RIT School of Mathematics and Statistics (SMS) Colloquiums

Stephanie Dodson,  Krener Assistant Professor, Department of Mathematics, University of California, Davis

Title: Traveling waves, reflections, and the onset of cardiac arrhythmias

 Abstract: When propagated action potentials in cardiac tissue interact with local heterogeneities, reflected waves can sometimes be induced. These reflected waves have been associated with the onset of cardiac arrhythmias. While their generation is not well understood, their existence is linked to that of one-dimensional (1D) spiral waves. Thus, understanding the existence and stability of 1D spirals plays a crucial role in determining the likelihood of unwanted reflected pulses. Mathematically, we probe these issues by viewing the 1D spiral as a time-periodic antisymmetric source defect pattern that arises in a reaction-diffusion system. Through a combination of root-finding and continuation methods, we numerically solve for the 1D spiral wave pattern to investigate its existence and stability and determine how the system's propensity for reflections is influenced by system parameters. Our results support and extend a previous hypothesis that the 1D spiral is an unstable periodic orbit that emerges through a global rearrangement of heteroclinic orbits. We identify key parameters and physiological processes that promote and deter reflection behavior. 

Bio:  Stephanie is currently a Krener Visiting Assistant Professor in the Department of Mathematics at UC Davis. Previously, she received her Ph.D. in Applied Mathematics from Brown University, where she was advised by Bjorn Sandstede and received an NSF Graduate Fellowship. Stephanie's research spans the fields of dynamical systems, nonlinear waves, and mathematical biology. In the fall, Stephanie will start as a tenure-track Assistant Professor in the Mathematics Department at Colby College.

Jason Ritt, Scientific Director of Quantitative Neuroscience, Carney Institute for Brain Science, Brown University

Title: Data science applications and challenges in brain science

Abstract: Brain science draws on a wide array of disciplines, from psychology to physiology to genetics to computational modeling and more, demonstrating the challenge of mechanistically connecting extraordinarily complex neural systems to behavior and subjective experience. In the last decade, due in part to the BRAIN Initiative and to a proliferation of powerful new open-source tools, the scale and sophistication of brain science experiments rapidly expanded, creating new data analysis and computational problems not met within these traditionally organized fields. I will describe experimental and theoretical brain science applications and highlight opportunities and challenges for data science to contribute to our understanding of the function of neural systems.

Bio:  Dr. Ritt is the Scientific Director of Quantitative Neuroscience at the Carney Institute for Brain Research at Brown University. His primary research areas include the neural basis of active touch, dynamical models of neural systems, and neural engineering for brain stimulation and control. Within the Carney, he collaboratively supports research and quantitative training across institute-affiliated labs working in neuroscience, cognitive science, molecular biology, linguistics, and other fields spanning the Carney mission.

Speaker: Dr. Elise Lockwood, Oregon State University

Bio: Elise Lockwood is an Associate Professor in the Department of Mathematics at Oregon State University and currently serves as a rotating program officer in the Division of Undergraduate Education at the National Science Foundation. She received her Ph.D. from Portland State University and was a postdoctoral scholar at the University of Wisconsin – Madison. Her research focuses on undergraduate students’ reasoning about combinatorics, and she is passionate about improving the teaching and learning of discrete mathematics. More recently, she has investigated the role of computing within mathematics education -- both within combinatorics and in other content domains. Her work has been funded by the National Science Foundation and Google. She received the 2018 John and Annie Selden Award and the 2019 Promising Scholar Award at Oregon State University. She was a 2019 Fulbright Scholar in Oslo, Norway, where she collaborated with researchers at the Center for Computing in Science Education at the University of Oslo. Elise’s favorite part of her work is collaborating with wonderful colleagues and students, and she finds it particularly rewarding when ideas are developed and refined through rich conversations. In her free time, Elise enjoys cooking, reading, running, traveling, playing board games, cheering for the Portland Trail Blazers, and spending time with her two Ragdoll cats.

