7 q(t). In the module of Kahler differentials this element corresponds to a1 dt + 2a2 tdt + . . . + mam tm1 dt but all these summands are null-homologous except for the first one. So t 7 a1 t 6= 0 and this, along with Lemma 4.5, proves the claim. We denote by m0 (q(t)) the element (q(t))1m0 . If m0 > 1, then the diagonal element m0 (t) maps to m X m0 (q(t)) = ai m0 (ti ) i=m0 and this is homologous to (m0 )!am0 volm0 + terms of higher t-degree by (4.12). Hence m0 (t) maps to a nontrivial element and again Lemma 4.5 gives the claim. 22  4.4. Truncated polynomial algebras in prime characteristic. We know that for commutative Hopf algebras A over k the Loday construction is stable, so Loday constructions of truncated polynomial algebras of the form Fp [t]/tp have the same homotopy groups when evaluated on an n-torus and on the corresponding bouquet of spheres. However, we show that there is a discrepancy for truncated polynomial algebras Fp [t]/tn for 2 6 n < p. Theorem 4.18. Assume that 2 6 n < p and n 6 m, then F F (LTpm (Fp [t]/tn ; Fp )) (LWpm k=1 In particular for all 2 6 n < p the pair (Fp [t]/tn ; F p) W m k ( ) Sk (Fp [t]/tn ; Fp )). is not stable. Proof. We consider the case m = n. The cases n < m follow by an argument similar to that for Proposition 4.16. As Fp [t] is smooth over Fp , we know that Fp Fp [t] is stable, so that F F (LTpn (Fp [t]; Fp )) = (LWpn k=1 [k],Fp and HH W n k ( ) (Fp [t]; Fp )) = Sk n O O k=1 [k],Fp HH (Fp [t]; Fp ) n k ( ) (Fp [t]; Fp ) is calculated in [4, 8] so that we obtain [k],Fp HH (Fp [t]; Fp ) = Bk+1 B B where B1 = Fp [t] and Bk+1 = Tor,k (Fp , Fp ) where the grading on Tor,k (Fp , Fp ) is the total F [2],F grading. Thus in low degrees this gives HH p (Fp [t]; Fp ) = Fp (t) with |t| = 1, HH p (Fp [t]; Fp ) = N F (0 t) with |0 t| = 2. As F (0 t) Fp [k t]/(k t)p we can iterate the result. = p i>0 p [n],F Note that in HHn p (Fp [t]; Fp ) there is always an indecomposable generator of the form 0 . . . 0 t or 0 0 . . . 0 t in degree n and we call this generator n . We also obtain a volume class F F voln := t1 . . . tn n LSp1 ...S 1 (Fp [t]; Fp ) n LTpn (Fp [t]; Fp ). The results from Proposition 4.11 work over the integers. If n < p, then n! is invertible in Fp and therefore the class n maps to n!voln . An argument analogous to Lemma 4.5 finishes the proof.  References [1] Katharine Adamyk, Teena Gerhardt, Kathryn Hess, Inbar Klang, Hana Jia Kong, Computational tools for twisted topological Hochschild homology of equivariant spectra, preprint arXiv:2001.06602. [2] Vigleik Angeltveit, Andrew J. Blumberg, Teena Gerhardt, Michael A. Hill, Tyler Lawson, and Michael A. Mandell, Topological cyclic homology via the norm, Doc. Math. 23 (2018), 21012163. [3] Yuri Berest, Ajay C. Ramadoss and Wai-Kit Yeung, Representation homology of spaces and higher Hochschild homology, Algebr. Geom. Topol. 19 (2019), no. 1, 281339. [4] Irina Bobkova, Ayelet Lindenstrauss, Kate Poirier, Birgit Richter, Inna Zakharevich On the higher topological Hochschild homology of Fp and commutative Fp -group algebras, Women in Topology: Collaborations in Homotopy Theory. Contemporary Mathematics 641, AMS, (2015), 97122. [5] Irina Bobkova, Eva Honing, Ayelet Lindenstrauss, Kate Poirier, Birgit Richter, Inna Zakharevich, Splittings and calculational techniques for higher THH , Algebr. Geom. Topol. 19 (2019), no. 7, 37113753. [6] James W. Cannon, Shrinking cell-like decompositions of manifolds. Codimension three, Ann. of Math. (2) 110 (1979), no. 1, 83112. [7] Bjrn Ian Dundas, Andrea Tenti, Higher Hochschild homology is not a stable invariant, Math. Z. 290 (2018), no. 1-2, 145154. [8] Anthony D. Elmendorf, Igor Kriz, Michael A. Mandell, J. Peter May, Rings, modules, and algebras in stable homotopy theory. With an appendix by M. Cole. Mathematical Surveys and Monographs, 47. American Mathematical Society, Providence, RI, (1997), xii+249 23 [9] Paul G. Goerss, John F. Jardine, Simplicial homotopy theory, Modern Birkhauser Classics, Birkhauser Verlag 2009, xv+510 pp. [10] Gemma Halliwell, Eva Honing, Ayelet Lindenstrauss, Birgit Richter, Inna Zakharevich, Relative Loday constructions and applications to higher THH-calculations, Topology Appl. 235 (2018), 523545. [11] Lars Hesselholt, Ib Madsen, On the K-theory of finite algebras over Witt vectors of perfect fields, Topology 36 (1997), no. 1, 29101. [12] Mark Hovey, Brooke Shipley, Jeff Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000), no. 1, 149208. [13] Michael Larsen, Ayelet Lindenstrauss, Cyclic homology of Dedekind domains. K-Theory 6 (1992), no. 4, 301334. [14] Ayelet Lindenstrauss, Birgit Richter, Stability of Loday constructions, preprint arXiv:1905.05619. [15] Jean-Louis Loday, Cyclic Homology, Second edition. Grundlehren der Mathematischen Wissenschaften 301. Springer-Verlag, Berlin, (1998), xx+513 pp. [16] Jacob Lurie, Higher Topos Theory, Annals of Mathematics Studies vol. 170, 2009. [17] Michael A. Mandell, J. Peter May, Equivariant orthogonal spectra and S-modules, Mem. Amer. Math. Soc. 159 (2002), no. 755, x+108 pp. [18] J. Peter May, Simplicial objects in algebraic topology, Vol. 11. University of Chicago Press, 1992. [19] J. Peter May, The geometry of iterated loop