While "dimension" has a natural definition in arbitrary vector spaces, the situation for arbitrary topological spaces is more subtle. Over the past century, several different notions of dimension have been articulated, and a rich subject has grown up around the notion of dimension in topology. In this talk we'll review a few of the most basic definitions of dimension. We will then focus on the halfdirectional dimension and the neight (nested weight), which are similarly defined yet subtly different. We will look at the open question of whether these notions of dimension coincide for separable metric spaces. This question should be tractable for a non-specialist, and the main purpose of the talk is to get the listener to the point of being able to think about (and possible solve!) this question.
Location: Stanley Thomas 302
An Abstract Argument Framework (AAF) is simply a pair consisting of a set A whose elements are called arguments, and of a binary relation R on A, called the attack relation. An abstract argument is not assumed to have any specific structure: an argument is anything that may attack or be attacked by another argument. An argumentation semantics is a formal definition of a method ruling the justification state of arguments: intuitively, an argument is justified if it has some way to survive the attacks it receives. An extension-based semantics specifies how to derive a subset of A representing a set of arguments that are collectively justified. Computational models and tools are used to model and compute these semantics and their correspondents in Weighted AAFs, i.e., where attacks or nodes are weighted with a strength score. Benchmarks based on small-world networks need to be assembled to test the scalability and applicability of these tools, even considering the hard problems related to Weighted AAFS.
Abstract: Asymptotic Formulas for Shifted Stacks and Unimodal Sequences
I will discuss recent results on the enumeration of unimodal sequences of natural numbers. This includes the combinatorial and asymptotic study of Euler's integer partitions, Auluck's generalized Ferrers diagrams, Wright's stacks, and Andrews' convex compositions. One result provides the asymptotic main term for the enumeration of shifted stacks, which answers an open problem in statistical mechanics due to Temperley.
Time: 11:00 AM
Abstract: Identifying Genetic Variants for Alcohol and Nicotine Co-Addiction in Minorities
Human twin studies suggest a shared genetic predisposition to develop alcohol and nicotine dependence. Specific pleiotropic genes, however, remain unknown and their function modes need to be elucidated. Existing statistical methods are underpowered to identify pleiotropic variants from DNA sequence data of minorities. Such methods neglect or oversimplify the causal mechanism of genetic determinants and their ancestries. It has become a standard practice, for example, to linearly adjust for local ancestries as traditional covariates. In this talk, I will introduce our (1) novel single-trait and bivariate trait causality models, (2) respective score tests and, (3) application to the DNA sequence data on co-addiction of African Americans. Our causality models allow traditional covariates to ensure that our score tests control false positive rate. Our score tests exploit ancestry-gene mechanism and prove more powerful than existing methods. Being applied to SAGE data of African Americans, our methods identified several susceptible pleiotropic genes for alcohol-nicotine co-abuse.
Location: Gibson 310
Time: 3:30 PM
Abstract: An Introduction to Digital Forensics: Privacy, Practice, and Research
Digital forensics is an important aspect of information assurance (IA) and plays an increasingly vital role in detecting and responding to cyberattacks, supporting civil and criminal litigation, protecting intellectual property, protecting minors from predators, and more. Recoverable digital evidence exists on a wide variety of electronic devices, from traditional computers, to smartphones, printers, video surveillance systems, voice recorders, and game consoles.
This talk provides an introduction to digital forensics, the art and science of discovering, preserving, and analyzing digital evidence, from three perspectives: privacy, practical digital investigation, and research. The talk covers basic concepts and investigative challenges before briefly addressing current research directions, most of which are concerned with techniques and tools for allowing investigators to deal with the ever-increasing size and complexity of forensic targets and the growing impact of malware in forensic investigations. These research approaches cover a wide spectrum, including the use of parallel and distributed architectures for forensics tools, Graphics Processing Units (GPUs), advanced file carving techniques, virtual machine introspection, and tools for live investigation and memory analysis.
The impact of digital forensics techniques on personal privacy is addressed throughout.
Time: 3:00 PM
Abstract: Invariant Negative Spheres in G-Hirzebruch Surfaces
Location: Gibson 400D
Time: 12:30 PM
Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 firstname.lastname@example.org