Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.

Particle Competition and Cooperation in Networks for Semi-Supervised Learning

Semi-supervised learning is one of the important topics in machine learning, concerning with pattern classification where only a small subset of data is labeled. In this paper, a new network-based (or graph-based) semi-supervised classification model is proposed. It employs a combined random-greedy walk of particles, with competition and cooperation mechanisms, to propagate class labels to the whole network. Due to the competition mechanism, the proposed model has a local label spreading fashion, i.e., each particle only visits a portion of nodes potentially belonging to it, while it is not allowed to visit those nodes definitely occupied by particles of other classes. In this way, a "divide-and-conquer" effect is naturally embedded in the model. As a result, the proposed model can achieve a good classification rate while exhibiting low computational complexity order in comparison to other network-based semi-supervised algorithms. Computer simulations carried out for synthetic and real-world data sets provide a numeric quantification of the performance of the method.

The sigma-isotypic decomposition and the sigma-index of reversible-equivariant systems

This work is concerned with dynamical systems in presence of symmetries and reversing symmetries. We describe a construction process of subspaces that are invariant by linear Gamma-reversible-equivariant mappings, where Gamma is the compact Lie group of all the symmetries and reversing symmetries of such systems. These subspaces are the sigma-isotypic components, first introduced by Lamb and Roberts in (1999) [10] and that correspond to the isotypic components for purely equivariant systems. In addition, by representation theory methods derived from the topological structure of the group Gamma, two algebraic formulae are established for the computation of the sigma-index of a closed subgroup of Gamma. The results obtained here are to be applied to general reversible-equivariant systems, but are of particular interest for the more subtle of the two possible cases, namely the non-self-dual case. Some examples are presented. (C) 2011 Elsevier BM. All rights reserved.

Algebraic-graph method for identification of islanding in power system grids

In this paper, a new algebraic-graph method for identification of islanding in power system grids is proposed. The proposed method identifies all the possible cases of islanding, due to the loss of a equipment, by means of a factorization of the bus-branch incidence matrix. The main features of this new method include: (i) simple implementation, (ii) high speed, (iii) real-time adaptability, (iv) identification of all islanding cases and (v) identification of the buses that compose each island in case of island formation. The method was successfully tested on large-scale systems such as the reduced south Brazilian system (45 buses/72 branches) and the south-southeast Brazilian system (810 buses/1340 branches). (C) 2011 Elsevier Ltd. All rights reserved.

Multi-planet extrasolar systems - detection and dynamics

20 years after the discovery of the first planets outside our solar system, the current exoplanetary population includes more than 700 confirmed planets around main sequence stars. Approximately 50% belong to multiple-planet systems in very diverse dynamical configurations, from two-planet hierarchical systems to multiple resonances that could only have been attained as the consequence of a smooth large-scale orbital migration. The first part of this paper reviews the main detection techniques employed for the detection and orbital characterization of multiple-planet systems, from the (now) classical radial velocity (RV) method to the use of transit time variations (TTV) for the identification of additional planetary bodies orbiting the same star. In the second part we discuss the dynamical evolution of multi-planet systems due to their mutual gravitational interactions. We analyze possible modes of motion for hierarchical, secular or resonant configurations, and what stability criteria can be defined in each case. In some cases, the dynamics can be well approximated by simple analytical expressions for the Hamiltonian function, while other configurations can only be studied with semi-analytical or numerical tools. In particular, we show how mean-motion resonances can generate complex structures in the phase space where different libration islands and circulation domains are separated by chaotic layers. In all cases we use real exoplanetary systems as working examples.

Flexible and conservative features of social systems in tufted capuchin monkeys: comparing the socioecology of Sapajus libidinosus and Sapajus nigritus