Speaker: Dr. Ruth Haas, the University of Hawaii at Manoa
Title: Integrating Computing into STEM Education: A Case of Python Programming in Combinatorial Contexts

Abstract: Computational activity, and programming, in particular, comprise an increasingly essential aspect of scientific activity, and engaging in computing is as accessible as ever. In STEM education, there is a need to investigate how students’ computational activity can support students reasoning about mathematical and scientific concepts. In this talk, I present results from a study in which undergraduate students engaged with Python programming tasks designed to elicit particular combinatorial ideas. I highlight noteworthy aspects of students’ experiences with computing in this mathematical context, including the benefits and drawbacks of working in a computational environment. I suggest that even for students with little programming experience, the computational environment supported their combinatorial reasoning in valuable ways. I conclude by addressing practical issues related to implementation and discussing pedagogical implications. Overall, I seek to frame these specific findings about Python programming in mathematics as an instance of a broader phenomenon, namely highlighting how computing may be leveraged to support students’ engagement with scientific concepts and practices.

Bio: Ruth Haas is an American mathematician and professor at the University of Hawaii at Manoa. Previously she was the Achilles Professor of Mathematics at Smith College. She received the M. Gweneth Humphreys Award from the Association for Women in Mathematics (AWM) in 2015 for her mentorship of women in mathematics. Haas was named an inaugural AWM Fellow in 2017. In 2017 she was elected President of the AWM, and on February 1, 2019, she assumed that position. Her research is in combinatorics and includes graph theory and algebraic combinatorics.

Speaker: Dr. Gaik Ambartsoumian, University of Texas, Arlington
Title: Reconfiguration in graph coloring and graph domination

Abstract: In mathematics, as in life, there are often multiple solutions to a question. Reconfiguration studies the relationship between various solutions to a problem. In particular, is it possible to move from one solution to another following a given set of rules? This talk will consider the reconfiguration of graph coloring and graph domination. A proper coloring of a graph is an assignment of a color to each vertex of the graph so that neighboring vertices have different colors. The standard reconfiguration rule is to change the color of just one vertex at a time. What conditions allow us to get from one coloring to another by a sequence of vertex changes with the condition that each step along the way is a proper coloring? We give some motivating applications and some results. In a graph with vertex set V, a dominating set is a subset S of vertices such that every vertex in V is either in S or adjacent to a vertex in S. We consider reconfiguring dominating sets by adding and subtracting vertices from a set and describe some recent results.

BIO: Dr. Ambartsoumian is an associate professor in the University of Texas, Arlington math department. His research interests are computerized tomography, integral geometry, inverse problems, and mathematical imaging problems.

Title: Broken Rays, Cones, and Stars in Tomography
Abstract: Mathematical models of various imaging modalities are based on integral transforms mapping a function (representing the image) to its integrals along specific families of curves or surfaces. Those integrals are generated by external measurements of physical signals, which are sent into the imaging object, modified as they pass through its medium, and captured by sensors after exiting the object. The mathematical task of image reconstruction is then equivalent to recovering the image function from the appropriate family of its integrals, i.e., inverting the corresponding integral transform (often called a generalized Radon transform).  A classical example is a computerized tomography (CT), where the measurements of the reduced intensity of X-rays that have passed through the body correspond to the X-ray transform of the attenuation coefficient of the medium. Image reconstruction in CT is achieved through inversion of the X-ray transform.  In this talk, we will discuss several novel imaging techniques using scattered particles, which lead to the study of generalized Radon transforms integrating along trajectories and surfaces containing a ``vertex''.The relevant applications include single-scattering X-ray tomography, single-scattering optical tomography, and Compton camera imaging. We will present recent results about injectivity, inversion, stability, and other properties of the broken ray, conical Radon, and star transform.

