Related papers: A Short Research Note on Calculating Exact Distrib…
We study the differential energy distribution of dark matter halos, carrying out cosmological N-body simulation.We give an analytical formula of the differential energy distribution of dark matter in the halos obtained by the numerical…
In order to study their interplay with large scale cosmic evolution and with relativistic effects, such as gravitational lenses, quintessence sources or gravitational waves, we construct a post-Newtonian fluid framework for the…
The one-point probability distribution function (PDF) is a powerful summary statistic for non-Gaussian cosmological fields, such as the weak lensing (WL) convergence reconstructed from galaxy shapes or cosmic microwave background (CMB)…
We introduce analytical expressions for a pseudo fully analytical elliptical projected Navarro, Frenk & White (NFW) mass profile to be used in lensing equations. We propose a formalism that incorporates the ellipticity into the expression…
We propose a new method for generating equilibrium models of spherical systems of collisionless particles that are finite in extent, but whose central regions resemble dark matter halos from cosmological simulations. This method involves…
An analytic galaxy model with $\rho \sim r^{-1}$ at small radii and $\rho \sim r^{-3.5}$ at large radii is presented. The asymptotic density fall-off is slower than the Hernquist model, but faster than the Navarro-Frenk-White (NFW) profile…
The density profile and the clustering of dark matter (DM) halos are two very important ingredients for understanding many observations of galaxies. In this talk, I present our new results for these two quantities from a large set of high…
The profile of Navarro, Frenk, and White (the NFW profile), which was derived from the {\it N}-body simulations of cold dark-matter halos, is a strong candidate for a galaxy or cluster profile. In order to check the usability of the NFW…
We consider the problem of finding the minimizer of a convex function $F: \mathbb R^d \rightarrow \mathbb R$ of the form $F(w) := \sum_{i=1}^n f_i(w) + R(w)$ where a low-rank factorization of $\nabla^2 f_i(w)$ is readily available. We…
More precise measurements of galaxy clustering will be provided by the next generation of galaxy surveys such as DESI, WALLABY and SKA. To utilize this information to improve our understanding of the Universe, we need to accurately model…
We study the diversity of the density profiles of dark matter halos based on a large set of high-resolution cosmological simulations of 256^3 particles. The cosmological models include four scale-free models and three representative cold…
In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields…
Since being proposed, Neural Radiance Fields (NeRF) have achieved great success in related tasks, mainly adopting the hierarchical volume sampling (HVS) strategy for volume rendering. However, the HVS of NeRF approximates distributions…
Given a CNF formula and a weight for each assignment of values to variables, two natural problems are weighted model counting and distribution-aware sampling of satisfying assignments. Both problems have a wide variety of important…
Distribution functions (DFs) for dynamically warm thin stellar disks residing in arbitrary axisymmetric potentials are presented which approximately reproduce pre-described surface-density and velocity-dispersion profiles. The functional…
We introduce a new type of Wannier functions (WFs) obtained by minimizing the conventional spread functional with a penalty term proportional to the variance of the spread distribution. This modified Wannierisation scheme is less prone to…
We study the statistical complexity of estimating partition functions given sample access to a proposal distribution and an unnormalized density ratio for a target distribution. While partition function estimation is a classical problem,…
The statistical characterization of the sum of random variables (RVs) are useful for investigating the performance of wireless communication systems. We derive exact closed-form expressions for the probability density function (PDF) and…
The use of summary statistics beyond the two-point correlation function to analyze the non-Gaussian clustering on small scales is an active field of research in cosmology. In this paper, we explore a set of new summary statistics -- the…
The cumulative distribution and quantile functions for the one-sided one sample Kolmogorov-Smirnov probability distributions are used for goodness-of-fit testing. While the Smirnov-Birnbaum-Tingey formula for the CDF appears straight…