Araceli N. Proto

Condensed matter theories

Topological Phase Transitions in Strongly Interacting Fermi Systems (J W Clark) Semifluxon Dynamics in Extended Josephson Junctions (H Farhan) On the Quantum Hall Effect in Graphene (S Fujita) Ergodicity and Chaos in a System of Harmonic Oscillators (M H Lee) Fluid Helium-4 in Thermal Equilibrium (M Ristig) On the Generalised Slater Approximation (E Suraud) An Informative Method for the Diagnostics of Superconductors (K Rostami) Numerical Study of Pi-Junction Using Spin Filtering Barriers (S Kawabata) RPA Approach to Nonlinear Transport in Quantum Dots (B Tanatar) and other papers.

Blind spectral unmixing by local maximization of non-Gaussianity

We approach the estimation of material percentages per pixel (endmember fractional abundances) in hyperspectral remote-sensed images as a blind source separation problem. This task is commonly known as spectral unmixing. Classical techniques require the knowledge of the existing materials and their spectra, which is an unrealistic situation in most cases. In contrast to recently presented blind techniques based on independent component analysis, we implement here a dependent component analysis strategy, namely the MaxNG (maximum non-Gaussianity) algorithm, which is capable to separate even strongly dependent signals. We prove that, when the abundances verify a separability condition, they can be extracted by searching the local maxima of non-Gaussianity. We also provide enough theoretical as well as experimental facts that indicate that this condition holds true for endmember abundances. In addition, we discuss the implementation of MaxNG in a noisy scenario, we introduce a new technique for the removal of scale ambiguities of estimated sources, and a new fast algorithm for the calculation of a Parzen windows-based NG measure. We compare MaxNG to commonly used independent component analysis algorithms, such as FastICA and JADE. We analyze the efficiency of MaxNG in terms of the number of sensor channels, the number of available samples and other factors, by testing it on synthetically generated as well as real data. Finally, we present some examples of application of our technique to real images captured by the MIVIS airborne imaging spectrometer. Our results show that MaxNG is a good tool for spectral unmixing in a blind scenario.

Wavelet statistical complexity analysis of the classical limit

Abstract We introduce the notion of wavelet statistical complexity (WSC) and investigate the classical limit of the non-linear dynamics of two interacting harmonic oscillators. It is shown that a rather special relationship between entropy and chaos ensues that, using the WSC tool, sheds some light on the intricacies of the classical–quantum transition. The associated transition region is seen to consists of two sub-zones, each with quite different properties. In one of them, a solid–gas like (smooth) transition seems to take place.

Dynamic peer-to-peer competition

The dynamic behavior of a multiagent system in which the agent size si is variable it is studied along a Lotka–Volterra approach. The agent size has hereby the meaning of the fraction of a given market that an agent is able to capture (market share). A Lotka–Volterra system of equations for prey–predator problems is considered, the competition factor being related to the difference in size between the agents in a one-on-one competition. This mechanism introduces a natural self-organized dynamic competition among agents. In the competition factor, a parameter σ is introduced for scaling the intensity of agent size similarity, which varies in each iteration cycle. The fixed points of this system are analytically found and their stability analyzed for small systems (with n=5 agents). We have found that different scenarios are possible, from chaotic to non-chaotic motion with cluster formation as function of the σ parameter and depending on the initial conditions imposed to the system. The present contribution aim is to show how a realistic though minimalist nonlinear dynamics model can be used to describe the market competition (companies, brokers, decision makers) among other opinion maker communities.

Semiquantum chaos and the uncertainty principle

With reference to a recently advanced semi-classical model (Cooper et al., Phys. Rev. Lett. 72 (1994) 1337), we study the quantum-averaged behaviour of the coupling between a classical and a quantum system. This composite system is seen to be described in the language of a classical dynamical system. We show that some characteristics of the putative classical-quantum border become amenable to a type of quantitative analysis involving the uncertainty principle.

Nontrivial dynamics induced by a nonlinear Jaynes-Cummings Hamiltonian

Abstract The addition of a nonlinear term to the Jaynes-Cummings Hamiltonian induced a nontrivial discrete dynamics for the number of possible transitions of a given order, represented by a Fibonacci series. We describe the physics of the problem in terms of relevant operators which close a semi-Lie algebra under commutation with the Hamiltonian and therefore extending the generalized Bloch equations, already obtained for the linear case, to the nonlinear one. The initial conditions as well as a thermodynamical treatmetn of the problem is analyzed via the maximum entropy principle density operator. Finally, a generalized solution for the time-independent case is obtained and the solution for the field in a thermal state is recovered.

A Minimax Entropy Method for Blind Separation of Dependent Components in Astrophysical Images

We develop a new technique for blind separation of potentially non independent components in astrophysical images. Given a set of linearly mixed images, corresponding to different measurement channels, we estimate the original electromagnetic radiation sources in a blind fashion. Specifically, we investigate the separation of cosmic microwave background (CMB), thermal dust and galactic synchrotron emissions without imposing any assumption on the mixing matrix. In our approach, we use the Gaussian and non‐Gaussian features of astrophysical sources and we assume that CMB‐dust and CMB‐synchrotron are uncorrelated pairs while dust and synchrotron are correlated which is in agreement with theory. These assumptions allow us to develop an algorithm which associates the Minimum Entropy solutions with the non‐Gaussian sources (thermal dust and galactic synchrotron emissions) and the Maximum Entropy solution as the only Gaussian source which is the CMB. This new method is more appropriate than ICA algorithms becaus...

INFORMATION ENTROPY AND NONLINEAR SEMIQUANTUM DYNAMICS

We describe how, departing from the Shannon entropy, it is possible to deal with semiquantum time-independent nonlinear Hamiltonians. The interplay between the quantal and classical degrees of freedom can be easily seen, and the set of differential equations that govern the temporal evolution of the quantal mean values and the classical variables is obtained. We find invariants of motion and, particularly, we describe under which conditions, the uncertainty principle remains as an invariant of motion too. Through the analysis of these invariants, it is possible to follow the transition of the system from quantum to classical regime and to conclude that the uncertainty principle behaves as an indicator telling us whether the system is in regular or irregular regime. A simple example is shown.

Rank-correlations and value-correlations of Gross Domestic Product per Capita in Latin American countries

This work describes a method for searching for globalization evidence within Latin American countries using correlation networks methods. Two correlation measures are used, one based on the usual Pearsons Correlation Coefficient and the other based on Mutual Information. First, it is pointed out there is a core of globalization, where no trade blocs appear, within Latin American countries and second, a hierarchy, from a globalization point of view, is found within these countries. There is no intention to enter into a political consideration here, though any politically prone reader may guess that some further consideration is in order.

Blind source separation applied to spectral unmixing: comparing different measures of nongaussianity

We report some of our results of a particular blind source separation technique applied to spectral unmixing of remote-sensed hyperspectral images. Different nongaussianity measures are introduced in the learning procedure, and the results are compared to assess their relative efficiencies, with respect to both the output signal-to-interference ratio and the overall computational complexity. This study has been conducted on both simulated and real data sets, and the first results show that skewness is a powerful and unexpensive tool to extract the typical sources that characterize remote-sensed images.