Related papers: Local Lagrangian Approximations for the Evolution …
Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…
Recently a mechanism was proposed whereby the primordial density perturbations are generated at the end of inflation. We continue the analysis of the proposed model of this mechanism and calculate the maximum extent to which the density…
We establish the convergence of the densities of a sequence of nonlinear functionals of an underlying Gaussian process to the density of a Gamma distribution. The key idea of our work is a new density formula for random variables in the…
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…
We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz…
We use the IllustrisTNG cosmological hydrodynamical simulation to study the evolution of star formation rate (SFR)-density relation over cosmic time. We construct several samples of galaxies at different redshifts from $z=2.0$ to $z=0.0$,…
We quantitatively study the probability distribution function (PDF) of cosmological nonlinear density fluctuations from N-body simulations with Gaussian initial condition. In particular, we examine the validity and limitations of one-point…
This study leverages the basic insight that the gradient-flow equation associated with the relative Boltzmann entropy, in relation to a Gaussian reference measure within the Hellinger-Kantorovich (HK) geometry, preserves the class of…
We derive the equation of matter density perturbations on sub-horizon scales around a flat Friedmann-Lema\^\i tre-Robertson-Walker background for the general Lagrangian density $f(R,\GB)$ that is a function of a Ricci scalar $R$ and a…
We have reconstructed the three-dimensional density fluctuation maps to z ~ 1.5 using the distribution of galaxies observed in the VVDS-Deep survey. We use this overdensity field to measure the evolution of the probability distribution…
Given a decision process based on the approximate probability density function returned by a data assimilation algorithm, an interaction level between the decision making level and the data assimilation level is designed to incorporate the…
The local galaxy bias formalism relies on the energy constraint equation at the formation time to relate the metric perturbation to the matter density contrast. In the Newtonian approximation, this relationship is linear, which allows us to…
The Jacob's ladder of density functional theory (DFT) proposes the compelling view that by extending the form of successful approximations -- being guided by exact conditions and selected (least empirical) norms -- upper rungs will do…
We use the ellipsoidal collapse approximation to investigate the nonlinear redshift space evolution of the density field with primordial non-Gaussianity of the local f_{nl}-type. We utilize the joint distribution of eigenvalues of the…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the non-linear evolution of…
We present an application of Large Deviation Theory to the problem of structure growth on large-scale structure cosmology. Starting from gaussian distributed overdensities on concentric spherical shells, we show that a Large Deviation…
Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…
We develop a mixture model for transition density approximation, together with soft model selection, in the presence of noisy and heterogeneous nonlinear dynamics. Our model builds on the Gaussian mixture transition distribution (MTD) model…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…