Related papers: On the Random Batch Method for second order intera…
We analyze and discuss convergence properties of a numerically exact algorithm tailored to study the dynamics of interacting two-dimensional lattice systems. The method is based on the application of the time-dependent variational principle…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
This overview paper describes the particle methods developed for the implementation of the a class of Bayes filters formulated using the random finite set formalism. It is primarily intended for the readership already familiar with the…
Randomized measurements are useful for analyzing quantum systems especially when quantum control is not fully perfect. However, their practical realization typically requires multiple rotations in the complex space due to the adoption of…
The need for strategies able to accurately manipulate quantum dynamics is ubiquitous in quantum control and quantum information processing. We investigate two scenarios where randomized dynamical decoupling techniques become more…
We devise a functional renormalization group treatment for a chain of interacting spinless fermions which is correct up to second order in the interaction strength. We treat both inhomogeneous systems in real-space as well as the…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not…
Consider a swarm of particles controlled by global inputs. This paper presents algorithms for shaping such swarms in 2D using boundary walls. The range of configurations created by conforming a swarm to a boundary wall is limited. We…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…
We review recently introduced numerical methods for the unbiased detection of the order parameter and/or dominant correlations, in many-body interacting systems, by using reduced density matrices. Most of the paper is devoted to the…
This paper proposes a framework of L-BFGS based on the (approximate) second-order information with stochastic batches, as a novel approach to the finite-sum minimization problems. Different from the classical L-BFGS where stochastic batches…
With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…
In many applications, data is collected in batches, some of which are corrupt or even adversarial. Recent work derived optimal robust algorithms for estimating discrete distributions in this setting. We consider a general framework of…
Irreversible random sequential deposition of interacting particles is widely used to model aggregation phenomena in physical, chemical, and biophysical systems. We show that in one dimension the exact time dependent solution of such…
We present an efficient finite difference method for the approximation of second derivatives, with respect to system parameters, of expectations for a class of discrete stochastic chemical reaction networks. The method uses a coupling of…
Similarities between models of fragmenting nuclei and disordered systems in condensed matter suggest corresponding methods. Several theoretical models of fragmentation investigated in this fashion show marked differences, indicating…
This article is an introductory review of random matrix theory (RMT) and its applications, with special focus on quantum chaos. Random matrices were first used by Wigner to understand the spectra of complex nuclei from a statistical…
We set up Restricted Boltzmann Machines (RBM) to reproduce the Long Range Ising (LRI) models of the Ohmic type in one dimension. The RBM parameters are tuned by using the standard machine learning procedure with an additional method of…