Speaker: David Neilsen (Professor, Department of Physics and Astronomy, Brigham Young University)

TITLE: A fast wavelet transform for numerically solving hyperbolic PDEs

ABSTRACT: Many solutions of nonlinear, hyperbolic PDEs have solutions with fine-scale features or even discontinuities, which are difficult to capture numerically. These solutions, however, often have a sparse representation in a wavelet basis, which has multiple scales to efficiently encode information. The interpolating wavelet basis is well adapted to solving PDEs numerically, the fast transform uses polynomial interpolation on dyadic grids, and we add adaptivity by thresholding the wavelet coefficients in the expansions. We have developed a new computer platform, Dendro-GR, to solve PDEs using the interpolating wavelet basis to robustly adapt the spatial resolution. I will present examples from computational fluid dynamics and general relativity.

BIO: David Neilsen researches numerical relativity, relativistic fluids, and computational physics at Brigham Young University, where he is Professor of Physics and Astronomy.  He received his PhD at the Center for Relativity at the University of Texas at Austin, and was a post-doctoral researcher at UT Austin and Louisiana State University before joining BYU.

Speaker: Minghao W. Rostami (Assistant Professor, Department of Mathematics, Syracuse University)

Title: Fast algorithms for the simulation of biofluids

Abstract: 
The simulation of fluid around dynamic biological structures, such as bacteria, cilia, and sperm, entails the solution of challenging systems of linear and differential equations. In this talk, we present several efficient numerical algorithms for tackling them. The talk consists of the following two parts: joint work with Sarah Olson (WPI) and Weifan Liu (Syracuse), respectively.

Some of the most popular methods for calculating fluid-structure interactions give rise to dense matrices, that is, matrices with very few zero entries. They tend to be large and very costly to work with for practical models in which the number of structures is large. We extend the Kernel-Independent Fast Multipole Method (KIFMM) to calculate the matrix-vector products involving these large, dense matrices and develop efficient preconditioners for solving the linear systems involving them as well. The methods that we propose are matrix-free; that is, they do not require explicit construction of the matrices.

To track the biological structures' dynamics over time, we need to solve a system of nonlinear Ordinary Differential Equations (ODEs). When multiple computer cores are available, we can parallelize the computation of fluid-structure interactions at each time step; however, the parallel speedup of this approach tends to “saturate” as the number of cores increases. We propose to apply the Para real algorithm to parallelize the solution of the ODEs in the time domain instead. We roughly divide the time domain into “slices” and simultaneously solve the ODEs on these slices. To further improve its speedup, we develop several new ODE solvers by extrapolating existing ones.

Bio: 
Minghao received her Ph.D. degree in Applied Mathematics and Scientific Computation from University of Maryland, College Park, in 2012. She was a postdoctoral researcher at Worcester Polytechnic Institute from 2013 to 2016. She has been a tenure-track Assistant Professor at the Department of Mathematics, Syracuse University, since 2016.

Minghao’s research interests lie in numerical linear algebra, computational fluid dynamics, and mathematical biology.

Speaker: Rediet Abebe (Assistant Professor of Computer Science at the University of California, Berkeley)

Title: Modeling the Dynamics of Poverty

Abstract:  The dynamic nature of poverty presents a challenge in designing effective assistance policies. A significant gap in our understanding of poverty is related to the role of income shocks in triggering or perpetuating cycles of poverty. Such shocks can constitute unexpected expenses -- such as a medical bill or a parking ticket -- or an interruption to one’s income flow. Shocks have recently garnered increased public attention due to prevalent evictions and food insecurity during the COVID-19 pandemic. However, shocks do not play a corresponding central role in designing and evaluating poverty-alleviation programs. 

To bridge this gap, we present a model of economic welfare that incorporates dynamic experiences with shocks and poses algorithmic questions related to subsidy allocations. We then computationally analyze the impact of shocks on poverty using a longitudinal, survey-based dataset. We reveal insights about the multi-faceted and dynamic nature of shocks and poverty. We discuss how these insights can inform the design of poverty-alleviation programs and highlight directions at this emerging interface of algorithms, economics, and social work. 

