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

We study quantum algorithms for spatial search on finite dimensional grids. Patel et al. and Falk have proposed algorithms based on a quantum walk without a coin, with different operators applied at even and odd steps. Until now, such…

Sampling-based motion-planning algorithms typically rely on nearest-neighbor (NN) queries when constructing a roadmap. Recent results suggest that in various settings NN queries may be the computational bottleneck of such algorithms.…

It is shown that the hopping of a single excitation on certain triangular spin lattices with non-uniform couplings and local magnetic fields can be described as the projections of quantum walks on graphs of the ordered Hamming scheme of…

Dzhaparidze and Spreij [5] showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This…

\textsc{cut} is a class of partition games played on a finite number of finite piles of tokens. Each version of \textsc{cut} is specified by a cut-set $\mathcal{C}\subseteq\mathbb{N}$. A legal move consists of selecting one of the piles and…

Physics-informed neural network (PINN) is a data-driven approach to solve equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory when it is used to solve multiscale equations. Homogenization…

Occupation of an interval by self-replicating initial pulses is studied numerically. Two different approximates in different categories are proposed for the numerical solutions of some initial-boundary value problems. The sinc differential…

Let game B be Toral's cooperative Parrondo game with (one-dimensional) spatial dependence, parameterized by N (3 or more) and p_0,p_1,p_2,p_3 in [0,1], and let game A be the special case p_0=p_1=p_2=p_3=1/2. Let mu_B (resp., mu_(1/2,1/2))…

We investigate the complexity of finding a winning strategy for the mis\`ere version of three games played on graphs : two variants of the game $\text{NimG}$, introduced by Stockmann in 2004 and the game $\text{Vertex Geography}$ on both…

A partially parallel dynamical noisy binary choice (Ising) game in discrete time of $N$ players on complete graphs with $k$ players having a possibility of changing their strategies at each time moment called $k$-flip Ising game is…

We present a new form of a Parrondo game using discrete-time quantum walk on a line. The two players A and B with different quantum coins operators, individually losing the game can develop a strategy to emerge as joint winners by using…

The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new…

Here, we present a variant of Nim with two piles. In the first pile, we have stones with a weight of 1, and in the second pile, we have stones with a weight of -2. Two Players take turns to take stones from one of the piles, and the total…

We make a conjecture that characterizes the periods of the nim values in subtraction games with subtraction set of size 3.

Physics-informed Neural Networks (PINNs) often have, in their loss functions, terms based on physical equations and derivatives. In order to evaluate these terms, the output solution is sampled using a distribution of collocation points.…

The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…

We study the periodicity of nim-sequences for subtraction games having subtraction sets with three elements. In particular, we give solutions in several cases, and we describe how these subtraction sets can be augmented by additional…

We consider a subclass of $n$-player stochastic games, in which players have their own internal state/action spaces while they are coupled through their payoff functions. It is assumed that players' internal chains are driven by independent…

We study pursuit-evasion in a polygonal environment with polygonal obstacles. In this turn based game, an evader $e$ is chased by pursuers $p_1, p_2, ..., p_{\ell}$. The players have full information about the environment and the location…

This paper presents an efficient algorithm for the sequential positioning, also called nested dissection, of two planes in an arbitrary polyhedron. Two planar interfaces are positioned such that the first plane truncates a given volume from…