Black Strings in Our World

The brane world scenario is a new approach to resolve the problem on how to compactify the higher dimensional spacetime to our 4-dimensional world. One of the remarkable features of this scenario is the higher dimensional effects in classical gravitational interactions at short distances. Due to this feature, there are black string solutions in our 4-dimensional world. In this paper, assuming the simplest model of complex minimally coupled scalar field with the local U(1) symmetry, we show a possibility of black-string formation by merging processes of type I long cosmic strings in our 4-dimensional world. No fine tuning for the parameters in the model might be necessary.Comment: 11pages, no figur

Coreference detection of low quality objects

The problem of record linkage is a widely studied problem that aims to identify coreferent (i.e. duplicate) data in a structured data source. As indicated by Winkler, a solution to the record linkage problem is only possible if the error rate is sufficiently low. In other words, in order to succesfully deduplicate a database, the objects in the database must be of sufficient quality. However, this assumption is not always feasible. In this paper, it is investigated how merging of low quality objects into one high quality object can improve the process of record linkage. This general idea is illustrated in the context of strings comparison, where strings of low quality (i.e. with a high typographical error rate) are merged into a string of high quality by using an n-dimensional Levenshtein distance matrix and compute the optimal alignment between the dirty strings. Results are presented and possible refinements are proposed

A three-dimensional scalar field theory model of center vortices and its relation to k-string tensions

In d=3 SU(N) gauge theory, we study a scalar field theory model of center vortices that furnishes an approach to the determination of so-called k-string tensions. This model is constructed from string-like quantum solitons introduced previously, and exploits the well-known relation between string partition functions and scalar field theories in d=3. Center vortices corresponding to magnetic flux J (in units of 2\pi /N) are composites of J elementary J=1 constituent vortices that come in N-1 types, with repulsion between like constituents and attraction between unlike constituents. The scalar field theory involves N scalar fields \phi_i (one of which is eliminated) that can merge, dissociate, and recombine while conserving flux mod N. The properties of these fields are deduced directly from the corresponding gauge-theory quantum solitons. Every vacuum Feynman graph of the theory corresponds to a real-space configuration of center vortices. We study qualitatively the problem of k-string tensions at large N, whose solution is far from obvious in center-vortex language. We construct a simplified dynamical picture of constituent-vortex merging, dissociation, and recombination, which allows in principle for the determination of vortex areal densities and k-string tensions. This picture involves point-like "molecules" (cross-sections of center vortices) made of constituent "atoms" that combine and disassociate dynamically in a d=2 test plane . The vortices evolve in a Euclidean "time" which is the location of the test plane along an axis perpendicular to the plane. A simple approximation to the molecular dynamics is compatible with k-string tensions that are linear in k for k<< N, as naively expected.Comment: 21 pages; RevTeX4; 4 .eps figure

Branch merging on continuum trees with applications to regenerative tree growth

We introduce a family of branch merging operations on continuum trees and show that Ford CRTs are distributionally invariant. This operation is new even in the special case of the Brownian CRT, which we explore in more detail. The operations are based on spinal decompositions and a regenerativity preserving merging procedure of $(\alpha, \theta)$-strings of beads, that is, random intervals $[0, L_{\alpha, \theta}]$ equipped with a random discrete measure $dL^{-1}$ arising in the limit of ordered $(\alpha, \theta)$-Chinese restaurant processes as introduced recently by Pitman and Winkel. Indeed, we iterate the branch merging operation recursively and give an alternative approach to the leaf embedding problem on Ford CRTs related to $(\alpha, 2-\alpha)$-regenerative tree growth processes.Comment: 40 pages, 5 figure