A continuous model of human dynamics

Ideas and tools from statistical physics have recently been applied to the investigation of human dynamics. The timing of human activities, in particular, has been studied both experimentally and analytically. Empirical data show that, in many different situations, the time interval separating two consecutive tasks executed by an individual follows a heavy-tailed probability distribution rather than Poisson statistics. To account for this data, human behaviour has been viewed as a decision-based queuing system where individuals select and execute tasks belonging to a finite list of items as an increasing function of a task priority parameter. It is then possible to obtain analytically the empirical result P(τ)∼1/τ, where P(τ) is the waiting time probability distribution.Here a continuous model of human dynamics is introduced using instead an infinite queuing list. In contrast with the results obtained by other models in the finite case we find a waiting time distribution explicitly depending on the priority distribution density function ρ. The power-law scaling P(τ)∼1/τ is then recovered when ρ is exponentially distributed.     

Cluster growth poised on the edge of break-up: Size distributions with small exponent power-laws

In many naturally occurring growth processes, cluster size distributions of power-law form n(s)∝s^−τ with small exponents 0<τ<1 are observed. We suggest here that such distributions emerge naturally from cluster growth, where size dependent aggregation is counterbalanced by size dependent break-up. The model used in the study is a simple reaction kinetic model including only monomer-cluster processes. It is shown that under such conditions power-law size distributions with small exponents are obtained. Therefore, the results suggest that the ubiquity of small exponent power-law distributions is related to the growth process, where aggregation driven cluster growth is poised on the edge of cluster break-up.     

Detection of collective motions in dielectric spectra and the meaning of the generalized Vogel-Fulcher-Tamman equation

Based on the reduction property of dielectric spectra associated with the power-law function [∼(jωτ)^±ν] that appears in the frequency domain, one can develop an effective procedure for detection of different reduced motions (described by the corresponding power-law exponents) in temperature domain. If the power-law exponent ν is related to characteristic relaxation time τ by the relationship ν=ν₀ ln(τ/τ_s)/ln(τ/τ₀) (here τ_s, τ₀ are the characteristic times characterizing a movement over fractal cluster that is defined in Ref. [Ya.E. Ryabov, Yu. Feldman, J. Chem. Phys. 116 (2002) 8610]) and the simple temperature dependence of τ(T)=τ_A exp(E/T) obeys the traditional Arrhenius relationship, then one can prove that any extreme point figuring in the complex permittivity ε(jω) spectra (characterized by the values [ω_m, y(ω_m)]) obeys the generalized Vogel-Fulcher-Tamman (VFT) equation. This important statement confirms the existence of the ‘universal’ response (UR) (discovered and classified by Jonscher in frequency domain) and opens new possibilities in the detection of the ‘hidden’ collective motions in temperature region for self-similar (heterogeneous) systems. It gives also the extended interpretation of the VFT equation and allows one to differentiate collective motions passing through an extreme point. This differentiation, in turn, allows one to select the proper fitting function containing one or two (at least) relaxation times for the fitting of the complex permittivity function ε(jω) in the limited frequency domain. This conclusion can allow for the classification of dielectric spectroscopy as the spectroscopy of the reduced (collective) motions, which are described by different power-law exponents on the mesoscale region. The verification of this approach on available DS data (poly(ethylene glycol)-based-single-ion conductors) completely confirms the basic statements of this theory and opens new possibilities in general classification of different motions that can be detected in the analysis of the different dielectric permittivity spectra.     

Effect of particle size distribution and dynamics on the performance of two-dimensional packing

Extensive computer simulation is used to revisit and to generalize two classical problems: (i) the random car-parking dynamics of A. Rényi and (ii) the irreversible random sequential adsorption (RSA) of parallel squares of same size on a planar substrate of area L². In this paper, differently from the classical RSA, the squares obey the size distribution n(a)=n(1)a^−τ, where a=1,2,3,… is the area of the squares. Using this scaling distribution and three classes of packing dynamics we study the final packing fraction of particles, ?(τ,L), and in particular its thermodynamic limit L→∞. We show that the efficiency to attain a high/low packing density of particles on the substrate is strongly dependent on the value of the exponent τ and on the characteristics of the dynamics.     

