Related papers: The descriptive theory of represented spaces

Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…

These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…

A representation embedding between cartesian theories can be defined to be a functor between respective categories of models that preserves finitely-generated projective models and that preserves and reflects certain epimorphisms. This…

Lexical semantics theories differ in advocating that the meaning of words is represented as an inference graph, a feature mapping or a vector space, thus raising the question: is it the case that one of these approaches is superior to the…

We discuss an extension of classical combinatorics theory to the case of spatially distributed objects.

Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…

The perception-related origins of physical measures and standards are considered within the framework of the general observer theory. The impact of observer characteristics on the development of observer-centric physics, physical concepts…

Predicting the structure of a discourse is challenging because relations between discourse segments are often implicit and thus hard to distinguish computationally. I extend previous work to classify implicit discourse relations by…

The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…

Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…

In recent years, the field of neuroscience has gone through rapid experimental advances and a significant increase in the use of quantitative and computational methods. This growth has created a need for clearer analyses of the theory and…

This paper surveys the significant progress over the past couple of decades in the theory of stratified spaces through the application of controlled methods as well as through the application of intersection homology.

Semantic role theory considers roles as a small universal set of unanalyzed entities. It means that formally there are no restrictions on role combinations. We argue that the semantic roles co-occur in verb representations. It means that…

Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep…

The purpose of this brief article is to clarify certain distortions of the history of ideas about the quantum theory of de Sitter space that have appeared in recent literature.

We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…

Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by…

The task of this survey is to present various results on intersection patterns of convex sets. One of main tools for studying intersection patterns is a point of view via simplicial complexes. We recall the definitions of so called…

Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed…

Visualization researchers and visualization professionals seek appropriate abstractions of visualization requirements that permit considering visualization solutions independently from specific problems. Abstractions can help us design,…