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A combined variational and diagrammatic quantum Monte Carlo approach to the many-electron problem.

ABSTRACT: Two of the most influential ideas developed by Richard Feynman are the Feynman diagram technique and his variational approach. Here we show that combining both, and introducing a diagrammatic quantum Monte Carlo method, results in a powerful and accurate solver to the generic solid state problem, in which a macroscopic number of electrons interact by the long range Coulomb repulsion. We apply it to the quintessential problem of solid state, the uniform electron gas, which is at the heart of the density functional theory success in describing real materials, yet it has not been adequately solved for over 90 years. Our method allows us to calculate numerically exact momentum and frequency resolved spin and charge response functions. This method can be applied to a number of moderately interacting electron systems, including models of realistic metallic and semiconducting solids.

SUBMITTER: Chen K

PROVIDER: S-EPMC6700185 | biostudies-literature | 2019 Aug

REPOSITORIES: biostudies-literature

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A combined variational and diagrammatic quantum Monte Carlo approach to the many-electron problem.

Chen Kun K Haule Kristjan K

Nature communications 20190819 1

Two of the most influential ideas developed by Richard Feynman are the Feynman diagram technique and his variational approach. Here we show that combining both, and introducing a diagrammatic quantum Monte Carlo method, results in a powerful and accurate solver to the generic solid state problem, in which a macroscopic number of electrons interact by the long range Coulomb repulsion. We apply it to the quintessential problem of solid state, the uniform electron gas, which is at the heart of the ...[more]

PMID: 31427574

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Project description:High-throughput gene expression data are often obtained from pure or complex (heterogeneous) biological samples. In the latter case, data obtained are a mixture of different cell types and the heterogeneity imposes some difficulties in the analysis of such data. In order to make conclusions on gene expresssion data obtained from heterogeneous samples, methods such as microdissection and flow cytometry have been employed to physically separate the constituting cell types. However, these manual approaches are time consuming when measuring the responses of multiple cell types simultaneously. In addition, exposed samples, on many occasions, end up being contaminated with external perturbations and this may result in an altered yield of molecular content. In this paper, we model the heterogeneous gene expression data using a Bayesian framework, treating the cell type proportions and the cell-type specific expressions as the parameters of the model. Specifically, we present a novel sequential Monte Carlo (SMC) sampler for estimating the model parameters by approximating their posterior distributions with a set of weighted samples. The SMC framework is a robust and efficient approach where we construct a sequence of artificial target (posterior) distributions on spaces of increasing dimensions which admit the distributions of interest as marginals. The proposed algorithm is evaluated on simulated datasets and publicly available real datasets, including Affymetrix oligonucleotide arrays and national center for biotechnology information (NCBI) gene expression omnibus (GEO), with varying number of cell types. The results obtained on all datasets show a superior performance with an improved accuracy in the estimation of cell type proportions and the cell-type specific expressions, and in addition, more accurate identification of differentially expressed genes when compared to other widely known methods for blind decomposition of heterogeneous gene expression data such as Dsection and the nonnegative matrix factorization (NMF) algorithms. MATLAB implementation of the proposed SMC algorithm is available to download at https://github.com/moyanre/smcgenedeconv.git.

Dataset Information

A combined variational and diagrammatic quantum Monte Carlo approach to the many-electron problem.

Publications

A combined variational and diagrammatic quantum Monte Carlo approach to the many-electron problem.

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