Related papers: Statistical structure of concave compositions
A new statistical ensemble is examined using the example of classical one-component simple fluid. It's logical to call it an open ensemble, because its peculiarity is the inclusion in the consideration some surrounding area. Calculations…
Measuring the structure factor, S(q), of a dispersion of particles by Small-Angle X-ray Scattering provides a unique method to investigate the spatial arrangement of colloidal particles. However, it is impossible to find the exact location…
To the families of geometric measures of convex bodies (the area measures of Aleksandrov-Fenchel-Jessen, the curvature measures of Federer, and the recently discovered dual curvature measures) a new family is added. The new family of…
We generalize classical triangular Schubert puzzles to puzzles with convex polygonal boundary. We give these puzzles a geometric Schubert calculus interpretation and derive novel combinatorial commutativity statements, using purely…
We describe the Gerstenhaber algebra structure on the Hochschild cohomology HH*$(A)$ when $A$ is a quadratic string algebra. First we compute the Hochschild cohomology groups using Barzdell's resolution and we describe generators of these…
We present the geometric solutions to some variational problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape…
In the paper two important theorems about complete affine spheres are generalized to the case of statistical structures on abstract manifolds. The assumption about constant sectional curvature is replaced by the assumption that the…
We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is…
Suppose we partition the integers into finitely many cells. Can we always find a solution of the equation $x^2+y^2=z^2$ with $x,y,z$ on the same cell? What about more general homogeneous quadratic equations in three variables? These are…
Jacobi structures are known to generalize Poisson structures, encompassing symplectic, cosymplectic, and Lie-Poisson manifolds. Notably, other intriguing geometric structures -- such as contact and locally conformal symplectic manifolds --…
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…
This paper studies stochastic optimization for a sum of compositional functions, where the inner-level function of each summand is coupled with the corresponding summation index. We refer to this family of problems as finite-sum coupled…
We consider the moduli space of bordered Riemann surfaces with boundary and marked points. Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds. We consider a…
The purpose of the present paper is to show few examples of nonlinear PDEs (mostly with strong geometric features) for which there is a hidden convex structure. This is not only a matter of curiosity. Once the convex structure is…
This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the…
Partial cubes are isometric subgraphs of hypercubes. Structures on a graph defined by means of semicubes, and Djokovi\'{c}'s and Winkler's relations play an important role in the theory of partial cubes. These structures are employed in the…
In this paper, we give a study of the $\mathbb{C}[\partial]$-split extending structures problem for associative conformal algebras. Using the unified product as a tool, which includes interesting products such as bicrossed product, cocycle…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…
The intrinsic volumes of a convex cone are geometric functionals that return basic structural information about the cone. Recent research has demonstrated that conic intrinsic volumes are valuable for understanding the behavior of random…
A number of results related to statistical classification on convex sets are presented. In particular, the focus is on the case where some of the covariates in the data and observation being classified can be missing. The form of the…