Related papers: Hyper-sparsity of the density matrix in a wavelet …
Boostlets are spatiotemporal functions that decompose nondispersive wavefields into a collection of localized waveforms parametrized by dilations, hyperbolic rotations, and translations. We study the sparsity properties of boostlets and…
We use deep sparsely connected neural networks to measure the complexity of a function class in $L^2(\mathbb R^d)$ by restricting connectivity and memory requirement for storing the neural networks. We also introduce representation system -…
We consider quantum light-matter interfaces comprised of multiple layers of two-dimensional atomic arrays, whose lattice spacings exceed the wavelength of light. While the coupling of light to a single layer of such a ``superwavelength"…
The rapid development of quantum computers has enabled demonstrations of quantum advantages on various tasks. However, real quantum systems are always dissipative due to their inevitable interaction with the environment, and the resulting…
We clarify the meaning of spatial densities of hadrons. A physical density is given by the expectation value of a local operator for a physical state, and depends on both internal structure and the hadron's wave packet. In some particular…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
We study the imprint of Dark Energy on the density profile of Dark Matter halos using a set of high-resolution large volume cosmological N-body simulations from the Dark Energy Universe Simulation Series (DEUSS). We first focus on the…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
Due to considerable recent interest in the use of density matrices for a wide variety of purposes, including quantum computation, we present a general method for their parameterizations in terms of Euler angles. We assert that this is of…
Predicting the optical response of macroscopic arrangements of individual scatterers is a computational challenge, as the problem involves length scales across multiple orders of magnitude. We present a full-wave optical method to highly…
A new scheme for the computation of dispersive interactions from first principles is presented. This cost-effective approach relies on a Wannier function representation compatible with density function theory descriptions. This is an…
We study the properties of a non-Gaussian density matrix for a O(N) scalar field in the context of the incomplete description picture. This is of relevance for studies of decoherence and entropy production in quantum field theory. In…
We consider signals and operators in finite dimension which have sparse time-frequency representations. As main result we show that an $S$-sparse Gabor representation in $\mathbb{C}^n$ with respect to a random unimodular window can be…
Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected…
This is the first of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The non-zero entries in the output are chosen to…
The density profiles of dark matter halos are typically modeled using empirical formulae fitted to the density profiles of relaxed halo populations. We present a neural network model that is trained to learn the mapping from the raw density…
Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual…
Deep neural networks (NNs) are known to lack uncertainty estimates and struggle to incorporate new data. We present a method that mitigates these issues by converting NNs from weight space to function space, via a dual parameterization.…
We introduce an analytical iterative method, the density matrix recursion method, to generate arbitrary reduced density matrices of superpositions of short-range dimer coverings on periodic or non-periodic quantum spin-1/2 ladder lattices,…
We propose a simple scheme to estimate potential energy surface (PES) with which the accuracy can be easily controlled and improved up to the level of the density functional theory (DFT) calculations. It is based on a model selection within…