spaces, Lectures Notes in Mathematics, Vol. 271. SpringerVerlag, Berlin-New York, 1972. viii+175 pp. [20] Thomas Nikolaus, The group completion theorem via localizations of ring spectra, expository notes, available at https://www.uni-muenster.de/IVV5WS/WebHop/user/nikolaus/Papers/Group_completion.pdf [21] Teimuraz Pirashvili, Hodge decomposition for higher order Hochschild homology, Ann. Sci. Ecole Norm. Sup. (4) 33 (2000), no. 2, 151179. [22] Nima Rasekh, Bruno Stonek, Gabriel Valenzuela, Thom spectra, higher THH and tensors in -categories, preprint arXiv:1911.04345. [23] Christoph Schaper, Suspensions of affine arrangements, Math. Ann. 309 (1997), no. 3, 463473. [24] Graeme Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973), 213221. [25] Christian Schlichtkrull, Higher topological Hochschild homology of Thom spectra, J. Topol. 4 (2011), no. 1, 161189. Department of Mathematics, University of Oslo, Box 1053, Blindern, NO - 0316 Oslo, Norway E-mail address: aliceph@math.uio.no Department of Mathematics, Michigan State University, 619 Red Cedar Rd, East Lansing, MI 48840, USA E-mail address: klander2@msu.edu Department of Mathematics, Indiana University, 831 East 3rd Street, Bloomington, IN 47405, USA E-mail address: alindens@indiana.edu Fachbereich Mathematik der Universitat Hamburg, Bundesstrae 55, 20146 Hamburg, Germany E-mail address: birgit.richter@uni-hamburg.de Department of Mathmatics, University of Chicago, 5734 S University Ave, Chicago, IL 60637, USA E-mail address: foling@math.uchicago.edu 24  ...

... American Journal of Biomedical Science & Research www.biomedgrid.com ISSN: 2642-1747 --------------------------------------------------------------------------------------------------------------------------------- Review Article Copy Right@ Aaron Schmid Preventing Pandemics and Containing Disease: A Proposed Symptoms-Based Syndromic Surveillance System Benjamin M Abraham1, Aaron Schmid1*, Israt Khan1, Samina Akbar1 and Minal Mulye1,2 1 Marian University-College of Osteopathic Medicine, Indianapolis, IN, USA 2 Philadelphia College of Osteopathic Medicine, Philadelphia, PA, USA *Corresponding author: Aaron Schmid, Marian University College of Osteopathic Medicine, Indianapolis, IN, USA. To Cite This Article: Benjamin M Abraham, Aaron Schmid, Israt Khan, Samina Akbar, Minal Mulye. Preventing Pandemics and Containing Disease: A Proposed Symptoms-Based Syndromic Surveillance System. Am J Biomed Sci & Res. 2022 - 15(3). AJBSR.MS.ID.002108. DOI: 10.34297/AJBSR.2022.15.002108 Received: January 11, 2022; Published: January 26, 2022 Abstract Background: Due to globalization, spread of a pandemic is inevitable as we have seen with COVID-19. Further, increased ease of travel increases the potential and frequency of pandemics. Hence, it is imperative to find solutions to stop the spread of future pandemics at onset. The proposed solution is a self-reported, symptoms-based syndromic surveillance system that is universal, interactive, integrative, and combined with artificial intelligence. Once developed, this framework has the potential to stop any future epidemics and pandemic in urban and rural areas worldwide. Methods: We conducted a thorough literature review of existing short message service (SMS, text messaging) and interactive voice response (IVR, calling) surveillance systems, identified and addressed the shortcomings. We considered artificial intelligence applicability in this paradigm and cost-versus-benefit analysis in a myriad of economies. Results: Utilizing social psychology studies regarding user compliance, high-quality systematic analyses of SMS/IVR-based reporting tools, artificial intelligence prediction models, and a review of data-sharing laws, we have found that many of the previous syndromic surveillance models suffer from data fragmentation, thus hindering their scalability to a global setting. Conclusions: This proposal will allow decision-making officials and healthcare professionals to robustly identify local disease outbreaks, thus thwarting unchecked spread while preventing a breakdown in the supply chain. Since communicable pathogens can cause high morbidity and mortality as well as a negative impact on economies, we call upon todays high-tech companies as well as governmental bodies to be the impetus for the change that will decrease the multifaceted burdens on our global society. Keywords: COVID-19, SARS-CoV-2, Syndromic Surveillance, Pandemic, Epidemic, Prevention Introduction Syndromic surveillance refers to the collection of individual and population information regarding clinical features, signs, and symptoms to provide an early means of outbreak detection in the public health landscape [1]. The central objective of the initially developed syndromic surveillance systems was to identify outbreaks, hotspots, and disease clusters early, and to mobilize a rapid response, thereby reducing morbidity and mortality [2]. Using machine learning (ML) algorithms, future syndromic surveillance systems can be trained on datasets that include previous disease outbreaks to be able to detect and predict any This work is licensed under Creative Commons Attribution 4.0 License AJBSR.MS.ID.002107. 