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Links : Interdisciplinary Center for Quantitative Modeling in Biology (ICQMB) seminar

UCR Math Department seminar

In Fall 2022, the PDE & Applied math seminar will be held both through zoom and in person. Specific information about format of each talk will be provided in the email announcement and posted below. If you're interested in attending the seminar, please contact Dr. Yat Tin Chow (yattinc@ucr.edu) and Dr. Mykhailo Potomkin (mykhailp@ucr.edu).

Fall 2022 Schedule

Sep 28 10:00 (Wed) Organizational meeting

Oct 5 10:00 (Wed) Tsz Lik (Woody) Chan, University of California, Riverside

Oct 12 10:00 (Wed) Dr. Gaoyang (Bridget) Fan, University of Houston

Oct 19 10:00 (Wed) Dr. Weiqi Chu, University of California, Los Angeles

Oct 26 10:00 (Wed) Dr. Yuhua Zhu, University of California, San Diego

Nov 2 10:00 (Wed) Dr. Sylvia Herbert, University of California, San Diego

Nov 9 10:00 (Wed) Fatima Afzali, University of California, Riverside

Nov 16 10:00 (Wed) Dr. Christina Athanasouli, Georgia Institute of Technology

Nov 30 10:00 (Wed) Dr. Kaitlyn Hood, Purdue University

Upcoming talk:

Nov 30, 2022, 10:00-10:50 AM PT

Dr. Kaitlyn Hood, Purdue University

Title: Modeling pairwise particle interactions in an inertial microfluidic channel

Abstract: In microfluidic devices, inertia drives particles to focus on a finite number of inertial focusing streamlines. Particles on the same streamline interact to form one-dimensional microfluidic crystals (or “particle trains”). Here we develop an asymptotic theory to describe the pairwise interactions underlying the formation of a one-dimensional crystal. Surprisingly, we show that particles assemble into stable equilibria, analogous to the motion of a damped spring. The damping of the spring is due to inertial focusing forces, and the spring force arises from the interplay of viscous particle-particle and particle-wall interactions. The equilibrium spacing can be represented by a quadratic function in the particle size and therefore can be controlled by tuning the particle radius.

Detailed talk announcements:

Sep 28, 2022, 10:00-10:50 AM PT

Dr. Yat Tin Chow (UC Riverside) and Dr. Mykhailo Potomkin (UC Riverside)

Title: Organizational meeting

Oct 5, 2022, 10:00-10:50 AM PT

Tsz Lik (Woody) Chan, University of California, Riverside

Title: Modeling COVID-19 Transmission Dynamics With Self-Learning Population Behavioral Change

Abstract: Many regions observed recurrent outbreaks of COVID-19 cases after relaxing social distancing measures. It suggests that maintaining sufficient social distancing is important for limiting the spread of COVID-19. The change of population behavior responding to the social distancing measures becomes an important factor for the pandemic prediction. In this talk, I will present a SEAIR model for studying the dynamics of COVID-19 transmission with population behavioral change. In the model, the population is divided into several groups with their own social behavior in response to the delayed information about the number of the infected population. The transmission rate depends on the behavioral changes of all the population groups, forming a feedback loop to affect the COVID-19 dynamics. Based on the data of Hong Kong, the simulations of the model demonstrate how the perceived cost after infection and the information delay affect the level and the time period of the COVID-19 waves.

Oct 12, 2022, 10:00-10:50 AM PT

Dr. Gaoyang (Bridget) Fan, University of Houston

Title: Pattern formation and bistability in a synthetic intercellular genetic toggle

Abstract: Differentiation within multicellular organisms is a complex process that helps to establish spatial patterning and tissue formation within the body. Often, the differentiation of cells is governed by morphogens and intercellular signaling molecules that guide the fate of each cell, frequently using toggle-like regulatory components. Here, we couple a synthetic co-repressive toggle switch with intercellular signaling pathways to create a “quorum-sensing toggle.” We show that this circuit not only exhibits population-wide bistability in a well-mixed liquid environment, but also generates patterns of differentiation in colonies grown on agar containing an externally supplied morphogen. We develop a mechanistic mathematical model of the system, to explain how degradation, diffusion, and sequestration of the signaling molecules and inducers determine the observed patterns.

Oct 19, 2022, 10:00-10:50 AM PT

Dr. Weiqi Chu, University of California, Los Angeles

Title: A mean-field opinion model and inference of the interaction kernel

Abstract: The perspectives and opinions of people change and spread through social interactions on a daily basis. In the study of opinion dynamics on networks, one often models entities as nodes and their social relationships as edges, and examines how opinions evolve as dynamical processes on networks, including graphs, hypergraphs, multi-layer networks, etc. In this talk, I will introduce a model of opinion dynamics and derive its mean-field limit, where the opinion density satisfies a kinetic equation of Kac type. We prove properties of the solution of this equation, including nonnegativity, conservativity, and steady-state convergence. We also study how to infer the interaction kernel from limited partial observations. We give sufficient conditions of measurement for two scenarios, such that one is able to reconstruct the kernel uniquely. We also provide a numerical algorithm of the inverse problem, when the data set only has a limited number of data points.

