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We consider a 3-dimensional lattice model of a network-forming fluid, which has been recently investigated by Girardi and coworkers by means of Monte Carlo simulations [J. Chem. Phys. \textbf{126}, 064503 (2007)], with the aim of describing…
We present a detailed description of the diagrammatic technique, recently devised in [V. V. Kuzmin et.al., npj Quantum Information 5, 115 (2019)], for semi-analytical description of large-scale quantum-repeater networks. The technique takes…
A new Monte Carlo algorithm for phase-space sampling, named (MC)**3, is presented. It is based on Markov Chain Monte Carlo techniques but at the same time incorporates prior knowledge about the target distribution in the form of suitable…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
Several quantum and classical Monte Carlo algorithms for Betti Number Estimation (BNE) on clique complexes have recently been proposed, though it is unclear how their performances compare. We review these algorithms, emphasising their…
The Monte Carlo dropout method has proved to be a scalable and easy-to-use approach for estimating the uncertainty of deep neural network predictions. This approach was recently applied to Fault Detection and Di-agnosis (FDD) applications…
Based on the scheme of variational Monte Carlo sampling, we develop an accurate and efficient two-dimensional tensor-network algorithm to simulate quantum lattice models. We find that Monte Carlo sampling shows huge advantages in dealing…
Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models…
In several implementations of Sequential Monte Carlo (SMC) methods it is natural, and important in terms of algorithmic efficiency, to exploit the information of the history of the samples to optimally tune their subsequent propagations. In…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…
It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem…
Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$,…
A numerical technique is introduced that reduces exponentially the time required for Monte Carlo simulations of non-equilibrium systems. Results for the quasi-stationary probability distribution in two model systems are compared with the…
Markov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, whenever either the distribution does not exist in closed form, or, if it does, no efficient method to simulate an independent sample from…
Quasi-stationary distributions (QSDs)arise from stochastic processes that exhibit transient equilibrium behaviour on the way to absorption QSDs are often mathematically intractable and even drawing samples from them is not straightforward.…
We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…
Monte Carlo methods approximate integrals by sample averages of integrand values. The error of Monte Carlo methods may be expressed as a trio identity: the product of the variation of the integrand, the discrepancy of the sampling measure,…
Discrepancy is a well-known measure for the irregularity of the distribution of a point set. Point sets with small discrepancy are called low-discrepancy and are known to efficiently fill the space in a uniform manner. Low-discrepancy…
1. Temporal trends in species distributions are necessary for monitoring changes in biodiversity, which aids policymakers and conservationists in making informed decisions. Dynamic species distribution models are often fitted to ecological…