Bio:  Rediet Abebe is an Assistant Professor of Computer Science at the University of California, Berkeley, and a Junior Fellow at the Harvard Society of Fellows. Abebe holds a Ph.D. in computer science from Cornell University and graduates degrees in mathematics from Harvard University and the University of Cambridge. Her research is in artificial intelligence and algorithms, focusing on equity and justice concerns. Abebe co-founded and co-organizes Mechanism Design for Social Good (MD4SG) -- a multi-institutional, interdisciplinary initiative. Her dissertation received 2020 ACM SIGKDD Dissertation Award and an honorable mention for the ACM SIGEcom Dissertation Award for offering the foundations of this emerging research area. Abebe's work has informed policy and practice at the National Institute of Health (NIH) and the Ethiopian Ministry of Education. She has been honored in the MIT Technology Reviews' 35 Innovators Under 35 and the Bloomberg 50 list as a one to watch. Abebe also co-founded Black in AI, a non-profit organization tackling equity issues in AI. Her research is influenced by her upbringing in her hometown of Addis Ababa, Ethiopia.

Title: Mathematical Justification of Slender Body Theory

Abstract:
Systems in which thin filaments interact with the surrounding fluid abound in science and engineering. The computational and analytical difficulties associated with treating thin filaments as 3D objects has led to the development of slender body theory, in which filaments are approximated as 1D curves in a 3D fluid. In the 70-80s, Keller, Rubinow, Johnson and others derived an expression for the Stokesian flow field around a thin filament given a one-dimensional force density along the center-line curve. Through the work of Shelley, Tornberg and others, this slender body approximation has become firmly established as an important computational tool for the study of filament dynamics in Stokes flow. An issue with slender body approximation has been that it is unclear what it is an approximation to. As is well-known, it is not possible to specify some value along a 1D curve to solve the 3D exterior Stokes problem. What is the PDE problem that slender body approximation is approximating? Here, we answer this question by formulating a physically natural PDE problem with non-conventional boundary conditions on the filament surface, which incorporates the idea that the filament must maintain its integrity (velocity along filament cross sections must be constant). We prove that this PDE problem is well-posed, and show furthermore that the slender body approximation does indeed provide an approximation to this PDE problem by proving error estimates. This is joint work with Laurel Ohm, Will Mitchell and Dan Spirn.

Short Bio:
Yoichiro Mori received his Ph.D from New York University in 2006. After a postdoc at the University of British Columbia, he joined the faculty of the University of Minnesota in 2008. He recently moved to the University of Pennsylvania, where he is the Calabi-Simons Professor in Mathematics and Biology, and is co-director of the Center for Mathematical Biology. His research interests are in mathematical physiology/biophysics and applied/numerical analysis.

Title: Computational Literacy: The Very Idea

Speaker: Andrea A diSessa, Graduate School of Education, University of California at Berkeley

My central claim is that achieving a new literacy with computation is the very best thing we can imagine for the future of computers and learning. That achievement will be transformative on par with the achievement of mass literacy for text; it will be fundamental to (future) society.

Then, I must fill in:
   What is “computational literacy”?
   What will it look like? Is there an existence proof?
   How can we conceive of its emergence? How can we nurture its advancement?

Finally, I’ll briefly look at a very visible competitor to the idea of computational literacy: computational thinking. I will argue that (1) the scientific basis for computational thinking is suspect, at best, and (2) while computational thinking has generated huge public visibility and funding, it is a detour best avoided on the track to achieving computational literacy.

Brief Bio:

Andrea diSessa holds degrees in physics from MIT (PhD) and Princeton (AB). He is a member of the National Academy of Education, a Fellow of the American Educational Research Association, and Corey Professor Emeritus at UC Berkeley. His research centers on the role of intuitive knowledge in learning scientific concepts, and computational literacies. He is the prime designer of Boxer, a medium to support computational literacy. diSessa has authored over 100 articles and chapters and authored or edited seven volumes, including Changing Minds: Computers, Learning and Literacy, and Turtle Geometry: The Computer as a Medium for Exploring Mathematics.