Related papers: A Realization of Discrete Geometry by String Model
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…
We introduce a combinatorial model based on measured foliations in surfaces which captures the phenomenology of open/closed string interactions. The predicted equations are derived in this model, and new equations can be discovered as well.…
Given a differential equation with infinite-dimensional symmetry pseudo-group it is shown, using an example, that it is generally not possible to construct enough joint invariants to form an invariant numerical scheme of the equation. To…
A graph based matching is used to construct aggregation for algebraic multigrid. Effects of inexact coarse grid solve is analyzed numerically for a highly discontinuous convection diffusion coefficient matrix and problems from Florida…
The modular symmetries of string loop threshold corrections for gauge coupling constants are studied in the presence of discrete Wilson lines for all examples of abelian orbifolds, where the point group is realised by the action of Coxeter…
In the framework of on nonassociative geometry, we introduce a new effective model that extends the statistical treatment of complex networks with hidden geometry. The small-world property of the network is controlled by nonlocal curvature…
We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a…
A covariant calculus for the construction of effective string theories is developed. Effective string theory, describing quantum string-like excitations in arbitrary dimension, has in the past been constructed using the principles of…
In an earlier paper [arXiv:1408.0484] gauge invariant and background covariant equations for closed string modes were obtained from the exact renormalization group equation of the world sheet theory. The background metric (but not the…
We discuss how to compute connected matrix model correlators for operators related to the gravitational descendants of the puncture operator, for the topological A model on P^1. The relevant correlators are determined by recursion relations…
In these lecture notes we discuss a body of work in which Morse theory is used to construct various homology and cohomology operations. In the classical setting of algebraic topology this is done by constructing a moduli space of graph…
An internal characterization of complete metric mappings (by means of Cauchy nets tied at a point) is given and a construction of the completion of a metric mapping is presented.
A linkage is a finite graph with lengths assigned to each edge. A planar realization is a map to the plane which preserves edge lengths. It can be thought of as a mechanical device formed from stiff rods and rotating joints. We look at the…
The discrete states of $c=1$ string theory at the self-dual radius are associated with modes of $W_{1+\infty}$ currents and their genus zero correlators are computed. An analogy to a recent suggestion based on the integrable structure of…
In the domain of geometry and topology optimization, discovering geometries that optimally satisfy specific problem criteria is a complex challenge in both engineering and scientific research. In this work, we propose a new approach for the…
We complete the set of string vertices of non-negative dimension by introducing in a consistent manner those moduli spaces which had previously been excluded. As a consequence we obtain a `geometrised' string action taking the simple form…
We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed in this framework and several examples are…
An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution equations and an answer to why there exist…
We propose that gaugino condensation in the hidden sector may dynamically induce intermediate gauge symmetry breaking and specify the compactification scale. We also show that this scheme makes possible affine level one grand unified string…
A study of the gauged Wess-Zumino-Witten models is given focusing on the effect of topologically non-trivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with…