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.

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!

Update 4-22-2018: The paper Limit shapes via Bijections (with Igor Pak) has been accepted to the journal Combinatorics, Probability & Computing!

Update 12-6-2017: The paper The probability of avoiding consecutive patterns in the Mallows distribution (with Harry Crane and Sergi Elizalde) has been accepted to the journal Random Structures & Algorithms!

Summary: my research is primarily in the subject of combinatorial probability, and I have an extensive background in applied and computational mathematics with emphasis in industrial problems. I taught a year-long introduction to programming course at UCLA which covered C++11/14 (C++17 wasn't published at the time) as well as Qt. I am currently programming in Python with big data (cliche, yes, but in this case it is true), and making GUIs with PyQt.

Research interests (see published papers below):

Probability

Poisson approximation (Stein's method)
Local central limit theorems

Enumerative combinatorics

asymptotic analysis
integer partitions

Statistics (theory)

Contingency tables
Random sampling of conditional distributions

Computer Science (empirical)
Applied and Computational Mathematics

Predictive Policing
Mathematical Problems in Industry
C++11/14/17 Lecture notes and code base
Python, PyQt (GUI), Big Data
Image processing techniques
B-spline interpolation
Spatial fuzzy c-means clustering
Invariant manifolds of the Sun-Earth-satellite and Earth-Moon-satellite three body problems
PI3K Signal Transduction Pathway of Dictyostelium Discoideum
C Elegans worm morphology and simulation in silico

Below is a heat map describing these activities, with greater emphasis on published papers.

Postdoc at the University of California Los Angeles from 2012 to 2017, worked closely with Igor Pak and 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.

Recent Talks Teaching Coding Misc

Papers Submitted

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

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

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+

Limit shapes via Bijections (with Igor Pak). Combinatorics, Probability & Computing (to appear).

The probability of avoiding consecutive patterns in the Mallows distribution (with Harry Crane and Sergi Elizalde). Random Structures & Algorithms (to appear).

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.

2017

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

Extended abstract: Electronic Notes in Discrete Mathematics.
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.

2016

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

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

2015

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

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

2013

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

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).

2010

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

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)

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