February 20, 2025 Nicholas Timme & Christopher Parker (UC Medicine)

Examining maladaptive decision-making in neural models

Neuropsychiatric disorders are caused by many factors and produce a wide range of symptomatic maladaptive behaviors in patients. Despite this great variance in causes and resulting behavior, we believe the maladaptive behaviors that characterize neuropsychiatric disorders are most proximally determined by networks of neurons and that this forms a common conceptual link between these disorders. Operating from this premise, it follows that treating neuropsychiatric disorders to reduce maladaptive behavior can be accomplished by modifying the patient’s network of neurons. In this seminar, we will discuss recent work by our laboratory using several different types of computational models to examine how the models can be modified to reduce maladaptive behavior. This work focuses on aversion-resistant alcohol drinking – a key maladaptive behavior associated with alcohol use disorder – as a test case. In simple models, we demonstrated that it was possible to predict personalized network modifications that substantially reduced maladaptive behavior without inducing side effects. Furthermore, we found that it was possible to predict effective treatments with limited knowledge of the model and that information about neural activity during certain types of trials was more helpful in predicting treatment than information about model parameters. We will also discuss ongoing analyses of more complex and biologically realistic models.

February 13, 2025 Hanliang "Han" Guo (Ohio Wesleyan U)

What Math Taught Me about Driving

What causes a smooth highway drive to suddenly fall into traffic jam without any apparent reason? Would lane-changing do me any favor when I feel stuck? In this talk, we will explore how mathematics provides a powerful lens to understand—and even predict—this everyday mystery. Based on our computational framework that combines classical car-following models with driver psychology, we will investigate two fundamental sources of traffic instability: reaction time and human frustration. I will first show how simple models reveal a critical threshold of driver reaction time, beyond which small disturbances can snowball into the infamous "phantom traffic jams." Then, we'll shift gears and see how psychological factors, such as frustration from being stuck behind slower vehicles, can drive lane-changing behavior and influence traffic flow. Along the way, we'll demonstrate how to model aggressive drivers and what they do to the overall traffic. This talk will blend differential equations, stability analysis, stochastic modeling, and a dash of behavioral science to uncover the fascinating interplay between mathematics and traffic.

February 6, 2025 Ryosuke Omori (Hokkaido U)

Mathematical modelling of infectious disease epidemics in the setting of aquaculture and its application for data analysis

Recently aquaculture has attracted attention due to its sustainability in terms of food supply. Infectious disease epidemic in aquaculture is one of the most serious obstacles for stable harvest. Control of infectious disease epidemics is required, however, several difficulties exist. To reveal and solve the bottleneck to control infectious disease epidemic in aquaculture, we conducted epidemiological studies. Generally, epidemiological analysis of infectious diseases is a time-series analysis of the number of infected individuals. As for fish diseases, only the time-series data of deaths is available due to the difficulty in the diagnosis coming from unclear symptoms and cost. We constructed the framework for coupling experiment and field observation by mathematical modeling to understand fish disease outbreaks, when only the time-series data of dead fish is available. As a case study we analyzed the time-series data of the number of deaths in outbreaks of Oncorhynchus masou virus (OMV) disease in reared rainbow trout. As another case study we analyzed White spot syndrome virus (WSSV) outbreak in farmed Kuruma shrimps. WSSV triggers white spot disease which causes quite high mortality in farmed shrimp. To control WSSV, understanding WSSV epidemic character is required. To this end, the epidemiological data of WSSV in the setting of aquaculture is required especially for measuring transmissibility including basic reproduction number (R0). However, the detailed epidemiological data is difficult to obtain due to the rapid and high mortality. In this study we proposed a framework for estimation of transmissibility of WSSV from the combination of i) the epidemiological data in the early phase of outbreak, ii) the infection experiment of WSSV and iii) the feeding experiment of dead shrimp eaten by healthy shrimp using a mathematical model describing WSSV transmission by cannibalism of dead and infected shrimp.

January 30, 2025 Selena Laikos (UC Grad Student, Journal Club)

Review on mathematical modeling of honeybee population dynamics

Abstract can be found here: https://doi.org/10.3389/fmolb.2021.681696

November 21, 2025 Don French (UC Math)

From the Numerical Analysis Bench: Method of Particular Solutions - Introduction & Beginnings

A range of primarily Engineering papers from roughly the 2010's introduced the method of particular solutions (MPS) which is often combined with the method of fundamental solutions (MFS) to solve a range of initial and boundary value problems.  In this talk, we introduce MPS and MPS/MFS as well as some beginning theoretical error analyses.

