The number of inversions of a permutation is the number of pairs (i < j) for which w_i > w_j. This important statistic that arises in many contexts, including as the minimum number of simple transpositions needed to express the permutation and, equivalently, as the rank function for weak Bruhat order on the symmetric group.…
Borosilicate glass is the material predominately used for encasing carbon fiber (CF) microelectrodes for fast-scan cyclic voltammetry (FSCV) experiments. These capillaries insulate unexposed CF from the surrounding environment, while leaving a 150-200 um exposed CF tip in vivo that allows for electrochemical measurements of neurotransmitters. However, borosilicate glass commonly breaks during implantation; this can leave…
This will be an informal discussion for graduate students about the opportunities and benefits available through the Society for Industrial and Applied Mathematics (SIAM).
Reception to follow in SAS Hall Atrium. Recent advances in large scale sequencing of microbial DNA without culturing or isolation gives us easy and direct access to “wild” microbial metagenomes that are otherwise virtually impossible to study. However, because these data sets are large and relatively unstructured, analyzing them requires advancing data science techniques…
The P-partition generating function of a (naturally labeled) poset P is a quasisymmetric function enumerating order-preserving maps from P to Z^+. Using the Hopf algebra of posets, we give necessary conditions for two posets to have the same generating function. In particular, we show that they must have the same number of antichains of each…
What to do when the size and complexity of your model essentially prevent you from using it? Well, get a smaller and simpler model... At the heart of this dimension reduction process is the notion of parameter importance which, ultimately, is part of the modeling process itself. Global Sensitivity Analysis (GSA) aims at efficiently identifying important…
In this talk we will discuss new classes of models that seek to describe evolution of a congregation of agents based on laws of self-organization. These models appear in a broad range of applications -- from biological sciences to social behavior. We focus on two long time phenomena: flocking and alignment. It has been a mathematical challenge…
This talk describes tips and tricks for building a successful career in the quantitative sciences. It covers research strategies, work/life balance, networking, and management of the portfolio of activities needed for different kinds of careers (academic, government, and industry). There is particular emphasis on how the professional societies can help advance your career. All graduate…
Mathematical modeling is a way for researchers to visualize components of a system and analyze how those components interact. When these models become significantly large, many problems arise. Here are a few: 1. As models increasingly complex with a myriad of parts, it is prudent for the researcher to ask whether all of these…
Target Audience: First and Second Years
Following Beilinson and Drinfeld, we describe vertex algebras as Lie algebras in a certain pseudo-tensor category. More precisely, starting from a vector superspace V with a linear operator on it, we introduce the operad of n-ary chiral operations on V. When V is equipped with a vertex algebra structure, this allows us to define the cohomology of V with…
Accurate estimation of microseismic events (small earthquakes) generated during hydraulic fracturing of low permeability rocks such as shale enables important characterization of hydraulic fracture networks. Determining the orientation of the fracture is important in characterizing the effectiveness of the stimulation process. We consider the source as separable in time and space and invert for a…
The finite minuscule and d-complete posets generalize Young and shifted Young diagrams. They have many nice combinatorial properties; for example, minuscule posets are Gaussian and Sperner, and d-complete posets have the hook length and jeu de taquin properties. Infinite analogs of the colored minuscule posets were used by R.M. Green to construct representations of many…
Poro-elastic and poro-visco-elastic models describe fluid flow through porous, deformable media. They are relevant in many applications in bioengineering and medicine, such as tissue perfusion and fluid flow inside cartilages and bones. In this talk, I will discuss the application of these models specifically to optical perfusion and its relation to glaucoma, as well as…
Geophysical seismic exploration, as well as radar and sonar imaging, require the solution of large scale forward and inverse problems for hyperbolic systems of equations. In this talk, I will show how model order reduction can be used to address some intrinsic difficulties of these problems. In model order reduction, one approximates the response (transfer…