CSUF Applied Mathematics Seminar

The CSUF Applied Mathematics Seminar features speakers in applied mathematics and related areas.

Fall 2024 Schedule:

  • Friday, November 7 in MH 476 from 11AM-Noon

    FRAMEWORKS FOR ASSESSING STABILITY, COMPLEXITY AND STATE CHANGES IN REAL AND MODEL ECOSYSTEMS

    Dr. John C. Moore, Colorado State University Abstract:     Ecosystem food web models describe the trophic interactions, material transfers, and dynamics of living and non-living components within the environment. For equation-based models of ecosystems with set structure, asymptotic stability (e.g., all eigenvalues ofthe Jacobian matrix are negative) captures the condition that for the system to persist the population densities of all species must be greater than zero else species go locally extinct, and that the species are all active (May 1973). We tend to think of food webs as possessing single structure that defines it complexity, with energy flux and interaction strength represented by average values that were functions of the population densities of species and their physiological and life history attributes. Here I’ll present different frameworks for assessing the structure, function, and dynamics of food webs. I’ll present the notion of apparent complexity wherein the food web structure is dynamic with nodes and interactions emerging and disappearing at given spatial or temporal scale (Moore and de Ruiter 2012). The static food web structure is rarely fully realized, but rather represents an aggregate of multiple dynamic sub-webs of itself that occur over space and time. With dynamic food web structure, transient rather than asymptotic dynamics may be pervasive to point ofthe system persisting in a perpetual transient dynamic state (Hastings and Higgins 1994, Hastings 2004). Whether perpetual transient dynamics are plausible in an ecological sense depends on our willingness to break from the strict notion of mathematic stability and embrace persistence.  I will present an emerging framework to study the persistence of dynamic food web structures using soil food webs as guide. I will explore how sub-webs of species and interactions arise from different types of resources, plant phenology, the distribution of water, and spatial heterogeneity of organic matter within soils. What appears asymptotically stable may be better characterized as persistent under perpetually transient conditions.
  • Friday, October 18  in MH 480 from  11AM-Noon

DECODING SPATIAL STOCHASTIC RNA DYNAMICS WITH POINT PROCESSES

Dr. Chris Miles, UC Irvine
Abstract: Advances in microscopy can now provide snapshot images of individual RNA molecules within a nucleus. Inferring the underlying spatiotemporal dynamics is important for understanding gene expression, but challenging due to the static, heterogeneous, and stochastic nature of the data. I will write down a stochastic reaction-diffusion model and show that observations of this process follow a spatial point (Cox) process constrained by a stochastic reaction-diffusion PDE. Inference on this data resembles a classical inverse problem but differs in several interesting ways, especially observations of individual particles rather than concentrations. We have promising results on both forward modeling aspects and inference with data. However, many open computational and modeling challenges remain in the development of scalable and extendable techniques for this inverse problem. This work is in collaboration with the Fangyuan Ding lab of Biomedical Engineering at UCI.

Spring 2023 Schedule:

  • Friday, March 24 in MH 480 from 11AM-Noon

Manipulating Transport Properties

of Passive Tracers in Fluid Channels via Cross Section

Dr. Manuchehr Aminian, CSU Pomona

Abstract: Traditionally, theory developed for dispersion of a solute in a
fluid flow has focused on predicting enhanced diffusion which can be
observed, even with smooth fluid flow. A distribution will appear to
spread much more rapidly than could be explained as the result of
molecular diffusion alone, and decades of theory have been
developed to successfully explain this. In our prior work, we
developed asymptotic theory which predicts not only spread
(variance), but also the sign differences in the distribution's skewness
depending on cross section. This theory has had success matching
with both experiment and numerical simulation.
I will introduce the setting with these past results, then present
a computational framework to extend this work past idealized cross
sections and explore some questions in shape optimization towards
more precise control of the tracer distribution, exploring the ability to
design channels to match a given specification.