Invasion percolation between two sites in two, three, and four dimensions

The mass distribution of invaded clusters in non-trapping invasion percolation between an injection site and an extraction site has been studied, in two, three, and four dimensions. This study is an extension of the recent study focused on two dimensions by Araújo et al. [A.D. Araújo, T.F. Vasconcelos, A.A. Moreira, L.S. Lucena, J.S. Andrade Jr., Phys. Rev. E 72 (2005) 041404] with respect to higher dimensions. The mass distribution exhibits a power-law behavior, P(m)∝m^−α. It has been found that the index α for p_e<p_c, p_c being the percolation threshold of a regular percolation, appears to be independent of the value of p_e and is also independent of the lattice dimensionality. When p_e=p_c, α appears to depend marginally on the lattice dimensionality, and the relation α=τ−1, τ being the exponent associated with cluster size distribution of a regular percolation via n_s∝s^−τ, appears to be valid.     

Study on probability distributions for evolution in modified extremal optimization

It is widely believed that the power-law is a proper probability distribution being effectively applied for evolution in τ-EO (extremal optimization), a general-purpose stochastic local-search approach inspired by self-organized criticality, and its applications in some NP-hard problems, e.g., graph partitioning, graph coloring, spin glass, etc. In this study, we discover that the exponential distributions or hybrid ones (e.g., power-laws with exponential cutoff) being popularly used in the research of network sciences may replace the original power-laws in a modified τ-EO method called self-organized algorithm (SOA), and provide better performances than other statistical physics oriented methods, such as simulated annealing, τ-EO and SOA etc., from the experimental results on random Euclidean traveling salesman problems (TSP) and non-uniform instances. From the perspective of optimization, our results appear to demonstrate that the power-law is not the only proper probability distribution for evolution in EO-similar methods at least for TSP, the exponential and hybrid distributions may be other choices.     

Scale-free networks by super-linear preferential attachment rule

A network growth model with geographic limitation of accessible information about the status of existing nodes is investigated. In this model, the probability Π(k) of an existing node of degree k is found to be super-linear with Π(k)∼k^α and α>1 when there are links from new nodes. The numerical results show that the constructed networks have typical power-law degree distributions P(k)∼k^−γ and the exponent γ depends on the constraint level. An analysis of local structural features shows the robust emergence of scale-free network structure in spite of the super-linear preferential attachment rule. This local structural feature is directly associated with the geographical connection constraints which are widely observed in many real networks.     

Coevolutionary extremal dynamics on gasket fractal

We considered a Bak-Sneppen model on a Sierpinski gasket fractal. We calculated the avalanche size distribution and the distribution of distances between subsequent minimal sites. To observe the temporal correlations of the avalanche, we estimated the return time distribution, the first-return time, and the all-return time distribution. The avalanche size distribution follows the power law, P(s)∼s−τ, with the exponent τ=1.004(7). The distribution of jumping sites also follows the power law, P(r)∼r−π, with the critical exponent π=4.12(4). We observe the periodic oscillation of the distribution of the jumping distances which originated from the jumps of the level when the minimal site crosses the stage of the fractal. The first-return time distribution shows the power law, Pf(t)∼t−τf, with the critical exponent τf=1.418(7). The all-return time distribution is also characterized by the power law, Pa(t)∼t−τa, with the exponent τa=0.522(4). The exponents of the return time satisfy the scaling relation τf+τa=2 for τf?2.     

