stephendesalvo

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Welcome to Stephen DeSalvo's home page!

I am currently a quantitative developer at Praedicat. The technological aspects are what really got me excited to explore this opportunity, and I found the people involved to be quite exceptional and inspiring.

I am no longer scheduled to teach any more PIC classes in the future.

Below you will find my research interests and papers, many of which are still under review by refereed journals. Please feel free to reach out if you have any questions or comments with respect to these topics!

Below is a heat map describing the various fields I have worked in.

My research interests include probability, asymptotic analysis, enumerative combinatorics, 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) for parallel computing; 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, in the form of calculating channel capacity under various forms of noise; PI3K signal transduction pathway for Dictyostelium Discoideum; I also implemented many numerical and statistical algorithms from numerical linear algebra and statistical regression analysis in MathStudio. I also recently participated in several workshops in applied mathematics: predictive policing in Providence, Rhode Island, where we looked at dispatch data to design an optimal allocation of police resources at a district level; and also a workshop for mathematical problems in industry at Duke University, where I worked with ReVon on analyzing triage data for asthma and COPD patients using various machine learning and statistical tools.

Postdoc at the University of California Los Angeles working with Igor Pak and more recently Georg Menz.

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 August 9, 2017):

The paper with Harry Crane and pattern avoidance for random permutations has been accepted into a special issue of Discrete Mathematics and Theoretical Computer Science, Permutation Patterns. I presented the work at the Permutation Patterns conference in the summer of 2016 at Howard University in Washington, DC.

Recent Talks Teaching Mathematical and Biological Applications Coding Misc

Papers Submitted

Random sampling of Latin squares via binary contingency tables and probabilistic divide-and-conquer.

Limit shapes via Bijections (with Igor Pak).

A robust quantitative local central limit theorem with applications to enumerative combinatorics and random combinatorial structures (with Georg Menz).

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).

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

2018+

Pattern Avoidance for Random Permutations (with Harry Crane). Discrete Mathematics and Theoretical Computer Science, Permutation Patterns 2016 (to appear).

Probabilistic Divide-and-Conquer: Deterministic Second Half. Advances in Applied Mathematics (2018).

2017

Improvements to exact Boltzmann samplers using probabilistic divide-and-conquer and the recursive method.

Extended abstract: Electronic Notes in Discrete Mathematics (2017).
Full Article: Pure Mathematics and Applications (to appear).

Completely effective error bounds for Stirling numbers of the first and second kinds via Poisson approximation (with Richard Arratia). Annals of Combinatorics. (2017)

2016

Exact sampling algorithms for Latin squares and Sudoku matrices via probabilistic divide-and-conquer. Algorithmica. (2016)

Probabilistic divide-and-conquer: a new exact simulation method, with integer partitions as an example (with Richard Arratia) Combinatorics, Probability, and Computing. (2016)

2015

On the Random Sampling of Pairs, with Pedestrian examples (with Richard Arratia), Advances in Applied Probability (2015).

Log-Concavity of the Partition Function (with Igor Pak) The Ramanujan Journal (2015). Update.

2013

On the singularity of random Bernoulli matrices - novel integer partitions and lower bound expansions (with Richard Arratia) Annals of Combinatorics (2013)

2011

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), (2011).

2010

The Shannon entropy of Sudoku matrices (with Paul K. Newton) Proceedings of the Royal Society A (2010).

2007

"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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