Related papers: Local Hypercomplex Analyticity
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…
We introduce a local multifractal formalism adapted to functions, measures or distributions which display multifractal characteristics that can change with time, or location. We develop this formalism in a general framework and we work out…
We revisit the definition of effective local compactness, and propose an approach that works for arbitrary countably-based spaces extending the previous work on computable metric spaces. We use this to show that effective local compactness…
We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…
Non-local correlations are usually understood through the outcomes of alternative measurements (on two or more parts of a system) that cannot altogether actually be carried out in an experiment. Indeed, a joint input/output -- e.g.,…
Several approaches and corresponding definitions of complexity have been developed in different fields. Urban systems are the archetype of complex socio-technical systems concerned with these different viewpoints. We suggest in this chapter…
This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…
The notion of supershift generalizes that one of superoscillation and expresses the fact that the sampling of a function in an interval allows to compute the values of the function outside the interval. In a previous paper we discussed the…
We propose a more general definition of generic-case complexity, based on using a random process for generating inputs of an algorithm and using the time needed to generate an input as a way of measuring the size of that input.
This paper presents a short introduction to local fractional complex analysis. The generalized local fractional complex integral formulas, Yang-Taylor series and local fractional Laurent's series of complex functions in complex fractal…
Several sets of quaternionic functions are described and studied with respect to hyperholomorphy, addition and (non commutative) multiplication, on open sets of $\mathbb H$. The aim is to get a local function theory.
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
This paper provides a general result on controlling local Rademacher complexities, which captures in an elegant form to relate the complexities with constraint on the expected norm to the corresponding ones with constraint on the empirical…
Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…
We introduce a novel parsing concept called local lexing. It integrates the classically separated stages of lexing and parsing by allowing lexing to be dependent upon the parsing progress and by providing a simple mechanism for constraining…
This note provides a detailed algorithm to the application of local (perturbation) analysis of differential equations which is normally taught at graduate math courses. Exercise books often present more abstract and simplified versions of…
In the framework of superanalysis we get a functions theory close to complex analysis, under a suitable condition (A) on the real superalgebras in consideration. Under the condition (A), we get an integral representation formula for the…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
A physical system is in local equilibrium if it cannot be distinguished from a global equilibrium by ``infinitesimally localized measurements''. This should be a natural characterization of local equilibrium, but the problem is to give a…