Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model.

Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by a non-Markovian dynamics: memory effects play an essential role in the spreading of diseases. Including memory effects in the susceptible-infected-recovered (SIR) epidemic model seems very appropriate for such an investigation. Thus, the memory prone SIR model dynamics is investigated using fractional derivatives. The decay of long-range memory, taken as a power-law function, is directly controlled by the order of the fractional derivatives in the corresponding nonlinear fractional differential evolution equations. Here we assume "fully mixed" approximation and show that the epidemic threshold is shifted to higher values than those for the memoryless system, depending on this memory "length" decay exponent. We also consider the SIR model on structured networks and study the effect of topology on threshold points in a non-Markovian dynamics. Furthermore, the lack of access to the precise information about the initial conditions or the past events plays a very relevant role in the correct estimation or prediction of the epidemic evolution. Such a "constraint" is analyzed and discussed.

Effects of competition and cooperation interaction between agents on networks in the presence of a market capacity.

A network effect is introduced taking into account competition, cooperation, and mixed-type interaction among agents along a generalized Verhulst-Lotka-Volterra model. It is also argued that the presence of a market capacity undoubtedly enforces a definite limit on the agent's size growth. The state stability of triadic agents, i.e., the most basic network plaquette, is investigated analytically for possible scenarios, through a fixed-point analysis. It is discovered that: (i) market demand is only satisfied for full competition when one agent monopolizes the market; (ii) growth of agent size is encouraged in full cooperation; (iii) collaboration among agents to compete against one single agent may result in the disappearance of this single agent out of the market; and (iv) cooperating with two rivals may become a growth strategy for an intelligent agent.

Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices.

Nowadays, strict finite size effects must be taken into account in condensed matter problems when treated through models based on lattices or graphs. On the other hand, the cases of directed bonds or links are known to be highly relevant in topics ranging from ferroelectrics to quotation networks. Combining these two points leads us to examine finite size random matrices. To obtain basic materials properties, the Green's function associated with the matrix has to be calculated. To obtain the first finite size correction, a perturbative scheme is hereby developed within the framework of the replica method. The averaged eigenvalue spectrum and the corresponding Green's function of Wigner random sign real symmetric N×N matrices to order 1/N are finally obtained analytically. Related simulation results are also presented. The agreement is excellent between the analytical formulas and finite size matrix numerical diagonalization results, confirming the correctness of the first-order finite size expression.

Cooperative peer-to-peer multiagent-based systems.

A multiagent based model for a system of cooperative agents aiming at growth is proposed. This is based on a set of generalized Verhulst-Lotka-Volterra differential equations. In this study, strong cooperation is allowed among agents having similar sizes, and weak cooperation if agents have markedly different "sizes", thus establishing a peer-to-peer modulated interaction scheme. A rigorous analysis of the stable configurations is presented first examining the fixed points of the system, next determining their stability as a function of the model parameters. It is found that the agents are self-organizing into clusters. Furthermore, it is demonstrated that, depending on parameter values, multiple stable configurations can coexist. It occurs that only one of them always emerges with probability close to one, because its associated attractor dominates over the rest. This is shown through numerical integrations and simulations, after analytic developments. In contrast to the competitive case, agents are able to increase their capacity beyond the no-interaction case limit. In other words, when some collaborative partnership among a relatively small number of partners takes place, all agents act in good faith prioritizing the common good, when receiving a mutual benefit allowing them to surpass their capacity.

Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series.

A nonlinear dynamics approach can be used in order to quantify complexity in written texts. As a first step, a one-dimensional system is examined: two written texts by one author (Lewis Carroll) are considered, together with one translation into an artificial language (i.e., Esperanto) are mapped into time series. Their corresponding shuffled versions are used for obtaining a baseline. Two different one-dimensional time series are used here: one based on word lengths (LTS), the other on word frequencies (FTS). It is shown that the generalized Hurst exponent h(q) and the derived f(α) curves of the original and translated texts show marked differences. The original texts are far from giving a parabolic f(α) function, in contrast to the shuffled texts. Moreover, the Esperanto text has more extreme values. This suggests cascade model-like, with multiscale time-asymmetric features as finally written texts. A discussion of the difference and complementarity of mapping into a LTS or FTS is presented. The FTS f(α) curves are more opened than the LTS ones.

Retrieving true images through fine grid steps for enhancing the resolution beyond the classical limits: theory and simulations.

We developed the theory of, and tested by extended simulations, a novel method for retrieving true images in a grid step much finer than both the acquisition and the optical microscope limits. We believe that the method is promising in view of avoiding the limitations on the resolution improvement in direct imaging mode systems. Two basic concepts are involved: (i) random (up to 3D) relative displacements of objects with respect to the receiving matrix and (ii) the use of a reference object firmly fixed to small signal objects for avoiding the displacement measurements. The retrieved images are created by rearranging a set of true images acquired with a lower resolution equal to the matrix pixel size. We demonstrate the good quality of the retrieved images and the possibility to visualize and detect small (convolved) objects not observed into the captured images. The method provides good opportunities for effective applications of different inverse algorithms for improving the resolution requiring, as a rule, more precisely sampled images, but at arbitrary relations between the pixel size and the optical diffraction limit. We further demonstrated the application of some deconvolution procedures for extracting highly resolved images in the object and image planes in the presence of noise. The possibility to resolve small objects beyond the two classical limits is shown by means of simulations. The estimates for the method's limiting resolution, combined with proper deconvolution processing, show that resolution in the lower nano-dimension scale (below 10 nm) could be achieved. The requirements to the implementation of the novel method are commented as well.

Majority model on a network with communities.

