Ideological Complex Systems: Mathematical Theory

The goal of this article is to build an abstract mathematical theory rather than a computational one of the process of transmission of ideology. The basis of much of the argument is Patten's Environment Theory that characterizes a system with its double environment (input or stimulus and output or response) and the existing interactions among them. Ideological processes are semiotic processes, and if in Patten's theory, the two environments are physical, in this theory ideological processes are physical and semiotic, as are stimulus and response.

Techniques for distributed theory synthesis in multiagent systems

Data sources are often dispersed geographically in real life applications. Finding a knowledge model may require to join all the data sources and to run a machine learning algorithm on the joint set. We present an alternative based on a Multi Agent System (MAS): an agent mines one data source in order to extract a local theory (knowledge model) and then merges it with the previous MAS theory using a knowledge fusion technique. This way, we obtain a global theory that summarizes the distributed knowledge without spending resources and time in joining data sources. New experiments have been executed including statistical significance analysis. The results show that, as a result of knowledge fusion, the accuracy of initial theories is significantly improved as well as the accuracy of the monolithic solution.

Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity

Dynamical Chern-Simons gravity is an extension of general relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard general relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.

Dynamical models for computer viruses propagation

Nowadays, digital computer systems and networks are the main engineering tools, being used in planning, design, operation, and control of all sizes of building, transportation, machinery, business, and life maintaining devices. Consequently, computer viruses became one of the most important sources of uncertainty, contributing to decrease the reliability of vital activities. A lot of antivirus programs have been developed, but they are limited to detecting and removing infections, based on previous knowledge of the virus code. In spite of having good adaptation capability, these programs work just as vaccines against diseases and are not able to prevent new infections based on the network state. Here, a trial on modeling computer viruses propagation dynamics relates it to other notable events occurring in the network permitting to establish preventive policies in the network management. Data from three different viruses are collected in the Internet and two different identification techniques, autoregressive and Fourier analyses, are applied showing that it is possible to forecast the dynamics of a new virus propagation by using the data collected from other viruses that formerly infected the network. Copyright (c) 2008 J. R. C. Piqueira and F. B. Cesar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The role of magnetic reconnection on jet/accretion disk systems

Context. It was proposed earlier that the relativistic ejections observed in microquasars could be produced by violent magnetic reconnection episodes at the inner disk coronal region (de Gouveia Dal Pino & Lazarian 2005). Aims. Here we revisit this model, which employs a standard accretion disk description and fast magnetic reconnection theory, and discuss the role of magnetic reconnection and associated heating and particle acceleration in different jet/disk accretion systems, namely young stellar objects (YSOs), microquasars, and active galactic nuclei (AGNs). Methods. In microquasars and AGNs, violent reconnection episodes between the magnetic field lines of the inner disk region and those that are anchored in the black hole are able to heat the coronal/disk gas and accelerate the plasma to relativistic velocities through a diffusive first-order Fermi-like process within the reconnection site that will produce intermittent relativistic ejections or plasmons. Results. The resulting power-law electron distribution is compatible with the synchrotron radio spectrum observed during the outbursts of these sources. A diagram of the magnetic energy rate released by violent reconnection as a function of the black hole (BH) mass spanning 10(9) orders of magnitude shows that the magnetic reconnection power is more than sufficient to explain the observed radio luminosities of the outbursts from microquasars to low luminous AGNs. In addition, the magnetic reconnection events cause the heating of the coronal gas, which can be conducted back to the disk to enhance its thermal soft X-ray emission as observed during outbursts in microquasars. The decay of the hard X-ray emission right after a radio flare could also be explained in this model due to the escape of relativistic electrons with the evolving jet outburst. In the case of YSOs a similar magnetic configuration can be reached that could possibly produce observed X-ray flares in some sources and provide the heating at the jet launching base, but only if violent magnetic reconnection events occur with episodic, very short-duration accretion rates which are similar to 100-1000 times larger than the typical average accretion rates expected for more evolved (T Tauri) YSOs.

CHARACTERIZATION OF EXPONENTIAL DIVERGENCE OF THE KALMAN FILTER FOR TIME-VARYING SYSTEMS

This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included.