Socioecological models assume that primates adapt their social behavior to ecological conditions, and predict that food availability and distribution, predation risk and risk of infanticide by males affect patterns of social organization, social structure and mating system of primates. However, adaptability and variation of social behavior may be constrained by conservative adaptations and by phylogenetic inertia. The comparative study of closely related species can help to identify the relative contribution of ecological and of genetic determinants to primate social systems. We compared ecological features and social behavior of two species of the genus Sapajus, S. nigritus in Carlos Botelho State Park, an area of Atlantic Forest in Sao Paulo state, and S. libidinosus in Fazenda Boa Vista, a semi-arid habitat in Piaui state, Brazil. S. libidinosus perceived higher predation risk and fed on clumped, high quality, and usurpable resources (fruits) all year round, whereas S. nigritus perceived lower predation risk and relied on evenly distributed, low-quality food sources (leaves) during periods of fruit shortage. As predicted by socioecology models, S. libidinosus females were philopatric and established linear and stable dominance hierarchies, coalitions, and grooming relationships. S. nigritus females competed less often, and could transfer between groups, which might explain the lack of coalitions and grooming bonds among them. Both populations presented similar group size and composition and the same polygynous mating system. The species differed from each other in accordance with differences in the characteristics of their main food sources, as predicted by socioecological models, suggesting that phylogenetic inertia does not constrain social relationships established among female Sapajus. The similarity in mating systems indicates that this element of the social system is not affected by ecological variables and thus, is a more conservative behavioral feature of the genus Sapajus. Am. J. Primatol. 74:315331, 2012. (c) 2011 Wiley Periodicals, Inc.

Implant Stability Measurements of Two Immediate Loading Protocols for the Edentulous Mandible: Rigid and Semi-rigid Splinting of the Implants

Aim: Primary and secondary stabilities of immediately loaded mandibular implants restored with fixed prostheses (FP) using rigid or semirigid splinting systems were clinically and radiographically evaluated. Methods: Fifteen edentulous patients were rehabilitated using hybrid FP; each had 5 implants placed between the mental foramens. Two groups were randomly divided: group 1-FP with the conventional rigid bar splinting the implants and group 2-semi-rigid cantilever extension system with titanium bars placed in the 2 distal abutment cylinders. Primary stability was evaluated using resonance frequency analysis after installation of the implant abutments. The measurements were made at 3 times: T0, at baseline; T1, 4 months after implant placement; and T2, 8 months after implant placement. Presence of mobility and inflammation in the implant surrounding regions were checked. Stability data were submitted to statistical analysis for comparison between groups (P, 0.05). Results: Implant survival rate for the implants was of 100% in both groups. No significant differences in the mean implant stability quotient values were found for both groups from baseline and after the 8-month follow-up. Conclusion: The immediate loading of the implants was satisfactory, and both splinting conditions (rigid and semi-rigid) can be successfully used for the restoration of edentulous mandibles. (Implant Dent 2012;21:486-490)

Dynamics of the 3:1 resonant planetary systems

Many of the discovered exoplanetary systems are involved inside mean-motion resonances. In this work we focus on the dynamics of the 3:1 mean-motion resonant planetary systems. Our main purpose is to understand the dynamics in the vicinity of the apsidal corotation resonance (ACR) which are stationary solutions of the resonant problem. We apply the semi-analytical method (Michtchenko et al., 2006) to construct the averaged three-body Hamiltonian of a planetary system near a 3:1 resonance. Then we obtain the families of ACR, composed of symmetric and asymmetric solutions. Using the symmetric stable solutions we observe the law of structures (Ferraz-Mello,1988), for different mass ratio of the planets. We also study the evolution of the frequencies of σ1, resonant angle, and Δω, the secular angle. The resonant domains outside the immediate vicinity of ACR are studied using dynamical maps techniques. We compared the results obtained to planetary systems near a 3:1 MMR, namely 55 Cnc b-c, HD 60532 b-c and Kepler 20 b-c.

Stability and dynamics of terrestrial planets in binary star systems: application on Alpha Centauri

Binary stars are frequent in the universe, with about 50% of the known main sequence stars being located at a multiple star system (Abt, 1979). Even though, they are universally thought as second rate sites for the location of exo-planets and the habitable zone, due to the difficulties of detection and high perturbation that could prevent planet formation and long term stability. In this work we show that planets in binary star systems can have regular orbits and remain on the habitable zone. We introduce a stability criterium based on the solution of the restricted three body problem and apply it to describe the short period planar and three-dimentional stability zones of S-type orbits around each star of the Alpha Centauri system. We develop as well a semi-analytical secular model to study the long term dynamics of fictional planets in the habitable zone of those stars and we verify that planets on the habitable zone would be in regular orbits with any eccentricity and with inclination to the binary orbital plane up until 35 degrees. We show as well that the short period oscillations on the semi-major axis is 100 times greater than the Earth's, but at all the time the planet would still be found inside the Habitable zone.