# Event category: Spring 2021

## Events

### Nancy Rodriguez
(University of Colorado Boulder)

A story on relocation strategies, the Allee effect, and the Ideal Free Distribution

Show/Hide Abstract
It is well known that relocation strategies in ecology and in economics can make the difference between extinction and persistence. In this talk I present a unifying model for the dynamics of ecological populations and street vendors, an important part of many informal economies. I discuss the effects of chemotactic movement of populations subject to the Allee Effect by discussing the existence of equilibrium solutions subject to various boundary conditions and the evolution problem when the chemotaxis effect is small. On an interesting note, I present numerical simulations, which show that in fact chemotaxis can help overcome the Allee effect as well as some partial analytical results in this direction on a bounded domain. We can make this precise in unbounded domains. I will conclude by making a connection to the Ideal Free Distribution and other movement strategies under competition.

### Naoki Masuda
(SUNY Buffalo)

Temporal network epidemiology

Show/Hide Abstract
Contact networks on which epidemic spreading occurs vary over time. Epidemic processes on such temporal networks are complicated by complexity of both network structure and temporal dimensions. We discuss two mathematical modeling topics on “temporal network epidemiology. First, we analyze how concurrency, i.e., the number of partnerships that an individual (i.e., node of the network) simultaneously owns affects the epidemic threshold. We particularly use a temporal network model with which we can vary the degree of concurrency while preserving the structure of the aggregate, static network. Second, we analyze the epidemic threshold and dynamics when each node switches between a high-activity state and a low-activity state in a Markovian manner. This assumption facilitates theoretical analyses and also allows us to produce distributions of inter-event times resembling heavy-tailed distributions, which are prevalent in empirical data. We argue that it is not the tail of the distribution but the small values of inter-event time that impact epidemic dynamics.

### Richard Bonneau
(Flatiron Institute)

Contracting ML and probabilistic methods for navigating time and space in genomics

Show/Hide Abstract
I will describe new methods for spatial transcriptomics and spacial genomics and contrast these methods with previous single cell and longitudinal genomics analysis approaches. I will focus first on methods for determining differential expression for spatial transcriptomic methods. I will then contract these early probabilistic methods with new methods built on variational auto encoders and generative ML approaches. Lastly I will describe bottlenecks, such as integrating imaging and genomic data in these studies. Prospects for building computational pipelines to integrate time, space and genomic coordinate will not be discussed, but will become apparent after deep reflection following the talk (but only if you pay attention).

### Adrian Lam
(Ohio State University)

Some PDEs in Evolution of Dispersal

Show/Hide Abstract
In the first part of the talk, we discuss the multi-species competition in a spatial domain, particularly the result of A. Hastings and some recent progress on the conjecture by Dockery et al. concerning the evolution of slow dispersal, i.e. when other things are equal, the slowest diffuser can competitively exclude other competitors. We then discuss the effect of adding passive drift and how it changes the evolutionary dynamics so that fast/intermediate diffuser is selected. In the second part, we will discuss the effect of mutation, and the associated moving Dirac solutions in a nonlocal PDE model proposed by Perthame and Souganidis. This latter equation describes a population structured by space and a phenotypic trait, and can be understood as competition of infinitely many species with different rate of dispersal.

### Lisa Fauci
(Tulane University)

Spinning helices, heaving panels, and waving tails

Show/Hide Abstract
The observed gait of a swimmer arises from the interplay of internal force generation, the passive elastic properties of its body, and environmental features such as fluid viscosity, boundaries, and obstacles. One could question whether optimal swimming of a fish occurs when it is actuated at a frequency near a natural frequency determined by its material bending rigidity. We will share some insights that we have gained using computational models of a few systems that range from the Stokes regime to others where inertial forces are important.

### Jordan Rozum
(Pennsylvania State University)

Boolean Networks

Show/Hide Abstract
Boolean networks are a common modeling tool for studying the phenotypic changes that cells undergo in response stimuli. Examples include cell differentiation during embryogenesis, metastasis of cancer cells, and apoptosis. In these models, genes and proteins are represented by nodes in a network, and each node is assigned a Boolean activity variable that evolves in discrete time-steps such that the attractors of the resulting dynamics correspond to phenotypes of interest. In this talk, I will focus on the techniques we use to analyze these discrete dynamical systems. These techniques rely on the construction and iterative reduction of an auxiliary network that encodes dynamical information as graph structure (an example is diagrammed in the accompanying figure). Our goals include finding all attractors, identifying key feedback loops that govern attractor selection, and driving the system to a desired attractor from an arbitrary initial state. I will briefly cover several recent applications of these methods to empirical and statistical models. I will also discuss ways in which these discrete models — and the techniques we use to analyze them — are related to their ODE counterparts.

