相关论文: Three-pile Sharing Nim and the quadratic time winn…

Let $\mathbf{T}_{\mathbf{a},\mathbf{b}}$ be the number of $3$-way contingency tables of size $m \times n \times p$ with two of its three plane-sum margins fixed by $\mathbf{a}=(a_1, \ldots, a_m) \in \mathbb{N}^m$ and $\mathbf{b}=(b_1,…

The Sprague-Grundy (SG) theory reduces the sum of impartial games to the classical game of $NIM$. We generalize the concept of sum and introduce $\cH$-combinations of impartial games for any hypergraph $\cH$. In particular, we introduce the…

Physics-informed neural networks (PINN) is a extremely powerful paradigm used to solve equations encountered in scientific computing applications. An important part of the procedure is the minimization of the equation residual which…

The problem of minimization of a quadratic functional depending on great number of binary variables is examined. 3 variants of minimization procedure are studied with the aid of computer simulation for spin-glass matrices. It is shown that…

In 1901, Bouton proved that a winning strategy of the game of Nim is given by the bitwise XOR, called the nim-sum. But, why does such a weird binary operation work? Led by this question, this paper introduces a categorical reinterpretation…

We present a simple randomized scheme for triangulating a set $P$ of $n$ points in the plane, and construct a kinetic data structure which maintains the triangulation as the points of $P$ move continuously along piecewise algebraic…

We present a new scheme for a discrete-time quantum walk on two- and three-dimensional lattices using a two-state particle. We use different Pauli basis as translational eigestates for different axis and show that the coin operation, which…

We study 2-player impartial games of the form take-away which produce P-positions (second player winning positions) corresponding to complementary Beatty sequences, given by the continued fractions (1;k,1,k,1,...) and (k+1;k,1,k,1,...). Our…

We consider a particle moving in a one dimensional potential which has a symmetric deterministic part and a quenched random part. We study analytically the probability distributions of the local time (spent by the particle around its mean…

We consider algorithmic problems motivated by modular robotic reconfiguration in the sliding square model, in which we are given $n$ square-shaped modules in a (labeled or unlabeled) start configuration and need to find a schedule of…

We propose a greedy algorithm to select $N$ important features among $P$ input features for a non-linear prediction problem. The features are selected one by one sequentially, in an iterative loss minimization procedure. We use neural…

Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular…

The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…

We consider several extensions of the fractional bin packing problem, a relaxation of the traditional bin packing problem where the objects may be split across multiple bins. In these extensions, we introduce load-balancing constraints…

We study sequences of partitions of a non decreasing sequence I n of intervals into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according…

We study a class of stochastic processes of the type $\frac{d^n x}{dt^n}= v_0\, \sigma(t)$ where $n>0$ is a positive integer and $\sigma(t)=\pm 1$ represents an `active' telegraphic noise that flips from one state to the other with a…

We propose a new approach to represent nonparametrically the linear dependence structure of a spatio-temporal process in terms of latent common factors. Though it is formally similar to the existing reduced rank approximation methods…

Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the…

In the paper a novel stochastic algorithm designed to study of chain-like bodies dynamics is introduced. This algorithm models chain movements induced by the tension propagation and its main idea relies on the sequentialization of each…

We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…