November 14, 2025 Gayashan Jayavilal (UC Math)

How competition shapes collective decision-making

November 7, 2025 Chethana Godage (UC Grad Student, Journal Club)

Review on mathematical modeling of honeybee population dynamics

Honeybees have an irreplaceable position in agricultural production and the stabilization of natural ecosystems. Unfortunately, honeybee populations have been declining globally. Parasites, diseases, poor nutrition, pesticides, and climate changes contribute greatly to the global crisis of honeybee colony losses. Mathematical models have been used to provide useful insights on potential factors and important processes for improving the survival rate of colonies. In this review, we present various mathematical tractable models from different aspects: 1) simple bee-only models with features such as age segmentation, food collection, and nutrient absorption; 2) models of bees with other species such as parasites and/or pathogens; and 3) models of bees affected by pesticide exposure. We aim to review those mathematical models to emphasize the power of mathematical modeling in helping us understand honeybee population dynamics and its related ecological communities. We also provide a review of computational models such as VARROAPOP and BEEHAVE that describe the bee population dynamics in environments that include factors such as temperature, rainfall, light, distance and quality of food, and their effects on colony growth and survival. In addition, we propose a future outlook on important directions regarding mathematical modeling of honeybees. We particularly encourage collaborations between mathematicians and biologists so that mathematical models could be more useful through validation with experimental data. [paper link]

October 31, 2025 Junghyun Lee (UC Grad Student, Journal Club)

Bayesian Model Calibration and Sensitivity Analysis for Oscillating Biological Experiments

Understanding the oscillating behaviors that govern organisms’ internal biological processes requires interdisciplinary efforts combining both biological and computer experiments, as the latter can complement the former by simulating perturbed conditions with higher resolution. Harmonizing the two types of experiment, however, poses significant statistical challenges due to identifiability issues, numerical instability, and ill behavior in high dimension. This article devises a new Bayesian calibration framework for oscillating biochemical models. The proposed Bayesian model is estimated relying on an advanced Markov chain Monte Carlo (MCMC) technique which can efficiently infer the parameter values that match the simulated and observed oscillatory processes. Also proposed is an approach to sensitivity analysis based on the intervention posterior. This approach measures the influence of individual parameters on the target process by using the obtained MCMC samples as a computational tool. The proposed framework is illustrated with circadian oscillations observed in a filamentous fungus, Neurospora crassa. [paper link]

October 24, 2025 Selena Laikos (UC Grad Student, Journal Club)

Swimming bacteria in Poiseuille flow: The quest for active Bretherton-Jeffery trajectories

Using a 3D Lagrangian tracking technique, we determine experimentally the trajectories of non-tumbling E. coli mutants swimming in a Poiseuille flow. We identify a typology of trajectories in agreement with a kinematic “active Bretherton-Jeffery” model, featuring an axisymmetric self-propelled ellipsoid. In particular, we recover the “swinging” and “shear tumbling” kinematics predicted theoretically by Zottl and Stark (Phys. Rev. Lett., 108 (2012) 218104). Moreover using this model, we derive analytically new features such as quasi-planar piecewise trajectories, associated with the high aspect ratio of the bacteria, as well as the existence of a drift angle around which bacteria perform closed cyclic trajectories. However, the agreement between the model predictions and the experimental results remains local in time, due to the presence of Brownian rotational noise. [paper link]

October 17, 2025 Jared Barber (IU Indianapolis)

Viscoelastic computational models of bone cells and migrating cells

Cellular forces, whether due to external or internal sources, have been implicated in a number of important biological processes.  Here we focus on two such processes:  Bone regulation by osteocytes, bone cells that respond to external forces in useful ways, and cell migration, which plays a role in cancer metastasis, wound healing, and other areas.  Our models in both cases use a network of interconnected damped springs, or viscoelastic elements, to model the cell.

With osteocytes, the external and internal fluid is coupled to our viscoelastic meshwork using a lattice-Boltzmann immersed boundary method.  The external fluid surrounds the cell which, in turn, is surrounded by rigid bone material.  Leveraging our approach’s relatively strong ability to handle complex geometries, we constructed four osteocyte models of varying complexity to consider what forces osteocytes tend to experience when in their natural environment.  We will share our approaches and findings that include suggestions that high force may arise where arms or processes of osteocytes connect to the main portion of the cell and that osteocytes may experience higher forces when inlets preferentially outnumber outlets in the region.

We will also shortly share our preliminary cell migration models and their ability to predict motion and force distribution.  In contrast with our osteocyte models, these models do not include fluid and take into account active cellular components that assist with migration.  We will share how we add in such active cellular components, if time allows, for both of our models.  Currently our main result is that such models, despite relative simplicity, can produce reasonable and interesting migratory behaviors.

September 19, 2025 Robert Buckingham (UC Math)

Pattern Formation and Wave Breaking in Nonlinear Dispersive Equations

Wave propagation in optical fibers, bodies of water, the atmosphere, plasmas, and Bose-Einstein condensates can all be described by nonlinear dispersive wave equations.  Solutions of these equations typically display both smooth and highly oscillatory behavior.  While qualitatively similar, the oscillations can be generated by a variety of different mechanisms.  We will discuss recent progress in understanding patterns formed by pure radiation, soliton ensembles, high-order solitons, and interacting energy modes.  We will also consider the onset of wave breaking and look at different types of behavior that can occur in the transition from smooth to oscillatory regions.  Special attention will be paid to a specific type of rogue-wave focusing that in the past few years has been shown to be universal for a number of different equations and initial conditions.