UNIQUENESS AND NONUNIQUENESS RESULTS FOR A CERTAIN CLASS OF ALMOST PERIODIC DISTRIBUTIONS

We consider distributions u is an element of S'(R) of the form u(t) = Sigma(n is an element of N) a(n)e(i lambda nt), where (a(n))(n is an element of N) subset of C and Lambda = (lambda n)(n is an element of N) subset of R have the following properties: (a(n))(n is an element of N) is an element of s', that is, there is a q is an element of N such that (n(-q) a(n))(n is an element of N) is an element of l(1); for the real sequence., there are n(0) is an element of N, C > 0, and alpha > 0 such that n >= n(0) double right arrow vertical bar lambda(n)vertical bar >= Cn(alpha). Let I(epsilon) subset of R be an interval of length epsilon. We prove that for given Lambda, (1) if Lambda = O(n(alpha)) with alpha < 1, then there exists epsilon > 0 such that u vertical bar I(epsilon) = 0 double right arrow u 0; (2) if Lambda = O(n) is uniformly discrete, then there exists epsilon > 0 such that u vertical bar I(epsilon) = 0 double right arrow u 0; (3) if alpha > 1 and. is uniformly discrete, then for all epsilon > 0, u vertical bar I(epsilon) = 0 double right arrow u = 0. Since distributions of the above mentioned form are very common in engineering, as in the case of the modeling of ocean waves, signal processing, and vibrations of beams, plates, and shells, those uniqueness and nonuniqueness results have important consequences for identification problems in the applied sciences. We show an identification method and close this article with a simple example to show that the recovery of geometrical imperfections in a cylindrical shell is possible from a measurement of its dynamics.

The Effect of Spatial Scale on Predicting Time Series: A Study on Epidemiological System Identification

A susceptible-infective-recovered (SIR) epidemiological model based on probabilistic cellular automaton (PCA) is employed for simulating the temporal evolution of the registered cases of chickenpox in Arizona, USA, between 1994 and 2004. At each time step, every individual is in one of the states S, I, or R. The parameters of this model are the probabilities of each individual (each cell forming the PCA lattice ) passing from a state to another state. Here, the values of these probabilities are identified by using a genetic algorithm. If nonrealistic values are allowed to the parameters, the predictions present better agreement with the historical series than if they are forced to present realistic values. A discussion about how the size of the PCA lattice affects the quality of the model predictions is presented. Copyright (C) 2009 L. H. A. Monteiro et al.

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.

Border figure detection using a phase oscillator network with dynamical coupling

Oscillator networks have been developed in order to perform specific tasks related to image processing. Here we analytically investigate the existence of synchronism in a pair of phase oscillators that are short-range dynamically coupled. Then, we use these analytical results to design a network able of detecting border of black-and-white figures. Each unit composing this network is a pair of such phase oscillators and is assigned to a pixel in the image. The couplings among the units forming the network are also dynamical. Border detection emerges from the network activity.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

System Identification and Prediction of Dengue Fever Incidence in Rio de Janeiro

Identification, prediction, and control of a system are engineering subjects, regardless of the nature of the system. Here, the temporal evolution of the number of individuals with dengue fever weekly recorded in the city of Rio de Janeiro, Brazil, during 2007, is used to identify SIS (susceptible-infective-susceptible) and SIR (susceptible-infective-removed) models formulated in terms of cellular automaton (CA). In the identification process, a genetic algorithm (GA) is utilized to find the probabilities of the state transition S -> I able of reproducing in the CA lattice the historical series of 2007. These probabilities depend on the number of infective neighbors. Time-varying and non-time-varying probabilities, three different sizes of lattices, and two kinds of coupling topology among the cells are taken into consideration. Then, these epidemiological models built by combining CA and GA are employed for predicting the cases of sick persons in 2008. Such models can be useful for forecasting and controlling the spreading of this infectious disease.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Rumor Propagation Model: An Equilibrium Study

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.

Fully Connected PLL Networks: How Filter Determines the Number of Nodes

Synchronization plays an important role in telecommunication systems, integrated circuits, and automation systems. Formerly, the masterslave synchronization strategy was used in the great majority of cases due to its reliability and simplicity. Recently, with the wireless networks development, and with the increase of the operation frequency of integrated circuits, the decentralized clock distribution strategies are gaining importance. Consequently, fully connected clock distribution systems with nodes composed of phase-locked loops (PLLs) appear as a convenient engineering solution. In this work, the stability of the synchronous state of these networks is studied in two relevant situations: when the node filters are first-order lag-lead low-pass or when the node filters are second-order low-pass. For first-order filters, the synchronous state of the network shows to be stable for any number of nodes. For second-order filter, there is a superior limit for the number of nodes, depending on the PLL parameters. Copyright (C) 2009 Atila Madureira Bueno et al.

