The problem of finding a low dimensional structure amongst inputs that have been sampled from high dimensional manifold is known as dimensionality reduction. When viewed from a machine learning perspective, it can be directly compared with feature selection. Another way of looking at dimensionality reduction is as a preprocessing mechanism wherein, the data of high dimensionality can be process...

Abstract Simulating quantum systems is believed to be one of the first applications for which computers may demonstrate a useful advantage. For many problems in physics, we are interested studying evolution electron–phonon Hamiltonian, efficient digital computing schemes exist. Yet date, no accurate simulation this system has been produced on real hardware. In work, consider absolute resource c...

Abstract We consider a velocity field with linear viscous interactions defined on one dimensional lattice. Brownian baths different parameters can be coupled to the boundary sites and bulk sites, determining kinds of non-equilibrium steady states or free-cooling dynamics. Analytical results for spatial temporal correlations are provided by analytical diagonalisation system’s equations in infini...

We show that the recently observed class of long-range ion-Rydberg molecules can be divided into two families states, which are characterised by their unique electronic structures resulting from ion-induced admixture quantum defect-split Rydberg $n$P states with different low-field seeking high-$l$ states. predict in both cases these diatomic molecular bind additional ground state atoms lying w...

This article aims <span lang="EN-US">to estimate the load profiling of electricity that provides information on electrical demand. In achieving this research implemented neural network algorithm joint approximate diagonalisation eigen-matrices (JADE) to describe profile pattern for each point. Nowadays, utility providers claim natural sources are used generate power by rising consumer dem...

Abstract With the increase in volume of climate model simulations for past, present and future climate, from various institutions across globe, there is a need efficient robust methods comparison and/or evaluation. This manuscript discusses common empirical orthogonal function analysis with step-wise algorithm, which can be used above objective. The method looks simultaneous diagonalisation sev...

We put the Density-of-States (DoS) approach to Monte-Carlo (MC) simulations under a stress test by applying it physical problem with worst possible sign problem: real time evolution of non-integrable quantum spin chain. Benchmarks against numerical exact diagonalisation and stochastic reweighting are presented. Both MC methods, DoS reweighting, allow for chains as long $L=40$, far beyond diagon...