Analytic crystals of solitons in the four dimensional gauged non-linear sigma model

The first analytic topologically non-trivial solutions in the (3+1)-dimensional gauged non-linear sigma model representing multi-solitons at finite volume with manifest ordered structures generating their own electromagnetic field are presented. The complete set of seven coupled non-linear field equations of the gauged non-linear sigma model together with the corresponding Maxwell equations are reduced in a self-consistent way to just one linear Schrodinger-like equation in two dimensions. The corresponding two dimensional periodic potential can be computed explicitly in terms of the solitons profile. The present construction keeps alive the topological charge of the gauged solitons. Both the energy density and the topological charge density are periodic and the positions of their peaks show a crystalline order. These solitons describe configurations in which (most of) the topological charge and total energy are concentrated within three-dimensional tube-shaped regions. The electric and magnetic fields vanish in the center of the tubes and take their maximum values on their surface while the electromagnetic current is contained within these tube-shaped regions. Electromagnetic perturbations of these families of gauged solitons are shortly discussed.Comment: 18 pages, 22 figures, accepted for publication on EUROPEAN PHYSICAL JOURNAL

D=10 dyonic black holes in string inspired models

We consider string-inspired models in D=10 spacetime dimensions, which include couplings with 1- and 3-form fields as well as R4 higher-curvature corrections to the gravitational action. For such models, we explicitly construct a family of black hole solutions with both electric and magnetic charges, and with different horizon topologies. The solutions exhibit some features similar to those of self-gravitating monopoles in Einstein-Yang-Mills theory, which we discuss. When higher-curvature corrections are switched off, our solutions reduce to charged p-brane solutions previously studied in the literature. Novel qualitative features appear due to the R4 terms, though. Such is the case for the emergence of branch singularities for charged solutions that, nonetheless, can be shielded by the event horizon.Fil: Giribet, Gaston Enrique. University of New York; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Lagos, Marcela. Universidad de Concepción; ChileFil: Oliva, Julio. Universidad de Concepción; ChileFil: Vera, Aldo. Universidad de Concepción; Chil

Multi Split Conformal Prediction

Split conformal prediction is a computationally efficient method for performing distribution-free predictive inference in regression. It involves, however, a one-time random split of the data, and the result depends on the particular split. To address this problem, we propose multi split conformal prediction, a simple method based on Markov's inequality to aggregate single split conformal prediction intervals across multiple splits.Comment: 12 pages, 1 figure, 2 tabl

Non-Parametric Classification of Time Series Using Permutation Ordinal Statistics

The present thesis explores some approaches to classify time series without prior statistical information using the concept of permutation entropy. Motivated by the results from a previous published and relevant work that set similarity relationships between EEG time series, a reproduction of the proposed approach was performed giving negative results. The failure to reproduce those results led to the conclusion that the approach of building statistics from permutation patterns have to be complemented with another metric in order to be used for classification purposes. The concept of Total Variation Distance (TVD) was then used to develop three algorithms to classify time series in a non-parametric way. At first, the developed algorithms were tested using EEG time series. Even though the results using the developed algorithms were better than previous results, they were not as satisfactory as desired. However, the inherent complexity of brain measurements led to switch to self-generated data to test the algorithms. Using time series coming from different sets of filtered versions of Gaussian white noise the classification was performed. For comparison purposes a parametric classification approach using the Maximum Likelihood Estimation was also used. Results showed that when each set of data came from the same filtering equation the classification using the developed algorithms was optimal reaching 100% success rate in many cases, being as good as the ML approach. On the other hand, when each set of data came from a mixture of different filter equations that generate the time series (reflecting the complex situations we faced when processing EEG data) , results were fairly successful with variations with respect to the ML approach, which was outperformed in some cases but also not surpassed in others. The results obtained pointed the permutation entropy analysis to be an approach in the right direction to efficiently classify time series, however more research needs to be done to adjust the correct metric to get better results

Crystals of superconducting Baryonic tubes in the low energy limit of QCD at finite density

The low energy limit of QCD admits (crystals of) superconducting Baryonic tubes at finite density. We begin with the Maxwell-gauged Skyrme model in (3+1)-dimensions (which is the low energy limit of QCD in the leading order of the large N expansion). We construct an ansatz able to reduce the seven coupled field equations in a sector of high Baryonic charge to just one linear Schrodinger-like equation with an effective potential (which can be computed explicitly) periodic in the two spatial directions orthogonal to the axis of the tubes. The solutions represent ordered arrays of Baryonic superconducting tubes as (most of) the Baryonic charge and total energy is concentrated in the tube-shaped regions. They carry a persistent current (which vanishes outside the tubes) even in the limit of vanishing U(1) gauge field: such a current cannot be deformed continuously to zero as it is tied to the topological charge. Then, we discuss the subleading corrections in the 't Hooft expansion to the Skyrme model (called usually \mathcal{L}_{6}$,$\mathcal{L}_{8}$ and so on). Remarkably, the very same ansatz allows to construct analytically these crystals of superconducting Baryonic tubes at any order in the 't Hooft expansion. Thus, no matter how many subleading terms are included, these ordered arrays of gauged solitons are described by the same ansatz and keep their main properties manifesting a universal character. On the other hand, the subleading terms can affect the stability properties of the configurations setting lower bounds on the allowed Baryon density.Comment: 30 pages, 19 figures. Accepted for publication in European Physical Journal