Related papers: Optimized replica gas estimation of absolute integ…
Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly…
Bose-Einstein condensation has been experimentally found to take place in finite trapped systems when one of the confining frequencies is increased until the gas becomes effectively two-dimensional (2D). We confirm the plausibility of this…
An integral representation of the partition function for general $n$-dimensional Ising models with nearest or non-nearest neighbours interactions is given. The representation is used to derive some properties of the partition function. An…
Fractionation of isotopes among distinct molecules or phases is a quantum effect which is often exploited to obtain insights on reaction mechanisms, biochemical, geochemical and atmospheric phenomena. Accurate evaluation of isotope ratios…
We explore a well-known integral representation of the logarithmic function, and demonstrate its usefulness in obtaining compact, easily-computable exact formulas for quantities that involve expectations and higher moments of the logarithm…
The accurate description of non-ideal quantum many-body systems is of prime importance for a host of applications within physics, quantum chemistry, material science, and related disciplines. At finite temperatures, the gold standard is…
Importance sampling (IS) is a powerful Monte Carlo methodology for the approximation of intractable integrals, very often involving a target probability density function. The performance of IS heavily depends on the appropriate selection of…
We evaluate using programmable superconducting flux qubit D-Wave quantum annealers to approximate the partition function of Ising models. We propose the use of two distinct quantum annealer sampling methods: chains of Monte Carlo-like…
We formulate the optimal flow problem in a multi-area integrated electrical and gas system as a mixed-integer optimization problem by approximating the non-linear gas flows with piece-wise affine functions, thus resulting in a set of…
We present a novel quantum algorithm for estimating Gibbs partition functions in sublinear time with respect to the logarithm of the size of the state space. This is the first speed-up of this type to be obtained over the seminal…
The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition…
We propose a simple estimator that allows to calculate the absolute value of a system's partition function from a finite sampling of its canonical ensemble. The estimator utilizes a volume correction term to compensate the effect that the…
The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo…
Integration by parts identities (IBPs) can be used to express large numbers of apparently different d-dimensional Feynman Integrals in terms of a small subset of so-called master integrals (MIs). Using the IBPs one can moreover show that…
Depth estimation is an essential component in understanding the 3D geometry of a scene, with numerous applications in urban and indoor settings. These scenes are characterized by a prevalence of human made structures, which in most of the…
Estimating a Gibbs density function given a sample is an important problem in computational statistics and statistical learning. Although the well established maximum likelihood method is commonly used, it requires the computation of the…
We design a recursive algorithm to compute the partition function of the Ising model, summed over cubic maps with fixed size and genus. The algorithm runs in polynomial time, which is much faster than methods based on a Tutte-like, or…
We perform calculations of the {3D} finite-temperature homogeneous electron gas (HEG) in the warm-dense regime ({r_{s} \equiv (3/4\pi n)^{1/3}a_{B}^{- 1} = 1.0- 40.0} and {\Theta \equiv T/T_{F} = 0.0625- 8.0}) using restricted path integral…
We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition…
This article presents an Integral Gaussian Process (IntegralGP) framework for volumetric estimation of subterranean properties in mineral deposits. It provides a unified representation for data with different spatial supports, which enables…