Growing networks with preferential deletion and addition of edges

A preferential attachment model for a growing network incorporating the deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t=1,2,…, with probability π₁>0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π₂ a vertex is chosen proportionally to its degree and an edge is added between this vertex and a randomly chosen other vertex, and with probability π₃=1−π₁−π₂<1/2 a vertex is chosen proportionally to its degree and a random edge of this vertex is deleted. The model is intended to capture a situation where high-degree vertices are more dynamic than low-degree vertices in the sense that their connections tend to be changing. A recursion formula is derived for the expected asymptotic fraction p_k of vertices with degree k, and solving this recursion reveals that, for π₃<1/3, we have p_k∼k^{−(3−7π₃)/(1−3π₃)}, while, for π₃>1/3, the fraction p_k decays exponentially at rate (π₁+π₂)/2π₃. There is hence a non-trivial upper bound for how much deletion the network can incorporate without losing the power-law behavior of the degree distribution. The analytical results are supported by simulations.     

Random pseudofractal networks with competition

In this paper, we present a simple rule which assigns fitness to each edge to generate random pseudofractal networks (RPNs). This RPN model is both scale-free and small-world. We obtain the theoretical results that the power-law exponent is γ=2+1/(1+α) for the tunable parameter α>-1, and that the degree distribution is of an exponential form for others. Analytical results also show that an RPN has a large clustering coefficient and can process hierarchical structure as C(k)∼k^-1 that is in accordance with many real networks. And we prove that the mean distance L(N) scales slower logarithmically with network size N. In particular, we explain the effect of nodes with degree 2 on the clustering coefficient. These results agree with numerical simulations very well.     

Lepton mixing under the lepton charge nonconservation, neutrino masses and oscillations and the “forbidden” decay µ− → e − + γ

The lepton-charge (L _e , L _μ , L _τ ) nonconserving interaction leads to the mixing of the electron, muon, and tau neutrinos, which manifests itself in spatial oscillations of a neutrino beam, and also to the mixing of the electron, negative muon, and tau lepton, which, in particular, may be the cause of the “forbidden” radiative decay of the negative muon into the electron and γ quantum. Under the assumption that the nondiagonal elements of the mass matrices for neutrinos and ordinary leptons, connected with the lepton charge nonconservation, are the same, and by performing the joint analysis of the experimental data on neutrino oscillations and experimental restriction for the probability of the decay µ^? → e ^? + γ per unit time, the following estimate for the lower bound of neutrino mass has been obtained: m ^(ν) > 1.5 eV/c ².     

Dynamic and spatial behavior of a corrugated interface in the driven lattice gas model

The spatiotemporal behavior of an initially corrugated interface in the two-dimensional driven lattice gas (DLG) model with attractive nearest-neighbors interactions is investigated via Monte Carlo simulations. By setting the system in the ordered phase, with periodic boundary conditions along the external field axis. i.e. horizontal, and open along the vertical directions respectively, an initial interface was imposed, that consists in a series of sinusoidal profiles with amplitude A₀ and wavelength λ set parallel to the applied driving field axis. We studied the dynamic behavior of its statistical width or roughness W(t), defined as the root mean square of the interface position. We found that W(t) decays exponentially for all λ and lattice longitudinal sizes L_x, i.e., the lattice side that runs along the axis of the external field. We determined its relaxation time τ, and found that depends on λ as a power law τ∝λ^p, where p depends on the temperature and L_x. At low T’s (T?T_c(E)) and large L_x, p approaches to p=3/2. At intermediate T’s (T<T_c(E)), p decreases up to p≈1, and is free of finite effects. This indicates that the interface stabilizes faster than in the equilibrium model, i. e. the Ising lattice gas (E=0) where p=3. At higher T’s p increases for T?T_c(E), and the finite size dependence is recovered. Also, if T is fixed, p increases with L_x until it saturates at large values of it, while this regime is vanishing at T?T_c(E). In this way, the dynamic relaxation process of a sinusoidal interface is improved by the external driving field with respect to its equilibrium counterpart, if the system is set in an intermediate temperature stage far from T_c(E) and in a lattice with a sufficiently large longitudinal side. The behavior of τ was also investigated as a function of E and in the intermediate stage T<T_c(E). It was found that τ decreases exponentially with E in the interval 0<E?1, while for higher fields it remains constant. The exponential decay depends on the wavelength of the initial profile.In order to study the spatial evolution of the profiles, we evaluated the structure factor of the interface, and the Fourier coefficients corresponding to the same wave vector of the initial profile. The obtained results allowed us to conclude that the spatial evolution of the profile maintains its initial wavelength, does not travel along the external field axis, and its shape is preserved over all the relaxation process.     