### Katrina Podsypanina
(Institut des Hautes Études Scientifiques [IHES])

Cancer cells and their epithelial neighbors

Show/Hide Abstract
I am a cancer researcher working on a framework for a new mathematical model of metastasis. The reason for making a new model is that, in mice, metastases can grow from cells that are still normal at the time of arriving to the future metastasis site. If the same happens in humans, it would be pretty important for cancer therapy. First, it would explain why anti-cancer therapies fail to prevent metastases in some patients: if the cells are yet non-malignant at the time of therapy, they would be spared by the treatment. Second, it may be possible to identify improved treatments based on the ability to kill these non-malignant cells. I hypothesize that dissemination of non-malignant epithelial cells occurs in parallel with tumor cells, and subsequent transformation at the ectopic sites is a source of some metastases. This scenario ties together two contradictory observations: that metastases are associated with large and rapidly growing primary tumors, while metastatic tumors themselves often take a long time to appear. During my recent sabbatical at the Institut des Hautes Etudes Scientifiques, together with Misha Gromov and his colleagues I started to interrogate publicly available data on mutation rates and/or profiles from cancer patients and healthy individuals to determine whether the earliest common ancestor predicted using phylogenetic methods in some primary-metastasis pairs has features of a non-malignant cell.

### Cengiz Pehlevan
(Harvard University)

Inductive Bias of Neural Networks

Show/Hide Abstract
Predicting a previously unseen example from training examples is unsolvable without additional assumptions about the nature of the task at hand. A learner’s performance depends crucially on how its internal assumptions, or inductive biases, align with the task. I will present a theory that describes the inductive biases of neural networks using kernel methods and statistical mechanics. This theory elucidates an inductive bias to explain data with “simple functions, which are identified by solving a related kernel eigenfunction problem on the data distribution. This notion of simplicity allows us to characterize whether a network is compatible with a learning task, facilitating good generalization performance from a small number of training examples. I will present applications of this theory to artificial and biological neural systems, and real datasets.

### Arnold Mathijssen
(University of Pennsylvania)

Fluid mechanics of the respiratory system and active coating materials

Show/Hide Abstract
Our airways are continuously exposed to potentially harmful particles like dust and viruses. The first line of defence against these pathogens is a network of millions of cilia, whip-like organelles that pump flows by beating over a thousand times per minute. In this talk, I will first discuss the connection between local ciliary architecture and the topology of the flows they generate. We image the mouse airway from the sub-cellular (nm) to the organ scales (mm), characterising quantitatively its ciliary arrangement and the resulting flows. Interestingly, we find that disorder in the ciliary alignment can actually be beneficial for this pathogen clearance [1]. Second, I would also like to discuss how systems can be driven out of equilibrium by such active carpets. Combining techniques from statistical and fluid mechanics, I will demonstrate how we can derive the diffusivity of particles near an active carpet, and how we can generalise Fick’s laws to describe their non-equilibrium transport [2]. These results may be used for designing self-cleaning materials, much like our airways.
[1] Ramirez San-Juan, Mathijssen et al., “Multi-scale spatial heterogeneity enhances particle clearance in airway ciliary arrays”, Nature Physics 16, 958–964 (2020)
[2] Guzman-Lastra, Löwen & Mathijssen, “Active carpets drive non-equilibrium diffusion and enhanced molecular fluxes”, in press, Nature Communications (2021)
Note: We also have an informal discussion session after the seminar. Please stay in the Zoom seminar room to chat together with Professor Arnold Mathijssen!

### Hye-Won Kang
(University of Maryland Baltimore County)

Stochastic Modeling of Reaction-Diffusion Processes in Biology

Show/Hide Abstract
Inherent fluctuations may play an important role in biochemical and biophysical systems when the system involves some species with low copy numbers. This talk will present the recent work on the stochastic modeling of reaction-diffusion processes in glucose metabolism. The first part of the talk introduces a compartment-based model for a simple glycolytic pathway using a continuous-time Markov jump process, which describes system features at different scales of interest. Then, we will see how the multiscale approximate method reduces the model complexity. We will briefly discuss how the compartment size in the spatial domain can affect the spatial patterns of the system. In the second part of the talk, I will show another example for glucose metabolism where we see different-sized enzyme complexes. We hypothesized that the size of multienzyme complexes is related to their functional roles. We will see two models: one using a system of differential equations and the other using the Langevin dynamics.

0

0

https://mathbio.sas.upenn.edu/event_listing_category/spring-2021/page/2/

https://mathbio.sas.upenn.edu/event_listing_category/spring-2021/