Related papers: De Rham model for string topology
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
We discuss the relation between open and closed string correlators using topological string theories as a toy model. We propose that one can reconstruct closed string correlators from the open ones by considering the Hochschild cohomology…
We discuss three closely related questions; i)~Given a conformal field theory, how may we deform it? ii)~What are the symmetries of string theory? and iii)~Does string theory have free parameters? We show that there is a distinct…
We continue our study of the large N phase transition in q-deformed Yang-Mills theory on the sphere and its role in connecting topological strings to black hole entropy. We study in detail the chiral theory defined in terms of uncoupled…
Template and prunning front are calculated for an experimental chaotic time series from a mechanical string experiment. An empirical synchronized model is also created for the data set. To appear in Physical Review E.
In this note we introduce a notion of a morphism between two hyperbolic iterated function systems. We prove that the graph of a morphism is the attractor of an iterated function system, giving a Closed Graph Theorem, and show how it can be…
We describe a class of systems theory based neural networks called "Network Of Recurrent neural networks" (NOR), which introduces a new structure level to RNN related models. In NOR, RNNs are viewed as the high-level neurons and are used to…
Motivated by orbifold string theory, we introduce orbifold cohomology group for any almost complex orbifold and orbifold Dolbeault cohomology for any complex orbifold. Then, we show that our new cohomology group satisfies Poincare duality…
By considering a cigar-shaped trapping potential elongated in a proper curvilinear coordinate, we discover a new form of wave localization which arises from the interplay of geometry and topological protection. The potential is modulated in…
An algebraic deformation theory of dialgebra morphisms is obtained.
We present a generalized notion of degree for rotating solutions of planar systems. We prove a formula for the relation of such degree with the classical use of Brouwer's degree and obtain a twist theorem for the existence of periodic…
Examples of non-trivial higher string topology operations have been regrettably rare in the literature. In this paper, working in the context of string topology of classifying spaces, we provide explicit calculations of a wealth of…
Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…
The chapter presents mathematical models intended for creating a topological drawing of a non-separable non-planar graph based on the methods of G. Ringel's vertex rotation theory. The induced system of cycles generates a topological…
We introduce \emph{topological density estimation} (TDE), in which the multimodal structure of a probability density function is topologically inferred and subsequently used to perform bandwidth selection for kernel density estimation. We…
We study topological strings on local toric del Pezzo surfaces by a method called remodeling the B-model which was recently proposed by Bouchard, Klemm, Marino and Pasquetti. For a large class of local toric del Pezzo surfaces we prove a…
Using the topological membrane approach to string theory, we suggest a geometric origin for the heterotic string. We show how different membrane boundary conditions lead to different string theories. We discuss the construction of closed…
In this paper, we analyze the numerical stability of the popular Longley-Rice Irregular Terrain Model (ITM). This model is widely used to plan wireless networks and in simulation-validated research and hence its stability is of fundamental…
We construct a model for the string group as an infinite-dimensional Lie group. In a second step we extend this model by a contractible Lie group to a Lie 2-group model. To this end we need to establish some facts on the homotopy theory of…
This is a survey of the theory of real trees and their applications.