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.

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.

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.

Critical behavior of the susceptible-infected-recovered model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic asynchronous susceptible-infected-recovered model on a square lattice is found to be c(0)=0.176 500 5(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda(c)=(1-c(0))/c(0)=4.665 71(3) and a net transmissibility of (1-c(0))/(1+3c(0))=0.538 410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.

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.

Dynamic transitions in a three dimensional associating lattice gas model

The aggregation of interacting Brownian particles in sheared concentrated suspensions is an important issue in colloid and soft matter science per se. Also, it serves as a model to understand biochemical reactions occurring in vivo where both crowding and shear play an important role. We present an effective medium approach within the Smoluchowski equation with shear which allows one to calculate the encounter kinetics through a potential barrier under shear at arbitrary colloid concentrations. Experiments on a model colloidal system in simple shear flow support the validity of the model in the concentration range considered. By generalizing Kramers' rate theory to the presence of shear and collective hydrodynamics, our model explains the significant increase in the shear-induced reaction-limited aggregation kinetics upon increasing the colloid concentration.

Dynamic transitions in a two dimensional associating lattice gas model

Using Monte Carlo simulations we investigate some new aspects of the phase diagram and the behavior of the diffusion coefficient in an associating lattice gas (ALG) model on different regions of the phase diagram. The ALG model combines a two dimensional lattice gas where particles interact through a soft core potential and orientational degrees of freedom. The competition between soft core potential and directional attractive forces results in a high density liquid phase, a low density liquid phase, and a gas phase. Besides anomalies in the behavior of the density with the temperature at constant pressure and of the diffusion coefficient with density at constant temperature are also found. The two liquid phases are separated by a coexistence line that ends in a bicritical point. The low density liquid phase is separated from the gas phase by a coexistence line that ends in tricritical point. The bicritical and tricritical points are linked by a critical lambda-line. The high density liquid phase and the fluid phases are separated by a second critical tau-line. We then investigate how the diffusion coefficient behaves on different regions of the chemical potential-temperature phase diagram. We find that diffusivity undergoes two types of dynamic transitions: a fragile-to-strong transition when the critical lambda-line is crossed by decreasing the temperature at a constant chemical potential; and a strong-to-strong transition when the critical tau-line is crossed by decreasing the temperature at a constant chemical potential.

Anomalous lattice parameter of magnetic semiconductor alloys

The addition of transition metals to III-V semiconductors radically changes their electronic, magnetic, and structural properties. We show by ab initio calculations that in contrast to the conventional semiconductor alloys, the lattice parameter in magnetic semiconductor alloys, including those with diluted concentration, strongly deviates from Vegard's law. We find a direct correlation between the magnetic moment and the anion-transition metal bond lengths and derive a simple and general formula that determines the lattice parameter of a particular magnetic semiconductor by considering both the composition and magnetic moment. This dependence can explain some experimentally observed anomalies and stimulate other kind of investigations.

Higher Moments of Net Proton Multiplicity Distributions at RHIC

200 GeV corresponding to baryon chemical potentials (mu(B)) between 200 and 20 MeV. Our measurements of the products kappa sigma(2) and S sigma, which can be related to theoretical calculations sensitive to baryon number susceptibilities and long-range correlations, are constant as functions of collision centrality. We compare these products with results from lattice QCD and various models without a critical point and study the root s(NN) dependence of kappa sigma(2). From the measurements at the three beam energies, we find no evidence for a critical point in the QCD phase diagram for mu(B) below 200 MeV.

Soliton dynamics at an interface between a uniform medium and a nonlinear optical lattice

We study trapping and propagation of a matter-wave soliton through the interface between uniform medium and a nonlinear optical lattice. Different regimes for transmission of a broad and a narrow solitons are investigated. Reflections and transmissions of solitons are predicted as a function of the lattice phase. The existence of a threshold in the amplitude of the nonlinear optical lattice, separating the transmission and reflection regimes, is verified. The localized nonlinear surface state, corresponding to the soliton trapped by the interface, is found. Variational approach predictions are confirmed by numerical simulations for the original Gross-Pitaevskii equation with nonlinear periodic potentials.

Magnetoelastic and thermal effects in the BiMn(2)O(5) lattice: A high-resolution x-ray diffraction study

High-resolution synchrotron x-ray diffraction measurements were performed on single crystalline and powder samples of BiMn(2)O(5). A linear temperature dependence of the unit cell volume was found between T(N)=38 and 100 K, suggesting that a low-energy lattice excitation may be responsible for the lattice expansion in this temperature range. Between T(*)similar to 65 K and T(N), all lattice parameters showed incipient magnetoelastic effects, due to short-range spin correlations. An anisotropic strain along the a direction was also observed below T(*). Below T(N), a relatively large contraction of the a parameter following the square of the average sublattice magnetization of Mn was found, indicating that a second-order spin Hamiltonian accounts for the magnetic interactions along this direction. On the other hand, the more complex behaviors found for b and c suggest additional magnetic transitions below T(N) and perhaps higher-order terms in the spin Hamiltonian. Polycrystalline samples grown by distinct routes and with nearly homogeneous crystal structure above T(N) presented structural phase coexistence below T(N), indicating a close competition amongst distinct magnetostructural states in this compound.

Engineering interactions for quasiperfect transfer of polariton states through nonideal bosonic networks of distinct topologies

We present a scheme for quasiperfect transfer of polariton states from a sender to a spatially separated receiver, both composed of high-quality cavities filled by atomic samples. The sender and the receiver are connected by a nonideal transmission channel -the data bus- modelled by a network of lossy empty cavities. In particular, we analyze the influence of a large class of data-bus topologies on the fidelity and transfer time of the polariton state. Moreover, we also assume dispersive couplings between the polariton fields and the data-bus normal modes in order to achieve a tunneling-like state transfer. Such a tunneling-transfer mechanism, by which the excitation energy of the polariton effectively does not populate the data-bus cavities, is capable of attenuating appreciably the dissipative effects of the data-bus cavities. After deriving a Hamiltonian for the effective coupling between the sender and the receiver, we show that the decay rate of the fidelity is proportional to a cooperativity parameter that weighs the cost of the dissipation rate against the benefit of the effective coupling strength. The increase of the fidelity of the transfer process can be achieved at the expense of longer transfer times. We also show that the dependence of both the fidelity and the transfer time on the network topology is analyzed in detail for distinct regimes of parameters. It follows that the data-bus topology can be explored to control the time of the state-transfer process.

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.

Interface roughness in short-period InGaAs/InP superlattices

Electron mobility was studied in lattice-matched short-period InGaAs/InP superlattices as a function of the width of the wells. The decreasing mobility with decreasing well width was shown to occur due to the interface roughness. The roughnesses of InGaAs/InP and GaAs/AlGaAs interfaces were compared. Much smoother InGaAs/InP interfaces resulted in higher electron mobility limited by interface roughness.

Statistics of opinion domains of the majority-vote model on a square lattice

The existence of juxtaposed regions of distinct cultures in spite of the fact that people's beliefs have a tendency to become more similar to each other's as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we study an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors' opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size L and that they interact with their nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with L(2) whereas the size of the largest cluster grows with ln L(2). The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model-Axelrod's model-we found that these opinion domains are unstable to the effect of a thermal-like noise.