相关论文: Construction of Generalized Connections
A generalized bridge is the law of a stochastic process that is conditioned on N linear functionals of its path. We consider two types of representations of such bridges: orthogonal and canonical. The orthogonal representation is…
Letting $P$ be a convex polytope in $\mathbb{R}^d$ with $n>d$ vertices, we study geometric and analytical properties of the set of generalized barycentric coordinates relative to any point $p\in P$. We prove that such sets are polytopes in…
Normalizing flows leverage the Change of Variables Formula (CVF) to define flexible density models. Yet, the requirement of smooth transformations (diffeomorphisms) in the CVF poses a significant challenge in the construction of these…
Using projective limits as subsets of Cartesian products of homomorphisms from a lattice to the structure group, a consistent interaction measure and an infinite-dimensional calculus has been constructed for a theory of non-abelian…
Different versions for defining Ashtekar's generalized connections are investigated depending on the chosen smoothness category for the paths and graphs -- the label set for the projective limit. Our definition covers the analytic case as…
In this note, we provide several constructions of Deza Cayley graphs over groups having a generalized dihedral subgroup. These constructions are based on a usage of (relative) difference sets.
This article is a follow-up of ``Holonomy and Path Structures in General Relativity and Yang-Mills Theory" by Barrett, J. W. (Int.J.Theor.Phys., vol.30, No.9, 1991). Its main goal is to provide an alternative proof of this part of the…
A generalized translational invariant noncommutative field theory is analyzed in detail, and a complete description of translational invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar…
Compositional generalization is one of the main properties which differentiates lexical learning in humans from state-of-art neural networks. We propose a general framework for building models that can generalize compositionally using the…
We study the continuity properties of a generalized Davenport Fourier expansion we recently discovered, by imposing conditions on the coefficients. We also put our expansion into perspective from the position of Appell sequences.
We show that one can construct two equivalent gauge theories from a linking theory and give a general construction principle for linking theories which we use to construct a linking theory that proves the equivalence of General Relativity…
We analyze approaches to the partial or complete unification of gauge symmetries in theories with dynamical symmetry breaking. Several types of models are considered, including those that (i) involve sufficient unification to quantize…
In this work we investigate generalized kappa-deformed spaces. We develop a systematic method for constructing realizations of noncommutative (NC) coordinates as formal power series in the Weyl algebra. All realizations are related by a…
We are going to introduce a new algebraic, analytic structure that is a kind of generalization of the Hausdorff dimension and measure. We give many examples and study the basic properties and relations of such systems.
In this Note, we propose a line bundle approach to odd-dimensional analogues of generalized complex structures. This new approach has three main advantages: (1) it encompasses all existing ones; (2) it elucidates the geometric meaning of…
The relationship between various methods to calculate the physical degrees of freedom for gauge invariant systems of a general form is established. The set of hidden parameters caused for the superfluous degrees of freedom is revealed.
The Carath\'eodory theorem on the construction of a measure is generalized by replacing the outer measure with an approximation of it and generalizing the Carath\'eodory measurability. The new theorem is applied to obtain dynamically…
The geometry of the Lie algebroid generalized tangent bundle of a generalized Lie algebroid is developed. Formulas of Ricci type and identities of Cartan and Bianchi type are presented. Introducing the notion of geodesic of a mechanical…
With the goal to study and better understand algebraic Anosov actions of $\mathbb R^k$, we develop a higher codimensional analogue of the contact distribution on odd dimensional manifolds, call such structure a generalized $k$-contact…
There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of…