Abstract:  This talk will build a careful foundation for modeling knit objects using graphs in order to explore equivalences between knittable objects and well known graph structures and build theory for the complexity of determining knittability of graph structures. This discussion will also relate knitting properties with the topological genus of graphs and explore restrictions of general graph algorithms which are uniquely motivated by the knitting process. This foundation will be used to represent real-world knitting patterns and illustrate considerations of visualizing such patterns through force-directed graph layout algorithms.

Al Scott, a native of Worcester, Massachusetts, obtained a doctorate in Electrical Engineering from MIT in 1961. During the early 1970’s his research interests led to important contributions to the then emerging field of soliton mathematics and nonlinear wave propagation. He became one of the leading figures in the new field of nonlinear science and a founding editor of Physica D, the first journal devoted to the study of nonlinear phenomena. He was very interested in the role of nonlinear dynamics in modeling biological systems and, in particular, its applications to neuroscience.

In addition to many scholarly papers on a wide variety of topics he wrote several books on neuroscience and nonlinear science and was the editor of the comprehensive Encyclopedia of Nonlinear Science published in 2005. He joined the faculty of the Mathematics Department at the University of Arizona in 1985 and became a member of the University’s Program in Applied Mathematics. He retired from the University in 2000. His many contributions to the life of both the Program in Applied Mathematics and the Department of Mathematics were characterized by a civilized and good-humored approach to academic life. He was particularly encouraging of graduate students and it is this characteristic that is the basis for the Al Scott Prize and Lecture. The annually awarded prize is given to a senior student in the Program in Applied Mathematics and consists of a cash prize and a lecture in the Applied Mathematics Colloquium series.

Day 4: PDE learning and Scientific  with Julia 

Place: ENR2, S395

           1 - Scientific Computing Integration with AD in Julia and Custom Adjoints

            2 - Example Notebooks: GPU Computing in Julia

            3 - Example Notebooks: Neural PDE Learning in Julia

            4 - Example Notebooks: Data Processing and Cross language Integration

Zoom:   https://arizona.zoom.us/j/83738249833   Passcode: applied

Abstract: We will discuss how to turn our work into an engaging research talk, under constraints such as time and audience. I will provide my preferred structure for a talk to effectively motivate a problem and convey results and their significance, as well as some tips for how to make the inherent theatrics and technology work to our favor. In addition, we will review some best practices and resources for how to ensure that our talks are inclusive and accessible to a wide audience, including, for example, some nuances in formatting slides and figures. There will be time during the talk for open discussion, and other opinions and perspectives are welcome and appreciated!

Zoom Link: https://www.math.arizona.edu/~klin/rtg-zoom

Title: From computational biology to disease control: insights from bacterial zoonotic diseases

Abstract: Newly emerging bacterial diseases are major threats to public and animal health. Bacteria that have long latent periods and can jump the species barrier are especially difficult to diagnose and control. Animal tuberculosis caused by Mycobacterium bovis has been recognized as a problem in many parts of the world. Infections have been found in multiple wildlife and livestock populations, as well as in humans. Recognition of the epidemiologic circumstances involved in spillover events, amplification, and spread of animal TB is essential for prioritizing surveillance and predicting future disease emergence risk. Here, I will present research to investigate ecological and evolutionary questions in the wildlife-livestock animal TB system. Using multiple data streams and a combination of statistical and mechanistic models, I will explore the main drivers enabling M. bovis persistence at the population level, as well as the impacts of cross-species transmission events on the management and control of the disease.

In recent years, the study of evolution equations with a fractional Laplacian has received much attention due to the fact that they have been successfully applied to the modeling of a wide variety of phenomena ranging from biology to physics to finance. The stochastic process behind fractional operators is associated with an $\alpha$-stable process in all space, in contrast to the Laplacian operator, which is associated with a Brownian stochastic process.

In addition, evolution equations involving fractional Laplacians offer new interesting, and very challenging mathematical problems. There are several equivalent definitions of the fractional Laplacian in the entire domain. In a bounded domain, however, there are several possibilities depending on the stochastic process under consideration.

In this talk, we will present results on the rigorous transition from a velocity-jumping stochastic process in a bounded domain to a macroscopic evolution equation with a fractional Laplace operator. More precisely, we will consider the long-time/small mean-free path asymptotic behavior of the solutions of a rescaled linear kinetic transport equation in a smooth bounded domain.

Gaussian elimination with partial pivoting (GEPP) remains the most used dense linear solver. For a nxn matrix A, GEPP results in the factorization PA = LU where L and U are lower and upper triangular matrices and P is a permutation matrix. If A is a random matrix, then the associated permutation from the P factor is random. When is this a uniform permutation? How many disjoint cycles are in its cycle decomposition (which equivalently answers how many GEPP pivot movements are needed on A)? What is the longest increasing subsequence of this permutation? We will provide some statistical answers to these questions for select random matrix ensembles and transformations. For particular butterfly permutations, we will present full distributional descriptions for these particular statistics. Moreover, we introduce a random butterfly matrix ensemble that induces the Haar measure on the full 2-Sylow subgroup of the symmetric group on a set of size 2ⁿ.

Blood flow heterogeneity in the pulmonary and systemic circulations can cause significant reductions in oxygen transport, particularly under conditions of high oxygen demand such as exercise.  Heterogeneity in the microcirculation arises from both intrinsic factors and extrinsic factors.  Intrinsic factors include the structural heterogeneity of microcirculatory networks that arise in part due to geometric constraints and the stochastic nature of angiogenesis, and the resultant variations in blood flow and hematocrit.  Extrinsic factors include variations in oxygen supply and demand.  Various mechanisms of compensating for this heterogeneity to improve oxygen uptake and utilization have evolved, and include short-term mechanisms such as flow regulation and long-term mechanisms such as structural adaptation.  Quantitative modeling suggests that the matching of blood flow to ventilation in the lung and to metabolism in the systemic circulation is imperative for maintaining oxygen transport, particularly under conditions of high oxygen demand. Impairment of flow regulation under pathophysiological conditions can lead to low blood oxygen levels and organ failure, even under conditions of adequate overall tissue perfusion, suggesting new therapeutic approaches.

https://www.mayoclinic.org/biographies/roy-tuhin-k-m-d-ph-d/bio-20054451

For details, see https://science.arizona.edu/academics/graduation-convocation