Related papers: Benchmark computations for the polarization tensor…
In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…
For the coherently driven \Lambda-type three-level systems the general ready-to-calculate expression for the susceptibility tensor at the frequency of the weak probe field is obtained for the arbitrary polarization of the strong coupling…
Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of…
Effective non-parametric density estimation is a key challenge in high-dimensional multivariate data analysis. In this paper,we propose a novel approach that builds upon tensor factorization tools. Any multivariate density can be…
In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…
We consider the problem of identifying multiway block structure from a large noisy tensor. Such problems arise frequently in applications such as genomics, recommendation system, topic modeling, and sensor network localization. We propose a…
Change detection process has recently progressed from a post-classification method to an expert knowledge interpretation process of the time-series data. The technique finds applications mainly in remote sensing images and can be utilized…
We study the problem of sparse tensor principal component analysis: given a tensor $\pmb Y = \pmb W + \lambda x^{\otimes p}$ with $\pmb W \in \otimes^p\mathbb{R}^n$ having i.i.d. Gaussian entries, the goal is to recover the $k$-sparse unit…
It has recently been observed that certain extremely simple feature encoding techniques are able to achieve state of the art performance on several standard image classification benchmarks including deep belief networks, convolutional nets,…
An optical waveplate rotating light polarization can be modeled as a single-qubit unitary operator, whose action can be experimentally determined via quantum process tomography. Standard approaches to tomographic problems rely on the…
The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least…
Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…
We develop the tensor renormalization group (TRG) algorithm for statistical systems with open boundaries, which allows us to investigate not only the bulk but also the boundary property, such as the surface magnetization. We demonstrate…
We propose a block coordinate descent type algorithm for estimating the rank of a given tensor. In addition, the algorithm provides the canonical polyadic decomposition of a tensor. In order to estimate the tensor rank we use sparse…
In this paper, we propose a general algorithmic framework to solve a class of optimization problems on the product of complex Stiefel manifolds based on the matrix polar decomposition. We establish the weak convergence, global convergence…
This report aims at establishing a theoretical framework for dealing with the reconstruction problem of a small acoustic inclusion. The objective is to introduce the new concept of time-dependent polarization tensors for the Helmholtz…
Polarized neutrons are a powerful probe to investigate magnetism in condensed matter on length scales from single atomic distances to micrometers. With the ongoing advancement of neutron optics, that allow to transport beams with increased…
This publication presents an investigation of the performance of different analytical electron ptychography methods for low-dose imaging. In particular, benchmarking is performed for two model-objects, monolayer MoS$_2$ and apoferritin, by…
Polarized neutron reflectometry is a powerful technique to interrogate the structures of multilayered magnetic materials with depth sensitivity and nanometer resolution. However, reflectometry profiles often inhabit a complicated objective…
The contribution of gravitational wave (tensor metric) and energy density (scalar metric) fluctuations to the cosmic microwave background polarization is computed by numerically solving the relativistic radiation transfer equations. We find…