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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…
Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange (Forex) market time series. Fluctuations of high frequency exchange rates of eight major world currencies over 2010-2018 period are used to…
We present a scaling theory for the effect of thermal fluctuations on the characteristics of the depinning transition, and also in the closely related directed percolation model. Thermal effects act as a sort of external field that produces…
On the basis of the dynamical interpretation of Monte Carlo simulations, we discuss the relation of the equilibrium relaxation time, the susceptibility and the statistical error. We introduce a new quantity called {\it the statistical…
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the…
An average instantaneous cross-correlation function is introduced to quantify the interaction of the financial market of a specific time. Based on the daily data of the American and Chinese stock markets, memory effect of the average…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an…
Approximate expressions for correlation functions in binary inhomogeneous mixtures are derived in a framework of the mesoscopic theory [Ciach A., Mol. Phys., 2011, {\textbf{109}}, 1101]. Fluctuation contribution is taken into account in a…
In principle, the probability of configurations, determined by the system's partition function or wave function, encapsulates essential information about phases and phase transitions. Despite the exponentially large configuration space, we…
Data-collapse is a way of establishing scaling and extracting associated exponents in problems showing self-similar or self-affine characteristics as e.g. in equilibrium or non-equilibrium phase transitions, in critical phases, in dynamics…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…
The thresholding of time series of activity or intensity is frequently used to define and differentiate events. This is either implicit, for example due to resolution limits, or explicit, in order to filter certain small scale physics from…
The cross correlation matrix between equities comprises multiple interactions between traders with varying strategies and time horizons. In this paper, we use the Maximum Overlap Discrete Wavelet Transform to calculate correlation matrices…
In order to emphasize cross-correlations for fluctuations in major market places, series of up and down spins are built from financial data. Patterns frequencies are measured, and statistical tests performed. Strong cross-correlations are…
Commonalities and differences in correlation analysis in terms of phase space, conditioning and uncorrelatedness are discussed. The Poisson process is not generally appropriate as reference distribution for normalisation and cumulants, so…
Most data processing techniques, applied to biomedical and sociological time series, are only valid for random fluctuations that are stationary in time. Unfortunately, these data are often non stationary and the use of techniques of…
We use quantum Monte-Carlo simulations to calculate the phase diagram and the correlation functions for the quantum phase transitions in the two-dimensional dissipative XY model with and without four-fold anisotropy. Without anisotropy, the…
We study a statistical mechanics model of two species of bosons with mutual statistics $\theta=2\pi/n$ in (2+1) dimensions. This model realizes a fractionalized topological phase of bosons, which is a fractionalized version of the boson…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
We present an extension of the so-called cumulant crossing method which is used for determination of critical point in Monte Carlo simulations.The new method uses linear combination of several different order-parameter moments and almost…