290 Am J Biomed Sci & Res Copy@ Aaron Schmid such future outbreaks [3]. The monitoring and prediction of disease trends will continue to grow and improve as longitudinal data accumulates and as syndrome definitions are refined. There are many resources, brilliant minds, and accurate systems in place to track increase in existing as well as novel disease incidence [4-8] (Table 1); however, the current 2020 global landscape concerning the spread of coronavirus disease (SARS-CoV-2; COVID-19) has Table 1: Resources that Provide a Proof-of-Concept. Resource Description Blue Dot [11,52] Artificial intelligence driven, algorithm-based health monitoring platform that quantifies exposure risk and helps to detect outbreaks early. China Infectious Diseases Automatedalert and Response System (CIDARS) [53] COVID Worldwide Symptom Tracker [22] COVID Symptom Study (Previously COVID Symptom Tracker) [3] Early Warning, Alert, and Response System (EWARS) [55,56] Utilizes the Internet, computers, and mobile phones to accomplish rapid signal generation and dissemination (SMS), timely reporting, and reviewing of signal response results at the county, prefecture, provincial, and national levels to assist in early outbreak detection at local levels. Prompts reporting of unusual disease occurrences or potential outbreaks to CDCs throughout the country. Finland-based developer. Allows individual to report symptoms. Individuals using this program are given a unique identification number allowing them to update their symptoms in the future. Developed by Zoe Global in collaboration with Kings College London and Massachusetts General Hospital. Enables the capture of selfreported information related to COVID-19. Mobile application based, therefore user logs into app to report symptom status (age: 18+ and must provide consent). Mobile phone field-based reporting and management system. Is deployed in remote and challenging field settings where there is no access to reliable internet or electricity. The system is available in a prepackaged box that contains mobile phones, laptops, solar generators and chargers, and a local server. Phones are distributed in rural, remote areas. Data is collected and temporarily saved and stored off-line. Once the data is added to the server it is synced and uploaded for real-time analysis. highlighted the weaknesses in our syndromic surveillance efficacy. Hence, it is essential to develop a robust, worldwide surveillance system that would curb any future epidemic or pandemic at the outset. Here, we propose an adaptable and timeless model which, in the future, could be developed on a global scale to accurately identify disease outbreaks in different parts of the world, predict a pandemic and stop its spread in a timely manner. Is concept specifically mentioned in our model? Does current literature show promising results? Considers useful parameter(s) in development of proposed model? If so, how? Y, Y Y, predicts based on airline itinerary, mobile device data, climate conditions, animal and insect populations. Successfully predicted and validated the COVID-19, Zika (Florida, 2016), and Ebola (West Africa, 2014) outbreaks. Y, - Y, SMS delivery of unusual disease occurrences and potential outbreaks utilizing available means for early detection and prevention Y, N Y, allows individuals to update their symptoms in the program based on their de-identified ID number. Mostly used in Finland and neighboring countries, limitations include high falsepositives due to selfreporting without further verification. Project is largely in its infancy. Y, - Y, same as above. Added current applicability in US and UK (2.6 million participants). Accurately predicted that 17.4% tested positive for COVID-19. High false positives,but has means to verify COVID-19 status suspicion. Very interactive and highly userfriendly. Application based, therefore limitations where smartphones do not exist. Y, Y Y, allows for on-site investigation of rise in disease incidence. Evaluation by healthcare professionals verifies whether potential patient has communicable disease. American Journal of Biomedical Science & Research 293 Am J Biomed Sci & Res Copy@ Aaron Schmid Digital, mobile phone-based system in place for Malaria surveillance. This system offers real-time tracking of disease, identification, and management of outbreaks, and is run on a central server. It also allows for data collection from rural and slum areas via health activists. Information reported to this system is made immediately available to public health officials, in database form, for analysis. Decisions can then be made to enforce quarantine in those areas, send out mass-messages to warn others about potential outbreaks, and allocate medical supplies. Y, Y Y, streamlines information via digitalization from underserved areas to a centralized platform and enabled faster generation of information critical to disease prevention. Addressed underreporting issues that burdened India with economical latencies as a manifestation of unchecked/unknown disease spread/active cases. ProMED Mail (PMM) [63] worldwide, online, email-based system put on by the International Society for Infectious Disease. Y, Y Sproxil [65] System that helps