Related papers: An Introduction To The Web-Based Formalism

We make a short review of the formalism that describes Higgs and Yang Mills fields as two particular cases of an appropriate generalization of the notion of connection. We also comment about the several variants of this formalism, their…

This is a survey paper of the theory of crystal bases, global bases and the cluster algebra structure on the quantum coordinate rings.

A 2-categorical generalisation of elementary topos is provided and some of the properties of the yoneda structure it generates are explored. Examples relevant to the globular approach to higher category theory are discussed. This paper also…

In this paper we describe all, up to isomorphism, left unital, right unital and unital algebra structures on two-dimensional vector space over any algebraically closed field and $\mathbb{R}$. We tabulate the algebras with the units.

We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular, we utilize string diagrams, tools similar to tensor…

This a slightly expended version of my habilitation thesis, which is an overview of my research activities during the last 4 years, written in a rather informal style.

We refurbish our axiomatics of differential geometry introduced in [Mathematics for Applications,, 1 (2012), 171-182]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an…

We develop classical globally supersymmetric theories. As much as possible, we treat various dimensions and various amounts of supersymmetry in a uniform manner. We discuss theories both in components and in superspace. Throughout we…

This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…

We provide an extension of the recently constructed double field theory formulation of the low-energy limits of type II strings, in which the RR fields can depend simultaneously on the 10-dimensional space-time coordinates and linearly on…

These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…

We develop an extension of institution theory that accommodates implicitly the partiality of the signature morphisms and its syntactic and semantic effects. This is driven primarily by applications to conceptual blending, but other…

Following our previous work on fractional spin symmetries (FSS) \cite{6, 7}, we consider here the construction of field theoretical models that are invariant under the $D=2(1/3,1/3)$ supersymmetric algebra.

A general two dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by $(L_{-1}, L_{0},…

The aim of this article is twofold: first, improve the multiplicity estimate obtained by the second author for Drinfeld quasi-modular forms; and then, study the structure of certain algebras of "almost-$A$-quasi-modular forms"

This paper serves as a comprehensive system description of version 2.0 of the Marabou framework for formal analysis of neural networks. We discuss the tool's architectural design and highlight the major features and components introduced…

In this paper we develop the frame-like gauge invariant formulation for the massive two-column bosonic fields in (anti) de Sitter space-times. We begin with the partially massless cases in AdS and dS and then we combine these results into…

Motivated by the relationship between symplectic fibrations and classical Yang-Mills theories, we study the closeness of a $n$-form (n=2,3) defined on the total space of a fibration as a simple model for an abstract field theory. We…

In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…

Bases, mappings, projections and metrics, natural for Neural network training, are introduced. Graph-theoretical interpretation is offered. Non-Gaussianity naturally emerges, even in relatively simple datasets. Training statistics,…