Modeling and Comp Seminar

Learning Dynamics of Oscillators with Applications to Circadian Rhythms

The ability to accurately forecast the dynamics of a complex oscillating system is fundamental to the study of many physical and biological systems. This is especially important for understanding and predicting the bodies natural 24 hour oscillations in physiology and behavior known as circadian rhythms. The response of oscillators to external perturbations can be traced out either theoretically or experimentally into phase response curves. In this work, we study the application of model discovery techniques to complex nonlinear oscillator systems using phase response data. Using simulated data we examine how well these techniques perform when the perturbations are generalized from the training data. Finally, we discuss the application of these techniques to the study of circadian rhythms and discuss some preliminary results for using wearable data (apple watch, fitbit) to build personalized models of circadian rhythms.

Zoom:  https://arizona.zoom.us/j/94534134312   Password:  “arizona” (all lower case)

When

12:30 p.m. Thursday

Where

Online

Mathematical Modeling of COVID-19 Dynamics on a College Campus: A Story of Differential Equations, Network Theory and Presentations to Campus Leadership

In March 2020 the University of California, Merced (UC Merced), along with all higher educational institutions in the state of California, moved to an on-line only mode of course delivery as a means to decrease the spread of SARS-CoV-2, or COVID-19. In Summer 2020, a Public Health Working group was convened to plan for the Fall 2020 semester. As mathematical biologists, we were tasked to develop mathematical models to evaluate the effectiveness of proposed disease mitigation strategies in containing COVID-19 at UC Merced. In this talk, we discuss both the results of our modeling efforts as well as our perspective on how mathematicians can effectively engage with campus leadership in the decision-making process. Finally, we report on our on-going efforts to provide UC Merced with data for Spring 2021 planning.

We will present the two mathematical models we used to evaluate Fall 2020 re-opening strategies: a system of ordinary differential equations and an agent based model. Perhaps not surprisingly, our models demonstrated that even when the campus undertook strong disease mitigation measures (limiting the size of in-person courses, testing of symptomatic & asymptomatic individuals and mandatory mask-use) COVID-19 would continue to enter the UC Merced campus population through less restrictive contacts with the surrounding community. As such, the campus would have to be prepared for a steady stream of active cases all semester. In July 2020, UC Merced made the decision to hold all classes remotely and our models were used to determine a “safe number” of students to allow in on-campus housing.

Place:  Zoom:  https://arizona.zoom.us/j/94534134312   Password:  “arizona” (all lower case)

When

12:30 p.m. Oct. 15, 2020

Where

Zoom

A topological view of collective behavior

From nanoparticle assembly to synchronized neurons to locust swarms, collective behaviors abound anywhere in nature that objects or agents interact. Investigators modeling collective behavior face a variety of challenges involving data from simulation and/or experiment. These challenges include exploring large, complex data sets to understand and characterize the system, inferring the model parameters that most accurately reflect a given data set, and assessing the goodness-of-fit between experimental data sets and proposed models. Topological data analysis provides a lens through which these challenges may be addressed. In this talk, I introduce the core ideas of topological data analysis for newcomers to the field. I then highlight how these topological techniques can be applied to models arising from the study of groups displaying collective motion, such as bird flocks, fish schools, and insect swarms. The key approach is to characterize a system's dynamics via the time-evolution of topological invariants called Betti numbers, accounting for persistence of topological features across multiple scales.

Place:  Zoom:  https://arizona.zoom.us/j/94534134312   Password:  “arizona” (all lower case)

When

12:30 p.m. Oct. 8, 2020

Where

Zoom

ML-based feedback control in bioelectronics for biological control

In this talk, we refer to the achievement of an intended and predicted response in a biological system as controlling biology. Efforts towards controlling biology have evolved on different scales from controlling gene expression at the single-cell level to controlling large complex networks such as glucose regulation via an artificial pancreas. However, most approaches are not immune to the inherent properties of nature such as stochasticity and unmodeled dynamics. What allows nature to evolve and life to exist is what makes it challenging to control. New technology in synthetic biology and bioelectronics can give us unprecedent spatiotemporal control over nature. Through adaptive external “sense and respond” learning algorithms, we can gain improved control over cellular response. In this talk, will discuss work done towards developing NN-based predictors and feedback controllers in order to direct cellular response with no model a priori and no offline training. We demonstrate successful control of stem cell membrane potential for a period of 10hrs. A Lyapunov based stability analysis is provided to give insight to the effectiveness of the controller.

Bio: Marcella M. Gomez is an assistant professor at UC Santa Cruz in the department of Applied Mathematics. She received her PhD from Caltech in 2015 and a B.S. from UC Berkeley in 2009; both degrees in Mechanical Engineering. Her research interests are in synthetic and systems biology. She is also a proud Chicana, first generation Mexican-American from Riverside, CA.

