Department of Mathematics & Statistics
SAC Room 305, Villanova University
800 Lancaster Avenue
Villanova, PA 19085
Tom Corwin '69 (Corwin Associates)
Friday, November 13, 2015
Mendel Hall Room 154, 2:30-3:30
Title: The Mathematics of Search: Theory and Operational Examples
I will review the basic tenants of Optimal Search Theory and discuss its application to real-world searches. These include:
1. The search for the H-bomb lost off Polomares Spain — 1966
2. The search for the USS Scorpion — 1968
3. Clearance of the Suez Canal — 1974
4. ComSubPac Submarine searches — 1975 through 1977
5. Search for the Miramar F-14 — 1976
6. Search for the USS Central America — 1988
7. Air France 447 — 2009
8. Malaysian Air 370 — 2014
Robert Buchanan (Millersville University)
Friday, November 20, 2015
Mendel Hall Room 154, 2:20-3:30
Title: The Mathematics of Wagering
Abstract: Parimutuel wagering is a form of gambling in which the payoff of a bet is determined in part by the collective wagers of all the bettors. Parimutuel wagering in common in horse racing and lotteries. The past performance of horses and jockeys can be analyzed to model the probabilities associated with future performance outcomes. When private estimates of race outcome probabilities differ from the collective public’s estimates as measured by their wagers, bets may be made which have a positive rate of return. The amount wagered and the outcomes wagered on must be carefully chosen to optimize the utility of the bettor’s bankroll. Information present in the win betting pool can be used to estimate probabilities of outcomes in the exotic betting pools.
This talk will touch on topics in statistical modeling, parameter estimation, and nonlinear, numerical constrained optimization. It will be understandable by undergraduate mathematics students.
David Chuss '97 (Villanova University)
Tuesday, December 8, 2015
Mendel Hall 154, 2:30-3:30
Title: Searching for the Fingerprint of Inflation in the Cosmic Microwave Background
Abstract: The past two decades have brought a vast improvement in our understanding of cosmology during which the Big Bang paradigm has been quantified using a six parameter model. The observed geometric flatness of the universe, it's near homogeneity, and the small deviation from scale invariance of the small temperature fluctuations in the cosmic microwave background (the relic radiation from the early universe) have hinted that the universe underwent a period of brief, rapid expansion in the first fraction of a second. This expansion, called "inflation," is predicted to produce gravitational waves that would have imprinted a faint but distinct polarization pattern in the cosmic microwave background. The Cosmology Large Angular Scale Surveyor (CLASS) is currently being constructed in the Atacama Desert to search for this signal to test the inflation paradigm. I will review the state of the art of our current understanding of cosmology and discuss the CLASS instrument capabilities.
Chris Rorres (Drexel University)
Thursday, January 21, 2016
Saint Augustine Center Room 300, 6:00-8:00
Title: The Law of the Lever: Archimedes vs. Mach
Abstract: Over a century ago Ernst Mach, the famous Austrian physicist and philosopher of science, wrote a blistering criticism of Archimedes' celebrated proof of the Law of the Lever. Mach accused Archimedes of overusing his "Grecian mania for demonstration" and succeding in his proof only "by the help of the very propostion he sought to prove". His attack drew the expected objections from many historians and philosophers of science who, in turn, accused Mach of not understanding the subtleties of Archimedes' proof. I will give my own interpretation of this controversy from a mathematician's poin tof view, concluding with my belief that while Archimedes did indeed prove something, it can hardly be called a proof of the Law of the Lever.
Weiwen Miao (Haverford College)
Friday, February 12, 2016
Saint Augustine Center Room 300, 2:30-3:25
Title: New Statistical Tests for Detecting Disparate Impact Arising from Two-Stage Selection Processes
Abstract:Statistical evidence is often critical when a court decides whether an employment practice (e.g. a promotional exam) has a disparate impact on minority candidates. In many cases, the hiring or promotion process consists of two steps. Since disparate impact can occur at each step, parties submitting evidence may use statistical tests at each stage without accounting for a potential multiple comparisons problem. Because different courts have focused on data concerning either one or the other step or a composite of both, they have reached opposite conculsions when faced with similar data. After illustrating the issues, two two-step tests are recommended to alleviate the problem. The large sample properties of these tests are obtained. A simulation study shows that in most situation, the new tests have higher power than the ones in current use.
Erica Graham (Bryn Mawr College)
Friday, April 1, 2016
Mendel Hall Room 154, 2:30-3:25
Title: On Mathematical Models of Metabolic Dysfunction: Diabetes, Cells, and Sleep
Abstract: How are cells, sleep, and diabetes related? Type 2 diabetes, in particular, is a metabolic disease whose very presence results from a coodrinated dysfunction of cells within the body. Although the disease is well studied, there remain significant gaps in our understanding of its development. Genetic and environmental factors are known to determine individual susceptibility to diabetes. Overnutrition is commonly associated with disease, whereas circadian disruption is a less known contirbutor to enviironmental susceptibility. Because diabetes often takes decades to develop, mathematical modeling is a useful tool to study disease progression from various perspectives. In this talk, I will discuss mathematical models of metabolic dysfunction, in the context of both cellular mechanism and sleep-wake patterns.
Mark McKibben (West Chester U)
Friday, April 8, 2016
Mendel Hall Room 115, 2:30-3:25
Title: Holey Rocks, Indecisive Fluids, Vanishing Beaches & Fiery Neurons: The Unifying Nature of Implicit Evolution Equations
Abstract: Hidden connections often lurk beneath the surface that, once discovered, enable mathematical models of seemingly disparate phenomena to be studied within a single, unified abstract framework. When the models consist of partial differential equations, the form of this structure is an abstract evolution equation. In this talk, we shall begin by illustrating, in a sequence of steps, how an abstract evolution equation can be derived to unify the study of the models alluded to in the title. Then, we will incorporate environmental noise into the models and develop an even more encompassing stochastic theory governing the evolution of these processes. If time permits, commentary will be given on current and future directions of research in this area, including how one accounts for sharp blows to the system, time delays, and "not-so-nice" noise (e.g., fractional Brownian motion).