identify counterfeit medicine hotspots in Ghana, Nigeria, Kenya, and India. It is supported by regulatory bodies and governments and utilizes a mobile, text-message based reporting system to a central database. Y, reported many outbreaks before the World Health Organization (WHO) did. Addresses privacy concerns by de-identifying reported information for quicker turnover of data acquisition and meaningful usage. Open and free to use for global surveillance. Notably, PMM caught a Cholera outbreak in the Philippines almost three weeks before the WHO, Yellow Fever in Brazil days before the WHO, Cholera in Peru eight weeks before the WHO, and the SARS outbreak even before governments were able to issue reports [30]. PMM has also been the first system to detect and report on numerous major and minor disease outbreaks including SARS, MERS, Ebola, and Zika. PMM is an open and free to use global surveillance system [31]. N, Y This is an internet-based, self-reporting system that assesses an individuals risk and helps that individual decide on the next steps to take (whether that person should go to the doctor, call the disease control hotline, etc.) Y, parameters may be repurposed in terms of coding to lend wisdom in identification of hacking or malicious utilization of healthcare information. Y, N Y, in our current global landscape and due to reliance on current syndromic surveillance models, triaging algorithm may be useful until shifting is fully implemented into practice. Emergency response and disease surveillance system that is mobile based. It Utilizes a centralized, integrated virtual control room. Based on individual reporting their system can accurately make predictions of future outbreak areas and medical supply shortages. These predictions can be used to catch problems early on. Y, Y Mobile-Based Surveillance Quest Using IT (MoSQuIT) [57] Well Vis COVID-19 Triaging [23] Zenysis [54] Y, utilizes machine learning algorithms to inform decision making officials of evidence based prediction and near-real-time reporting of cases. AI enhancement made false positive prevalence lower than technology that did not use it. Integrated data sets into a single platform (virtual workspace), established a high-quality information flow to the public and partnering organizations, and allowed decision makers (government officials and healthcare professionals) to reduce cholera cases from 400 to 0 in three weeks (Sofala, Africa, 2019) A conglomeration of resources with concepts that are either well-studied, applicable to our proposal, or both. Legend: Y = Yes, N = No, - =significantly documented limitations that must be considered, and furtherly researched before definitive yes. The Problems Firstly, current national and international surveillance methods only track provider-reported symptoms and disease cases [4,9] where symptom reporting is dependent on a healthcare provider seeing the patient. Further, delay of care is a persistent and undesirable feature of current health care systems where nearly 33% of Americans report an inability to receive timely care for urgent needs [10]. Symptomatic patients hesitate to seek care for weeks and travel rates among asymptomatic patients allow for unchecked disease spread to others [11-15]. A second problem with current disease surveillance methods is access to healthcare. With global healthcare inaccessibility, people in afflicted communities either must wait days to weeks before healthcare professionals assessment or do not receive healthcare altogether and community transmission of disease goes unchecked [16-19]. Especially relevant in developing countries, lack of geographic accessibility hinders the distribution of healthcare-related items (i.e., drugs and vaccines) [16]. American Journal of Biomedical Science & Research 294 Am J Biomed Sci & Res Copy@ Aaron Schmid Limited access to electricity, supply-chain, internet, and cellular network further contribute to underreporting of true case volume via the current surveillance system structures [3,15]. The third problem with current methods is fragmented communication and integration [4-8]. When datasets are centralized, predictive power, detection, and prevention are greatly increased [3,20]. Overall, current methods do not allow for robust early containment of geographical hotspots, thus allowing future outbreaks and pandemics. With current methods, we can pair retrospective analytical tools with prospective, predictive software to develop an early notification system. Addressing Healthcare Provider-Dependent Reporting While several countries have previously implemented smallscale, local, mobile-based health surveillance systems in urban and rural areas (Table 1), the lack of central integration misses early detection of outbreaks at-large. Despite the current need for central integration, there is a place for mobile-based practice in public health. A systematic review in 2015 that looked at many high-quality metaanalyses and systematic research reviews substantially supports the value of integrating text-messaging interventions into public health practice, especially since the interactivity in the SMS format facilitated and correlated positively with use