Designing the Game to Play: Optimizing Payoff Structure in Security Games

Effective game-theoretic modeling of defender-attacker behavior is becoming increasingly important. In many domains, the defender functions not only as a player but also the designer of the game's payoff structure. We study Stackelberg Security Games where the defender, in addition to allocating defensive resources to protect targets from the attacker, can strategically manipulate the attacker's payoff under budget constraints in weighted L^p-norm form regarding the amount of change. Focusing on problems with weighted L^1-norm form constraint, we present (i) a mixed integer linear program-based algorithm with approximation guarantee; (ii) a branch-and-bound based algorithm with improved efficiency achieved by effective pruning; (iii) a polynomial time approximation scheme for a special but practical class of problems. In addition, we show that problems under budget constraints in L^0-norm form and weighted L^\infty-norm form can be solved in polynomial time. We provide an extensive experimental evaluation of our proposed algorithms

Empirical Bayes inference in sparse high-dimensional generalized linear models

High-dimensional linear models have been extensively studied in the recent literature, but the developments in high-dimensional generalized linear models, or GLMs, have been much slower. In this paper, we propose the use an empirical or data-driven prior specification leading to an empirical Bayes posterior distribution which can be used for estimation of and inference on the coefficient vector in a high-dimensional GLM, as well as for variable selection. For our proposed method, we prove that the posterior distribution concentrates around the true/sparse coefficient vector at the optimal rate and, furthermore, provide conditions under which the posterior can achieve variable selection consistency. Computation of the proposed empirical Bayes posterior is simple and efficient, and, in terms of variable selection in logistic and Poisson regression, is shown to perform well in simulations compared to existing Bayesian and non-Bayesian methods.Comment: 30 pages, 2 table

Junior Recital: Rachel Stein, soprano

This recital is presented in partial fulfillment of requirements for the degree Bachelor of Music in Performance. Ms. Stein studies voice with Eileen Moremen.https://digitalcommons.kennesaw.edu/musicprograms/1134/thumbnail.jp

Denoising Particle-In-Cell Data via Smoothness-Increasing Accuracy-Conserving Filters with Application to Bohm Speed Computation

The simulation of plasma physics is computationally expensive because the underlying physical system is of high dimensions, requiring three spatial dimensions and three velocity dimensions. One popular numerical approach is Particle-In-Cell (PIC) methods owing to its ease of implementation and favorable scalability in high-dimensional problems. An unfortunate drawback of the method is the introduction of statistical noise resulting from the use of finitely many particles. In this paper we examine the application of the Smoothness-Increasing Accuracy-Conserving (SIAC) family of convolution kernel filters as denoisers for moment data arising from PIC simulations. We show that SIAC filtering is a promising tool to denoise PIC data in the physical space as well as capture the appropriate scales in the Fourier space. Furthermore, we demonstrate how the application of the SIAC technique reduces the amount of information necessary in the computation of quantities of interest in plasma physics such as the Bohm speed

Low-redundancy codes for correcting multiple short-duplication and edit errors

Due to its higher data density, longevity, energy efficiency, and ease of generating copies, DNA is considered a promising storage technology for satisfying future needs. However, a diverse set of errors including deletions, insertions, duplications, and substitutions may arise in DNA at different stages of data storage and retrieval. The current paper constructs error-correcting codes for simultaneously correcting short (tandem) duplications and at most $p$ edits, where a short duplication generates a copy of a substring with length $\leq 3$ and inserts the copy following the original substring, and an edit is a substitution, deletion, or insertion. Compared to the state-of-the-art codes for duplications only, the proposed codes correct up to $p$ edits (in addition to duplications) at the additional cost of roughly $8p(\log_q n)(1+o(1))$ symbols of redundancy, thus achieving the same asymptotic rate, where $q\ge 4$ is the alphabet size and $p$ is a constant. Furthermore, the time complexities of both the encoding and decoding processes are polynomial when $p$ is a constant with respect to the code length.Comment: 21 pages. The paper has been submitted to IEEE Transaction on Information Theory. Furthermore, the paper was presented in part at the ISIT2021 and ISIT202