Classification of Triadic Chord Inversions Using Kohonen Self-organizing Maps

In this paper we discuss the application of the Kohonen Selforganizing Maps to the classification of triadic chords in inversions and root positions. Our motivation started in the validation of Schönberg´s hypotheses of the harmonic features of each chord inversion. We employed the Kohonen network, which has been generally known as an optimum pattern classification tool in several areas, including music, to verify that hypothesis. The outcomes of our experiment refuse the Schönberg´s assumption in two aspects: structural and perceptual/functional

Synchronization of Kauffman networks

We analyze the synchronization transition for a pair of coupled identical Kauffman networks in the chaotic phase. The annealed model for Kauffman networks shows that synchronization appears through a transcritical bifurcation, and provides an approximate description for the whole dynamics of the coupled networks. We show that these analytical predictions are in good agreement with numerical results for sufficiently large networks, and study finite-size effects in detail. Preliminary analytical and numerical results for partially disordered networks are also presented.Comment: 10 pages, 9 figure

Fractional Exclusion Statistics and the Universal Quantum of Thermal Conductance: A Unifying Approach

We introduce a generalized approach to one-dimensional (1D) conduction based on Haldane's concept of fractional statistics (FES) and the Landauer formulation of transport theory. We show that the 1D ballistic thermal conductance is independent of the statistics obeyed by the carriers and is governed by the universal quantum $(\pi^2 k^2_B T)/(3h)$ in the degenerate regime. By contrast, the electrical conductance of FES systems is statistics-dependent. This work unifies previous theories of electron and phonon systems and explains an interesting commonality in their behavior.Comment: 7 pages (Tex source file) + 2 ps figure

Big brake singularity is accommodated as an exotic quintessence field

We describe a big brake singularity in terms of a modified Chaplygin gas equation of state p=(\ga_{m}-1)\rho+\al\ga_{m}\rho^{-n}, accommodate this late-time event as an exotic quintessence model obtained from an energy-momentum tensor, and focus on the cosmological behavior of the exotic field, its kinetic energy and the potential energy. At the background level, the exotic field does not blow up whereas its kinetic energy and potential both grow without limit near the future singularity. We evaluate the classical stability of this background solution by examining the scalar perturbations of the metric along with the inclusion of entropy perturbation in the perturbed pressure. Within the Newtonian gauge, the gravitational field approaches a constant near the singularity plus additional regular terms. When the perturbed exotic field is associated with \al>0 the perturbed pressure and contrast density both diverge, whereas the perturbed exotic field and the divergence of the exotic field's velocity go to zero exponentially. When the perturbed exotic field is associated with \al<0 the contrast density always blows up, but the perturbed pressure can remain bounded. In addition, the perturbed exotic field and the divergence of the exotic field's velocity vanish near the big brake singularity. We also briefly look at the behavior of the intrinsic entropy perturbation near the singular event.Comment: 11 pages, no figures. Accepted for its publication in PR

Dark radiation and dark matter coupled to holographic Ricci dark energy

We investigate a universe filled with interacting dark matter, holographic dark energy, and dark radiation for the spatially flat Friedmann-Robertson-Walker (FRW) spacetime. We use a linear interaction to reconstruct all the component energy densities in terms of the scale factor by directly solving the balance's equations along with the source equation. We apply the $\chi^{2}$ method to the observational Hubble data for constraining the cosmic parameters, contrast with the Union 2 sample of supernovae, and analyze the amount of dark energy in the radiation era. It turns out that our model exhibits an excess of dark energy in the recombination era whereas the stringent bound $\Omega_{\rm x}(z\simeq 10^{10})<0.21$ at big-bang nucleosynthesis is fulfilled. We find that the interaction provides a physical mechanism for alleviating the triple cosmic coincidence and this leads to $\Omega_{\rm m0}/\Omega_{\rm x0} \simeq \Omega_{\rm r0}/\Omega_{\rm x0} \simeq {\cal O}(1)$.Comment: 8 pages, 5 figures, 2 tables. Accepted for its publication in The European Physical Journal C (2013). http://link.springer.com/article/10.1140/epjc/s10052-013-2352-7 arXiv admin note: substantial text overlap with arXiv:1210.550

Interacting dark matter and modified holographic Ricci dark energy plus a noninteracting cosmic component

We investigate a spatially flat Friedmann-Robertson-Walker universe that has an interacting dark matter, a modified holographic Ricci dark energy (MHRDE), plus a third, decoupled component that behaves as a radiation term. We consider a nonlinear interaction in the dark component densities and their derivatives up to second order. We apply the $\chi^{2}$ method to the observational Hubble data for constraining the cosmological parameters and analyze the amount of dark energy in the radiation era for both MHRDE and holographic Ricci dark energy models. The former is consistent with the bound $\Omega_{x}(z\simeq 1100)<0.1$ reported for the behavior of dark energy at early times while the latter does not fulfill it.Comment: 5 pages, 2 figures, Revtex 4.0. Phys. Rev. D 85, 127301 (2012