Related papers: Knot Logic: Logical Connection and Topological Con…

Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…

Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…

In this paper we sketch how some fundamental concepts of modern topology (as well as logic and category theory) can be understood philosophically in the light of Hegel's Science Logic as well how modern topological concepts can provide…

Document-level relation extraction is a complex human process that requires logical inference to extract relationships between named entities in text. Existing approaches use graph-based neural models with words as nodes and edges as…

This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with L-topological system and L-topological space are established.

We define two words in a language to be connected if they express similar concepts. The network of connections among the many thousands of words that make up a language is important not only for the study of the structure and evolution of…

Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…

This is an introductory article on high dimensional knots for the beginners. High dimensional knot theory is an exciting field. It is a field of knot theory, which is one of topology and is connected with many ones. In this article we use…

Inductive link prediction -- where entities during training and inference stages can be different -- has been shown to be promising for completing continuously evolving knowledge graphs. Existing models of inductive reasoning mainly focus…

Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…

Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as…

Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena…

Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent…

We present an algorithm to express Wilson lines that are defined on piecewise linear paths in function of their individual segments, reducing the number of diagrams needed to be calculated. The important step lies in the observation that…

This paper introduces a new algebra, the crossing algebra, that is applied to count the number of components for arborescent knots, links, tangles or states (of a state polynomial expansion such as the Kauffman bracket). This algebra is…

Knots are commonly represented and manipulated via diagrams, which are decorated planar graphs. When such a knot diagram has low treewidth, parameterized graph algorithms can be leveraged to ensure the fast computation of many invariants…

We give an introduction to the physics and mathematics involved in the recently observed relation between topological string theory and knot contact homology and then discuss this relation. The note is based on two lectures given at the…

The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…

We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such…