Enhanced Convergence and Robust Performance of Randomized Dynamical Decoupling

We demonstrate the advantages of randomization in coherent quantum dynamical control. For systems which are either time-varying or require decoupling cycles involving a large number of operations, we find that simple randomized protocols offer superior convergence and stability as compared to deterministic counterparts. In addition, we show how randomization always allows to outperform purely deterministic schemes at long times, including combinatorial and concatenated methods. General criteria for optimally interpolating between deterministic and stochastic design are proposed and illustrated in explicit decoupling scenarios relevant to quantum information storage.Comment: 4 pages, 3 figures, replaced with final versio

Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: An exact vacuum solution in five dimensions

As is well-known, Kerr-Schild metrics linearize the Einstein tensor. We shall see here that they also simplify the Gauss-Bonnet tensor, which turns out to be only quadratic in the arbitrary Kerr-Schild function f when the seed metric is maximally symmetric. This property allows us to give a simple analytical expression for its trace, when the seed metric is a five dimensional maximally symmetric spacetime in spheroidal coordinates with arbitrary parameters a and b. We also write in a (fairly) simple form the full Einstein-Gauss-Bonnet tensor (with a cosmological term) when the seed metric is flat and the oblateness parameters are equal, a=b. Armed with these results we give in a compact form the solution of the trace of the Einstein-Gauss-Bonnet field equations with a cosmological term and a different than b. We then examine whether this solution for the trace does solve the remaining field equations. We find that it does not in general, unless the Gauss-Bonnet coupling is such that the field equations have a unique maximally symmetric solution.Comment: 10 pages, no figures, references added. Last version for CQ

Métodos estatísticos para análise de Y-STRs em genética forense

Tese de mestrado em Bioestatística, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2011A implementação dos marcadores de DNA nas ciências forenses consistiu no maior avanço nesta área nos últimos vinte anos. Os fenómenos de mutação e recombinação genética contribuem para uma grande diversidade genética, o que se traduz no facto de todos os indivíduos, com excepção de gémeos verdadeiros, apresentarem sequências de DNA diferentes entre si, mas invariváveis em todas as suas células. Estas características permitem a sua aplicação na área forense em investigações criminais, relações de parentesco, imigração, pessoas desaparecidas em acidentes de massa e estudos históricos\antropológicos. Nos últimos dez anos os marcadores de DNA específicos dos indivíduos do sexo masculino, Y-STRs, foram estudados e aplicados em diferentes laboratórios na área forense. Estes marcadores permitem a identificação das linhagens paternas do indivíduos e esta informação pode ser de grande importância nos casos de abuso sexual e de investigação de parentesco. No entanto a sua correcta aplicação nos casos do Serviço de Genética e Biologia Forense implica a implementação de um método científico adequado para avaliar a probabilidade de coincidência de dois perfis genéticos. Para este objectivo foi implementado um kit de estudo de Y-STRs, designado por AmpFlSTR® Yfiler™ (Applied Biosystems), previamente desenvolvido e validado para a área forense e aplicado em 197 pares pai\filho, provenientes de uma base de dados da população de referência do Sul de Portugal. Este estudo permitiu realizar inferências populacionais, estimar taxas de mutação da linha germinal paterna e efectuar cálculos de probabilidade de coincidência de perfis genéticos (matching probabilities) em diferentes tipos de casos estudados. As inferências populacionais foram realizadas com diferentes conjuntos deY-STRs, designadas por Haplotipo minimo, Haplotipo Estendido e Haplotipo completo, de forma a verificar qual o conjunto de Y STRs que permite obter a maior diversidade genética A análise com os diferentes conjuntos de haplótipos revelou a presença de 171, 183 e 191 haplotipos diferentes, correspondendo a diversidades genéticas de 0.6411, 0.6403 e 0.6508. No que diz respeito à metodologia aplicada recorrendo à formulação bayesiana, verificou-se que a metodologia recorrendo à distribuição a priori Beta permite estimar valores de taxas de mutação mais próximos dos valores referenciados por outros autores, disponíveis no site www.yhrd.org. O valor mais baixo da taxa de mutação obtido foi de 6.010-4 (5.747-4 – 3.242-4 ) para o marcador DYS438. Estes resultados contribuiram para a estimativa das probabilidades de coincidência de dois perfis genéticos. Estes cálculos foram efetuados recorrendo a diferentes metodologias, nomeadamente, método frequencista, método de “haplotype survyeing” e método de Charles Brenner. Os resultados obtidos com as diferentes metodologias, permitiram concluir que a metodologia “Haplotype Surveying” é presentemente a mais adequada para aplicação na área forense como actualmente está implementada.DNA analysis has been the greatest technological advance in forensic science in the past twenty years. Due to mutation and recombination no two persons, except true twins, have the same DNA sequence, wich enables to determine DNA sequence in every biological sample, and this knowlodge can be used in the investigation of crime, kinship relationships, immigration, missing persons, mass disasters and historical cases. In the last ten years, among DNA markers with forensic interest, a few with potencial to identify male –specific DNA, Y-STRs, were described and implemented in most forensic genetic laboratorys. These markers are very important since they contribute to identify male lineages and this information can be invaluable in cases of sexual assault and in kinship testing, as well as in anthropological and population genetics studies. However to apply Y-STRs in Forensic Genetics Service from National Institute of Legal Medicine, it is convenient to have a scientific method to analyse and evaluate the evidential strength of a Y-haplotype match. For this purpose, a 17 locus microsatellite kit, AmpFlSTR® Yfiler™ (Applied Biosystems), previously developed and validated for forensic cases, was adopted in a 197 father son\pairs south Portugal reference database, in order to make population inferences, Y-STR germline mutation rates estimation, and matching probabilities evaluations. Population inferences were done with different sets of Y STRs markers, classified as Complete Haplotype, Extended Haplotype and Minimal Haplotype, in order to study which set can give the strongest genetic diversity. A total of 171,183, 191 haplotypes were observed when analysed the Minimal Haplotype, Extended Haplotype and Complete Haplotype, respectively, corresponding to genetic diversity 0.6411, 0.6403 and 0.6508. The locus specific mutation rates were estimated with Bayesian formulation, and the best approximation was obtained with a priori Beta distribution. These results contributed to estimate matching probabilities in different kind of cases, kinship and criminal ones, with three distinct methodologies, frequencist, haplotype surveying and Brenner’s, in order to distinguish the best one to apply in the laboratory