Entropy production in irreversible systems described by a Fokker-Planck equation

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.

Probability currents and entropy production in nonequilibrium lattice systems

The structure of probability currents is studied for the dynamical network after consecutive contraction on two-state, nonequilibrium lattice systems. This procedure allows us to investigate the transition rates between configurations on small clusters and highlights some relevant effects of lattice symmetries on the elementary transitions that are responsible for entropy production. A method is suggested to estimate the entropy production for different levels of approximations (cluster sizes) as demonstrated in the two-dimensional contact process with mutation.

Dynamical Lorentz symmetry breaking in 3D and charge fractionalization

We analyze the breaking of Lorentz invariance in a 3D model of fermion fields self-coupled through four-fermion interactions. The low-energy limit of the theory contains various submodels which are similar to those used in the study of graphene or in the description of irrational charge fractionalization.

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3526961]

Crossover between distinct mechanisms of microwave photoresistance in bilayer systems

We report on temperature-dependent magnetoresistance measurements in balanced double quantum wells exposed to microwave irradiation for various frequencies. We have found that the resistance oscillations are described by the microwave-induced modification of electron distribution function limited by inelastic scattering (inelastic mechanism), up to a temperature of T*similar or equal to 4 K. With increasing temperature, a strong deviation of the oscillation amplitudes from the behavior predicted by this mechanism is observed, presumably indicating a crossover to another mechanism of microwave photoresistance, with similar frequency dependence. Our analysis shows that this deviation cannot be fully understood in terms of contribution from the mechanisms discussed in theory.

Magnetoresistance oscillations in multilayer systems: Triple quantum wells

Magnetoresistance of two-dimensional electron systems with several occupied subbands oscillates owing to periodic modulation of the probability of intersubband transitions by the quantizing magnetic field. In addition to previous investigations of these magnetointersubband (MIS) oscillations in two-subband systems, we report on both experimental and theoretical studies of such a phenomenon in three-subband systems realized in triple quantum wells. We show that the presence of more than two subbands leads to a qualitatively different MIS oscillation picture, described as a superposition of several oscillating contributions. Under a continuous microwave irradiation, the magnetoresistance of triple-well systems exhibits an interference of MIS oscillations and microwave-induced resistance oscillations. The theory explaining these phenomena is presented in the general form, valid for an arbitrary number of subbands. A comparison of theory and experiment allows us to extract temperature dependence of quantum lifetime of electrons and to confirm the applicability of the inelastic mechanism of microwave photoresistance for the description of magnetotransport in multilayer systems.

Approximation to density functional theory for the calculation of band gaps of semiconductors

The local-density approximation (LDA) together with the half occupation (transitionstate) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half occupation is equivalent to introducing the hole self-energy (electrostatic and exchange correlation) into the Schrodinger equation. The argument then becomes simple: The eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the self- interaction correction equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self- energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.

Adiabatic intramolecular movements for water systems

An effective treatment of the intramolecular degrees of freedom is presented for water, where these modes are decoupled from the intermolecular ones, ""adiabatically"" allowing these coordinates to be positioned at their local minimum of the potential energy surface. We perform ab initio Monte Carlo simulations with the configurational energies obtained via density functional theory. We study a water dimer as a prototype system, and even in this simple case the intramolecular relaxations are very important to properly describe properties such as the dipole moment. We show that rigid simulations do not correctly sample the phase space, resulting in an average dipole moment smaller than the one obtained with the adiabatic model, which is closer to the experimental result. (c) 2008 American Institute of Physics.

Conservation laws, integrability, and transport in one-dimensional quantum systems

In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge current in the attractive Hubbard model at half filling, however, the current operator does not have overlap with any of the local conserved quantities. We show that in these situations transport at finite temperatures is dominated by a diffusive contribution with the Drude weight being either small or even zero. For the XXZ model we discuss in detail the relation between our results, the phenomenological theory of spin diffusion, and measurements of the spin-lattice relaxation rate in spin chain compounds. Furthermore, we study the Haldane-Shastry model where a conserved spin current exists.