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The stability and convergence analysis of high-order numerical approximations for the one- and two-dimensional nonlocal wave equations on unbounded spatial domains are considered. We first use the quadrature-based finite difference schemes…
Domain-specific quantitative reasoning remains a major challenge for large language models (LLMs), especially in fields requiring expert knowledge and complex question answering (QA). In this work, we propose Expert Question Decomposition…
The chase procedure is a fundamental algorithmic tool in database theory with a variety of applications. A key problem concerning the chase procedure is all-instances termination: for a given set of tuple-generating dependencies (TGDs), is…
Protocols for quantum position verification (QPV) which combine classical and quantum information are insecure in the presence of loss. We study the exact loss-tolerance of the most popular protocol for QPV, which is based on BB84 states,…
Current systems and formalisms for representing incomplete information generally suffer from at least one of two weaknesses. Either they are not strong enough for representing results of simple queries, or the handling and processing of the…
While Quantum Key Distribution (QKD) provides information-theoretic security, the transition from theory to physical hardware introduces side-channel vulnerabilities that traditional error metrics often fail to characterize. This paper…
Let $Q_d$ be the $d$-dimensional Hamming cube and $N=|V(Q_d)|=2^d$. An independent set $I$ in $Q_d$ is called balanced if $I$ contains the same number of even and odd vertices. We show that the logarithm of the number of balanced…
Generalized category discovery (GCD) aims at addressing a more realistic and challenging setting of semi-supervised learning, where only part of the category labels are assigned to certain training samples. Previous methods generally employ…
In this short note we give an example of a four-person finite positional game with perfect information that has no positions of chance and no Nash equilibria in pure stationary strategies. The corresponding directed graph has only one…
We present a comprehensive study of vortex structures in $d$-wave superconductors from large-scale renormalized mean-field theory of the square-lattice $t$-$t'$-$J$ model, which has been shown to provide a quantitative modeling for…
When solving k-in-a-Row games, the Hales-Jewett pairing strategy [4] is a well-known strategy to prove that specific positions are (at most) a draw. It requires two empty squares per possible winning line (group) to be marked, i.e., with a…
Coding theory plays a crucial role in ensuring data integrity and reliability across various domains, from communication to computation and storage systems. However, its reliance on trust assumptions for data recovery, which requires the…
The localization game is a variant of the game of Cops and Robber in which the robber is invisible and moves between adjacent vertices, but the cops can probe any $k$ vertices of the graph to obtain the distance between probed vertices and…
We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave…
Chess has experienced a large increase in viewership since the pandemic, driven largely by the accessibility of online learning platforms. However, no equivalent assistance exists for physical chess games, creating a divide between analog…
EvenQuads is a new card game that is a generalization of the SET game, where each card is characterized by three attributes, each taking four possible values. Four cards form a quad when, for each attribute, the values are the same, all…
The problem Defensive $\delta$-Covering, for some covering range $\delta > 0$, is a continuous facility location problem on undirected graphs where all edges have unit length. It is a generalization of Defensive Dominating Set and…
Identifying the configuration of chess pieces from an image of a chessboard is a problem in computer vision that has not yet been solved accurately. However, it is important for helping amateur chess players improve their games by…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
Formal verification is a promising method for producing reliable software, but the difficulty of manually writing verification proofs severely limits its utility in practice. Recent methods have automated some proof synthesis by guiding a…