and health outcomes [21]. Open-access symptom tracker tools equip users with unique identification numbers and resources to guide their next-steps [3,22,23]. Our proposal seeks to utilize the useful insights from these surveillance systems as it is mentioned in (Table 1). User Compliance While SMS-mediated communication allows for great penetrance [24,25] a limitation with user (i.e., patient) compliance must be addressed in governmental initiatives that empower the patient through SMS/IVR. One group showed that intrinsically and extrinsically motivated individuals (self-determination theory) are more likely to participate in governmental initiatives when users deemed it fun and enjoyable [26]. Therefore, a quintessential aspect in the development of our AIs interactivity function would be the cornerstone that it is exceptionally user-friendly. Furthermore, it has been reported that negative emotions (i.e., fear and anxiety) in response to the current pandemic are protective and account for adaptive public health-compliant behavior change [27]. However, over-sensationalized media coverage and fear of infection during health clinic visits have contributed to maladaptive levels of anxiety, which helps explain why some patients do not seek healthcare services [28,29]. As negative emotions can facilitate user compliance, especially in our proposals governmental, public-health initiative paradigm, we strongly recommend that media outlets responsibly report findings from evidence-based institutions. Increasing Predictivity Power, Learning, and Saving Money Integrating Deep As SARS-CoV-2 has inspired the advent of open-access symptom tracker tools [3,22], a mainstay limitation is a high rate of false-negatives and -positives in the database (attributed to leading questions and mainstream media influence). Nonetheless, when one group paired disease-specific symptoms (i.e., loss of taste and smell) with otherwise general symptoms (i.e., fatigue, persistent cough, and loss of appetite), they yielded a prediction model that most accurately determined true-positives [3]. Another group showed that ML and cloud computing end-user data can predict disease spread in real-time using the Robust Weibull model (e.g., allows user to weigh parameters to robustly deal with contaminated data), which made statistically better predictions than the baseline Gaussian model (e.g., a model that assumes a parabolic behavior near the origin of coordinates) [30]. These more accurate predictions allow for a better proactive governmental and citizen response to an emergence of disease in a country specific manner. As notorious overfilling of hospitals occurred in the face of the 2020 COVID-19 pandemic in countries across the world, a better system for triaging was made evident. In the clinical setting, a fully automated Deep Learning (DL) system for COVID-19 diagnosis and prognosis may better triage patients based on computed tomographic images of their lungs, thus optimizing medical resource usage in the clinical setting. Additionally, this DL system is also able to differentiate pneumonias (COVID-19 vs. other viral vs. bacterial), thus substantially decreasing the generation of falsepositives [31]. As ML predictive models are developed, DL methods may be employed to amplify important inputs that discriminate and suppress irrelevant variations [32]. On a geographical scale, Blue Dot and Zenysis (Table 1) are AI-based healthcare companies that have utilized aggregated data in thwarting previous epidemics. Their concepts provide prediction models based on meta-data parameters (airline itinerary, disease-carrying vector[s], and cellphone data). Analysis offered by Oxford Insights details the readiness index by which various countries governments have the capacity to implement AI technology into their daily practice [3337]. In a cost-versus-benefit analysis, financially limited countries may benefit the most in a universally accessible syndromic surveillance paradigm [32]. As larger datasets are integrated, ML and DL-associated costs are expected to increase; however, mitigating economic devastations warrant the investment. American Journal of Biomedical Science & Research 295 Am J Biomed Sci & Res Copy@ Aaron Schmid Applicability in Global Communities (Urban & Rural) Smartphone-based applications are powerful, but there is concern that their scalability is limited to affluent areas in developed countries, and the concept cannot be extrapolated to rural areas, impoverished cities, or developing countries [38]. Unavailability of transportation is associated with a lack of regular medical care and less use of healthcare services, therefore leading to adverse health outcomes that may be otherwise prevented [39]. Rural populations are less likely to have online access to health information [40], less access to information from primary care physicians and specialists [41], and lower levels of health literacy [42] compared to urban residents. Rural populations, especially minorities, are more unlikely to be able to see a physician for at least one year due to the related costs [43]. In (Table 2), we show extensive global utilization in both urban and rural demographics that have