Tau decays into kaons

Predictions for semi-leptonic decay rates of theτ lepton into two meson final statesK ^?π⁰ v _τ, $\overline {K^0 } \pi - v_\tau $ ,K ⁰ K ^? v _τ, and three meson final statesK ^?π^? K ⁺ v _τ, $K^0 \pi ^ - \overline {K^0 } v_\tau $ ,K _sπ^? K _s v _τ,K _sπ^? K _L v _τ,K _Lπ^? K _L v _τ,K ^?π⁰ K ⁰ v _τ, π⁰π⁰ K ^? v _τ,K ^?π^?π⁺ v _τ, π^? K ⁰π⁰ v _τ are derived. The hadronic matrix elements are expressed in terms of form factors, which can be predicted by chiral Lagrangians supplemented by informations about all possible low-lying resonances in the different channels. Isospin symmetry relations among the different final states are carefully taken into account. The calculated branching ratios are compared with measured decay rates where data are available.     

Epidemic outbreaks in growing scale-free networks with local structure

The class of generative models has already attracted considerable interest from researchers in recent years and much expanded the original ideas described in BA model. Most of these models assume that only one node per time step joins the network. In this paper, we grow the network by adding n interconnected nodes as a local structure into the network at each time step with each new node emanating m new edges linking the node to the preexisting network by preferential attachment. This successfully generates key features observed in social networks. These include power-law degree distribution p_k∼k^−(3+μ), where μ=(n−1)/m is a tuning parameter defined as the modularity strength of the network, nontrivial clustering, assortative mixing, and modular structure. Moreover, all these features are dependent in a similar way on the parameter μ. We then study the susceptible-infected epidemics on this network with identical infectivity, and find that the initial epidemic behavior is governed by both of the infection scheme and the network structure, especially the modularity strength. The modularity of the network makes the spreading velocity much lower than that of the BA model. On the other hand, increasing the modularity strength will accelerate the propagation velocity.     

Intermittency in the atmospheric surface layer: Unresolved or slowly varying?

We present streamwise velocity structure functions 〈δv_L(τ)〉=〈|v(t+τ)−v(t)|^p〉 (with p=1:5) obtained in the near neutral atmospheric surface layer at the Utah SLTEST site at the highest terrestrial Reynolds number Re_τ=O(10⁶). We show that the occurrence of very large scale coherent oscillations in the streamwise velocity throughout the wall region, interpreted as genuine structural features of the canonical turbulent boundary layer, affects the scaling exponents of the p>3 order structure functions. This results in a slight alteration of the intermittent behavior of the velocity field. It was found that for positive (fast) large scale oscillation of the low-pass filtered velocity signal, deviations from the Kolmogorov K41 prediction (absence of multiscaling) are more marked, as compared to negative (slow) excursion. The results are discussed in terms of convergence of statistics from atmospheric boundary layer measurements.     

