Brown University Graduate School Dissertation Defense Information Lefschetz Center for Dynamical Systems Seminar
Cognitive & Linguistic Sciences
Honors Presentations
Special Brown University Applied Mathematics Student Seminar
Abstract: For the last four years, the Default Swap market has seen a tremendous growth. This market has created a suite of derivative products, including indices, options on indices, and trenches of portfolios of Default Swaps, and options on these trenches. In this lecture, we will introduce the Default Swap contract and some elements of its pricing. We will then introduce portfolio products: the focus will be in the participants and the market forces that influence the trading levels. We will discuss the shortcoming in the current pricing and describe current efforts under investigation that are supposed to diminish the current inconsistencies. Focus will be on pricing and risk management. We have finally discussed additional complications brought by Collateralized Debt Obligations Squared (CDO Squared) or CDOs backed by pools of CDOs.
(This is an informal lecture and the focus will be on the challenges that market participants are facing).
PDE Seminar
Abstract: We discuss unique identification of elastic parameters from dynamic displacement-traction boundary measurements for anisotropic elastic media. Surface measurements are encoded in the so-called Dirichlet-to-Neumann or DN map. We first prove that there is a natural "obstruction to uniqueness" due to the covariance of the system of elastodynamics under diffeomorphisms fixing the boundary. It is known that the elastic moduli are uniquely determined by the DN map for isotropic media. We then consider a certain class of transversely isotropic media, for which elastic waves propagate along geodesic segments of three Riemannian metrics. Under mild conditions the light cone associated to one of the metrics is always disjoint from the others. By microlocally decoupling the equations of elastodynamics (following a result of M. Taylor), we show that the DN map uniquely determines the boundary distance function, or equivalently the travel times through the object, for this metric. This is joint work with L. Rachele.
Department of Mathematics Colloquium
Brown University -
Division of Biology and Medicine
Center for Statistical Sciences Seminar Series
Candidate for Open Rank Professor (research track) in the | |
Abstract: Measuring accuracy of diagnostic tests based on Receiver Operating Characteristic (ROC) curves often proves to be costly and time-consuming when tests are applied to screening populations in which the number of participants is large and the majority of test results are negative.
Therefore, we propose to study two-phase design that do not require verifying the disease status for every participant to reduce cost, while still ensuring enough diseased cases in low prevalence screening studies,
We approach the design and analysis of two-phase screening studies from a Bayesian perspective when diagnostic performance measures are based on ROC curves. For both estimation and sample size calculations, we adopt the Data Augmentation method and carry out the computations in MATLAB. In particular, the sample size for a particular study is calculated based on iterative simulations under a set of assumptions.
We conclude that two-phase designs for estimating and comparing ROC curves can be more efficient than single sample designs. The Bayesian approach makes it possible to incorporate available prior information in the study and to account for the uncertainty about the assumptions used in design considerations.
(Bernold Fiedler, John Mallet-Paret)