The Riemann integral is rather restricted, while the Lebesgue integral might be called rather complex.  Some mathematicians argue that for those reasons, the Riemann integral should be replaced in undergraduate analysis courses with the Henstock integral.  This talk will look into what the Henstock integral is and how it relates to other integrals.

How densely can we pack congruent balls into Euclidean space without making them overlap? This talk will give an overview of why we care, what has been proved, why the problems are hard, and what sort of mathematics is used in this area.

Recent studies have documented the importance of asymmetry and tail-fatness of returns on portfolio-choice, asset-pricing, value-at-risk, and option-valuation models.  This paper explores the nature of skewness and elongation in daily exchange-traded fund (ETF) return distributions using g, h and (g x h) distributions. 

In this talk, we present our study the geometrical properties of massive online social networks (MOSN). A MOSN can be represented as a graph, where the nodes are network members and the edges are "friendship" relationships. The graph induces a metric space with the distance between any two nodes defined as the length of the shortest path in the graph connecting the nodes. Thus, one can argue about the distance between the nodes, but not about their positions in the MOSN.

Online social networks made their way into the Internet and became an important (if not the most important) part of the socially oriented Web in the beginning of the 21st century. The structure of these networks resembles the structure of "traditional" human societies, but, unlike the latter, can be easily recorded. Understanding the online structure can help us understand the "traditional" structure and to find the differences between online and "traditional" societies.

Human eye movements are a very fast, effortless, and intuitive way of controlling a computer program. Therefore, eye-movement information can be used to facilitate human-computer interaction. Gaze-controlled interfaces are also beneficial to physically challenged computer users and enable them, for example, to type a text by just looking at letters arranged to form a virtual keyboard on a computer screen. However, eye movements are not completely under conscious control, which needs to be considered for the construction of gaze-controlled interfaces. This talk will present several interfaces developed in the Visual Attention Lab at UMass Boston and discuss research results on gaze-controlled human-computer interaction.