Related papers: Difficult Sudoku Puzzles Created by Replica Exchan…
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…
We showcase a collection of practical strategies to deal with a problem arising from an analysis of integral estimators derived via quasi-Monte Carlo methods. The problem reduces to a triple binomial sum, thereby enabling us to open up the…
Monte Carlo algorithms are a foundational pillar of modern computational science, yet their effective application hinges on a deep understanding of their performance trade offs. This paper presents a critical analysis of the evolution of…
An efficient Monte Carlo algorithm for the simulation of spin models with long-range interactions is discussed. Its central feature is that the number of operations required to flip a spin is independent of the number of interactions…
The Monte Carlo method, proposed by Dell'Amico and Filippone, estimates a password's rank within a probabilistic model for password generation, i.e., it determines the password's strength according to this model. We propose several ideas to…
Policy-guided Monte Carlo is an adaptive method to simulate classical interacting systems. It adjusts the proposal distribution of the Metropolis-Hastings algorithm to maximize the sampling efficiency, using a formalism inspired by…
Monte Carlo (MC) simulations of lattice models are a widely used way to compute thermodynamic properties of substitutional alloys. A limitation to their more widespread use is the difficulty of driving a MC simulation in order to obtain the…
In combinatorial reconfiguration, the reconfiguration problems on a vertex subset (e.g., an independent set) are well investigated. In these problems, some tokens are placed on a subset of vertices of the graph, and there are three natural…
Reciprocating interactions represent a central feature of all human exchanges. They have been the target of various recent experiments, with healthy participants and psychiatric populations engaging as dyads in multi-round exchanges such as…
Icosoku is a challenging and interesting puzzle that exhibits highly symmetrical and combinatorial nature. In this paper, we pose the questions derived from the puzzle, but with more difficulty and generality. In addition, we also present a…
In this paper we propose the approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance…
Sampling from hierarchical Bayesian models is often difficult for MCMC methods, because of the strong correlations between the model parameters and the hyperparameters. Recent Riemannian manifold Hamiltonian Monte Carlo (RMHMC) methods have…
The work discusses a new low-rank Monte Carlo technique to solve Smoluchowski-like kinetic equations. It drastically decreases the computational complexity of modeling of size-polydisperse systems. For the studied systems it can outperform…
We advance the Cohn-Umans framework for developing fast matrix multiplication algorithms. We introduce, analyze, and search for a new subclass of strong uniquely solvable puzzles (SUSP), which we call simplifiable SUSPs. We show that these…
Rubik's Cube is one of the most famous combinatorial puzzles involving nearly $4.3 \times 10^{19}$ possible configurations. Its mathematical description is expressed by the Rubik's group, whose elements define how its layers rotate. We…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
While looking for abductive explanations of a given set of manifestations, an ordering between possible solutions is often assumed. The complexity of finding/verifying optimal solutions is already known. In this paper we consider the…
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…
We present an algorithm for the optimization and thermal equilibration of spin glasses - or more generally, cost functions of the Ising form $H=\sum_{\langle i j\rangle} J_{ij} s_i s_j + \sum_i h_i s_i$, defined on graphs with arbitrary…
We explore the capabilities of physical computing with Oscillatory Neural Networks (ONN) to solve combinatorial optimization problems. To solve Sudokus with ONNs, we define a novel mapping strategy that utilizes the unique characteristics…