Research
Research
Research
Research
6,875+ open-access research outputs.
J. Conway defined useful operations on the Class of combinatorial games and also introduced a notion of equivalence between games. Conway showed that, under his equivalence, games form a Group. Howeve…
In this letter, we study a model-based inverse problem for infinite-horizon linear-quadratic differential games with descriptor dynamics. Specifically, we seek to identify the set of all cost function…
Revealing the interaction topology underlying strategic behavior is fundamental to prediction, intervention, and policy design in networked systems. Yet the interaction matrix is often unobservable, a…
We study stochastic differential games with $N$ players, where interactions are determined by sequences of graphs in which the number of neighbours of each node remains bounded as $N$ grows, such as c…
Lutwak's affine quermassintegral theory is a foundational component of modern affine Brunn--Minkowski theory. Developed in the 1980s, it provides affine analogues of the classical quermassintegrals an…
Hill functions, dominant in gene regulatory network modeling, carry fundamental limitations: at non-integer cooperativity exponents, routine when fitting dose-response data, derivatives diverge at the…
This paper develops a deep policy iteration method for high-dimensional finite-horizon mean-field games. We reformulate the game as a regenerative problem with deterministic cycles, which allows polic…
This paper studies the Nash equilibrium seeking problem for stochastic games under heavy-tailed noise. The gradient noise is considered to have a finite $\delta$-th moment ($1<\delta\le 2$), which gen…
For the boundary value problem $$\left\{ \begin{array}{rcll} -\Delta_p u+u^{p-1}&=&|x|^{\alpha}u^{q-1}&\mbox{in }\Omega,\\ \frac{\displaystyle\partial u}{\displaystyle\partial{\bf n}}&=&0&\mbox{on }\p…
We show the subgroup of 20 nonzero fourth powers in the finite field of order 81 is a cap set. Similarly, the subgroup of 9 nonzero seventh powers in the field of order 64 is a cap set. These are the …
Our research is closely related to ontological studies in mathematics. It provides crucial insights into the nature of decisions and strategies characterized by Markov moments. In a stopping game, a…
We consider the two families of even polynomials $\Xi_n$ and $\Lambda_n$ studied in~\cite{TallaWaffo2026arxiv2602.16761}, together with the rescaled polynomials $\widetilde{\Xi}_n(x):=\Xi_n(\sqrt{x})$…
We compute the Atiyah Real $K$-theory of $C_2$-equivariant projective spaces and construct immersions of such spaces into multiples of the regular representation. These computations are made tractable…
We study the control of rumor propagation in large networked populations by using Stackelberg graphon games. We first introduce a principal who wants to incentivize the spread of her preferred news an…
We develop a terminal-defect method for the double Dixie cup problem and use it to prove the finite-variance extremality conjecture of Doumas and Papanicolaou. For every \(m\ge1\) and \(N\ge2\), among…
We prove explicit finite-$N$ lower bounds for $\mathbb P(\bigcup_{k=1}^N A_k)$ when the $\sigma$-algebras generated by an event sequence satisfy quantitative $\varphi$- or $\alpha$-mixing bounds. The …
Game-theoretic characterizations of selection principles provide a powerful framework for analyzing covering properties through strategic interactions. For a Tychonoff space $X$ and a non-trivial metr…
In many applications, including Stackelberg games, machine learning, and power systems \cite{Mackay2018Selftuning,Heinrich1952The,Wang2021Bi-Level}, the decisions in a minimax optimization problem can…
This paper investigates a class of linear-quadratic-Gaussian risk-sensitive graphon mean-field games, involving an asymptotically infinite population of heterogeneous agents distributed across an asym…
For every nonzero integer $m$ and every integer $n \ge 1$, the $n$\textsuperscript{th} harmonic number $H_n = 1 + \tfrac12 + \dots + \tfrac1n$ satisfies the identity \[ H_n \;=\; \frac{1}{m}\,\sum_{…
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