Density matrix based time-dependent density functional theory and the solution of its linear response in real time domain

A density matrix based time-dependent density functional theory is extended in the present work. Chebyshev expansion is introduced to propagate the linear response of the reduced single-electron density matrix upon the application of a time-domain δ -type external potential. The Chebyshev expansion method is more efficient and accurate than the previous fourth-order Runge-Kutta method and removes a numerical divergence problem. The discrete Fourier transformation and filter diagonalization of the first-order dipole moment are implemented to determine the excited state energies. It is found that the filter diagonalization leads to highly accurate values for the excited state energies. Finally, the density matrix based time-dependent density functional is generalized to calculate the energies of singlet-triplet excitations. © 2007 American Institute of Physics.published_or_final_versio

Robust Distributed Fusion with Labeled Random Finite Sets

This paper considers the problem of the distributed fusion of multi-object posteriors in the labeled random finite set filtering framework, using Generalized Covariance Intersection (GCI) method. Our analysis shows that GCI fusion with labeled multi-object densities strongly relies on label consistencies between local multi-object posteriors at different sensor nodes, and hence suffers from a severe performance degradation when perfect label consistencies are violated. Moreover, we mathematically analyze this phenomenon from the perspective of Principle of Minimum Discrimination Information and the so called yes-object probability. Inspired by the analysis, we propose a novel and general solution for the distributed fusion with labeled multi-object densities that is robust to label inconsistencies between sensors. Specifically, the labeled multi-object posteriors are firstly marginalized to their unlabeled posteriors which are then fused using GCI method. We also introduce a principled method to construct the labeled fused density and produce tracks formally. Based on the developed theoretical framework, we present tractable algorithms for the family of generalized labeled multi-Bernoulli (GLMB) filters including $\delta$-GLMB, marginalized $\delta$-GLMB and labeled multi-Bernoulli filters. The robustness and efficiency of the proposed distributed fusion algorithm are demonstrated in challenging tracking scenarios via numerical experiments.Comment: 17pages, 23 figure

Perturbative Analysis of Adaptive Smoothing Methods in Quantifying Large-Scale Structure

Smoothing operation to make continuous density field from observed point-like distribution of galaxies is crucially important for topological or morphological analysis of the large-scale structure, such as, the genus statistics or the area statistics (equivalently the level crossing statistics). It has been pointed out that the adaptive smoothing filters are more efficient tools to resolve cosmic structures than the traditional spatially fixed filters. We study weakly nonlinear effects caused by two representative adaptive methods often used in smoothed hydrodynamical particle (SPH) simulations. Using framework of second-order perturbation theory, we calculate the generalized skewness parameters for the adaptive methods in the case of initially power-law fluctuations. Then we apply the multidimensional Edgeworth expansion method and investigate weakly nonlinear evolution of the genus statistics and the area statistics. Isodensity contour surfaces are often parameterized by the volume fraction of the regions above a given density threshold. We also discuss this parameterization method in perturbative manner.Comment: 42 pages including 9 figure, ApJ 537 in pres

Likelihood Analysis of Power Spectra and Generalized Moment Problems

We develop an approach to spectral estimation that has been advocated by Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance extension problem, by Enqvist and Karlsson. The aim is to determine the power spectrum that is consistent with given moments and minimizes the relative entropy between the probability law of the underlying Gaussian stochastic process to that of a prior. The approach is analogous to the framework of earlier work by Byrnes, Georgiou and Lindquist and can also be viewed as a generalization of the classical work by Burg and Jaynes on the maximum entropy method. In the present paper we present a new fast algorithm in the general case (i.e., for general Gaussian priors) and show that for priors with a specific structure the solution can be given in closed form.Comment: 17 pages, 4 figure

Systematic approach to nonlinear filtering associated with aggregation operators. Part 1. SISO-filters

There are various methods to help restore an image from noisy distortions. Each technique has its advantages and disadvantages. Selecting the appropriate method plays a major role in getting the desired image. Noise removal or noise reduction can be done on an image by linear or nonlinear filtering. The more popular linear technique is based on average (on mean) linear operators. Denoising via linear filters normally does not perform satisfactorily since both noise and edges contain high frequencies. Therefore, any practical denoising model has to be nonlinear. In this work, we introduce and analyze a new class of nonlinear SISO-filters that have their roots in aggregation operator theory. We show that a large body of non-linear filters proposed to date constitute a proper subset of aggregation filters. (C) 2017 The Authors. Published by Elsevier Ltd.This work was supported by grants the RFBR No. 17-07-00886 and by Ural State Forest Engineering's Center of Excellence in "Quantum and Classical Information Technologies for Remote Sensing Systems"