Oct 26, 2022, 10:00-10:50 AM PT

Dr. Yuhua Zhu, University of California, San Diego

Title: Continuous-in-time Limit for Bayesian Bandits

Abstract: This talk revisits the bandit problem in the Bayesian setting. The Bayesian approach formulates the bandit problem as an optimization problem, and the goal is to find the optimal policy which minimizes the Bayesian regret. One of the main challenges facing the Bayesian approach is that computation of the optimal policy is often intractable, especially when the length of the problem horizon or the number of arms is large. In this paper, we first show that under a suitable rescaling, the Bayesian bandit problem converges to a continuous Hamilton-Jacobi-Bellman (HJB) equation. The optimal policy for the limiting HJB equation can be explicitly obtained for several common bandit problems, and we give numerical methods to solve the HJB equation when an explicit solution is not available. Based on these results, we propose an approximate Bayes-optimal policy for solving Bayesian bandit problems with large horizons. Our method has the added benefit that its computational cost does not increase as the horizon increases.

Nov 2, 2022, 10:00-10:50 AM PT

Dr. Sylvia Herbert, University of California, San Diego

Title: Safe Control from Value Functions: Blending Control Barrier Functions and Hamilton-Jacobi Reachability Analysis

Abstract: Value functions have been used extensively for generating safe control policies for robots and other nonlinear systems. The output of the function provides the current “safety level” of the system, and its gradient informs the allowable control inputs to maintain safety. Two common approaches for value functions are control barrier functions (CBFs) and Hamilton-Jacobi (HJ) reachability value functions. Each method has its own advantages and challenges. HJ reachability analysis is a constructive and general method that struggles from computational complexity. CBFs are typically much simpler, but are challenging to find, often resulting in conservative or invalid hand-tuned or data-driven approximations. In this talk I will discuss our work in exploring the connections between these two approaches in order to blend the theory and tools from each. I’ll introduce the “control barrier-value function,” and show how we can refine CBF approximations to recover the maximum safe set and corresponding control policy for a system.

Nov 9, 2022, 10:00-10:50 AM PT

Fatima Afzali, University of California, Riverside

Title: An Active Inference Approach to Modeling Auditory Verbal Hallucinations

Abstract: Hallucinations, imaginary as they are, nonetheless follow real psychophysical principles determining their genesis, medium, and content. Auditory verbal hallucination, in which spoken words are perceived in the absence of external stimuli, is the most common mode, present from sleep deprivation to schizophrenia; etiology distinguishes between in-context (semantically contiguous with prior percepts) or out-of-context hallucinations. Computational theories of perception have often provided explanations for the former, but explanations for out-of-context hallucinations, more often clinically relevant, have remained elusive. Towards this end, I'll introduce the active inference framework, in which biological systems are seen as developing internal world models via variational approximations to Bayesian updates on sensory input. By using this to elucidate the computational mechanisms behind sensory processing, we'll consider an account of hallucination that simulates an agent processing sensory information according to priors on dialogical roles such as speaking and listening in order to reproduce a variety of phenomena associated with both in-context and out-of-context hallucination. Notably, the appearance of hallucinations is shown to be dependent not just on pathologically strong priors over sensory stimuli, but by disordered priors that lead to the generation of implausible content.

Note: the talk will be a review of the paper by Benrimoh, D., Parr, T., Adams, R.A. and Friston, K., 2019. Hallucinations both in and out of context: an active inference account. PLoS One, 14(8), p.e0212379. [link]

Nov 16, 2022, 10:00-10:50 AM PT

Dr. Christina Athanasouli, Georgia Institute of Technology

Title: Bifurcations in patterns of human sleep under homeostatic and circadian variation

Abstract: The timing of human sleep is strongly modulated by the 24 hour circadian rhythm, our internal biological clock, and the homeostatic sleep drive, one’s need for sleep which depends on prior awakening. The parameters dictating the evolution of the homeostatic sleep drive may vary with development and have been identified as important parameters for generating the transition from multiple sleeps to a single sleep episode per day. In this talk, I will present the mathematical framework we employ to analyze bifurcations characterizing transitions in sleep patterning under variation of the homeostatic time constants in a physiologically-based two-state model of sleep-wake regulation. This model produces two states, namely sleep and wake. Our framework includes the construction of a circle map that captures the timing of sleep onsets on successive days. Analysis of the structure and bifurcations in the map reveals changes in the average number of sleep episodes per day in a period-adding-like structure. We also show that changes in the circadian waveform influence this transition. Time permitting, I will present how the dynamics of a three-state model of sleep-wake regulation, that captures wake, rapid eye movement (REM) sleep, and non-REM sleep, complicate the bifurcations describing transitions in sleep patterns.

Nov 30, 2022, 10:00-10:50 AM PT

Dr. Kaitlyn Hood, Purdue University

Title: Modeling pairwise particle interactions in an inertial microfluidic channel

Abstract: In microfluidic devices, inertia drives particles to focus on a finite number of inertial focusing streamlines. Particles on the same streamline interact to form one-dimensional microfluidic crystals (or “particle trains”). Here we develop an asymptotic theory to describe the pairwise interactions underlying the formation of a one-dimensional crystal. Surprisingly, we show that particles assemble into stable equilibria, analogous to the motion of a damped spring. The damping of the spring is due to inertial focusing forces, and the spring force arises from the interplay of viscous particle-particle and particle-wall interactions. The equilibrium spacing can be represented by a quadratic function in the particle size and therefore can be controlled by tuning the particle radius.