Events
Department of Mathematics and Statistics
Texas Tech University
Locusts gather in large numbers to feed on crops, destroying agricultural fields. Wingless juveniles marching together through a field demonstrate collective behavior that forms a coherent front of advancing insects. We examine this front through two models: an agent-based model and a set of partial differential equations. We construct the agent-based model using observations of individual behavior from the biological literature. The PDE model yields insight into collective behavior of the front. We demonstrate that resource-dependent behavior can explain the density distribution observed in locust hopper bands.
Let $(R,\mathfrak{m},k)$ be a commutative local ring and $\mathbf{K_{tac}}(R)$ the category of totally acyclic $R$-complexes. In this talk, I will define an extension of critical degree for $R$-modules to totally acyclic complexes. In addition, I will discuss how the critical and cocritical degrees of an $R$-complex change under certain operations, with a focus on operations involving tensor products of complexes.
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Glycans are one of the most widely investigated biomolecules, due to their roles in numerous vital biological processes. This involvement makes it critical to understand their structure-function relationships. Few system-independent, LC-MS/MS (Liquid chromatography tandem mass spectrometry) based studies have been developed with this particular goal, however. When studied, the employed methods generally rely on normalized retention times as well as m/z-mass to charge ratio of an ion value. Due to these limitations, there is need for quantitative characterization methods which can be used independent of m/z values, thus utilizing only normalized retention times. As such, the primary goal of this article is to construct an LC-MS/MS based classification of the permethylated glycans derived from standard glycoproteins and human blood serum, using a Glucose Unit Index (GUI) as the reference frame in the space of compound parameters. For the reference frame we develop a closed-form analytic formula, which is obtained from Green’s function of a relevant convection-diffusion-absorption equation used to model composite material transport. The aforementioned equation is derived from an Einstein-Brownian motion paradigm, which provides a physical interpretation of the time-dependence at the point of observation for molecular transport in the experiment. The necessary coefficients are determined via a data-driven learning procedure. The methodology is presented in an abstract manner which allows for immediate application to related physical and chemical processes. Results employing the proposed classification method are validated via comparison to experimental mass spectrometer data.Refining the previous shape operation to possess the infinitesimal property that the “points-to-pieces” transformation ♭X → ∫X is an equivalence of ∞-groupoids, we explain how this condition axiomatizes certain infinitesimal behavior in a cohesive ∞-topos. However, it is also not enough for differential geometry. We explain that this equivalence holds, in particular, when there is a universal internal notion of “tangent space” for objects X, computed by a universal object of contractible infinitesimal shape. This is the richer setting of differential cohesion, where all the cohesion modalities factor through a sub-∞-topos of infinitesimal shapes. This extends the setting of fundamental path ∞-groupoids and differential cohomology given by ordinary cohesion to one where the constructions of higher Cartan geometry can be carried out. Important examples are given by the categories of jets on Cartesian spaces and ∞-sheaves on jets of Cartesian spaces, which we will show subsumes the classical framework of synthetic differential geometry.