Related papers: Gaussian dynamics equation in normal product form
Though Gaussian graphical models have been widely used in many scientific fields, relatively limited progress has been made to link graph structures to external covariates. We propose a Gaussian graphical regression model, which regresses…
The time dependence of deviations from the Gaussian state in a freely cooling homogeneous system of smooth inelastically colliding spheres is investigated by kinetic theory. We determine the full time dependence of the coefficients of an…
In this work, we propose a novel generative model for mapping inputs to structured, high-dimensional outputs using structured conditional normalizing flows and Gaussian process regression. The model is motivated by the need to characterize…
The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude…
The Lindblad (GKLS) master equation, which represents the mathematical form for the general evolution of a density matrix, is a versatile and widely-used tool in open quantum systems. In contrast with the typical approach of imposing…
Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…
We show that the eigenvalue density of a product X=X_1 X_2 ... X_M of M independent NxN Gaussian random matrices in the large-N limit is rotationally symmetric in the complex plane and is given by a simple expression rho(z,\bar{z}) =…
The transient dynamics of quantum coherence of Gaussian states are investigated. The state is coupled to an external environment which can be described by a Fano-Anderson type Hamiltonian. Solving the quantum Langevin equation, we obtain…
We examine the real-time dynamics of a system of one or more black holes interacting with long wavelength gravitational fields. We find that the (classical) renormalizability of the effective field theory that describes this system…
We develop a finite-dimensional formulation of the recently introduced notion of ``timelike entanglement'', defined in terms of two-point functions between operators supported on different Cauchy slices. Using a local orthonormal operator…
A numerical approach to ground-state dynamical correlation functions from Density Matrix Renormalization Group (DMRG) is developed. Using sum rules, moments of a dynamic correlation function can be calculated with DMRG, and with the moments…
We construct a family of random matrix models for the q-deformed Gaussian random variables G_\mu=a_\mu+a^\star_\mu where the annihilation operators a_\mu and creation operators a^\star_\nu fulfil the q-deformed commutation relation a_\mu…
Friction modeling has always been a challenging problem due to the complexity of real physical systems. Although a few state-of-the-art structured data-driven methods show their efficiency in nonlinear system modeling, deterministic…
Starting with the average particle distribution function for bosons and fermions for non-extensive thermodynamics , as proposed in \cite{CMP}, we obtain the corresponding density matrix operators and hamiltonians. In particular, for the…
We propose a strictly local quantum tomography protocol for a bipartite system. We show that the joint density matrix of an arbitrary two-mode Gaussian state, entangled or not, is obtained via local operations and classical communication…
We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research communities surrounding the two concepts often pursue…
We propose an energy-driven stochastic master equation for the density matrix as a dynamical model for quantum state reduction. In contrast, most previous studies of state reduction have considered stochastic extensions of the Schr\"odinger…
Let $\bf{x}$ be a random variable with density $\rho(x)$ taking values in ${\mathbb R}^d$. We are interested in finding a representation for the shape of $\rho(x)$, i.e. for the orbit $\{ \rho(g\cdot x) | g\in E(d) \}$ of $\rho$ under the…
This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…