SMS and IVR technologies currently employed. We summarized these findings to show the current successes in utilizing the SMS/IVR route as a means for data collection and information distribution done in an accurate manner. Taken together, user compliance may be enhanced by an automated, streamlined, and digitalized SMS/ IVR syndromic surveillance model, therefore leading to the early detection and prevention of epidemic and pandemic pathogens. Table 2: Feasibility of Proposed Program Worldwide based on Similarly Employed Technologies. (Urban/Rural) Country SMS, IVR, or Both? Category Results Philippines [34] Both Crime India [57] SMS Health (Malaria) -20% of population with cellphones subscribed -Overall reduction of crime -Decreased time of data transfer (21 days to instantaneous) -Decreased time of lab results (7 days to 1 day) - Increased medical stock visibility (7 days to instantaneous) - Increased epidemiological report generation (1 month to 1 hour) -82.9% of text messages sent received a response Referred 9% of asymptomatic close contacts for testing (from 14.6% of total asymptomatic close contacts) Ireland [35] SMS Health (COVID-19) Sierra Leone [36] Both Health (Ebola) Rural Nepal [37] SMS Rural Western Uganda [45] SMS (Diarrheal & Respiratory Diseases) Rural Madagascar [46] Rural Ghana [47] Health Health (General) SMS Health (Influenza- - 85.8% of cell phone alerts were followed-up within 24 hours - Data collected via SMS modestly correlated with clinical/ hospital data - Effectively provided a snapshot at current health state before reaching the hospital - Reporting of symptoms was found to be 75.2% accurate -86.7% of the data was analyzed in real-time of 24 hours - Caregivers were able to triage childrens symptoms effectively based on severity Like IVR - 2.6% of total text message recipients tested positive for COVID-19 Diseases) Health (General) - Reporting of symptoms was found to be 95% accurate for fever and 87% accurate for diarrhea Examples of countries utilizing SMS and IVR technologies to mitigate a variety of issues (i.e, crime, specific- and general-health issues). Results are summarized from primary literature sources. Countries considered were those of both urban and rural geographical location. Proposed Solution Our proposed symptoms-based addresses three main objectives: syndromic surveillance Focus on early detection of known and unknown diseases to improve overall health surveillance. Prevent potential disease transmission within the community, thereby mitigating outbreaks at-large. Consider mass distribution and market penetration through current economic and medical landscape. The proposed solution (Figure 1) is a self-reported, symptomsbased syndromic surveillance system that is universal, interactive, integrative, and combined with artificial intelligence. The system aims to be integrated, meaning data input and analysis is handled by one central system. It utilizes short message service (SMS; text-messaging) and interactive voice response (IVR; calling; for American Journal of Biomedical Science & Research 296 Am J Biomed Sci & Res Copy@ Aaron Schmid those unable to text) to identify and contain hot spots during the early stages of an outbreak. Our proposed system interacts with users (educating them on evidence based/recommended next- steps) and with the virtual workspace (communicating findings in [near]-real-time) using an artificial intelligence (AI)-enhanced communication pipeline. Figure 1. The key to the success of our solution is funding provided by international health agencies and legislative bodies. The proposal includes collaboration between different regional, national, and global, governing bodies to construct a centralized, mobile-based reporting network. Previous success has been shown with diseaseoutbreak prevention systems utilizing cellphones at local and regional levels. Two groups have successfully used similar ideas in the United States and United Kingdom. The first was used to predict geographical hotspots of COVID-19 incidence five to seven days before public health reports, and the second to predict COVID-19 cases, based on self-reported symptoms, before patients were seen and diagnosed [3,44]. In the United States, contact tracing is done via SMS, telephone, or in-person follow-ups. When compared to the robust SMS system in Ireland, the United States had a significantly lower yield of 0.5% positive COVID-19 cases from 445 close contacts [45-48]. Therefore, while cognizant of its current limitations, we consider a system based in mobile technology best suited for the early detection needs of a pandemic. AI has equipped its users with robust predictive power which provides accurate case reporting while simultaneously mitigating false-positive cases. It also offers low-cost alternatives such as virtual, data-integrated workspaces to ease the workload by any single individual that can work in both urban and rural settings. In an artificial intelligence (AI)-based manner, big-data companies, such as Blue Dot and Zenysis (Table 1), have increased the availability of the technologys benefits to entire regions despite economic shortage. By having an AI-enhanced SMS/IVR system, we