A Universal Construction for (Co)Relations

Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic interpretation for diagrams is given in terms of relations or corelations (generalised equivalence relations) of some kind. In this paper we show how semantic categories of both relations and corelations can be characterised as colimits of simpler categories. This modular perspective is important as it simplifies the task of giving a complete axiomatisation for semantic equivalence of string diagrams. Moreover, our general result unifies various theorems that are independently found in literature and are relevant for program semantics, quantum computation and control theory

UD_Japanese-CEJC: Dependency Relation Annotation on Corpus of Everyday Japanese Conversation

Conference name: the 24th Meeting of the Special Interest Group on Discourse and Dialogue, Conference place: Prague, Czechia, Session period: 2023/09/11-15, Organizer: Association for Computational Linguisticsapplication/pdfNational Institute for Japanese Language and LinguisticsTohoku UniversityMegagon Labs, Tokyo, Recruit Co., LtdNational Institute for Japanese Language and LinguisticsIn this study, we have developed Universal Dependencies (UD) resources for spoken Japanese in the Corpus of Everyday Japanese Conversation (CEJC). The CEJC is a large corpus of spoken language that encompasses various everyday conversations in Japanese, and includes word delimitation and part-of-speech annotation. We have newly annotated Long Word Unit delimitation and Bunsetsu (Japanese phrase)-based dependencies, including Bunsetsu boundaries, for CEJC. The UD of Japanese resources was constructed in accordance with hand-maintained conversion rules from the CEJC with two types of word delimitation, part-of-speech tags and Bunsetsu-based syntactic dependency relations. Furthermore, we examined various issues pertaining to the construction of UD in the CEJC by comparing it with the written Japanese corpus and evaluating UD parsing accuracy.conference pape

Universal Constructions for (Co)Relations: categories, monoidal categories, and props

Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic interpretation for diagrams is given in terms of relations or corelations (generalised equivalence relations) of some kind. In this paper we show how semantic categories of both relations and corelations can be characterised as colimits of simpler categories. This modular perspective is important as it simplifies the task of giving a complete axiomatisation for semantic equivalence of string diagrams. Moreover, our general result unifies various theorems that are independently found in literature and are relevant for program semantics, quantum computation and control theory.Comment: 22 pages + 3 page appendix, extended version of arXiv:1703.0824

An introduction to quantized Lie groups and algebras

We give a selfcontained introduction to the theory of quantum groups according to Drinfeld highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After having defined Poisson-Lie groups we study their relation to Lie-bi algebras and the classical Yang-Baxter equation. Then we explain in detail the concept of quantization for them. As an example the quantization of $sl_2$ is explicitly carried out. Next we show how quantum groups are related to the Yang-Baxter equation and how they can be used to solve it. Using the quantum double construction we explicitly construct the universal $R$-matrix for the quantum $sl_2$ algebra. In the last section we deduce all finite dimensional irreducible representations for $q$ a root of unity. We also give their tensor product decomposition (fusion rules) which is relevant to conformal field theory.Comment: 38 page

Universal homotopy theories

Given a small category C, we show that there is a universal way of expanding C into a model category, essentially by formally adjoining homotopy colimits. The technique of localization becomes a method for imposing `relations' into these universal gadgets. The paper develops this formalism and discusses various applications, for instance to the study of homotopy colimits, the Dwyer-Kan theory of framings, and to the homotopy theory of schemes

Cross Product Bialgebras - Part II

This is the central article of a series of three papers on cross product bialgebras. We present a universal theory of bialgebra factorizations (or cross product bialgebras) with cocycles and dual cocycles. We also provide an equivalent (co-)modular co-cyclic formulation. All known examples as for instance bi- or smash, doublecross and bicross product bialgebras as well as double biproduct bialgebras and bicrossed or cocycle bicross product bialgebras are now united within a single theory. Furthermore our construction yields various novel types of cross product bialgebras.Comment: 52 pages, LaTeX. Modified proof of the central theorem and updated references included. Accepted for publication in Journal of Algebr

The universal C*-algebra of the electromagnetic field

A universal C*-algebra of the electromagnetic field is constructed. It is represented in any quantum field theory which incorporates electromagnetism and expresses basic features of this field such as Maxwell's equations, Poincar\'e covariance and Einstein causality. Moreover, topological properties of the field resulting from Maxwell's equations are encoded in the algebra, leading to commutation relations with values in its center. The representation theory of the algebra is discussed with focus on vacuum representations, fixing the dynamics of the field.Comment: 17 pages, 1 figure; v2: minor corrections, version as to appear in Lett. Math. Phys. Dedicated to the memory of D. Kastler and J.E. Roberts; v3 improvement of layou

A Universal Approach to Vertex Algebras

We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.Comment: To appear in the Journal of Algebr