Modern applications of strong gravitational lensing require the ability to use precise and varied observational data to constrain complex lens models. I discuss two sets of computational methods for lensing calculations. The first is a new algorithm for solving the lens equation for general mass distributions. This algorithm makes it possible to apply arbitrarily complicated models to observed ...

I read this book by Peyret and Taylor with pleasure. At last there is an introductory book on computational fluid dynamics that is intelligent, fairly wellinformed, and reasonably up-to-date. Its perspective is not, however, fully consistent with a mathematician's point of view. Computational fluid dynamics (CFD) is the process of solving problems in fluid dynamics numericallyon a computer. It ...

Oblivious equilibrium is a new solution concept for approximating Markov perfect equilibrium in dynamic models of imperfect competition among heterogeneous firms. In this paper, we present algorithms for computing oblivious equilibrium and for bounding approximation error. We report results from computational case studies that serve to assess both efficiency of the algorithms and accuracy of ob...

How is the information from a thousand gene-expression arrays, the location of more than two hundred regulatory factors, and nine sequenced genomes to be integrated into a global view of the regulatory network in budding yeast? Computational methods that fit incomplete noisy data provide the outlines of regulatory pathways, but the errors are not quantified. In the fly, embryonic patterning has...

Explicit Runge–Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge–Kutta schemes available in literature. Furthermore, they have a small principal error n...

OF THE DISSERTATION Computational Methods in Permutation Patterns by Brian Koichi Nakamura Dissertation Director: Doron Zeilberger Given two permutations σ ∈ Sk and π = π1 . . . πn ∈ Sn, the permutation π is said to contain the pattern σ if there exists 1 ≤ i1 < . . . < ik ≤ n such that πi1 . . . πik is order-isomorphic to σ. Each such subsequence is called an occurrence of σ in π. Over the pas...

Individuality is the state or quality of being an individual. We establish a computational methodology to determine whether a particular modality of data is sufficient to establish the individuality of every individual or even a demographic group. To test the individuality, generative models are given or learned to represent the distribution of certain characteristics such as birthday, human he...

A computational method is described for option replication. In particular, a procedure is provided for computing the projection basis that corresponds to a positive basis of R m. Application of this procedure in order to compute maximal submarkets that replicate any option is demonstrated. Specifically, we provide a computational study for replication of options in security markets with a finit...

[Note: The presentation in this publication is oriented toward the synthesis properties per se of SPRUCE in view of the general theme of the conference. However, the main objective of the overall SPRUCE project was and remains the building of a computational model of human speech production. This objective should not be confused with what we perceive to be the ‘simpler’ task of engineering a de...