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We give very simple algorithms for best play in the simplest kind of Dots & Boxes endgames: those that consist entirely of loops and long chains. In every such endgame we compute the margin of victory, assuming both players maximize the…
Deep architectures consist of tens or hundreds of convolutional layers (CLs) that terminate with a few fully connected (FC) layers and an output layer representing the possible labels of a complex classification task. According to the…
Continuous variable quantum key distribution (CVQKD) with discrete modulation combines advantages of CVQKD, such as the implementability using readily available technologies, with advantages of discrete variable quantum key distribution,…
Correlated equilibria are a fundamental solution concept in game theory. However, despite decades of research, the complexity beyond games of polynomial type -- such as extensive-form games, congestion or routing games, and more broadly…
The game of SET is a popular card game in which the objective is to form Sets using cards from a special deck. In this paper we study single- and multi-round variations of this game from the computational complexity point of view and…
We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal…
We study central configurations when the set of positions is symmetric. We use a theorem from representation theory of finite groups to explore the symmetry properties of equations for central configurations. This approach simplifies…
We prove that the strong immersion order is a well-quasi-ordering on the class of semi-complete digraphs, thereby strengthening a result of Chudnovsky and Seymour that this holds for the class of tournaments.
We introduce a generalization of "Solo Chess", a single-player variant of the game that can be played on chess.com. The standard version of the game is played on a regular 8 x 8 chessboard by a single player, with only white pieces, using…
Generalizations of Redfield's master theorem and superposition theorem are proved by using decomposition of the tensor product of several induced monomial representations of the symmetric group $S_d$ into transitive constituents. As direct…
In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement, and the…
Dynamical decoupling (DD) is a key technique for suppressing decoherence and preserving the performance of quantum algorithms. We introduce a measurement-based DD (MDD) protocol that determines control unitary gates from partial…
Table recognition is using the computer to automatically understand the table, to detect the position of the table from the document or picture, and to correctly extract and identify the internal structure and content of the table. After…
We study copositive matrices which admit a decomposition into a sum of a positive semidefinite matrix and a matrix with nonnegative entries. Our main result shows that if the off-diagonal entries of a copositive matrix are nondecreasing in…
We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…
Let $\mathbf{C}$ be a Cauchy-complete category. The subtoposes of $[\mathbf{C}^{\mathrm{op}},\mathbf{Set}]$ are sometimes all of the form $[\mathbf{D}^{\mathrm{op}},\mathbf{Set}]$ where $\mathbf{D}$ is a full subcategory of $\mathbf{C}$.…
Deep equilibrium (DEQ) models have emerged as a promising class of implicit layer models, which abandon traditional depth by solving for the fixed points of a single nonlinear layer. Despite their success, the stability of the fixed points…
A fundamental challenge for quantum information processing is reducing the impact of environmentally-induced errors. Quantum error detection (QED) provides one approach to handling such errors, in which errors are rejected when they are…
We establish a fixed-point theorem for the face maps that consist in deleting the $i$th entry of an ordered set. Furthermore, we show that there exists random finite sets of integers that are almost invariant under such deletions.…
Game theory is a very profound study on distributed decision-making behavior and has been extensively developed by many scholars. However, many existing works rely on certain strict assumptions such as knowing the opponent's private…