Quantum Process Tomography: Resource Analysis of Different Strategies

Characterization of quantum dynamics is a fundamental problem in quantum physics and quantum information science. Several methods are known which achieve this goal, namely Standard Quantum Process Tomography (SQPT), Ancilla-Assisted Process Tomography (AAPT), and the recently proposed scheme of Direct Characterization of Quantum Dynamics (DCQD). Here, we review these schemes and analyze them with respect to some of the physical resources they require. Although a reliable figure-of-merit for process characterization is not yet available, our analysis can provide a benchmark which is necessary for choosing the scheme that is the most appropriate in a given situation, with given resources. As a result, we conclude that for quantum systems where two-body interactions are not naturally available, SQPT is the most efficient scheme. However, for quantum systems with controllable two-body interactions, the DCQD scheme is more efficient than other known QPT schemes in terms of the total number of required elementary quantum operations.Comment: 15 pages, 5 figures, published versio

Un algoritmo secuencial, aleatorio y óptimo para problemas de factibilidad robusta

[ES] En este trabajo (del cual se presentó una versión preliminar en Alamo et al. (2007)) se propone un algoritmo aleatorio para determinar la factibilidad robusta de un conjunto de desigualdades lineales matriciales (Linear Matrix Inequalities, LMI). El algoritmo está basado en la solución de una secuencia de problemas de optimización semidefinida sujetos a un bajo número de restricciones. Se aporta además una cota superior del número máximo de iteraciones que requiere el algoritmo para resolver el problema de factibilidad robusta. Finalmente, los resultados se ilustran mediante un ejemplo numérico. [EN] This paper proposes a randomized algorithm for feasibility of uncertain LMIs. The algorithm is based on the solution of a sequence of semidefinite optimization problems involving a reduced number of constraints. A bound of the maximum number of iterations required by the algorithm is given. Finally, the performance and behaviour of the algorithm are illustrated by means of a numerical example. Los autores agradecen la financiacion del Ministerio de Ciencia e Innovación mediante el proyecto DPI2010-21589-C05-01. Álamo, T.; Tempo, R.; Ramírez, D.; Luque, A.; Camacho, E. (2013). Un algoritmo secuencial, aleatorio y óptimo para problemas de factibilidad robusta. Revista Iberoamericana de Automática e Informática industrial. 10(1):50-61. https://doi.org/10.1016/j.riai.2012.11.005 OJS 50 61 10

Second-Order Formalism for 3D Spin-3 Gravity

A second-order formalism for the theory of 3D spin-3 gravity is considered. Such a formalism is obtained by solving the torsion-free condition for the spin connection \omega^a_{\mu}, and substituting the result into the action integral. In the first-order formalism of the spin-3 gravity defined in terms of SL(3,R) X SL(3,R) Chern-Simons (CS) theory, however, the generalized torsion-free condition cannot be easily solved for the spin connection, because the vielbein e^a_{\mu} itself is not invertible. To circumvent this problem, extra vielbein-like fields e^a_{\mu\nu} are introduced as a functional of e^a_{\mu}. New set of affine-like connections \Gamma_{\mu M}^N are defined in terms of the metric-like fields, and a generalization of the Riemann curvature tensor is also presented. In terms of this generalized Riemann tensor the action integral in the second-order formalism is expressed. The transformation rules of the metric and the spin-3 gauge field under the generalized diffeomorphims are obtained explicitly. As in Einstein gravity, the new affine-like connections are related to the spin connection by a certain gauge transformation, and a gravitational CS term expressed in terms of the new connections is also presented.Comment: 40 pages, no figures. v2:references added, coefficients of eqs in apppendix D corrected, minor typos also corrected, v3:Version accepted for publication in Classical and Quantum Gravit

