On the r−r-stability of spacelike hypersurfaces

In this paper we study the strong stability of spacelike hypersurfaces with constant $r$-th mean curvature in Generalized Robertson-Walker spacetimes of constant sectional curvature. In particular, we treat the case in which the ambient spacetime is the de Sitter space

Tripartite Graph Clustering for Dynamic Sentiment Analysis on Social Media

The growing popularity of social media (e.g, Twitter) allows users to easily share information with each other and influence others by expressing their own sentiments on various subjects. In this work, we propose an unsupervised \emph{tri-clustering} framework, which analyzes both user-level and tweet-level sentiments through co-clustering of a tripartite graph. A compelling feature of the proposed framework is that the quality of sentiment clustering of tweets, users, and features can be mutually improved by joint clustering. We further investigate the evolution of user-level sentiments and latent feature vectors in an online framework and devise an efficient online algorithm to sequentially update the clustering of tweets, users and features with newly arrived data. The online framework not only provides better quality of both dynamic user-level and tweet-level sentiment analysis, but also improves the computational and storage efficiency. We verified the effectiveness and efficiency of the proposed approaches on the November 2012 California ballot Twitter data.Comment: A short version is in Proceeding of the 2014 ACM SIGMOD International Conference on Management of dat

A quantitative evaluation of the role of the Argentinean Col and the Low Pressure Tongue East of the Andes for frontogenesis in the South American subtropics

Previous studies have found the South American subtropics to exhibit high climatological frontogenesis in equivalent potential temperature during the austral summer. An important contribution to this pattern is given by frontogenesis over the Argentinean Col (AC), which separates the Northwestern Argentinean Low (NAL) from transient troughs to the south of it. The NAL and the Low Pressure Tongue east of the Andes (LPT) promote efficient transport of Amazonian humidity to the subtropics during the incursion of transient disturbances over the continent. The convergence of this strong warm and humid flow with mid-latitude air brought into the subtropics by the disturbance occurs preferentially in the neighborhood of the AC. The main difficulty in quantifying the contribution of the NAL, AC and LPT structure to frontogenesis in the South American subtropics is the automatic detection of the AC and LPT. In this paper an algorithm developed to this end is briefly presented and applied to obtain statistics on the role of these structures in frontogenesis. Six-hourly data from ECMWF ERA-40 Reanalysis over 21 austral summer periods (December–March) is used. Occurrences of the AC are highly concentrated between 34–39° S and 66–69° W, being present in this region in 42% of the time instants analyzed. The spatial average of the positive values of the frontogenesis over this region was calculated for each time step as a measure of intensity and histograms were built for the cases when the AC was and was not found inside this region. Mean, median and mode are larger for the distribution of cases with the presence of the AC. In addition, we present the frequency of occurrence of the AC as a function of the frontogenesis, showing that it grows with the intensity of the frontogenesis, rising above the 0.955 quantile. We have not found any correlation between the AC frequency and the frontolysis intensity

Phenomenological model for symmetry breaking in chaotic system

We assume that the energy spectrum of a chaotic system undergoing symmetry breaking transitions can be represented as a superposition of independent level sequences, one increasing on the expense of the others. The relation between the fractional level densities of the sequences and the symmetry breaking interaction is deduced by comparing the asymptotic expression of the level-number variance with the corresponding expression obtained using the perturbation theory. This relation is supported by a comparison with previous numerical calculations. The predictions of the model for the nearest-neighbor-spacing distribution and the spectral rigidity are in agreement with the results of an acoustic resonance experiment.Comment: accepted for publication in Physical Review

Experimental analysis of lateral impact on planar brittle material: spatial properties of the cracks

The breakup of glass and alumina plates due to planar impacts on one of their lateral sides is studied. Particular attention is given to investigating the spatial location of the cracks within the plates. Analysis based on a phenomenological model suggests that bifurcations along the cracks' paths are more likely to take place closer to the impact region than far away from it, i. e., the bifurcation probability seems to lower as the perpendicular distance from the impacted lateral in- creases. It is also found that many observables are not sensitive to the plate material used in this work, as long as the fragment multiplicities corresponding to the fragmentation of the plates are similar. This gives support to the universal properties of the fragmentation process reported in for- mer experiments. However, even under the just mentioned circumstances, some spatial observables are capable of distinguishing the material of which the plates are made and, therefore, it suggests that this universality should be carefully investigated