Many seminars during the year will be delivered by the Purdue University Fort Wayne LDS Team on topics of interest to students, researchers, and local and global communities. The regular time of the seminars is Wednesday from 1:30pm to 2:30pm.

Abstract

Most social & behavioral science (SBS) research investigates dynamical systems, although the research approaches commonly used are not dynamic. The reasons for the paucity of dynamical systems use in SBS research go beyond simple lack of awareness, however; SBS data are often much different than the data for which dynamical systems approaches were developed. Beginning with an introduction to dynamical systems, we will examine the differences between dynamical systems approaches and common SBS data science approaches, how dynamical systems approaches can be applied to SBS research, and the likely need for interdisciplinary teams to take full advantage of dynamical systems in SBS research.

Abstract

C. elegans produce many behaviors, such as foraging, by switching between forward and reversal states with turns ending reversals.  While experimentalists have identified subsets of neurons that drive forward and reversal states, these premotor neurons are highly integrated into a larger network whose collective dynamics ultimately determine which behaviors are sustained and terminated.  Analyzing collective network dynamics presents a major challenge in C. elegans and other biological networks where a subsystem of interest is embedded in a complex larger system.  In this talk, I will introduce a dynamical systems model of the C. elegans neural network that is amenable to analysis and treats subnetworks relevant to behavior as perturbed holistic components.  Our model elucidates how nonlinear intrinsic dynamics in conjunction with connectivity structure may produce stochastic switching activity underlying foraging behavior and highlights different roles for gap junctions and synaptic connections.

Abstract

A metapopulation consists of a group of spatially distanced subpopulations, each occupying a separate patch. It is usually assumed that each localized patch is well-mixed. In this talk, we will discuss the spread of an epidemic in a system of weakly connected patches, where the disease dynamics of each patch occurs on a network. The SIR dynamics in a single patch is governed by the rate of disease transmission, the disease duration, and the node degree distribution of a network. Monte-Carlo simulations of the model reveal the phenomenon of spatial disease propagation. The speed of front propagation and its dependence on the single patch parameters and on the strength of interaction between the patches was determined analytically, and a good agreement with simulation results was observed [1]. Next, we will discuss front propagation in case of an Allee effect, where the effective transmission rate depends on the fraction of infected, and the state of no epidemic is linearly stable. We discovered [2] a novel phenomenon of front stoppage: in some regime of parameters, the front solution ceases to exist, and the propagating pulse of infection decays despite the initial outbreak. 

[1]. E. Khain and M. Iyengar, Phys. Rev. E 107, 034309 (2023). 

[2]. E. Khain, Phys. Rev. E 107, 064303 (2023).

Abstract

Breast cancer is a significant health challenge for women worldwide. Managing breast cancer not only plays an important role in extending life expectancy but also offers the possibility of complete remission. The proposed expert system serves as a clinical decision support tool to aid healthcare professionals in making informed treatment recommendations. It adopts a patient-centric approach by taking specific details from the patient to provide a detailed treatment plan. The expert system integrates forward chaining as its core reasoning mechanism, ensuring tailored treatment plans. In addition to the knowledge base, our expert system also incorporates a machine learning model which is trained on the NKI breast cancer dataset, predicting optimal treatment combinations. It also combines the generative capabilities of the latest Chat GPT release, which allows users to engage in dialogue and seek specific answers to questions. This integration amplifies the depth of understanding regarding treatment plans beyond traditional forward chaining. While this system is not designed to replace the expertise of healthcare professionals, it empowers medical professionals with a tool to aid and enhance their decision-making process. With personalized and detailed medical plans at the disposal of medical professionals, this system contributes to the effective management of breast cancer.

Abstract

We introduce a method to identify phase equations that include N-body interactions for general coupled oscillators, valid beyond the weak coupling approximation. This strategy is an extension of the theory from [Y. Park and D. Wilson, SIAM J. Appl. Dyn. Syst., 20 (2021), pp. 1464--1484] and yields coupling functions for N general limit-cycle oscillators with arbitrary types of coupling, in a similar spirit to the classic theory of weakly coupled oscillators. These coupling functions enable the study of oscillator networks in terms of phase-locked states, whose stability can be determined using straightforward linear stability arguments. We demonstrate the utility of this approach by reducing and analyzing N = 3 conductance-based thalamic neuron models: the reduction correctly predicts a loss in stability of a splay state for nonweak synaptic coupling. We conclude with a brief remark on recent extensions to n:m phase-locking with heterogeneous oscillators.

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