Using state space differential geometry for nonlinear blind source separation

Given a time series of multicomponent measurements of an evolving stimulus, nonlinear blind source separation (BSS) seeks to find a "source" time series, comprised of statistically independent combinations of the measured components. In this paper, we seek a source time series with local velocity cross correlations that vanish everywhere in stimulus state space. However, in an earlier paper the local velocity correlation matrix was shown to constitute a metric on state space. Therefore, nonlinear BSS maps onto a problem of differential geometry: given the metric observed in the measurement coordinate system, find another coordinate system in which the metric is diagonal everywhere. We show how to determine if the observed data are separable in this way, and, if they are, we show how to construct the required transformation to the source coordinate system, which is essentially unique except for an unknown rotation that can be found by applying the methods of linear BSS. Thus, the proposed technique solves nonlinear BSS in many situations or, at least, reduces it to linear BSS, without the use of probabilistic, parametric, or iterative procedures. This paper also describes a generalization of this methodology that performs nonlinear independent subspace separation. In every case, the resulting decomposition of the observed data is an intrinsic property of the stimulus' evolution in the sense that it does not depend on the way the observer chooses to view it (e.g., the choice of the observing machine's sensors). In other words, the decomposition is a property of the evolution of the "real" stimulus that is "out there" broadcasting energy to the observer. The technique is illustrated with analytic and numerical examples.Comment: Contains 14 pages and 3 figures. For related papers, see http://www.geocities.com/dlevin2001/ . New version is identical to original version except for URL in the bylin

Electromagnetic radiation from collisions at almost the speed of light: an extremely relativistic charged particle falling into a Schwarzschild black hole

We investigate the electromagnetic radiation released during the high energy collision of a charged point particle with a four-dimensional Schwarzschild black hole. We show that the spectra is flat, and well described by a classical calculation. We also compare the total electromagnetic and gravitational energies emitted, and find that the former is supressed in relation to the latter for very high energies. These results could apply to the astrophysical world in the case charged stars and small charged black holes are out there colliding into large black holes, and to a very high energy collision experiment in a four-dimensional world. In this latter scenario the calculation is to be used for the moments just after the black hole formation, when the collision of charged debris with the newly formed black hole is certainly expected. Since the calculation is four-dimensional, it does not directly apply to Tev-scale gravity black holes, as these inhabit a world of six to eleven dimensions, although our results should qualitatively hold when extrapolated with some care to higher dimensions.Comment: 6 pages, 2 figure

Late-Time Tails of Wave Propagation in Higher Dimensional Spacetimes

We study the late-time tails appearing in the propagation of massless fields (scalar, electromagnetic and gravitational) in the vicinities of a D-dimensional Schwarzschild black hole. We find that at late times the fields always exhibit a power-law falloff, but the power-law is highly sensitive to the dimensionality of the spacetime. Accordingly, for odd D>3 we find that the field behaves as t^[-(2l+D-2)] at late times, where l is the angular index determining the angular dependence of the field. This behavior is entirely due to D being odd, it does not depend on the presence of a black hole in the spacetime. Indeed this tails is already present in the flat space Green's function. On the other hand, for even D>4 the field decays as t^[-(2l+3D-8)], and this time there is no contribution from the flat background. This power-law is entirely due to the presence of the black hole. The D=4 case is special and exhibits, as is well known, the t^[-(2l+3)] behavior. In the extra dimensional scenario for our Universe, our results are strictly correct if the extra dimensions are infinite, but also give a good description of the late time behaviour of any field if the large extra dimensions are large enough.Comment: 6 pages, 3 figures, RevTeX4. Version to appear in Rapid Communications of Physical Review

Numerical analysis of quasinormal modes in nearly extremal Schwarzschild-de Sitter spacetimes

We calculate high-order quasinormal modes with large imaginary frequencies for electromagnetic and gravitational perturbations in nearly extremal Schwarzschild-de Sitter spacetimes. Our results show that for low-order quasinormal modes, the analytical approximation formula in the extremal limit derived by Cardoso and Lemos is a quite good approximation for the quasinormal frequencies as long as the model parameter $r_1\kappa_1$ is small enough, where $r_1$ and $\kappa_1$ are the black hole horizon radius and the surface gravity, respectively. For high-order quasinormal modes, to which corresponds quasinormal frequencies with large imaginary parts, on the other hand, this formula becomes inaccurate even for small values of $r_1\kappa_1$. We also find that the real parts of the quasinormal frequencies have oscillating behaviors in the limit of highly damped modes, which are similar to those observed in the case of a Reissner-Nordstr{\" o}m black hole. The amplitude of oscillating ${\rm Re(\omega)}$ as a function of ${\rm Im}(\omega)$ approaches a non-zero constant value for gravitational perturbations and zero for electromagnetic perturbations in the limit of highly damped modes, where $\omega$ denotes the quasinormal frequency. This means that for gravitational perturbations, the real part of quasinormal modes of the nearly extremal Schwarzschild-de Sitter spacetime appears not to approach any constant value in the limit of highly damped modes. On the other hand, for electromagnetic perturbations, the real part of frequency seems to go to zero in the limit.Comment: 9 pages, 7 figures, to appear in Physical Review

