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For Majorana-Wilson lattice fermions in two dimensions we derive a dimer representation. This is equivalent to Gattringer's loop representation, but is made exact here on the torus. A subsequent dual mapping leads to yet another…
A review of the Loop Algorithm, its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a Quantum Monte Carlo procedure which employs nonlocal changes of worldline configurations,…
Monte Carlo simulations are a crucial component when analysing the Standard Model and New physics processes at the Large Hadron Collider. This paper aims to explore the performance of generative models for complementing the statistics of…
The pseudo-random number generators (PRNGs), sampling algorithms, and algorithms for generating random integers in some common statistical packages and programming languages are unnecessarily inaccurate, by an amount that may matter for…
This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and $1/t$ algorithms. The classical algorithms are modified by the use of $m$…
Short autocorrelation times are essential for a reliable error assessment in Monte Carlo simulations of lattice systems. In many interesting scenarios, the decay of autocorrelations in the Markov chain is prohibitively slow. Generative…
A natural approach to software quality assurance consists in writing unit tests securing programmer-declared code invariants. Throughout the literature a great body of work has been devoted to tools and techniques automating this…
In the Monte Carlo simulation of both Lattice field-theories and of models of Statistical Mechanics, identities verified by exact mean-values such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well known…
We discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model. By using the perspective of probability theory, we detail the nature of a cluster algorithm,…
We introduce a method for non-uniform random number generation based on sampling a physical process in a controlled environment. We demonstrate one proof-of-concept implementation of the method that reduces the error of Monte Carlo…
Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard…
Fabrication process variations are a major source of yield degradation in the nano-scale design of integrated circuits (IC), microelectromechanical systems (MEMS) and photonic circuits. Stochastic spectral methods are a promising technique…
We propose a new effective cluster algorithm of tuning the critical point automatically, which is an extended version of Swendsen-Wang algorithm. We change the probability of connecting spins of the same type, $p = 1 - e^{- J/ k_BT}$, in…
Semi-supervision in Machine Learning can be used in searches for new physics where the signal plus background regions are not labelled. This strongly reduces model dependency in the search for signals Beyond the Standard Model. This…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
In variable or graph selection problems, finding a right-sized model or controlling the number of false positives is notoriously difficult. Recently, a meta-algorithm called Stability Selection was proposed that can provide reliable…
We study the ability of Transformer models to learn sequences generated by Permuted Congruential Generators (PCGs), a widely used family of pseudo-random number generators (PRNGs). PCGs introduce substantial additional difficulty over…
Standard formulations of GANs, where a continuous function deforms a connected latent space, have been shown to be misspecified when fitting different classes of images. In particular, the generator will necessarily sample some low-quality…
Systematic error, which is not determined by chance, often refers to the inaccuracy (involving either the observation or measurement process) inherent to a system. In this paper, we exhibit some long-neglected but frequent-happening…
We report on a particular example of noise and data representation interacting to introduce systematic error. Many instruments collect integer digitized values and appy nonlinear coding, in particular square-root coding, to compress the…