Related papers: Homogeneity
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
This work defines two classes of processes, that we term {\it tempered fractional multistable motion} and {\it tempered multifractional stable motion}. They are extensions of fractional multistable motion and multifractional stable motion,…
One deals with arbitrary reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus. A particular emphasis is given to both…
The prevalence of many urban phenomena changes systematically with population size. We propose a theory that unifies models of economic complexity and cultural evolution to derive urban scaling. The theory accounts for the difference in…
A brief review is presented of the scaling of complex fluids, polymers and polyelectrolytes in solution and in confined geometry, in thermodynamical, structural and rheology properties using equilibrium and nonequilibrium dissipative…
Topological collections allow to consider uniformly many data structures in programming languages and are handled by functions defined by pattern matching called transformations. We present two type systems for languages with topological…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
We investigate the homological behaviour of compactly generated triangulated categories under separable extensions. We show that homological invariants (finiteness of global dimension, gorensteinness and regularity) are preserved under such…
A homogenizable structure $\mathcal{M}$ is a structure where we may add a finite amount of new relational symbols to represent some $\emptyset-$definable relations in order to make the structure homogeneous. In this article we will divide…
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in…
We discuss general formation of complementary behaviors, functions and forms in biological species competing for resources. We call orthogonalization the related processes on macro and micro-level of a self-organized formation of…
By the early 1960's advances in statistical physics had established the existence of universality classes for systems with second-order phase transitions and characterized these by critical exponents which are different to the classical…
Let $\mathcal{F}\subset\mathcal{M}(D)$ and let $a, b$ and $c$ be three distinct complex numbers. If, there exist a holomorphic function $h$ on $D$ and a positive constant $\rho$ such that for each $f\in\mathcal{F},$ $f$ and $f^{'}$…
We study the homogenization of a class of non-local functionals featuring a rapidly oscillating periodic weight. By means of two-scale convergence, we explicitly evaluate the {\Gamma}-limit for constant target functions, revealing how the…
In the present work, we explore homogenization techniques for a class of switching diffusion processes whose drift and diffusion coefficients, and jump intensities are smooth, spatially periodic functions; we assume full coupling between…
Many natural combinatorial quantities can be expressed by counting the number of homomorphisms to a fixed relational structure. For example, the number of 3-colorings of an undirected graph $G$ is equal to the number of homomorphisms from…
We generalize and complete some of Maxim's recent results on Alexander invariants of a polynomial transversal to the hyperplane at infinity. Roughly speaking, and surprisingly, such a polynomial behaves both topologically and algebraically…
In order to have a better description of homogenization for parabolic partial differential equations with periodic coefficients, we define the notion of parametric two-scale convergence. A compactness theorem is proved to justify this…