Black holes in three dimensional higher spin gravity: A review

We review recent progress in the construction of black holes in three dimensional higher spin gravity theories. Starting from spin-3 gravity and working our way toward the theory of an infinite tower of higher spins coupled to matter, we show how to harness higher spin gauge invariance to consistently generalize familiar notions of black holes. We review the construction of black holes with conserved higher spin charges and the computation of their partition functions to leading asymptotic order. In view of the AdS/CFT correspondence as applied to certain vector-like conformal field theories with extended conformal symmetry, we successfully compare to CFT calculations in a generalized Cardy regime. A brief recollection of pertinent aspects of ordinary gravity is also given.Comment: 49 pages, harvmac, invited contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie

Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity

The theory of massive gravity in three dimensions recently proposed by Bergshoeff, Hohm and Townsend (BHT) is considered. At the special case when the theory admits a unique maximally symmetric solution, a conformally flat space that contains black holes and gravitational solitons for any value of the cosmological constant is found. For negative cosmological constant, the black hole is characterized in terms of the mass and the "gravitational hair" parameter, providing a lower bound for the mass. For negative mass parameter, the black hole acquires an inner horizon, and the entropy vanishes at the extremal case. Gravitational solitons and kinks, being regular everywhere, are obtained from a double Wick rotation of the black hole. A wormhole solution in vacuum that interpolates between two static universes of negative spatial curvature is obtained as a limiting case of the gravitational soliton with a suitable identification. The black hole and the gravitational soliton fit within a set of relaxed asymptotically AdS conditions as compared with the ones of Brown and Henneaux. In the case of positive cosmological constant the black hole possesses an event and a cosmological horizon, whose mass is bounded from above. Remarkably, the temperatures of the event and the cosmological horizons coincide, and at the extremal case one obtains the analogue of the Nariai solution, $dS_{2}\times S^{1}$. A gravitational soliton is also obtained through a double Wick rotation of the black hole. The Euclidean continuation of these solutions describes instantons with vanishing Euclidean action. For vanishing cosmological constant the black hole and the gravitational soliton are asymptotically locally flat spacetimes. The rotating solutions can be obtained by boosting the previous ones in the $t-\phi$ plane.Comment: Talk given at the "Workshop on Gravity in Three Dimensions," 14-24 April 2009, ESI, Vienna. 30 pages, 6 figures. V2: minor changes and section 6 slightly improved. Last version for JHE

Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes

Field theories with anisotropic scaling in 1+1 dimensions are considered. It is shown that the isomorphism between Lifshitz algebras with dynamical exponents z and 1/z naturally leads to a duality between low and high temperature regimes. Assuming the existence of gap in the spectrum, this duality allows to obtain a precise formula for the asymptotic growth of the number of states with a fixed energy which depends on z and the energy of the ground state, and reduces to the Cardy formula for z=1. The holographic realization of the duality can be naturally inferred from the fact that Euclidean Lifshitz spaces in three dimensions with dynamical exponents and characteristic lengths given by z, l, and 1/z, l/z, respectively, are diffeomorphic. The semiclassical entropy of black holes with Lifshitz asymptotics can then be recovered from the generalization of Cardy formula, where the ground state corresponds to a soliton. An explicit example is provided by the existence of a purely gravitational soliton solution for BHT massive gravity, which precisely has the required energy that reproduces the entropy of the analytic asymptotically Lifshitz black hole with z=3. Remarkably, neither the asymptotic symmetries nor central charges were explicitly used in order to obtain these results.Comment: 17 pages, no figures, references corrected and update

Analysis of Stochastic Strategies in Bacterial Competence: A Master Equation Approach

Competence is a transiently differentiated state that certain bacterial cells reach when faced with a stressful environment. Entrance into competence can be attributed to the excitability of the dynamics governing the genetic circuit that regulates this cellular behavior. Like many biological behaviors, entrance into competence is a stochastic event. In this case cellular noise is responsible for driving the cell from a vegetative state into competence and back. In this work we present a novel numerical method for the analysis of stochastic biochemical events and use it to study the excitable dynamics responsible for competence in Bacillus subtilis. Starting with a Finite State Projection (FSP) solution of the chemical master equation (CME), we develop efficient numerical tools for accurately computing competence probability. Additionally, we propose a new approach for the sensitivity analysis of stochastic events and utilize it to elucidate the robustness properties of the competence regulatory genetic circuit. We also propose and implement a numerical method to calculate the expected time it takes a cell to return from competence. Although this study is focused on an example of cell-differentiation in Bacillus subtilis, our approach can be applied to a wide range of stochastic phenomena in biological systems