Synchronization of Discrete-Time Chaotic Systems in Bandlimited Channels

Over the last couple of decades, many methods for synchronizing chaotic systems have been proposed with communications applications in view. Yet their performance has proved disappointing in face of the nonideal character of usual channels linking transmitter and receiver, that is, due to both noise and signal propagation distortion. Here we consider a discrete-time master-slave system that synchronizes despite channel bandwidth limitations and an allied communication system. Synchronization is achieved introducing a digital filter that limits the spectral content of the feedback loop responsible for producing the transmitted signal. Copyright (C) 2009 Marcio Eisencraft et al.

Homeotropic surface anchoring and the layer-thinning transition in free-standing films

In this work, we investigate the interplay between surface anchoring and finite-size effects on the smectic-isotropic transition in free-standing smectic films. Using an extended McMillan model, we study how a homeotropic anchoring stabilizes the smectic order above the bulk transition temperature. In particular, we determine how the transition temperature depends on the surface ordering and film thickness. We identify a characteristic anchoring for which the transition temperature does not depend on the film thickness. For strong surface ordering, we found that the thickness dependence of the transition temperature can be well represented by a power-law relation. The power-law exponent exhibits a weak dependence on the range of film thicknesses, as well as on the molecular alkyl tail length. Our results reproduce the main experimental findings concerning the layer-thinning transitions in free-standing smectic films.

LOCAL HEAD LOSS OF NON-COAXIAL EMITTERS INSERTED IN POLYETHYLENE PIPE

The design of a lateral line for drip irrigation requires accurate evaluation of head losses in not only the pipe but in the emitters as well. A procedure was developed to determine localized head losses within the emitters by the formulation of a mathematical model that accounts for the obstruction caused by the insertion point. These localized losses can be significant when compared with tire total head losses within the system due to the large number of emitters typically installed along the lateral line. Air experiment was carried out by altering flow characteristics to create Reynolds numbers (R) from 7,480 to 32,597 to provide turbulent flow and a maximum velocity of 2.0 m s(-1). The geometry of the emitter was determined by an optical projector and sensor An equation was formulated to facilitate the localized head loss calculation using the geometric characteristics of the emitter (emitter length, obstruction ratio, and contraction coefficient). The mathematical model was tested using laboratory measurements on four emitters. The local head loss was accurately estimated for the Uniram (difference of +13.6%) and Drip Net (difference of +7.7%) emitters, while appreciable deviations were found for the Twin Plus (-21.8%) and Tiran (+50%) emitters. The head loss estimated by the model was sensitive to the variations in the obstruction area of the emitter However, the variations in the local head loss did not result in significant variations in the maximum length of the lateral lines. In general, for all the analyzed emitters, a 50% increase in the local head loss for the emitters resulted in less than an 8% reduction in the maximum lateral length.

AtPIN: Arabidopsis thaliana Protein Interaction Network

Background: Protein-protein interactions (PPIs) constitute one of the most crucial conditions to sustain life in living organisms. To study PPI in Arabidopsis thaliana we have developed AtPIN, a database and web interface for searching and building interaction networks based on publicly available protein-protein interaction datasets. Description: All interactions were divided into experimentally demonstrated or predicted. The PPIs in the AtPIN database present a cellular compartment classification (C(3)) which divides the PPI into 4 classes according to its interaction evidence and subcellular localization. It has been shown in the literature that a pair of genuine interacting proteins are generally expected to have a common cellular role and proteins that have common interaction partners have a high chance of sharing a common function. In AtPIN, due to its integrative profile, the reliability index for a reported PPI can be postulated in terms of the proportion of interaction partners that two proteins have in common. For this, we implement the Functional Similarity Weight (FSW) calculation for all first level interactions present in AtPIN database. In order to identify target proteins of cytosolic glutamyl-tRNA synthetase (Cyt-gluRS) (AT5G26710) we combined two approaches, AtPIN search and yeast two-hybrid screening. Interestingly, the proteins glutamine synthetase (AT5G35630), a disease resistance protein (AT3G50950) and a zinc finger protein (AT5G24930), which has been predicted as target proteins for Cyt-gluRS by AtPIN, were also detected in the experimental screening. Conclusions: AtPIN is a friendly and easy-to-use tool that aggregates information on Arabidopsis thaliana PPIs, ontology, and sub-cellular localization, and might be a useful and reliable strategy to map protein-protein interactions in Arabidopsis. AtPIN can be accessed at http://bioinfo.esalq.usp.br/atpin.

Anomalous diffusion in non-Markovian walks having amnestically induced persistence

We report numerically and analytically estimated values for the Hurst exponent for a recently proposed non-Markovian walk characterized by amnestically induced persistence. These results are consistent with earlier studies showing that log-periodic oscillations arise only for large memory losses of the recent past. We also report numerical estimates of the Hurst exponent for non-Markovian walks with diluted memory. Finally, we study walks with a fractal memory of the past for a Thue-Morse and Fibonacci memory patterns. These results are interpreted and discussed in the context of the necessary and sufficient conditions for the central limit theorem to hold.

Spontaneous symmetry breaking in amnestically induced persistence

We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of four phases, for this system: (i) classical nonpersistence, (ii) classical persistence, (iii) log-periodic nonpersistence, and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however, log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.