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We present algorithms to work with iterated Eisenstein integrals that have recently appeared in the computation of multi-loop Feynman integrals. These algorithms allow one to analytically continue these integrals to all regions of the…
The partition function of the 2D Ising model coupled to an external magnetic field is studied. We show that the sum over the spin variables can be reduced to an integration over a finite number of variables. This integration must be…
Exchange symmetry in acceleration partitions the configuration space of an N particle, one-dimensional, gravitational system into N! equivalent cells. We take advantage of the resulting small angular extent of each cell to construct a…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature/energy range around the critical point. By combining the replica-exchange algorithm with cluster updates…
Analog quantum computing with Rydberg atoms is seen as an avenue to solve hard graph optimization problems, because they naturally encode the Maximum Independent Set (MIS) problem on Unit-Disk (UD) graphs, a problem that admits rather…
In this article, we present an improved version of the PULSE method (Partition function Unsupervised Learning Sampling and Evaluation) for estimating the thermodynamic properties of chemically disordered compounds. The aim is to reduce the…
We present a surprisingly simple approach to high-accuracy calculations of critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in…
We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…
Value Iteration is a widely used algorithm for solving Markov Decision Processes (MDPs). While previous studies have extensively analyzed its convergence properties, they primarily focus on convergence with respect to the infinity norm. In…
First of all, this paper presents some improvements of DSMC method in the form of new schemes and approaches, that, for a wide class of problems, increase performance and reduce the demands on computer resources. The most important…
Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function. We propose a new parameter fitting method, Minimum Probability Flow (MPF), which is applicable to any parametric model. We…
We introduce an algorithm to systematically improve the efficiency of parallel tempering Monte Carlo simulations by optimizing the simulated temperature set. Our approach is closely related to a recently introduced adaptive algorithm that…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
Automated Machine Learning encompasses a set of meta-algorithms intended to design and apply machine learning techniques (e.g., model selection, hyperparameter tuning, model assessment, etc.). TPOT, a software for optimizing machine…
The energy splitting $E_{0a}$ in two and four dimensional Ising models is measured in a cylindrical geometry on finite lattices. By comparing to exact results in the two dimensional Ising model we demonstrate that $E_{0a}$ can be extracted…
We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical…
Often in applications such as rare events estimation or optimal control it is required that one calculates the principal eigen-function and eigen-value of a non-negative integral kernel. Except in the finite-dimensional case, usually…
The multi-index matching problem (MIMP) generalizes the well known matching problem by going from pairs to d-uplets. We use the cavity method from statistical physics to analyze its properties when the costs of the d-uplets are random. At…
This paper presents an in-depth analysis of the generalized isotonic recursive partitioning (GIRP) algorithm for fitting isotonic models under separable convex losses, proposed by Luss and Rosset [J. Comput. Graph. Statist., 23 (2014), pp.…
Multiple raters are often needed to be used interchangeably in practice for measurement or evaluation. Assessing agreement among these multiple raters via agreement indices are necessary before their participation. While the intuitively…