相关论文: Relaxing the Geodesic Rule in Defect Formation Alg…
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…
The question of interest in the present study is: ``Given a body subject to mechanical loads, how to define the initial geometry so that the deformed one matches precisely a prescribed shape?'' This question is particularly relevant in…
We investigate the geodesics in the entire class of nonexpanding impulsive gravitational waves propagating in an (anti-)de Sitter universe using the distributional form of the metric. Employing a 5-dimensional embedding formalism and a…
The problem of learning tree-structured Gaussian graphical models from independent and identically distributed (i.i.d.) samples is considered. The influence of the tree structure and the parameters of the Gaussian distribution on the…
Non-convex optimization problems are challenging to solve; the success and computational expense of a gradient descent algorithm or variant depend heavily on the initialization strategy. Often, either random initialization is used or…
Ooguri, Vafa, and Verlinde have outlined an approach to two-dimensional accelerating string cosmology which is based on topological string theory, the ultimate objective being to develop a string-theoretic understanding of "creating the…
Geodesics deviation equation (GDE) is itroduced. In "adiabatic" approximation exact solution of the GDE if found. Perturbation theory in general case is formulated. Geometrical criterion of local instability which may lead to chaos is…
The language and methods of algebraic topology, particularly homotopy theory, have been extensively used in the study of the identification, the classification and the evolution of defects. Topological methods provide the means for the…
A randomised trapezoidal quadrature rule is proposed for continuous functions which enjoys less regularity than commonly required. Indeed, we consider functions in some fractional Sobolev space. Various error bounds for this randomised rule…
This paper addresses the computational challenges in reliability-based topology optimization (RBTO) of structures associated with the estimation of statistics of the objective and constraints using standard sampling methods, and overcomes…
We study the gradient method under the assumption that an additively inexact gradient is available for, generally speaking, non-convex problems. The non-convexity of the objective function, as well as the use of an inexactness specified…
Cosmic strings are one-dimensional topological defects which could have been formed in the early stages of our Universe. They triggered a lot of interest, mainly for their cosmological implications: they could offer an alternative to…
The experiments on verification of the Kibble-Zurek mechanism showed that topological defects are formed most efficiently in the systems of small size or low (quasi-)dimensionality, whereas in the macroscopic two- and three-dimensional…
Superconductors are the only experimentally accessible systems with spontaneously broken gauge symmetries which support topologically nontrivial defects, namely string defects. We propose two experiments whose aim is the observation of the…
Parameterless stopping criteria for recursive polynomial expansions to construct the density matrix in electronic structure calculations are proposed. Based on convergence order estimation the new stopping criteria automatically and…
We derive various consistency requirements for Vachaspati-Vilenkin type Monte-Carlo simulations of cosmic string formation or disclination formation in liquid crystals. We argue for the use of a tetrakaidekahedral lattice in such…
In [44], we qualitatively studied some classical results implied by the specification property for dynamical systems with non-uniform specification. In this paper, we perform quantitative studies on how properties of topological theory and…
We derive the geodesic equation of motion in the presence of weak gravitational fields produced by relativistic sources such as cosmic strings, decomposed into scalar, vector and tensor parts. We find that the vector (gravito-magnetic)…
Statistical modeling of spatiotemporal phenomena often requires selecting a covariance matrix from a covariance class. Yet standard parametric covariance families can be insufficiently flexible for practical applications, while…
We construct the Hamiltonian operator of the string field theory for $c=0$ string theory. It describes how strings evolve in the coordinate frame, which is defined by using the geodesic distance on the worldsheet. The Hamiltonian consists…