Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to nonreflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the nonlinear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the nonaxisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.

Free-fall in a uniform gravitational field in noncommutative quantum mechanics

We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics (NCQM). Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the (stationary) scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM. (C) 2010 American Institute of Physics. [doi:10.1063/1.3466812]

Regional scale analysis of landform configuration with base-level (isobase) maps

Base-level maps (or ""isobase maps"", as originally defined by Filosofov, 1960), express a relationship between valley order and topography. The base-level map can be seen as a ""simplified"" version of the original topographic surface, from which the ""noise"" of the low-order stream erosion was removed. This method is able to identify areas with possible tectonic influence even within lithologically uniform domains. Base-level maps have been recently applied in semi-detail scale (e.g., 1:50 000 or larger) morphotectonic analysis. In this paper, we present an evaluation of the method's applicability in regional-scale analysis (e.g., 1:250 000 or smaller). A test area was selected in northern Brazil, at the lower course of the Araguaia and Tocantins rivers. The drainage network extracted from SRTM30_PLUS DEMs with spatial resolution of approximately 900 m was visually compared with available topographic maps and considered to be compatible with a 1:1,000 000 scale. Regarding the interpretation of regional-scale morphostructures, the map constructed with 2nd and 3rd-order valleys was considered to present the best results. Some of the interpreted base-level anomalies correspond to important shear zones and geological contacts present in the 1:5 000 000 Geological Map of South America. Others have no correspondence with mapped Precambrian structures and are considered to represent younger, probably neotectonic, features. A strong E-W orientation of the base-level lines over the inflexion of the Araguaia and Tocantins rivers, suggest a major drainage capture. A N-S topographic swath profile over the Tocantins and Araguaia rivers reveals a topographic pattern which, allied with seismic data showing a roughly N-S direction of extension in the area, lead us to interpret this lineament as an E-W, southward-dipping normal fault. There is also a good visual correspondence between the base-level lineaments and geophysical anomalies. A NW-SE lineament in the southeast of the study area partially corresponds to the northern border of the Mosquito lava field, of Jurassic age, and a NW-SE lineament traced in the northeastern sector of the study area can be interpreted as the Picos-Santa Ines lineament, identifiable in geophysical maps but with little expression in hypsometric or topographic maps.

Lossless filter for multiple repeats with bounded edit distance

Background: Identifying local similarity between two or more sequences, or identifying repeats occurring at least twice in a sequence, is an essential part in the analysis of biological sequences and of their phylogenetic relationship. Finding such fragments while allowing for a certain number of insertions, deletions, and substitutions, is however known to be a computationally expensive task, and consequently exact methods can usually not be applied in practice. Results: The filter TUIUIU that we introduce in this paper provides a possible solution to this problem. It can be used as a preprocessing step to any multiple alignment or repeats inference method, eliminating a possibly large fraction of the input that is guaranteed not to contain any approximate repeat. It consists in the verification of several strong necessary conditions that can be checked in a fast way. We implemented three versions of the filter. The first is simply a straightforward extension to the case of multiple sequences of an application of conditions already existing in the literature. The second uses a stronger condition which, as our results show, enable to filter sensibly more with negligible (if any) additional time. The third version uses an additional condition and pushes the sensibility of the filter even further with a non negligible additional time in many circumstances; our experiments show that it is particularly useful with large error rates. The latter version was applied as a preprocessing of a multiple alignment tool, obtaining an overall time (filter plus alignment) on average 63 and at best 530 times smaller than before (direct alignment), with in most cases a better quality alignment. Conclusion: To the best of our knowledge, TUIUIU is the first filter designed for multiple repeats and for dealing with error rates greater than 10% of the repeats length.