Place:  Zoom:  https://arizona.zoom.us/j/94534134312   Password:  “arizona” (all lower case)

When

12:30 p.m. Oct. 1, 2020

Where

Zoom

Math Flips the Perspective in Contact Tracing

Contact tracing has emerged as an important technique in controlling COVID-19. Its test-trace-isolate-support paradigm focuses on identifying potentially contagious individuals and isolating them. This talk introduces an alternative and complementary approach which has just become achievable with present technology: for each positive case, do not only notify their direct contacts, but inform thousands of people of how far away they are from the positive case, as measured in network-theoretic distance in their relationship network (not geographical distance). This approach brings a new tool to bear on COVID-19, analogous to a weather satellite providing early warning of incoming hurricanes. It empowers individuals to observe the spread and directly avoid infection (a natural selfish instinct), reducing reliance on altruism. This could solve the behavior coordination problem which has hampered most other interventions to date. The speaker is a math professor whose ordinary research focus is in network theory, probability, and algorithms. This talk will be different in nature from a traditional math research seminar, and will be accessible to non-math-researchers. It will also share some of the experience of starting from several mathematical research insights (network theory and basic Fourier Analysis) to implement and deploy a practical system at scale: the NOVID app.  

Please join us for a post-seminar discussion from 1:30 to 2:30.  

At the speakers request this event will not be recorded.  Place:  Zoom:  https://arizona.zoom.us/j/94534134312   

When

12:30 p.m. Sept. 24, 2020

Where

Zoom

Quantifying risk of SARS-CoV-2 transmission for use in the Covid Watch app

Privacy-preserving exposure notification apps recommend quarantine based on Bluetooth signal. Apps deployed so far recommend quarantine using three binary decision points; when timing falls within a fixed window of infectiousness, duration is above a threshold, and attenuation is below a threshold. However, Bluetooth attenuation is not a reliable measure of distance, and infection risk is not a binary function of distance, nor duration, nor timing. Here we describe a method to integrate all sources of information (including new data on the relationship between distance and Bluetooth attenuation) to more accurately estimate relative infection risk. We also provide a method to calculate the probability of current or future infectiousness, which is a function of initial infection risk and the number of symptom-free days since exposure, and any negative test results. Public health authorities can use either probability, implemented in the Covid Watch app, to apply a threshold for quarantine.  Place:  Zoom:  https://arizona.zoom.us/j/94534134312   

When

12:30 p.m. Sept. 17, 2020

Where

Zoom

A Hamilton-Jacobi Formulation for Time-Optimal Paths of Rectangular Nonholonomic Vehicles

We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some of the ambient geometry by assuming the car is a point mass and/or buffering obstacle boundaries. We present a Hamilton-Jacobi formulation of the problem which resolves time-optimal paths and considers the geometry of the vehicle. In doing so, we avert the need for a hierarchical path planner or other obstacle avoidance considerations. We design an upwind fast sweeping scheme to solve the Hamilton-Jacobi equation numerically, and we conclude by briefly discussing some generalizations.  Zoom:  https://arizona.zoom.us/j/94534134312

 

When

12:30 p.m. Sept. 3, 2020

Where

Zoom

Organizational Meeting

The Modeling, Computation, Nonlinearity, Randomness, and Waves Seminar will have an organizational meeting on Thursday, 8/27  at 12:30 via Zoom.  If you would like to speak or suggest a potential speaker, please attend or email one of us.  Kevin Lin klin@math.arizona.edu & Laura Miller lauram9@math.arizona.edu  If you would like to receive email announcements and are not already on the Applied Math seminar list, please write appliedmath@math.arizona.edu to be added.

Place:    Zoom:  https://arizona.zoom.us/j/94534134312

When

12:30 p.m. Aug. 27, 2020

Where

Zoom

Spatio-Temporal Additive Regression Model Selection for Urban Water Demand

Understanding the factors influencing urban water use is critical for meeting demand and conserving resources. To analyze the relationships between urban household-level water demand and potential drivers, we develop a method for Bayesian variable selection in partially linear additive regression models, particularly suited for high-dimensional spatio-temporally dependent data. Our approach combines a spike-and-slab prior distribution with a modified version of the Bayesian group lasso to simultaneously perform selection of null, linear, and nonlinear models and to penalize regression splines to prevent overfitting. We investigate the effectiveness of the proposed method through a simulation study and provide comparisons with existing methods. We illustrate the methodology on a case study to estimate and quantify uncertainty of the associations between several environmental and demographic predictors and spatio-temporally varying household-level urban water demand in Tampa, FL.  Zoom: https://arizona.zoom.us/j/95834019930

When

12:30 p.m. April 30, 2020

Where

Zoom Session: TBA

Deep Learning for Efficient Modeling of High Dimensional Spatiotemporal Physics

Turbulence is an exceptionally complex and high-dimensional phenomena, exhibiting spatio-temporal dynamics, non-linearity and chaos. In an era where vast quantities of such DNS data are generated; building practical, physics-driven reduced order models (ROM) of such phenomena are crucial. While Deep neural networks for spatio-temporal data have shown considerable promise, they face severe computational bottlenecks in learning extremely high dimensional datasets, often with > 10^9 degrees of freedom. These application-agnostic networks may also lack physical constraints and interpretability that is desired in scientific ROMs. In this work, we present our efforts in integrating the strong mathematical and physical foundations underlying numerical methods and wavelet theory with deep neural networks. In this talk, we demonstrate computationally efficient learning of 3D turbulence with embedded physics constraints for improved interpretability and physics guarantees, and outline ongoing efforts.  Zoom: :  https://arizona.zoom.us/j/97722828578

When

12:30 p.m. April 23, 2020

Where

Zoom Session
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