Related papers: Information structure and general characterization…
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
We show that there is an isometry between the real ambient space of all Mueller matrices and the space of all Hermitian matrices which maps the Mueller matrices onto the positive semidefinite matrices. We use this to establish an optimality…
Linearly polarized emission is described, in general, in terms of the Stokes parameters $Q$ and $U$, from which the polarization intensity and polarization angle can be determined. Although the polarization intensity and polarization angle…
For $\pi^0\eta$-photoproduction on the nucleon formal expressions are developed for the five-fold differential cross section and the recoil polarization including beam and target polarizations. The polarization observables are described by…
In the mass-polariton (MP) theory of light formulated by us recently [Phys. Rev. A 95, 063850 (2017)], light in a medium is described as a coupled state of the field and matter. The key result of the MP theory is that the optical force of…
We introduce a uniform representation of general objects that captures the regularities with respect to their structure. It allows a representation of a general class of objects including geometric patterns and images in a sparse, modular,…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
Quantum Mechanics of the Early Universe is considered as deformation of a well-known Quantum Mechanics. Similar to previous works of the author, the principal approach is based on deformation of the density matrix with concurrent…
Starting from a model of nonlinear magnetoelasticity where magnetization is defined in the Eulerian configuration while elastic deformation is in the Lagrangean one, we rigorously derive a linearized model that coincides with the standard…
One introduces the notion of C*-algebra with polarization which could be considered as the quantum Kahler structure. The connection of these algebras with Kostant-Souriou geometric quantization is shown. The theory of polarized C*-algebra…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
The nonlinear oscillator model allows a basic understanding of all nonlinear processes and can be adopted to analyse optical vibrational modes and electronic transition in molecules and crystals, in order to derive general properties of…
Polarization observations yield otherwise unobtainable information about the geometrical structure of unresolved objects. In this talk we review the evidences for non-spherically symmetric structures around Luminous Hot Stars from…
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation…
The physical properties of matter are typically described by coefficient matrices governed by crystal symmetry. Applying spatial operations, such as rotation, inversion, and mirror, to these matrices provides an effective approach for…
We develop a nonperturbative approach to the bulk polarization of crystalline electric insulators in $d\geq1$ dimensions. Formally, we define polarization via the response to background fluxes of both charge and lattice translation…
This paper collects some characteristic aspects of the general model-building framework of the mechanics of complex bodies, that are bodies in which the material substructure influences prominently the gross behavior through interactions…