Stability of a two-sublattice spin-glass model

We study the stability of the replica-symmetric solution of a two-sublattice infinite-range spin-glass model, which can describe the transition from antiferromagnetic to spin glass state. The eigenvalues associated with replica-symmetric perturbations are in general complex. The natural generalization of the usual stability condition is to require the real part of these eigenvalues to be positive. The necessary and sufficient conditions for all the roots of the secular equation to have positive real parts is given by the Hurwitz criterion. The generalized stability condition allows a consistent analysis of the phase diagram within the replica-symmetric approximation.Comment: 21 pages, 5 figure

Reference Frames and the Physical Gravito-Electromagnetic Analogy

The similarities between linearized gravity and electromagnetism are known since the early days of General Relativity. Using an exact approach based on tidal tensors, we show that such analogy holds only on very special conditions and depends crucially on the reference frame. This places restrictions on the validity of the "gravito-electromagnetic" equations commonly found in the literature.Comment: 9 Pages, 1 figure. To appear in the Proceedings of the IAU Symposium 261 "Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis", Virginia Beach, USA, 27 April - 1 May 200

A Double Myers-Perry Black Hole in Five Dimensions

Using the inverse scattering method we construct a six-parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations, with U(1)^2 rotational symmetry. It describes the superposition of two Myers-Perry black holes, each with a single angular momentum parameter, both in the same plane. The black holes live in a background geometry which is the Euclidean C-metric with an extra flat time direction. This background possesses conical singularities in two adjacent compact regions, each corresponding to a set of fixed points of one of the U(1) actions in the Cartan sub-algebra of SO(4). We discuss several aspects of the black holes geometry, including the conical singularities arising from force imbalance, and the torsion singularity arising from torque imbalance. The double Myers-Perry solution presented herein is considerably simpler than the four dimensional double Kerr solution and might be of interest in studying spin-spin interactions in five dimensional general relativity.Comment: 23 pages, 7 figures, LaTeX. v2: minor changes, references added; version published in JHE

On the Efficiency of Data Representation on the Modeling and Characterization of Complex Networks

Specific choices about how to represent complex networks can have a substantial effect on the execution time required for the respective construction and analysis of those structures. In this work we report a comparison of the effects of representing complex networks statically as matrices or dynamically as spase structures. Three theoretical models of complex networks are considered: two types of Erdos-Renyi as well as the Barabasi-Albert model. We investigated the effect of the different representations with respect to the construction and measurement of several topological properties (i.e. degree, clustering coefficient, shortest path length, and betweenness centrality). We found that different forms of representation generally have a substantial effect on the execution time, with the sparse representation frequently resulting in remarkably superior performance

Evaluating partitioning and bucketing strategies for Hive-based Big Data Warehousing systems

Hive has long been one of the industry-leading systems for Data Warehousing in Big Data contexts, mainly organizing data into databases, tables, partitions and buckets, stored on top of an unstructured distributed file system like HDFS. Some studies were conducted for understanding the ways of optimizing the performance of several storage systems for Big Data Warehousing. However, few of them explore the impact of data organization strategies on query performance, when using Hive as the storage technology for implementing Big Data Warehousing systems. Therefore, this paper evaluates the impact of data partitioning and bucketing in Hive-based systems, testing different data organization strategies and verifying the efficiency of those strategies in query performance. The obtained results demonstrate the advantages of implementing Big Data Warehouses based on denormalized models and the potential benefit of using adequate partitioning strategies. Defining the partitions aligned with the attributes that are frequently used in the conditions/filters of the queries can significantly increase the efficiency of the system in terms of response time. In the more intensive workload benchmarked in this paper, overall decreases of about 40% in processing time were verified. The same is not verified with the use of bucketing strategies, which shows potential benefits in very specific scenarios, suggesting a more restricted use of this functionality, namely in the context of bucketing two tables by the join attribute of these tables.This work is supported by COMPETE: POCI-01-0145- FEDER-007043 and FCT—Fundação para a Ciência e Tecnologia within the Project Scope: UID/CEC/00319/2013, and by European Structural and Investment Funds in the FEDER com-ponent, through the Operational Competitiveness and Internationalization Programme (COMPETE 2020) [Project no. 002814; Funding Reference: POCI-01-0247-FEDER-002814]

Experimental Demonstration of a Structured Material with Extreme Effective Parameters at Microwaves

Following our recent theoretical studies [M. G. Silveirinha, C. A. Fernandes, Phys. Rev. B, 78, 033108, 2008], it is experimentally verified that an array of crossed metallic wires may behave as a nonresonant material with extremely large index of refraction at microwaves, and may enable the realization of ultra-subwavelength waveguides.Comment: accepted for publication in Applied Physics Letters (in press). Applied Physics Letters (in press) (2008