Related papers: Constellation Ensembles and Interpolation in Ensem…
A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and lower variance than the individual classifiers that…
We study arrangements of intervals in $\mathbb{R}^2$ for which many pairs form trapezoids. We show that any set of intervals forming many trapezoids must have underlying algebraic structure, which we characterise. This leads to some…
Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate…
Explicit expressions for multimatrix models with complex and unitary matrices allows to couple these models with well-known unitary, orthogonsl and sympletic ensembles. We consider examples of such mixed ensembles which are solvable in the…
We study several kinds of polynomial ensembles of derivative type which we propose to call P\'olya ensembles. These ensembles are defined on the spaces of complex square, complex rectangular, Hermitian, Hermitian anti-symmetric and…
We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary…
We present a generic framework for describing interacting, spinning, active polar particles, aimed at modelling dense cell aggregates, where cells are treated as polar, rotating objects that interact mechanically with one another and their…
Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein|Podolsky|Rosen (EPR) spin correlation is calculated and shown to coincide with the quantum mechanical one for the 1/2-spin particles.
We study the optic control for birefringence of a polarized light by an atomic ensemble with a tripod configuration, which is mediated by the electromagnetically induced transparency with a spatially inhomogeneous laser. The atom ensemble…
In this note, we propose a simple-looking but broad conjecture about star-algebras over the field of real numbers. The conjecture enables many matrix decompositions to be represented by star-algebras and star-ideals. This paper is written…
Coherent bremsstrahlung of high energy electrons moving in a three-dimensional imperfect periodic lattice consisting of a complicated system of atoms is considered. On the basis of the normalized probability density function of the…
The semiclassical approximation for electron wave-packets in crystals leads to equations which can be derived from a Lagrangian or, under suitable regularity conditions, in a Hamiltonian framework. In the plane, these issues are studied %in…
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
A new ansatz is presented for a Lax pair describing systems of particles on the line interacting via (possibly nonsymmetric) pairwise forces. Particular cases of this yield the known Lax pairs for the Calogero-Moser and Toda systems, as…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
We present a survey of some aspects and new results on configurations, i.e. disjoint unions of constellations of infinitely near points, local and global theory, with some applications and results on generalized Enriques diagrams, singular…
Let $G$ be a commutative algebraic group embedded in projective space and $\Gamma$ a finitely generated subgroup of $G$. From these data we construct a chain of algebraic subgroups of $G$ which is intimately related to obstructions to…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
We define combinatorial counterparts to the geometric string vertices of Sen-Zwiebach and Costello-Zwiebach, which are certain closed subsets of the moduli spaces of curves. Our combinatorial vertices contain the same information as the…
This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a…