Related papers: Chaos in Binary Category Computation
Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of…
As the Internet grows in size, so does the amount of text based information that exists. For many application spaces it is paramount to isolate and identify texts that relate to a particular topic. While one-class classification would be…
Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…
This paper provides an abstract definition of some kinds of logics, called diagrammatic logics, together with a definition of morphisms and of 2-morphisms between diagrammatic logics. The definition of the 2-category of diagrammatic logics…
Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…
Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…
We prove the Categorified Wrapping Number Conjecture for large classes of annular links, including alternating annular links and tangle closures exhibiting plumbed link phenomena. We do so by characterizing when a resolution is sufficient…
Categorization systems are widely studied in psychology, sociology, and organization theory as information-structuring devices which are critical to decision-making processes. In the present paper, we introduce a sound and complete…
Topological invariants such as characteristic classes are an important tool to aid in understanding and categorizing the structure and properties of algebraic varieties. In this note we consider the problem of computing a particular…
The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
A binary relation on graphs is recursively enumerable if and only if it can be computed by a formula in monadic second-order logic. The latter means that the formula defines a set of graphs, in the usual way, such that each "computation…
In the first part, we further advance the study of category theory in a strong balanced factorization category C [Pisani, 2008], a finitely complete category endowed with two reciprocally stable factorization systems such that X \to 1 is in…
Based on a Whitehead-type characterization of the sectional category we develop the notion of weak sectional category. This is a new lower bound of the sectional category, which is inspired by the notion of weak category in the sense of…
We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…
The counting grid is a grid of microtopics, sparse word/feature distributions. The generative model associated with the grid does not use these microtopics individually. Rather, it groups them in overlapping rectangular windows and uses…
In this paper we investigate a fractional order logistic map and its discrete time dynamics. We show some basic properties of the fractional logistic map and numerically study its period-doubling route to chaos.
Artificial intelligence (AI) is currently based largely on black-box machine learning models which lack interpretability. The field of eXplainable AI (XAI) strives to address this major concern, being critical in high-stakes areas such as…
We give a simple order-theoretic construction of a Cartesian closed category of sequential functions. It is based on bistable biorders, which are sets with a partial order -- the extensional order -- and a bistable coherence, which captures…
This paper explores the interplay between category theory, topology, and the algebraic theory of finite groups. Our analysis unfolds in three stages. First, we establish the foundational universe of our objects: the complete and cocomplete…