Related papers: A recipe for black box functors
In colored range counting (CRC), the input is a set of points where each point is assigned a ``color'' (or a ``category'') and the goal is to store them in a data structure such that the number of distinct categories inside a given query…
The graph isomorphism, subgraph isomorphism, and graph edit distance problems are combinatorial problems with many applications. Heuristic exact and approximate algorithms for each of these problems have been developed for different kinds…
Color Refinement, also known as Naive Vertex Classification, is a classical method to distinguish graphs by iteratively computing a coloring of their vertices. While it is mainly used as an imperfect way to test for isomorphism, the…
We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S,…
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…
Design patterns are elegant and well-tested solutions to recurrent software development problems. They are the result of software developers dealing with problems that frequently occur, solving them in the same or a slightly adapted way. A…
Building on recent progress at the intersection of combinatorial optimization and deep learning, we propose an end-to-end trainable architecture for deep graph matching that contains unmodified combinatorial solvers. Using the presence of…
It is proved that 1) the indicator function of some onefold or multifold independent set in a regular graph is a perfect coloring if and only if the set attain the Delsarte--Hoffman bound; 2) each transversal in a uniform regular hypergraph…
For groups of a topological origin, such as braid groups and mapping class groups, an important source of interesting and highly non-trivial representations is given by their actions on the twisted homology of associated spaces; these are…
In recent years, deep learning has become prevalent to solve applications from multiple domains. Convolutional Neural Networks (CNNs) particularly have demonstrated state of the art performance for the task of image classification. However,…
We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a…
We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…
In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…
In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will…
Community detection in graphs is a problem that is likely to be relevant whenever network data appears, and consequently the problem has received much attention with many different methods and algorithms applied. However, many of these…
Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…
We introduce collages of string diagrams as a diagrammatic syntax for glueing multiple monoidal categories. Collages of string diagrams are interpreted as pointed bimodular profunctors. As the main examples of this technique, we introduce…
Distributional compositional (DisCo) models are functors that compute the meaning of a sentence from the meaning of its words. We show that DisCo models in the category of sets and relations correspond precisely to relational databases. As…
The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social system represented as a directed graph. Central among these…