American Journal of Biomedical Science & Research 297 Am J Biomed Sci & Res Copy@ Aaron Schmid exponentially strengthen our otherwise lacking financial resources, human ability to manage big datasets, and disease prevention and mitigation strategies. By utilizing an SMS/IVR reporting system to obtain initial data in a potential public health crisis scenario, our proposal would be able to pre-screen users and effectively lessen the rapid demand on healthcare professionals and resources. Our end-users assigned an identification number and partnering health agencies can de-identify patient information since the user only needs a cellphone number when giving self-reported symptoms and demographic information. Users are then triaged and advised on follow-up that mitigates psychological distress and functional impairment among citizens, thus increasing user compliance. As AI-based technology to detect disease-causing agents is expected to increase, its current and expected applications on various levels may help to decrease inherent costs and curtail expenditures associated with a breakdown of the supply chain. population own mobile phones [49]. In advanced economies and the United States, 94% [50] and 96% [49] of the population own mobile phones, respectively. By relying on the current hardware distribution of cellphones allocated to individuals in the world, we drastically decrease the need for new hardware. Developing a syndromic surveillance network that relies on the utilization of existing hardware, combined with its expansive present-day utilization in both rural and urban societies, allows our proposed system to be highly scalable. Combined with AI and ML, a system like this would identify emerging patterns of disease exposure, symptom onset, disease trajectory, and clinical prognosis [51]. citizens informatively on the proper next steps. Mobile-based tools have previously been rapidly deployed in pandemic settings to address disease reporting and treatment needs [3,44]. Our proposal allows for the greatest market penetration in the current technological landscape and provides vital access to healthcare to vulnerable populations. In emerging economies, 78% of the (Table 1) so that they are readily available may require additional investment from the WHO. If the long-term feasibility of this program is adopted and governments wish to equip every individual with a mobile phone (smart or not), they may need additional funding for hardware needs if sensitivity is to be maximized. This may not be required as a smaller percentage of local populations rise in symptoms may be enough to alert of unusual disease activity. In a centralized manner, our proposal empowers legislative bodies, healthcare professionals, and individual decision-making Altruistic Behavior Remaining Challenges Secondary Costs Costs related to further engineering of software for AI, ML, and DL that seeks to integrate information from country-based syndromic surveillance systems into a centralized system will both need to be funded. Additionally, expanding EWARS-like systems Figure 2. American Journal of Biomedical Science & Research 298 Am J Biomed Sci & Res Copy@ Aaron Schmid Perhaps the greatest limitation of them all will be the desire for companies, governments, and other resources to work together if this idea would be proposed over the next five years (Figure 2). While organizations like the WHO may obtain individual governmental backing, we will need governmental contracts promising financial compensation for lasting partnerships. In addition, we will need a group of computer and AI engineers to collaborate in developing the algorithm and code for this centralized system. We may utilize algorithms like Blue Dots [52,53] or Zenysis [54] that will help setup the program for widespread distribution. Once developed, it can be deployed by individual local and national governments and increase the robustness of this system. With the added benefit of ML and DL, this system will be adaptable over time without needing to start from scratch [55-57]. Privacy Concerns One of the biggest concerns with big data communication networks is that only data that are meant to be transferred are obtained by the organizing bodies. This emphasizes the need for institutional regulations regarding the issues of privacy at all levels - patient and individual governments. Current legal precedents may help guide privacy rights and data sharing in our syndromic surveillance model. Importantly, all information collected from users is de-identified and HIPAA compliant, which is achievable if users are provided with a unique identification number that then redacts their personal information. United States federal law allows the sharing of healthcare-related information to those conducting public health surveillance [58]. International Health Regulations implemented by the Global Outbreak Alert and Response Network (GOARN) also permit the sharing of health information among countries [59]. These legislative bodies may be useful in checking that information cannot be linked to personal health information of any individual and ensure privacy compliance to ensure ethical utilization and enhanced