In this lecture we will present basis theoretical and algorithmic properties of Monte Carlo methods. In particular, their convergence properties and implementational simplicity will be highlighted. There are a variety of Monte Carlo methods but we will focus on two, namely, Monte Carlo integration and Markov Chain Monte Carlo. Prior knowledge of Monte Carlo methods…
High dimensional data exhibit distinct properties compared to its low dimensional counterpart; this causes a common performance decrease and a formidable computational cost increase of traditional approaches. Novel methodologies are therefore needed to characterize data in high dimensional spaces. Considering the parsimonious degrees of freedom of high dimensional data compared to its dimensionality, we study…
This tutorial will provide an introduction to nonlinear optimization. We will begin by presenting a general constrained nonlinear program, defining concepts like local versus global optimality, and examining the differences between convex and nonconvex problems. We will then present the Karush-Kuhn-Tucker optimality conditions. Students who have taken OR 706 (Nonlinear Programming) will find this tutorial…
Investigating through mathematical modelling the complex chemistry in cells has grown in the research community over the past ten years. However trying to understand the relationship between cellular (microscale) and larger scale lengths such as the vasculature upstream of the capillary bed has proved a more difficult task. The tutorial (if you want to call…
In recent years, Sandia National Laboratories has been accelerating research investments in data science and analytics. This change was motivated by a need for timely decisions about the state of the world in the context of increasingly large and diverse varieties of data. Data-centric challenges often cross discipline boundaries. To address these challenges, our group…
Control systems impact our lives on a daily basis, whether it is from our thermostat controlling the temperature in our home to cruise control in our car to surfing the worldwide web. Feedback control systems is a type of dynamical system where it uses feedback from the system and an algorithm to determine an input…
The Finite Element Method(FEM) is one of many numerical methods to approximate solutions to ordinary and partial differential equations. FEM has been applied to numerous problems found in the fields of Fluid Mechanics, Electromagnetics, Lagrangian Mechanics, etc. While there are many approaches to the Finite Element Method, I will present the Galerkin approach. I will…
In this talk, I will discuss a convex formulation of the clustering problem and its generalization to biclustering of matrices and more broadly to co-clustering of multiway arrays or tensor data. The key advantage in formulating clustering as a convex program is that doing so addresses well-known issues of instability and parameter selection that plague…
In full-tensor extensions of 1D interpolation or quadrature rules, the number of nodes will grow exponentially in the dimension—commonly called the “curse of dimensionality.” In this talk, we present an overview of sparse grids, in which the number of nodes grows only polynomially in the dimension. First, we will do an overview of 1D interpolation for…
One of the primary goals of text mining is to group together, organize and summarize textual information. In social network analysis, we typically tie individuals together through social connections — can we connect documents and their contents in a similar fashion? What can social network analysis tell us about the content of a document or…
Students are often given the impression that there is one way to have an academic career, the right way. Reality is much more complicated, but this can also be empowering. We will discuss such things informally, while drawing some examples from my own path: from particle physics at Fermilab and CERN to cancer research at…
The outgoing student chapter president Joey Hart will give a short presentation overviewing SIAM and the opportunities its provides for graduate student members. A discussion time will follow. Pizza will be served.
This will be an informal discussion for graduate students about the opportunities and benefits available through the Society for Industrial and Applied Mathematics (SIAM).
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…
This will be the first seminar in the SIAM Industry series, which is focused on presenting information about research opportunities in business, industry, and government jobs. Speakers will discuss their career paths and speak on projects they have worked on at their current industrial institution. The DOE Exascale Computing Project (ECP), a collaborative effort between…
This seminar will be an informal panel of some of our fellow graduate students speaking on their experiences with applying to and participating in internships in business, industry, and government. This will be an opportunity for graduate students to hear testimonies about the benefits and types of problems that are addressed when doing an internship…
Machine learning has become widely popular in fields like computer vision, natural language processing, and speech recognition, often performing tasks better than humans. A fundamental building block of many of these algorithms is a neural network known as a multilayer perceptron. In this tutorial we will discuss how to construct these networks and how to…
Kitware develops and supports modeling and simulation platforms that power medical training, planning, and predictive applications for improved patient treatment and outcomes. Our capabilities include whole-body computational physiology models for faster than real-time simulation, surgical planning, and guidance applications, high-fidelity computational fluid dynamics for patient-specific treatment planning, and virtual/augmented reality solutions for immersive training, and…
In this talk, I will present basic Bayesian statistics and multi-source Bayesian data fusion methods. It will start with basic statistical definitions, working through a coin flip problem. From there, I will outline multi-source fusion using several simple methods that require the previous Bayesian background. I will also provide several motivating examples, including one drawn…
This talk will report on my experiences as a Mathematician at Space and Naval Warfare (SPAWAR) Systems Center Atlantic. After an introduction, I will provide an overview of SPAWAR Atlantic, talk in general about my opportunities and experiences as a Mathematics PhD in the government, and then give examples of research projects I support. Finally,…