PIMS Voyageur Colloquium

Given a sample of random vectors drawn from the standard Gaussian distribution, there is a variety of associated random convex sets. For instance, taking the convex hull of the vectors gives rise to a Gaussian random polytope

We derive new identities for a polynomial analogue of the Stern sequence and define two subsequences of these polynomials. We obtain various properties for these two interrelated subsequences which have 0-1 coefficients and can be seen as extensions or analogues of the Fibonacci numbers. We also define two analytic functions as limits of these sequences.

As an application we obtain evaluations of certain finite and infinite continued fractions whose partial quotients are doubly exponential.

In a case of particular interest, the set of convergents has exactly two limit points. (Joint work with K.B. Stolarsky).

We derive new identities for a polynomial analogue of the Stern sequence and define two subsequences of these polynomials. We obtain various properties for these two interrelated subsequences which have 0-1 coefficients and can be seen as extensions or analogues of the Fibonacci numbers. We also define two analytic functions as limits of these sequences.

As an application we obtain evaluations of certain finite and infinite continued fractions whose partial quotients are doubly exponential. In a case of particular interest, the set of convergents has exactly two limit points. (Joint work with K.B. Stolarsky).

Computational noise in deterministic simulations is as ill-defined a concept as can be found in scientific computing. Roundoff errors, discretizations, numerical solutions to systems of equations, and adaptive techniques can destroy the smoothness of the processes underlying a simulation. Such noise complicates optimization, sensitivity analysis, and other applications that depend on the simulation output.

Modern probability theory, whose foundation is based on the axioms set forth by Kolmogorov, is  currently the major tool for performance analysis  in stochastic systems. While it offers insights in understanding such systems, probability theory is really not a  computationally tractable theory. Correspondingly, some of its major areas of application remain unsolved when the underlying systems become multidimensional: Queueing networks, network information theory, pricing multi-dimensional financial contracts, auction design in multi-item, multi-bidder auctions among others.

Taking advantage of Degeneracy in Cone Optimization; Applications to Euclidean Distance Completion Problems including: Sensor Network Localization and Molecular Conformation.

The elegant theoretical results for strong duality and strict complementarity for linear programming, LP, lie behind the success of current algorithms. However, the theory and preprocessing techniques that are successful for LP can fail for cone programming over nonpolyhedral cones.