privacy of the patient data that will be collected, guidelines such as Singapores Model Artificial Intelligence Governance Framework [60] can be used. Other guidelines were also established to encourage the use of data collected via public funds to be a public good [61]. However, these guidelines were not universally adopted due to privacy concerns. Blockchain, a distributed ledger system most commonly used for cryptocurrencies, can be used to combat these privacy issues and ultimately maintain confidentiality of health data [61]. De-identifying data or performing meta-analysis can be other ways to protect patient data while continuing to benefit from the valuable health information [62]. The use of ML will build prospective analyses, which then can be retrospectively verified to enhance future predictive power. Utilizing current datasets that do not require official clearance may curtail disease detection, and respect privacy concerns as data is inherently de-identified before reporting. Pro MED Mail (PMM) is a worldwide, online, email-based system put on by the International Society for Infectious Disease [63-65]. In contrast to the World Health Organization, PMM does not need clearance from officials before reporting on disease. Thus, by also sending this information to the AI-enhanced proposal we describe, we may afford national governments the preliminary preventative decision-making information before cases break into epidemic magnitude. Taken together, many legal avenues and resources allow for meaningful information to be aggregated while respecting patient privacy. Still, however, breaches in personal health information should be vigorously overseen to ensure this standard is being met. In the technological era of data sharing, safeguards that prevent malicious utilization of information and hacking should be active areas of research moving forward. Future Applications Due to the extensive applicability and reach of this proposal, there are several ways this system can be utilized in the future. Patients in rural areas can easily be seen and assessed by a provider through a central, virtual, telephone box-like telemedicine room. This method can also allow for remote monitoring of patients. Offering and providing a virtual system to receive healthcare may be an essential approach to reducing health disparities among rural and underserved populations [66,67]. Based on our proposal, more complex robotic telemedicine carts with cameras, interactive screens, and on-board medical equipment can be developed for these populations as well [66]. There is also potential to interact and treat disease hot spots without risking healthcare workers or additional exposure. Our system can also be used as a mass messaging system that provides health alerts or warnings and health or disease-related education [66,68]. Millions of people can be informed simultaneously via a simple text message, thereby increasing their health literacy. Regarding the COVID-19 pandemic and for future use, our system can also provide an enhanced contact tracing technique. The information can be easily attained and analyzed from patients who have reported symptoms in an efficient, timely manner. Conclusion Design and development of an automated, AI-enhanced SMS/ IVR syndromic surveillance system is of great interest to the global scientific and medical community and an active area of research. While some areas are better studied than others, the integration of associated technologies can be started locally and subsequently incorporated into a more centralized database as data and positive American Journal of Biomedical Science & Research 299 Am J Biomed Sci & Res Copy@ Aaron Schmid outcomes accumulate. With strong evidence showing the beauty in a system that increases communication and workflow through an AI-enhanced manner, healthcare and the medical landscape will inevitably progress in this direction. In our proposed solution to thwart any future epidemic and pandemic, we offer a conglomeration of evidence-based reports, real-life examples, and potential funding sources to perpetuate the beginning of what may just change the future of healthcare as we know it. While current economic constraints, altruistic-dependent behavior, and privacy concerns are considered, the proposal offers future savings, positive public health outcomes, and patient privacy protection as mainstays in our development toward its feasibility, applicability, sustainability, and scalability into the greater medical landscape. We describe current and future appliances of our solution that truly increase healthcare for all. In an integrated manner, we have essentially taken proficient pieces of the metaphorical puzzle and assembled them to offer a novel concept in stopping epidemics and pandemics in their tracks. Acknowledgement None. 12. Taber JM, Leyva B, Persoskie A (2015) Why do people avoid medical care? A qualitative study using national data. J gen int med 30(3): 290297. 13. Green CA, Johnson KM, Yarborough BJ (2014) Seeking, delaying, and avoiding routine health care services: patient perspectives. Am j health promot 28(5): 286-293. 14. 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