Related papers: Topological regluing of rational functions
Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some…
I discuss the general formalism of two-dimensional topological field theories defined on open-closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for…
Function (linear) spaces on which an arbitrary function operates (i.e. the space is stable w.r.t. the pointwise unary operation defined by the function) were investigated, for continuous real or complex operations, by deLeeuw-Katznelson,…
We study toroidal orbifold models with topologically invariant terms in the path integral formalism and give physical interpretations of the terms from an operator formalism point of view. We briefly discuss a possibility of a new class of…
There are two main results. The first states that isotropy subgroups of groups acting transitively on a rationally hyperbolic spaces have infinitely generated rational cohomology algebra. Using this fact, we prove that the analogous…
We establish a general result on the existence of partially defined semiconjugacies between rational functions acting on the Riemann sphere. The semiconjugacies are defined on the complements to at most one-dimensional sets. They are…
On objects of a triangulated category with a stability condition, we construct a topology.
Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits…
We consider a metapopulation version of the Schelling model of segregation over several complex networks and lattice. We show that the segregation process is topology independent and hence it is intrinsic to the individual tolerance. The…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
We analyze a real one-parameter family of quasiconformal deformations of a hyperbolic rational map known as {\em spinning}. We show that under fairly general hypotheses, the limit of spinning either exists and is unique, or else converges…
We describe an algorithm that constructs a list of all topological types of holomorphic actions of a finite group on a compact Riemann surface $C$ of genus at least $g \geq 2$ with $C/G \cong \mathbb{P}^1$.
The natural duality between "topological" and "regular," both considered as convergence space properties, extends naturally to p-regular convergence spaces, resulting in the new concept of a p-topological convergence space. Taking advantage…
In this work we consider topology optimization of systems, which are governed by the external Bernoulli free boundary problem. We utilize the so-called pseudo-solid approach to solve the governing free boundary problems during the…
The paper discuss the limit point concept of a subset in a group via ideal of the power set ring. This idea along with anti-ideal give the topological structure in a group. Homomorphic images of both ideal and anti-ideal are played the…
Regularization plays a crucial role in supervised learning. Most existing methods enforce a global regularization in a structure agnostic manner. In this paper, we initiate a new direction and propose to enforce the structural simplicity of…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
In this thesis we explore natural procedures through which topological structure can be constructed from specific semigroups. We will do this in two ways: 1) we equip the semigroup object itself with a topological structure, and 2) we find…
In the spirit of the geometric approach to two-dimensional conformal field theory, we explicitly associate to every holomorphic vertex operator algebra a section of a power of Hodge line bundle on the moduli space of curves of arbitrary…