Desmos Activity Builder is an online tool that can be used in a variety of ways in and out of the classroom. It can be used to introduce concepts or as a learning assessment during or outside of class. In this session we will explore some ways to use Desmos activities in your classroom. We…
The structure of algebras of differential invariants, particularly their generators, is based on the symbolic invariant calculus provided by the method of equivariant moving frames. I will discuss a new computational algorithm that will, in many cases, determine whether a given set of differential invariants is generating. As an example, we establish a new result…
Global sensitivity analysis (GSA) offers a flexible framework for understanding the structural importance of uncertain parameters in mathematical models. This dissertation focuses on forward and inverse problems arising in uncertainty quantification and the computation of Sobol’ indices, measures of variance-based sensitivity. The models involved in these prob- lems are often computationally expensive to evaluate. Sensitivity…
This talk will be in person in Cox 306 where snacks and refreshments will be provided, there will also be a virtual option for those who cannot attend in person. Speaker's website Zoom Link
We show how to use continued fraction representations of 2-bridge knots to compute the average value of different invariants of the set of 2-bridge knots with fixed crossing number c. Examples include the Seifert genus, braid index, and the absolute value of the signature. We also mention other properties of the probability distributions of these…
In this talk we define a new category of matroids, by working on matroid polytopes and rank preserving weak maps. This lets us introduce the concept of categorical valuativity for functors, which can be seen as a categorification of the ordinary valuativity on matroid polytope decompositions. We also show that this new theory agrees with…
Recent developments in the practice of numerical programming require optimization problems not only to be solved numerically, but also to be differentiated. This allows to integrate the computational operation of evaluating a solution in larger models, which are themselves trained or optimized using gradient methods. Most well known applications include bilevel optimization and implicit input-output…
Speaker's website
In this article, we study feature attributions of Machine Learning (ML) models originating from linear game values and coalitional values defined as operators on appropriate functional spaces. The main focus is on random games based on the conditional and marginal expectations. The first part of our work formulates a stability theory for these explanation operators…
Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is common to all particles. The interaction between the particles is due to the common noise and…
Programs Preparing Graduate Students to Teach Undergraduate Mathematics Zoom link
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A metric Lie algebra is a real Lie Algebra with an inner product. In this talk, we will outline a complete classification of all three-dimensional metric Lie algebras up to notions of equivalence determined by isomorphism and scaling and investigate the Ricci flow on the resulting parameter spaces of equivalence classes.
Polyhedral fans are geometric objects, which arise naturally in many areas of mathematics, for example in toric geometry, the theory of hyperplane arrangements and representation theory. In many cases, there are natural ways of identifying some of the polyhedral cones defining a fan, thus giving a "partition of the fan". To each such partitioned fan…
We will discuss a special family of 2D incompressible inviscid fluid flows in the form of logarithmic spiral vortex sheets. Such flows are determined by a vorticity distribution of a curve R^2, and they are notoriously hard to study analytically. In the talk we will discuss several results regarding logarithmic spiral vortex sheets: well-posedness of the spirals as…
Spreading (diffusion) of new products is a classical problem. Traditionally, it has been analyzed using the compartmental Bass model, which implicitly assumes that all individuals are homogeneous and connected to each other. To relax these assumptions, research has gradually shifted to the more fundamental Bass model on networks, which is a particle model for the…
We study Merton’s expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. We take the reinforcement learning (RL) approach to learn optimal portfolio policies directly by exploring the unknown market, without attempting to estimate the model parameters.…
Reduced-order models (ROMs) are a critical tool for sensitivity analysis, parameter inference, and uncertainty quantification where high-fidelity models would be computationally intractable. Galerkin POD-ROMs are one particular class of ROMs which project high-fidelity model equations onto a set of model solutions to construct ROMs retaining original model parameters and physics, enabling accurate sensitivity analysis, parameter inference,…
Gene co-expression graphs are a rich source of information, revealing critical insights into cellular functions, states, and activities. Yet, extracting meaningful signals from these graphs presents a formidable challenge. This complexity arises due to the presence of multiple, overlapping sources of information and the inherent noise, which is particularly pronounced in data derived from single-cell…