Related papers: Parallel Transport on Higher Loop Spaces

Complex analysis is a powerful tool to study classical integrable systems, statistical physics on the random lattice, random matrix theory, topological string theory,... All these topics share certain relations, called "loop equations" or…

In this paper we show an approach to electron transport in double barrier structures which unifies the well known sequential and resonant tunneling models in the widest range of transport regimes, from completely coherent to completely…

We generalise the fold map for the wedge sum and use this to give a loop space decomposition of topological spaces with a high degree of symmetry. This is applied to polyhedral products to give a loop space decomposition of polyhedral…

We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…

With vast amounts of spectrum available in the millimeter wave (mmWave) band, small cells at mmWave frequencies densely deployed underlying the conventional homogeneous macrocell network have gained considerable interest from academia,…

Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis. In numerous applications, it is necessary to align and jointly embed multiple datasets from different studies or experimental…

We provide a theory of manifold-valued rough paths of bounded 3 > p-variation, which we do not assume to be geometric. Rough paths are defined in charts, and coordinate-free (but connection-dependent) definitions of the rough integral of…

A vector bundle with connection over a supermanifold leads naturally to a notion of parallel transport along superpaths. In this note we show that {\it every} such parallel transport along superpaths comes form a vector bundle with…

In this article we define and investigate a notion of parallel transport on finite projective modules over finite matrix algebras. Given a derivation-based differential calculus on the algebra and a connection on the module, we construct…

The defect of a complex Hadamard matrix $H$ is an upper bound for the dimension of a continuous Hadamard orbit stemming from $H$. We provide a new interpretation of the defect as the dimension of the center subspace of a gradient flow and…

A topological hyperplane is a subspace of R^n (or a homeomorph of it) that is topologically equivalent to an ordinary straight hyperplane. An arrangement of topological hyperplanes in R^n is a finite set H such that k topological…

All living cells transport molecules and ions across membranes, often against concentration gradients. This active transport requires continual energy expenditure and is clearly a nonequilibrium process for which standard equilibrium…

Ordered (key-value) maps are an important and widely-used data type for large-scale data processing frameworks. Beyond simple search, insertion and deletion, more advanced operations such as range extraction, filtering, and bulk updates…

We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…

Using contact homology, we reobtain some recent results of Geiges and Gonzalo about the fundamental group of the space of contact structures on some 3-manifolds. We show that our techniques can be used to study higher dimensional contact…

In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized…

The set of homogeneous isotropic connections, as used in loop quantum cosmology, forms a line $l$ in the space of all connections $\cal A$. This embedding, however, does not continuously extend to an embedding of the configuration space…

In this work, following the Discrete de Rham (DDR) paradigm, we develop an arbitrary-order discrete divdiv complex on general polyhedral meshes. The construction rests 1) on discrete spaces that are spanned by vectors of polynomials whose…

We will construct differential forms on the embedding spaces Emb(R^j,R^n) for n-j>=2 using configuration space integral associated with 1-loop graphs, and show that some linear combinations of these forms are closed in some dimensions.…

The hopping model for cargo transport by molecular motors introduced in Refs. goldman1, goldman2, is extended here in order to incorporate the movement of cargo-motor complexes. In this context, hopping process expresses the possibility for…