We focus on the majority model in a topology consisting of two coupled fully connected networks, thereby mimicking the existence of communities in social networks. We show that a transition takes place at a value of the interconnectivity parameter. Above this value, only symmetric solutions prevail, where both communities agree with each other and reach consensus. Below this value, in contrast, the communities can reach opposite opinions and an asymmetric state is attained. The importance of the interface between the subnetworks is shown.

Brownian particle having a fluctuating mass.

We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behavior is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87, 180601 (2001)]. By performing numerical simulations of the Langevin equation, we check the theoretical predictions derived in the adiabatic limit, i.e. when the mass fluctuation time scale is much larger than the time for reaching the local equilibrium, and study deviations outside this limit. We compare the mass velocity distribution with truncated Tsallis distributions [J. Stat. Phys. 52, 479 (1988)] and find excellent agreement if the masses are chi-squared distributed. We also consider the diffusion of the Brownian particle by studying a Bernoulli random walk with fluctuating walk length in one dimension. We observe the time dependence of the position distribution kurtosis and find interesting behaviors. We point out a few physical cases, where the mass fluctuation problem could be encountered as a first approximation for agglomeration-fracture nonequilibrium processes.

Uncovering collective listening habits and music genres in bipartite networks.

In this paper, we analyze web-downloaded data on people sharing their music library, that we use as their individual musical signatures. The system is represented by a bipartite network, nodes being the music groups and the listeners. Music groups' audience size behaves like a power law, but the individual music library size is an exponential with deviations at small values. In order to extract structures from the network, we focus on correlation matrices, that we filter by removing the least correlated links. This percolation idea-based method reveals the emergence of social communities and music genres, that are visualized by a branching representation. Evidence of collective listening habits that do not fit the neat usual genres defined by the music industry indicates an alternative way of classifying listeners and music groups. The structure of the network is also studied by a more refined method, based upon a random walk exploration of its properties. Finally, a personal identification-community imitation model for growing bipartite networks is outlined, following Potts ingredients. Simulation results do reproduce quite well the empirical data.

N-body decomposition of bipartite author networks.

In this paper, we present a method to project co-authorship networks, that accounts in detail for the geometrical structure of scientists' collaborations. By restricting the scope to three-body interactions, we focus on the number of triangles in the system, and show the importance of multi-scientist (more than two) collaborations in the social network. This motivates the introduction of generalized networks, where basic connections are not binary, but involve arbitrary number of components. We focus on the three-body case and study numerically the percolation transition.

Clusters in a magnetic toy model for binary granular piles.

Results on a generalized magnetically controlled ballistic deposition model of granular piles are reported in order to search for the effect of "spin flip" probability q in building a granular pile. Two different regimes of spin cluster site distributions have been identified, a borderline q(c) (betaJ) where J is the interaction potential strength.

Dynamical model and nonextensive statistical mechanics of a market index on large time windows.

The shape and tails of partial distribution functions (PDF) for a financial signal, i.e., the S&P500 and the turbulent nature of the markets are linked through a model encompassing Tsallis nonextensive statistics and leading to evolution equations of the Langevin and Fokker-Planck type. A model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log returns for such a financial market index, for small and large time windows, and both for small and large log returns. These turbulent market volatility (of normalized log returns) distributions can be sufficiently well fitted with a chi(2) distribution. The transition between the small time scale model of nonextensive, intermittent process, and the large scale Gaussian extensive homogeneous fluctuation picture is found to be at ca. a 200 day time lag. The intermittency exponent kappa in the framework of the Kolmogorov log-normal model is found to be related to the scaling exponent of the PDF moments, thereby giving weight to the model. The large value of kappa points to a large number of cascades in the turbulent process. The first Kramers-Moyal coefficient in the Fokker-Planck equation is almost equal to zero, indicating "no restoring force." A comparison is made between normalized log returns and mere price increments.

Reexamination of the Branly effect.

The electrical resistance of a metallic granular packing has been recorded at room temperature. A nearby burster between which sparks are produced, induces a decrease in the resistance of the granular packing as described in the works of Branly. Our measurements emphasize that the decrease is continuous and the resistance variations behave like a stretched exponential law due to the creation of new electrical paths as in nucleation-growth soldering processes. This behavior has been identified to be a diffusionlike process.

Reply to "Comment on 'Power-law correlations in the southern-oscillation-index fluctuations characterizing El Niño'".

Earlier [Phys. Rev. E 63, 047201 (2001)] we studied the southern oscillation index (SOI). Our findings tended to favor specific physical models for the El Niño description. The Comment by Metzler [Phys. Rev. E 67, 018201 (2003)] on this publication does not give any argument in favor of another El Niño physical model. In contrast, the Comment points out that statistical properties of the SOI data can be explained with a model based on a linear autoregressive process, but such a modeling does not help in identifying the relevant physical mechanisms.

Power-law correlations in the southern-oscillation-index fluctuations characterizing El Niño.

The southern oscillation index (SOI) is a characteristic of the El Niño phenomenon. SOI monthly averaged data is analyzed for the time interval 1866-2000. The tail of the cumulative distribution of the fluctuations of SOI signal is studied in order to characterize the amplitude scaling of the fluctuations and the occurrence of extreme events. Large fluctuations are more likely to occur than the Gaussian distribution would predict. The time scaling of fluctuations is studied by applying the energy spectrum and the detrended fluctuation analysis statistical method. Self-affine properties are found to be pertinent to the SOI signal and therefore suggest power-law correlations of fluctuations of the signal. An antipersistent type of correlations exists for a time interval ranging from about 4 months to about 6 years. This leads to favoring specific physical models for El Niño description.