Related papers: Expansion systems
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
Science about optimization methods is rapidly developing today. In machine learning, computer vision, biology, medicine, construction and in many other different areas optimization methods have vast popularity and they appear as important…
In the empirical study of evolutionary algorithms, the solution quality is evaluated by either the fitness value or approximation error. The latter measures the fitness difference between an approximation solution and the optimal solution.…
This article will be a continuation of our research into self-justifying systems. It will introduce several new theorems and their applications. (One of these results will transform our previous infinite-sized self-verifying formalisms into…
In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor…
A new framework for analyzing Fejer convergent algorithms is presented. Using this framework we define a very general class of Fejer convergent algorithms and establish its convergence properties. We also introduce a new definition of…
Our goal is to finally settle the persistent problem in Diophantine Approximation of finding best linear approximates. Classical results from the theory of continued fractions provide the solution for the special homogeneous case in the…
In this paper we provide an exhaustive survey of the current state of the mathematics of filtration enlargement and an interpretation of the key results of the literature from the viewpoint of mathematical finance. The emphasis is on…
The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states $W(N)$ depends on the size $N$ of the system. Here we propose a scaling expansion of…
Previous work has demonstrated that efficient algorithms exist for computing Kan extensions and that some Kan extensions have interesting similarities to various machine learning algorithms. This paper closes the gap by proving that all…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…
We consider extension of a closure system on a finite set S as a closure system on the same set S containing the given one as a sublattice. A closure system can be represented in different ways, e.g. by an implicational base or by the set…
We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of…
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in…
Motivated by questions from program transformations, eight notions of isomorphisms between term rewriting systems are defined, analysed, and classified. The notions include global isomorphisms, where the renaming of variables and function…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…
Incrementality is ubiquitous in human-human interaction and beneficial for human-computer interaction. It has been a topic of research in different parts of the NLP community, mostly with focus on the specific topic at hand even though…
The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…
Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps, we investigate…