Related papers: The geometry of syntax and semantics for directed …
Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual…
We provide a pipeline for generating syntax diagrams (also called railroad diagrams) from context free grammars. Syntax diagrams are a graphical representation of a context free language, which we formalize abstractly as a set of mutually…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
Positive geometry provides a geometric framework where physical observables are encoded as canonical forms associated to regions of kinematic space. In this paper we consider a generalisation to an infinite union of line segments, which…
This review paper is concerned with the generalizations to field theory of the tangent and cotangent structures and bundles that play fundamental roles in the Lagrangian and Hamiltonian formulations of classical mechanics. The paper…
Many programming problems call for turning geometrical thoughts into code: tables, hierarchical structures, nests of objects, trees, forests, graphs, and so on. Linear text does not do justice to such thoughts. But, it has been the dominant…
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…
Tool support for language engineering has typically prioritises concrete syntax over abstract syntax by providing meta-languages for expressing concrete syntax and then mapping concrete to abstract structures. Text-based languages are…
To unify general relativity and quantum theory is hard in part because they are formulated in two very different mathematical languages, differential geometry and functional analysis. A natural candidate for bridging this language gap, at…
Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge…
Geospatial semantics is a broad field that involves a variety of research areas. The term semantics refers to the meaning of things, and is in contrast with the term syntactics. Accordingly, studies on geospatial semantics usually focus on…
We describe a guided proceduralization framework that optimizes geometry processing on architectural input models to extract target grammars. We aim to provide efficient artistic workflows by creating procedural representations from…
In order to gain a better understanding of the state space of programs, with the aim of making their verification more tractable, models based on directed topological spaces have been introduced, allowing to take in account equivalence…
This note clarifies the concept of syntax and semantics and their relationships. Today, a lot of confusion arises from the fact that the word "semantics" is used in different meanings. We discuss a general approach at defining semantics…
An understandable concrete syntax and a comprehensible abstract syntax are two central aspects of defining a modeling language. Both representations of a language significantly overlap in their structure and also information, but may also…
This paper exposes the language of geometric contexts and elementary schemes, which is a functorial formalism to study categories of geometric objects such as schemes, topological manifolds, differential manifolds, analytic manifolds, etc.…
Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…
Almost every programming language's syntax includes a notion of binder and corresponding bound occurrences, along with the accompanying notions of $\alpha$-equivalence, capture-avoiding substitution, typing contexts, runtime environments,…
The metric known to be relevant for standard quantization procedures receives a natural interpretation and its explicit use simultaneously gives both physical and mathematical meaning to a (coherent-state) phase-space path integral, and at…