# Search Research Symposium Abstracts

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## The three-dimensional generalized Hénon map: Bifurcations and attractors

We study dynamics of a generic quadratic diffeomorphism, a 3D generalization of the planar Hénon map. Focusing on the dissipative, orientation preserving case, we give a comprehensive parameter study of codimension-one and two bifurcations. Periodic orbits, born at resonant, Neimark–Sacker bifurcations, give rise to Arnold tongues in parameter space. [Read More...]

**Presenter:**Amanda E. Hampton, University of Colorado, Boulder

**Authors:**Amanda E. Hampton and James D. Meiss

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

## Learning Ability of Interpolating Deep Convolutional Neural Networks

It is frequently observed that overparameterized neural networks generalize well. Regarding such phenomena, existing theoretical work mainly devotes to linear settings or fully-connected neural networks. This paper studies the learning ability of an important family of deep neural networks, deep convolutional neural networks (DCNNs), under both [Read More...]

**Presenter:**Tian-Yi Zhou, Georgia Institute of Technology

**Authors:**Tian-Yi Zhou, Xiaoming Huo

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

## Impact of Noise on Topology and Geometry of Big Network Data

Noise within data can significantly impact prediction of any study and can lead to poor results and reducing accuracy. Noise is anything that is not the "true" signal. Noisy data unnecessarily increases the amount of storage space required and can also adversely affect the results of any data mining analysis. It may have values close to your true [Read More...]

**Presenter:**Tahmineh Azizi, University of Wisconsin-Madison

**Authors:**Tahmineh Azizi

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

## Visual Aspects of Gaussian Periods and Analogues

Gaussian periods have been studied for centuries in the realms of number theory, field theory, cryptography, and elsewhere. However, it was only within the last decade or so that they began to be studied from a visual perspective. By plotting Gaussian periods in the complex plane, many interesting and insightful patterns can be seen, leading to various [Read More...]

**Presenter:**Samantha Platt, University of Oregon

**Authors:**Samantha Platt

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

## An edge CLT for the Log determinant of Laguerre beta ensembles

We obtain a CLT for the logarithm of $|\rm{det}(M_n − s_n)|$ where $M_n$ is a scaled Laguerre beta ensemble and $s_n$ is near the upper edge of the limiting spectrum of the matrix. In the special cases of Laguerre orthogonal and unitary ensembles, the lower bound on $s_n$ can be relaxed. A similar result was proved for Wigner matrices by Johnstone, [Read More...]

**Presenter:**Han Gia Le, University of Michigan

**Authors:**Elizabeth Collins-Woodfin, Han Gia Le

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

## On perturbations of singular complex analytic curves

Suppose $V$ is a singular complex analytic curve inside $\mathbb{C}^{2}$. We investigate when a singular or non-singular complex analytic curve $W$ inside $\mathbb{C}^{2}$ with sufficiently small Hausdorff distance $d_{H}(V, W)$ from $V$ must intersect $V$. We obtain a sufficient condition on $W$ which when satisfied gives an affirmative answer to our [Read More...]

**Presenter:**Achinta Kumar Nandi,

**Authors:**Achinta Kumar Nandi

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

## Equivariant Global Hopf Bifurcation in Abstract Nonlinear Parabolic Equations

We propose a method for studying symmetric global Hopf bifurcation problems in a parabolic system. The objective is to detect unbounded branches of non-constant periodic solutions that arise from an equilibrium point and describe their symmetric properties in detail. The method is based on the twisted equivariant degree theory, which counts orbits of [Read More...]

**Presenter:**Arnaja Mitra, The University of Texas at Dallas

**Authors:**Zalman Balanov, Wieslaw Krawcewicz, Arnaja Mitra, Dmitrii Rachinskii

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

## Constructing Pair Operations

In his survey of closure operations, Epstein goes over several constructions which always produce closure operations. Pair operations were introduced by Epstein, R.G. and Vassilev as generalizations of closure and interior operations, but they are so general that they encompass other types of operations that don't behave like closure or interior [Read More...]

**Presenter:**Sarah Poiani, University of New Mexico

**Authors:**Sarah Poiani, Janet Vassilev

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

## High-Order Asymptotic Preserving IMEX-BDF-DG Schemes for Linear Kinetic Transport Equation

Kinetic transport equations are used to model phenomena such as radiative transfer and neutron transport. In particular, we consider a linear kinetic transport equation under a diffusive scaling that converges to a diffusion equation as the Knudsen number epsilon goes to 0. One challenge that arises when solving this equation is that it is multiscale in [Read More...]

**Presenter:**Kimberly Matsuda, Rensselaer Polytechnic Institute

**Authors:**Kimberly Matsuda, Fengyan Li

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

## Dynamics of a Multi-Layer Fluid System

A long-wave asymptotic model is used to analyze the linear stability of the Navier-Stokes equations. The impact of different parameters on the linear growth of the interfacial disturbances is investigated, when disturbances are small. The growth rate of the disturbances is computed by solving an eigenvalue problem, which helps determine where the system is [Read More...]

**Presenter:**Awa Traore, University of Alabama

**Authors:**Awa Traore, David Halpern

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

## Dynamic Entrainment: A data-driven process approach for synchronization in the Hodgkin-Huxley model

Resonance and synchronized rhythm are important phenomena and can be either constructive or destructive in dynamical systems in the nature, specifically in biology. There are many examples showing that the human’s body organs must maintain their rhythm in order to function properly. For instance, in the brain, synchronized or desynchronized electrical [Read More...]

**Presenter:**Lawan Wijayasooriya, Georgia State University

**Authors:**Pejman Sanaei, Soheil Saghaf

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

## Analysis and Numerical Simulations of Nanofluids with the Impact of Magnetic Field

Computational Fluid Dynamics predicts many fascinating fluid problems and conjectures for the behavior of solutions related to their flows characterized by conservation laws. The fundamental of all CFD problems are Navier-Stokes equations that describe fluid motion. Several analytical and numerical methods are designed to handle these coupled partial [Read More...]

**Presenter:**Mittu Walia, Indian Institute of Technology Roorkee

**Authors:**Mittu Walia

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

## Stability analysis and a priori error estimation for Nitsche-type CIP/GP-CutFEM multi-phase flow.

Two-phase flows are encountered in various industrial applications and natural phenomena. Since the interface is significantly thin in two-phase flow, it can be treated as a discontinuity in the flow field where localized surface tension forces act. Defining the interface implicitly means that elements may be intersected by the interface, and the [Read More...]

**Presenter:**Himali Gammanpila, Texas Tech University

**Authors:**Himali Gammanpila , Dr. Eugenio Aulisa

**Symposium Year:**2023

**Session:**Poster Presentation

**Presentation Time:**September 30, 2023; 4:10 pm

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