Related papers: Hamiltonian Reconstruction: the Correlation Matrix…
The correlation spectrum of fully developed one-dimensional mappings are studied near and at a weakly intermittent situation. Using a suitable infinite matrix representation, the eigenvalue equation of the Frobenius-Perron operator is…
A model subspace configuration interaction method is developed to obtain chemically accurate electron correlations by diagonalising a very compact effective Hamiltonian of realistic molecule. The construction of the effective Hamiltonian is…
A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…
We apply a data assimilation techniques, inspired from meteorological applications, to perform an optimal reconstruction of the neutronic activity field in a nuclear core. Both measurements, and information coming from a numerical model,…
Low rank model arises from a wide range of applications, including machine learning, signal processing, computer algebra, computer vision, and imaging science. Low rank matrix recovery is about reconstructing a low rank matrix from…
Hamiltonian Mechanics works for conserved systems and Quantum Mechanics is given in Hamiltonian language. It is considered that complexifying the quantum Hamiltonian, a balanced loss and gain model can be created. The usual mathematics of…
Based on the matrix realignment and partial transpose, we develop an approach to entangling power and operator entanglement of quantum unitary operators. We demonstrate efficiency of the approach by studying several unitary operators on…
Matrix completion, i.e., the exact and provable recovery of a low-rank matrix from a small subset of its elements, is currently only known to be possible if the matrix satisfies a restrictive structural constraint---known as {\em…
In this paper we introduce a Hilbert series approach to build the operator basis for a N = 1 supersymmetry theory with chiral superfields. We give explicitly the form of the corrections that remove redundancies due to the equations of…
In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…
In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…
In this paper, we study matrix representations of truncated Toeplitz operators with respect to orthonormal bases which are invariant under a canonical conjugation map. In particular, we determine necessary and sufficient conditions for when…
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…
One important property of imaging modalities and related applications is the resolution of image reconstructions which relies on various factors such as instrumentation or data processing. Restrictions in resolution can have manifold…
Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generality, we discuss the reduction of a Hamilton-Jacobi theory for…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
Machine learning often needs to model density from a multidimensional data sample, including correlations between coordinates. Additionally, we often have missing data case: that data points can miss values for some of coordinates. This…
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…