Related papers: Nim on Integer Partitions and Hyperrectangles

Here, we present a variant of the sliding coins game. Two coins are placed on distinct squares of a semi-infinite linear board with squares numbered $0, 1, 2, dots, $. Two players take turns and move a coin to a lower unoccupied square.…

Deciding the existence of an $l\times m\times n$ integer threeway table with given line-sums is NP-complete already for fixed $l=3$, but is in P with both $l,m$ fixed. Here we consider {\em huge} tables, where the variable dimension $n$ is…

In this paper we focus on comparing machine learning approaches for quantum graphs, which are metric graphs, i.e., graphs with dedicated edge lengths, and an associated differential operator. In our case the differential equation is a…

We introduce the strongly NP-complete pagination problem, an extension of BIN PACKING where packing together two items may make them occupy less volume than the sum of their individual sizes. To achieve this property, an item is defined as…

Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…

Graph similarity computation aims to predict a similarity score between one pair of graphs to facilitate downstream applications, such as finding the most similar chemical compounds similar to a query compound or Fewshot 3D Action…

Physics-informed neural networks (PINNs) hold the potential for supplementing the existing set of techniques for solving differential equations that emerge in the study of black hole quasinormal modes. The present research investigated them…

Node-Kayles is a well-known impartial combinatorial game played on graphs, where players alternately select a vertex and remove it along with its neighbors. By the Sprague-Grundy theorem, every position of an impartial game corresponds to a…

Physics-informed neural networks (PINNs) provide a means of obtaining approximate solutions of partial differential equations and systems through the minimisation of an objective function which includes the evaluation of a residual function…

This paper proposes a rank inspired neural network (RINN) to tackle the initialization sensitivity issue of physics informed extreme learning machines (PIELM) when numerically solving partial differential equations (PDEs). Unlike PIELM…

Physics-Informed Neural Networks (PINN) emerged as a powerful tool for solving scientific computing problems, ranging from the solution of Partial Differential Equations to data assimilation tasks. One of the advantages of using PINN is to…

A new approach for the study of social games and communications is proposed. Games are simulated between cognitive players who build the opponent's internal model and decide their next strategy from predictions based on the model. In this…

RSA exponent reduction and AES S-box inversion share a hidden commonality: both are governed by the same impartial combinatorial principle, which we call a Product-Congruence Game (PCG). A Product-Congruence Game tracks play via the modular…

PINN models have demonstrated capabilities in addressing fluid PDE problems, and their potential in solid mechanics is beginning to emerge. This study identifies two key challenges when using PINN to solve general solid mechanics problems.…

Physics-informed neural networks (PINNs) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…

The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community last years. Physics Informed Neural Networks (PINNs) is one of this methods and represent a…

There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed…

Physics-Informed Neural Networks (PINNs) are a powerful class of numerical solvers for partial differential equations, employing deep neural networks with successful applications across a diverse set of problems. However, their…

In this paper, we use a simple discrete dynamical model to study integer partitions and their lattice. The set of reachable configurations of the model, with the order induced by the transition rule defined on it, is the lattice of all…

The game of Antonim is a variant of the game Nim, with the additional rule that heaps are not allowed to be the same size. A winning strategy for three heap Antonim has been solved. We will discuss the solution to three-heap Antonim and…