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Welcome to Stephen DeSalvo's home page!

My email address is [firstname][lastname]@

math.ucla.edu

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Currently I am a Program in Computing Assistant Adjunct Professor at UCLA (it's basically a postdoc with some teaching).

My research interests include probability, asymptotic analysis, enumerative combinatorics, combinatorial stochastic processes, exact random sampling of conditional distributions, integer partitions, Poisson approximation (Stein's method), and local central limit theorems.

I also have an extensive applied mathematics background, see Mathematical and Biological Applications. I have been teaching using the new C++11/14 ISO Standard, and I have worked with MPI (message passing interface), B-spline interpolation, spatial fuzzy c-means clustering and other image processing techniques in Matlab, orbital mechanics (specifically, the restricted 3-body problem and the invariant manifolds of the Sun-Earth-S/C and Earth-Moon-S/C dynamical systems), satellite communications systems, PI3K signal transduction pathway for Dictyostelium Discoideum, and I implemented many numerical and statistical algorithms from numerical linear algebra and statistical regression analysis in MathStudio.

PhD in applied mathematics at the University of Southern California in 2012 under the direction of Richard Arratia.

Master's degree in statistics at the University of Southern California in 2009.

I worked with Fadil Santosa as an undergraduate student in conjunction with the Minnesota Supercomputing Institute and an REU at the University of Minnesota.

Some Recent Highlights (last updated September 15, 2016):

New paper with Harry Crane and Sergi Elizalde on the probability of avoiding consecutive patterns in the Mallows distribution is now on ArXiv.

New paper with Richard Arratia on the use of a Poisson process in order to approximation a family of random combinatorial structures called assemblies now on ArXiv.

Manuscript for my presentation at GASCOM 2016 in Corisca, France, on using probabilistic divide-and-conquer with the recursive method to obtain speedups for exact Boltzmann sampling.

Recent Talks Teaching Misc

Papers Submitted

The probability of avoiding consecutive patterns in the Mallows distribution (with Harry Crane and Sergi Elizalde).

Poisson and independent process approximation for random combinatorial structures with a given number of components, and near-universal behavior for low rank assemblies (with Richard Arratia).

Random Sampling of Contingency Tables via Probabilistic Divide-and-Conquer (with James Zhao).

Pattern Avoidance for Random Permutations (with Harry Crane).

An independent process approximation to sparse random graphs with a prescribed number of edges and triangles (with Puck Rombach).

Probabilistic Divide-and-Conquer: Deterministic Second Half.

Papers Published (or accepted)

Exact sampling algorithms for Latin squares and Sudoku matrices via probabilistic divide-and-conquer. Algorithmica. To appear.

Improvements to exact Boltzmann samplers using probabilistic divide-and-conquer and the recursive method. Electronic notes in discrete mathematics. To appear.

Completely effective error bounds for Stirling numbers of the first and second kinds via Poisson approximation (with Richard Arratia). Annals of Combinatorics. To appear.

Probabilistic divide-and-conquer: a new exact simulation method, with integer partitions as an example (with Richard Arratia) Combinatorics, Probability, and Computing, Volume 25, Issue 3, May 2016, pp 324--351

On the Random Sampling of Pairs, with Pedestrian examples (with Richard Arratia), Advances in Applied Probability (March 2015) 47, no. 1, 292--305.

Log-Concavity of the Partition Function (with Igor Pak) The Ramanujan Journal, October 2015, Volume 38, Issue 1, pp 61-73. Update.

On the singularity of random Bernoulli matrices - novel integer partitions and lower bound expansions (with Richard Arratia) Annals of Combinatorics. (June 2013), Volume 17, Issue 2, pp 251-274.

Reducing the Team Uncertainty Penalty: Empirical and Theoretical Approaches (with Scott Alfeld, Kumera Berkele, Tong Pham, Daniel Russo, Lisa Jing Yan, and Matthew E. Taylor). Proceedings of the Workshop on Multiagent Sequential Decision Making in Uncertain Domains (at AAMAS-11), (May, 2011).

The Shannon entropy of Sudoku matrices (with Paul K. Newton) Proceedings of the Royal Society A (2010), 466, pp 1957--1975.

"Image Processing for C. Elegans Movement Video Streams," Los Alamos National Laboratory Technical Report LA-UR-07-5069 (with Matt Sottile, Sharif Ibrahim, and Jennifer Treanor) (2007)

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