Abstract: • I consider myself a moderately well informed amateur in artificial intelligence. I started giving talks on artificial intelligence in UMD in 2017.
• I believe one can better understand how people think by discussing how AIs think. Such understanding might benefit our students. We can’t discuss questions about whether AI programs can think or have General Intelligence without understanding what these terms mean for people, without figuring out what we mean when we say people think. Do people hallucinate as often as LLMs (large language model AIs)?
• I will propose a mini model for testing how people or more specifically mathematicians/scientists think, and I will describe how AIs process ideas.
I will refer to a paper with B. Hasselblatt entitled Finding Tactics in Proofs- to appear in JJIAM: https://www.dropbox.com/scl/fi/mvjezmhinpgt9vvyj9cwu/FINDING-TACTICS-IN-PROOFS-B- HASSELBLATT-AND-JY-JJIAM-AUG-2025.pdf?rlkey=7o6hae0w9isgssuyqm8d1l0d6&dl=0
Abstract: Lyme disease, transmitted by ticks, is endemic in several regions of the United States (including the Northeast), and the lifecycle of ticks is significantly affected by changes in local climatic variables. In this study, we modeled the dynamics of Lyme disease across the U.S. state of Maryland. We used a mechanistic model, calibrated using case and temperature data, to assess the impact of temperature fluctuations on the geospatial distribution and burden of Lyme disease across Maryland. Our results demonstrate that tick activity and Lyme disease intensity peak when temperature reaches $17.0^{\circ}$C---$20.5^{\circ}$C. We estimate that moderate projected global warming will cause a range expansion of Lyme disease, increasing burden in Central Maryland and extending risk into Western counties, while reducing the
disease burden in Southern and most Eastern counties. High projected warming will cause a westward shift, with new Lyme disease hotspots emerging in Western counties, and reduction of burden in Central, Southern and Eastern regions. Maryland will experience reductions in overall Lyme disease burden under both projected global warming scenarios (with more reductions under the high warming scenario). Disease elimination is feasible using a hybrid strategy, which combines rodents baiting, habitat clearance, and personal protection against tick bites, with moderate coverages.
Abstract: The risk and intensity of mosquito-borne disease outbreaks are tightly linked to the frequency at which mosquitoes feed on blood, also known as the biting rate. Standard mosquito-borne disease transmission models assume that mosquitoes bite only once per reproductive cycle – an assumption commonly violated in nature. For example, host defensive behaviors or climate factors can increase the occurrence of multiple biting while simultaneously impacting the mosquito gonotrophic cycle duration (GCD), the quantity customarily used to determine biting rates.
We present a framework for incorporating complex mosquito biting behaviors into transmission models, to account for the heterogeneity in and linkages between the biting rate and the multiple biting number. We derive general formulas for the basic offspring number, N0, and basic reproduction number, R0, and introduce specific models arising from empirical, phenomenological, and mechanistic perspectives. Using the gonotrophic cycle duration as a standard quantity to compare these models, we show how assumptions about the biting process strongly affect the relationship between the GCD and R0. This work highlights the importance of behavioral dynamics on mosquito-borne disease transmission while providing a tool for evaluating how individual-level interventions against biting scale up to affect population-level disease risk.
Abstract: Evolutionary dynamics shape social and biological systems across scales, from the evolution of multicellularity to the emergence of underground fungal symbioses to the formation and maintenance of animal groups and human societies. In these complex adaptive systems, small-scale interactions and associations can lead to emergent, large-scale phenomena. These interactions are often greatly influenced by various forms of heterogeneity, such as personality differences in human populations and variation in altruistic tendencies in animals. In this talk, I will present several models of complex social and biological systems, motivated by real-world phenomena and observations. These models are driven by evolutionary game theory, opinion dynamics frameworks, and agent-based modeling, and employ tools from stochastic processes, differential equations, and dynamical network analysis. I will discuss applications such as the evolution of cooperation, social group formation, the effects of environmental shocks on political opinions and activism, and altruistic tensions in social insect populations.
Abstract: Social dynamics are an integral part of the spread of disease affecting contact rates and the adoption of pharmaceutical and non-pharmaceutical interventions. This talk will present behavioural-epidemiological models that feature tipping-point dynamics in which behaviour can undergo rapid changes. Health, economic costs, and social payoffs are all unified into payoff functions that determine changes in behaviour, potentially creating collective action problems. Key findings include: nonlinear responses to key epidemiological parameters, increased public awareness can undermine disease control, and behavioural synchronization. A discussion of optimal public policies in light of these findings will also be discussed.
Abstract: Inflation is a method to select a model from within a large hierarchy of models with the goal of finding the simplest model that economically simulates a small set of objective functions with near optimal fidelity. It begins with an extremely large model, the parameters of which each have an associated intrinsic uncertainty. A hierarchy of smaller models is constructed from a family of reductions of this large model. Starting from a small model in the hierarchy, adjoint sensitivity analysis is used to select a slightly larger model from within the hierarchy that improves the fidelity of a small set of objective functions. This process is repeated until the improved fidelity of these functions becomes comparable to their intrinsic fidelity. This model inflation method will be illustrated on a family of quadratic population models.
Abstract: We begin with a brief overview of the rapidly developing research area of active matter, a.k.a. active materials. These materials are intrinsically out of equilibrium resulting in novel physical properties whose modeling requires the development of new mathematical tools. We present a free boundary PDE model a cytoskeleton of a moving cell. The key features of our model are the Keller-Segel cross-diffusion term and nonlocal boundary conditions. We first present a recent result on the nonlinear stability of stationary and traveling wave solutions in this model. We discuss novel mathematical features of this free boundary model with a focus on non-self-adjointness, which plays a key role in the spectral stability analysis. We next consider the model above with nonlinear diffusion and prove this nonlinearity results in the change of the bifurcation from subcritical to subcritical. leading that to two drastically different scenarios of the onset of the cell motion. Finally we derive an explicit formula that governs the change of the bifurcation type in terms of measurable physical parameters and therefore can be used for both qualitative and quantitative biological predictions.
This work resulted in two published papers with A. Safsten and V. Rybalko ( Phys. Rev . E, 2022, Transactions of AMS, 2023) as well as recent papers with A. Safsten and L. Truskinovsky (ARMA, 2025, accepted subject to revision) and with O. Krupchytski and T. Laux (Nonlinear Science, 2025, accepted subject to revision).
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