Title: The Mathematics of Soap Films
Abstract: Every child knows that when you blow bubbles the surface that results is a sphere. But why? We’ll talk about this, more exotic examples, and a little bit about the group of Princeton mathematicians that became obsessed with soap films in the 1960s.
Title: Beyond Standard Scores: Using Item-level Responses From Clinical Measures to Detect Atypical Developmental Patterns
Abstract: Developmental deviance (DDEV) refers to the non-sequential attainment of milestones within a developmental domain. This observation is in contrast to developmental delay (DD), where milestones are reached in the typical sequence, but the timeline of attainments is delayed. There is evidence that DDEV is associated with certain neurobehavioral diagnoses, such as autism spectrum disorder (ASD). Clinically, the attainment of developmental milestones is assessed through standardized measures of developmental domains. Many psychometric tests are arranged hierarchically, and on the surface, two individuals with the same overall score on a clinical measure may appear to be impaired to a similar extent. However, at the itemized level, individuals with DDEV exhibit a more scattered pattern of incorrect answers. Differentiating between DDEV and DD may inform prognosis and predict long-term outcomes. We developed a measure of scatter, called deviance index (DI), to differentiate between DD and DDEV using standardized measures of language ability. We tested the accuracy of DI to predict ASD diagnosis, and by extension DDEV, among individuals from the New Jersey Language and Autism Genetics Study (NJLAGS) cohort. Using our DI metric, we found that individuals with ASD and a language impairment (LI) exhibit more DDEV across measures of expressive, pragmatic, and metalinguistic language compared to individuals with LI alone. By distinguishing between DDEV and DD, DI was able to predict ASD diagnosis among LI/LI+ASD probands. DI can be applied to measures across multiple developmental domains in order to characterize developmental profiles of individuals with DDEV/DD.
Title: Modeling lamprey swimming with mathematics and computation
Abstract: Locomotion — swimming, running, flying — is one of the most basic animal behaviors. In order for an animal (like a lamprey) to swim, a lot has to happen, including neural signaling, muscle contractions, interactions between the body and the water, and adjustments from sensory feedback. How do we use mathematics to better understand the underlying mechanisms that drive locomotion? We will explore how we can use mathematical models to describe these individual systems and then coordinate the systems to produce a naturally emerging behavior in computer simulations of swimming lampreys.
Title: 1+2+3+4+… = -1/12
Abstract: Infinite series. Every Calculus II student hates them; every mathematician loves them. So, why do mathematicians love infinite series? Well, ask one, and you’ll never hear the end of it… (just sum math humor).
We’ll see how two standard examples of series, the geometric series and the zeta function (p-series), lead to beautiful applications, such as in economics and signal processing. We’ll also see how even divergent series are fascinating.
Title: Losing Altitude: A story of airplanes, heart rate, and one “controversial” dataset
Abstract: When you ride in an airplane, the lowered pressure in the cabin causes your blood oxygen levels to decrease. If oxygen saturation levels go low enough, you may experience some interesting side effects (like temporary color blindness, for example), that much we know. What we don’t know is if there is also an impact on the functioning of the heart. Partially motivated by a rash of flight related medical case studies, a study was conducted in 2007 to more formally assess the effects of exposure to altitude on heart health while in flight. We will explore this study, the complex dataset it generated, and the “controversy” of conducting research a certain airline manufacturer would rather we not.
Title: What Did You Do Last Summer?
Moderator: Alexander Murph ’18
Presenters:
Trevor Adriaanse ’17 – Cryptanalysis & Exploitation Services Summer Program, at the NSA.
Alexander Murph ’18 – Research Apprentice for the Bucknell Geisinger Research Initiative (BGRI)
Laura Papili ’17 – Actuarial Internship at Genworth in Richmond, VA. Genworth’s Actuarial development program.
Ryan Buzzell ’17 – AEW Capital Management, L.P. (Boston Office). Real Estate Investment Firm.
Katie Lunceford ’17 – Susquehanna International Group LLP (SIG)/Statistical Options Trading/Intern – Bala Cynwyd, PA
Tung Phan ’17 – Susquehanna International Group LLP (SIG)/Statistical Options Trading/Intern – Bala Cynwyd, PA
Naba Mukhtar ’18 – REU: Partial Differential Equations and Dynamical Systems – Florida Institute of Technology
Abstract: There are many exciting summer opportunities for students in the mathematical sciences! These range from internships in financial companies to research experiences at other universities to leadership development programs. In this week’s colloquium, a panel of your peers will tell you their experiences. What did they enjoy about their experiences? When did they apply? There will also be ample time for questions and answers. These varied opportunities, as well as being terrific fun, are also immensely valuable as you begin to think about your careers after Bucknell.
Title: Electoral College Math: How to Become President with 20% of the Popular Vote
Abstract: The Electoral College makes it possible to become U. S. President with less than a majority of the popular vote. In a two-candidate election, what is the minimal percentage of the popular vote possible for a winning candidate? In this talk we’ll first mimic an approach suggested by George Pólya that to find a theoretical solution. We’ll then make use of of tools not readily available to Pólya – spreadsheets and binary linear integer problem software — to see if we can improve on his results using actual presidential election data. Anyone with a vague recollection of high school algebra has the mathematical background necessary to enjoy this talk.
Title: Sequential data mining
Abstract: Data representing DNA, proteins, literature, weather, and the stock market all share one common characteristic: their data are sequential. Sequence data present some of the most challenging problems for machine learning and data mining methods. In this talk, Professor Brian King will present a generalized, probabilistic framework for modeling sequential data. He will show how he and his students have adapted this model for classification and prediction tasks, reporting results from recent studies.
Title: Being fair in a world of limited resources
Abstract: Fair division is a problem that all of us encounter regularly. Every time you and another person or several people have to divide something – pizza, money, space, Neapolitan ice cream, band width, candy, etc. – you are working on a fair-division problem. How can several people share a limited resource and make sure that no person feels the resulting allocation is unfair? Before we can answer this question, we need to figure out what exactly is means to be ‘fair’. The mathematical development of this subject is fairly recent and the results touch issues in economics and game theory. We will do lots of examples.
Title: From airlines to healthcare: scheduling services with high variability
Abstract: What do the airline and healthcare industries have in common when it comes to managing their capacity? What makes scheduling surgeries so much more difficult than an airline’s management of its seat inventory? How can hospitals improve their surgical scheduling system? While most optimization models suffer from the curse of dimensionality, simulation-based optimization is often a better choice when dealing with demand that is highly variable. Drawing from revenue management techniques developed by the airline industry, I will show how simulation modeling can help hospitals to more efficiently schedule surgical procedures, in order to better address and balance over- and under-utilization of their resources.