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This is a review of recent developments in Monte Carlo methods in the field of ultra cold gases. For bosonic atoms in an optical lattice we discuss path integral Monte Carlo simulations with worm updates and show the excellent agreement…
In this paper we explore ways of numerically computing recursive dynamic monetary risk measures and utility functions. Computationally, this problem suffers from the curse of dimensionality and nested simulations are unfeasible if there are…
It is known that computing the permanent of the matrix $1+A$, where $A$ is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I…
The least-mean-squares (LMS) algorithm is the most popular algorithm in adaptive filtering. Several variable step-size strategies have been suggested to improve the performance of the LMS algorithm. These strategies enhance the performance…
Monte Carlo (MC) simulations of many systems, in particular those with conflicting constraints, can be considerably speeded up by using multicanonical or related methods. Some of these approaches sample with a-priori unknown weight factors.…
The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the…
We describe a regression-based method, generally referred to as the Least Squares Monte Carlo (LSMC) method, to speed up exposure calculations of a portfolio. We assume that the portfolio contains several exotic derivatives that are priced…
Efficient simulation of quantum computers is essential for the development and validation of near-term quantum devices and the research on quantum algorithms. Up to date, two main approaches to simulation were in use, based on either full…
The problem of assessing the performance of algorithms used for the minimization of an $\ell_1$-penalized least-squares functional, for a range of penalty parameters, is investigated. A criterion that uses the idea of `approximation…
Binary optimisation tasks are ubiquitous in areas ranging from logistics to cryptography. The exponential complexity of such problems means that the performance of traditional computational methods decreases rapidly with increasing problem…
A broad spectrum of physical systems in condensed-matter and high-energy physics, vibrational spectroscopy, and circuit and cavity QED necessitates the incorporation of bosonic degrees of freedom, such as phonons, photons, and gluons, into…
The partial least squares algorithm for dependent data realisations is considered. Consequences of ignoring the dependence for the algorithm performance are studied both theoretically and in simulations. It is shown that ignoring certain…
Continuous-time determinantal algorithm is proposed for the quantum Monte Carlo simulation of the interacting fermions. The scheme does not invoke Hubbard-Stratonovich transformation. The fermionic action is divided into two parts. One of…
We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and,…
Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
In this chapter we present the sums of Hermitian squares approach to noncommutative polynomial optimization problems. This is an extension of the sums of squares approach for polynomial optimization arising from real algebraic geometry. We…
The total least squares~(TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the…
This chapter [of a supplement to Prog. Theo. Phys.] reviews numerical simulations of quantum field theories based on stochastic quantization and the Langevin equation. The topics discussed include renormalization of finite step-size…
Quantum Monte-Carlo (QMC) simulations involving fermions have the notorious sign problem. Some well-known exceptions of the auxiliary field QMC algorithm rely on the factorizibility of the fermion determinant. Recently, a fermionic QMC…