Temperature oscillations of magnetization observed in nanofluid ferromagnetic graphite

We report on unusual magnetic properties observed in the nanofluid room-temperature ferromagnetic graphite (with an average particle size of l=10nm). More precisely, the measured magnetization exhibits a low-temperature anomaly (attributed to manifestation of finite size effects below the quantum temperature) as well as pronounced temperature oscillations above T=50K (attributed to manifestation of the hard-sphere type pair correlations between ferromagnetic particles in the nanofluid)

Manifestation of finite temperature size effects in nanogranular magnetic graphite

In addition to the double phase transition (with the Curie temperatures T_C=300K and T_{Ct}=144K), a low-temperature anomaly in the dependence of the magnetization is observed in the bulk magnetic graphite (with an average granular size of L=10nm), which is attributed to manifestation of the size effects below the quantum temperature. The best fits of the high-temperature data (using the mean-field Curie-Weiss and Bloch expressions) produced reasonable estimates for the model parameters, such as defects mediated effective spin exchange energy J=12meV (which defines the intragranular Curie temperature T_C) and proximity mediated interactions between neighboring grains (through potential barriers created by thin layers of non-magnetic graphite) with energy J_t=exp(-d/s)J=5.8meV (which defines the intergranular Curie temperature T_{Ct}) with d=1.5nm and s=2nm being the intergranular distance and characteristic length, respectively

Perfil de expressão gênica global no músculo esquelético de ovinos por meio de microarrays.

O perfil de expressão gênica global no músculo esquelético de cordeiros de quatro grupos genéticos de ovinos foi comparado por meio de microarrays de oligonucleotídeos. As análises indicaram 262 transcritos diferencialmente expressos entre os grupos genéticos. Um total de 23 transcritos de funções conhecidas foram diferencialmente expressos, sendo dez deles apenas na comparação Morada Nova x Somalis Brasileira. Dentre os genes diferencialmente expressos, aqueles envolvidos com características de importância para a produção de carne, destacaram-se: MyoD e IGFBP4 (desenvolvimento muscular), PGDS e SCD (biosíntese de ácidos graxos), C/EBP δ e PPARγ (adipogênese) e PYGL, GLUT-3, GGTA1 e ATP5G1 (metabolismo energético). Os resultados da técnica de microarray foram validados por meio de qPCR. Estes transcritos podem ser considerados marcadores expressos úteis para a seleção de cordeiros nas condições estudadas. A seleção para polimorfismos nestes genes pode conferir maior marmoreio e deposição de massa muscular, que são características ligadas diretamente a quantidade, a qualidade e a aceitação da carne. Global gene expression profile in skeletal muscle of sheep by microarray. Abstract: The global gene expression profile in muscle of four genetic groups of hair sheep were compared by oligonucleotide microarray. The analyses showed that 262 transcripts were differentially expressed among the four genetic groups. A total of 23 genes of known function were differentially expressed, with 10 transcripts differentially expressed only in the comparison between Morada Nova x Brazilian Somali. Among the differentially expressed genes, those involved with important features for the production of meat, stood out: IGFBP4 and MyoD (muscle growth), and PGDS (SCD biosynthesis of fatty acids), C/EBPδ and PPARγ (adipogenesis) and PYGL, GLUT-3, and GGTA1 ATP5G1 (energy metabolism). The results of the microarray were validated by qPCR. These transcripts can be considered useful markers expressed in the selection of lambs under the conditions studied here. Screening for polymorphisms in these genes may confer greater marbling deposition and muscle mass, which are features directly linked to quantity, quality and acceptability of meat

BPS dyons and Hesse flow

We revisit BPS solutions to classical N=2 low energy effective gauge theories. It is shown that the BPS equations can be solved in full generality by the introduction of a Hesse potential, a symplectic analog of the holomorphic prepotential. We explain how for non-spherically symmetric, non-mutually local solutions, the notion of attractor flow generalizes to gradient flow with respect to the Hesse potential. Furthermore we show that in general there is a non-trivial magnetic complement to this flow equation that is sourced by the momentum current in the solution.Comment: 25 pages, references adde