Related papers: Approximation Methods for Non-linear Gravitational…
Electron-positron clusters are studied using a quantum hydrodynamic model that includes Coulomb and exchange interactions. A variational Lagrangian method is used to determine their stationary and dynamical properties. The cluster static…
We present the methodology for deriving accurate and reliable cosmological constraints from non-linear scales (<50Mpc/h) with k-th nearest neighbor (kNN) statistics. We detail our methods for choosing robust minimum scale cuts and…
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic…
Local nonlinear approximations to the growth of cosmic perturbations are developed, resulting in relations, at a given epoch, between the peculiar velocity and gravity fields and their gradients. Only the equation of motion is approximated,…
We develop a theory of nonlinear cosmological perturbations on superhorizon scales where a characteristic length scale of perturbations is longer than the Hubble radius, in general theoretical frameworks. Our formalism is based on the…
We show that the formation of large-scale structures through gravitational instability in the expanding universe can be fully described through a path-integral formalism. We derive the action S[f] which gives the statistical weight…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
In many practical applications of clustering, the objects to be clustered evolve over time, and a clustering result is desired at each time step. In such applications, evolutionary clustering typically outperforms traditional static…
There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the…
I present a general discussion of the evolution and model-dependence of both the linear and nonlinear power spectrum of density fluctuations. The features of the linear power spectrum in cosmological models with cold dark matter (CDM) and…
This paper investigates whether nonlinear gravitational instability can account for the clustering of galaxies on large and small scales, and for the evolution of clustering with epoch. No CDM-like spectrum is consistent with the shape of…
The adhesion model has been proposed in the past as an improvement of the Zel'dovich approximation, providing a good description of the formation of the cosmic web. We recast the model as a field theory for cosmological large scale…
The mass and spin distributions of compact binary gravitational-wave sources are currently uncertain due to complicated astrophysics involved in their formation. Multiple sub-populations of compact binaries representing different…
Using a non-perturbative method developed in a previous work (paper II), we derive the probability distribution $P(\delta_R)$ of the density contrast within spherical cells in the quasi-linear regime for some non-Gaussian initial…
Clustering methods seek to partition data such that elements are more similar to elements in the same cluster than to elements in different clusters. The main challenge in this task is the lack of a unified definition of a cluster,…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
Observations of galaxy clusters (GC's) are a powerful tool to probe the evolution of the Universe at $z<2$. However, the determination of their real shape and structure is not completely understood and the assumption of asphericity is often…
Using an ensemble of high resolution 2D numerical simulations, we explore the scaling properties of cosmological density fluctuations in the non-linear regime. We study the scaling behaviour of the usual $N$--point volume-averaged…
Dynamic model reduction in power systems is necessary for improving computational efficiency. Traditional model reduction using linearized models or online analysis is not adequate to capture dynamic behaviors of the power system,…
This paper deals with nonparametric estimation of conditional den-sities in mixture models in the case when additional covariates are available. The proposed approach consists of performing a prelim-inary clustering algorithm on the…