Related papers: Information structure and general characterization…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
Numerical computations involving rational matrices often benefit from preserving underlying matrix structures such as symmetry, Hermitian properties, or sparsity that reflect physical, geometric, or algebraic characteristics of the system.…
Imaging Mueller polarimetry has already proved its potential for metrology, remote sensing and biomedicine. The real-time applications of this modality require both video rate image acquisition and fast data post-processing algorithms.…
We revisit the classification of polarization observables of the cosmic microwave background. There exists a unified approach to the $3 \times 3$ density matrix by which intensity, linear and circular polarization are treated on an equal…
Polarization is one of the basic properties of electromagnetic waves conveying valuable information in signal transmission and sensitive measurements. Conventional methods for advanced polarization control impose demanding requirements on…
This is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…
When we speak about parametric programming, sensitivity analysis, or related topics, we usually mean the problem of studying specified perturbations of the data such that for a given optimization problem some optimality criterion remains…
While optics and mechanics are two distinct branches of physics, they are connected. It is well known that geometrical/ray treatment of light has direct analogies to mechanical descriptions of particle motion. However, connections between…
The formalism is developed for a tree-dimensional ($3D$) nonlinear Stokes-Mueller polarimetry. The expressions are derived for the generalized $3D$ linear and nonlinear Stokes vectors, and the corresponding nonlinear Mueller matrix. The…
When polarized light is absorbed by an atom, the excited atomic system carries information about the initial polarization of light. For the light that carries an orbital angular momentum, or the twisted light, the polarization states are…
We give a probabilistic characterization of the set of measures that can be represented by the matrix product ansatz. By suitably enlarging the state space, we show that a probability measure can be described in terms of non negative…
Polarization is well known for its ability to decompose diffuse and specular reflections. However, the existing decomposition methods only focus on direct reflection and overlook multiple reflections, especially specular inter-reflection.…
We give a complete structural characterisation of the map the positive branch of a one-way pattern implements. We start with the representation of the positive branch in terms of the phase map decomposition, which is then further analysed…
Microwave background polarization, though presently undetected, is a fundamental prediction of any viable cosmological model. These lectures review the theoretical description of polarization, its physical interpretation, and potentially…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
Three quantitative measures of the spatiotemporal behavior of the coupled map lattices: reduced density matrix, reduced wave function, and an analog of particle number, have been introduced. They provide a quantitative meaning to the…
To discuss one-photon polarization states we find an explicit form of the Wigner's little group element in the massless case for arbitrary Lorentz transformation. As is well known, when analyzing the transformation properties of the…
We discuss the notion of linearization through examples, which include the Price map, PageRank, representation theory, the Euler characteristic and quantum invariants. We also review categorification, which adds an additional layer of…
Correlations disguised in various forms underlie a host of important phenomena in classical and quantum systems, such as information and energy exchanges. The quantum mutual information and the norm of the correlation matrix are both…
We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearisation. The main difference with respect to the previous studies…