Related papers: Parametrized Fixed Points on O-Categories and Appl…
We study holomorphic fixed point germs in two complex variables that are tangent to the identity and have a degenerate characteristic direction. We show that if that characteristic direction is also a characteristic direction for higher…
In this survey article (which hitherto is an ongoing work-in-progress) we present the formulation of the induction and coinduction principles using the language and conventions of each of order theory, set theory, programming languages'…
This paper develops a methodology for representing machine learning models as models of formal theories, grounded in the perspective that machine learning models are a form of database and that databases are models of theories in coherent…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
Local fixpoint iteration describes a technique that restricts fixpoint iteration in function spaces to needed arguments only. It has been studied well for first-order functions in abstract interpretation and also in model checking. Here we…
First introduced in the study of the Sturmian words, the iterated palindromic closure was recently generalized to pseudopalindromes. This operator allows one to construct words with an infinity of pseudopalindromic prefixes, called…
The aim of this paper is to present some fixed point theorems for generalized contractions by altering distance functions in a complete cone metric spaces endowed with a partial order. We also generalize fixed point theorems of J. Harjani,…
Coalgebras for an endofunctor provide a category-theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired…
Indices of fixed point classes play a central role in Nielsen fixed point theory. Jiang-Wang-Zhang proved that for selfmaps of graphs and surfaces, the index of any fixed point class has an upper bound called its characteristic. In this…
The author constructs a theory of dagger formal schemes over $R$ and then defines the de Rham cohomology for flat dagger formal schemes $X$ with integral and regular reductions $\bar{X}$ which generalizes the Monsky-Washnitzer cohomology.…
In this paper, we describe the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…
Through coarse-graining, tensor network representations of a two-dimensional critical lattice model flow to a universal four-leg tensor, corresponding to a conformal field theory (CFT) fixed-point. We computed explicit elements of the…
The aim of this article is to describe a new perspective on functoriality of persistent homology and explain its intrinsic symmetry that is often overlooked. A data set for us is a finite collection of functions, called measurements, with a…
Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…
In this paper, we present a deep learning architecture which addresses the problem of 3D semantic segmentation of unstructured point clouds. Compared to previous work, we introduce grouping techniques which define point neighborhoods in the…
We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…
Functional programming languages are particularly well-suited for building automated reasoning systems, since (among other reasons) a logical term is well modeled by an inductive type, traversing a term can be implemented generically as a…
We provide a categorical proof of convergence for martingales and backward martingales in mean, using enriched category theory. The enrichment we use is in topological spaces, with their canonical closed monoidal structure, which encodes a…
Operational semantics has established itself as a flexible but rigorous means to describe the meaning of programming languages. Oftentimes, it is felt necessary to keep a semantics small, for example to facilitate its use for model checking…
We present a novel approach to construction of a formal semantics for a programming language. Our approach, using a parametric denotational semantics, allows the semantics to be easily extended to support new language features, and…