Percolation in a network with long-range connections: Implications for cytoskeletal structure and function

Cell shape, signaling, and integrity depend on cytoskeletal organization. In this study we describe the cytoskeleton as a simple network of filamentary proteins (links) anchored by complex protein structures (nodes). The structure of this network is regulated by a distance-dependent probability of link formation as P=p/d^s, where p regulates the network density and s controls how fast the probability for link formation decays with node distance (d). It was previously shown that the regulation of the link lengths is crucial for the mechanical behavior of the cells. Here we examined the ability of the two-dimensional network to percolate (i.e. to have end-to-end connectivity), and found that the percolation threshold depends strongly on s. The system undergoes a transition around s=2. The percolation threshold of networks with s<2 decreases with increasing system size L, while the percolation threshold for networks with s>2 converges to a finite value. We speculate that s<2 may represent a condition in which cells can accommodate deformation while still preserving their mechanical integrity. Additionally, we measured the length distribution of F-actin filaments from publicly available images of a variety of cell types. In agreement with model predictions, cells originating from more deformable tissues show longer F-actin cytoskeletal filaments.     

A new deterministic complex network model with hierarchical structure

We introduce a new simple pseudo tree-like network model, deterministic complex network (DCN). The proposed DCN model may simulate the hierarchical structure nature of real networks appropriately and have the unique property of ‘skipping the levels’, which is ubiquitous in social networks. Our results indicate that the DCN model has a rather small average path length and large clustering coefficient, leading to the small-world effect. Strikingly, our DCN model obeys a discrete power-law degree distribution P(k)∝k^−γ, with exponent γ approaching 1.0. We also discover that the relationship between the clustering coefficient and degree follows the scaling law C(k)∼k⁻¹, which quantitatively determines the DCN's hierarchical structure.     

Power-law behavior in complex organizational communication networks during crisis

Communication networks can be described as patterns of contacts which are created due to the flow of messages and information shared among participating actors. Contemporary organizations are now commonly viewed as dynamic systems of adaptation and evolution containing several parts, which interact with one another both in internal and in external environment. Although there is limited consensus among researchers on the precise definition of organizational crisis, there is evidence of shared meaning: crisis produces individual crisis, crisis can be associated with positive or negative conditions, crises can be situations having been precipitated quickly or suddenly or situations that have developed over time and are predictable etc. In this research, we study the power-law behavior of an organizational email communication network during crisis from complexity perspective. Power law simply describes that, the probability that a randomly selected node has k links (i.e. degree k) follows P(k)∼k^−γ, where γ is the degree exponent. We used social network analysis tools and techniques to analyze the email communication dataset. We tested two propositions: (1) as organization goes through crisis, a few actors, who are prominent or more active, will become central, and (2) the daily communication network as well as the actors in the communication network exhibit power-law behavior. Our preliminary results support these two propositions. The outcome of this study may provide significant advancement in exploring organizational communication network behavior during crisis.     

The Incipient Infinite Cluster for High-Dimensional Unoriented Percolation

We consider bond percolation on $\mathbb{Z}^d$ at the critical occupation density p _c for d>6 in two different models. The first is the nearest-neighbor model in dimension d?6. The second model is a “spread-out” model having long range parameterized by L in dimension d>6. In the spread-out case, we show that the cluster of the origin conditioned to contain the site x weakly converges to an infinite cluster as |x|→∞ when d>6 and L is sufficiently large. We also give a general criterion for this convergence to hold, which is satisfied in the case d?6 in the nearest-neighbor model by work of Hara.⁽¹²⁾ We further give a second construction, by taking p<p _c , defining a measure $\mathbb{Q}^p $ and taking its limit as p↗p ^? _c . The limiting object is the high-dimensional analogue of Kesten's incipient infinite cluster (IIC) in d=2. We also investigate properties of the IIC such as bounds on the growth rate of the cluster that show its four-dimensional nature. The proofs of both the existence and of the claimed properties of the IIC use the lace expansion. Finally, we give heuristics connecting the incipient infinite cluster to invasion percolation, and use this connection to support the well-known conjecture that for d>6 the probability for invasion percolation to reach a site x is asymptotic to c|x|^?(d?4) as |x|→∞.     

An evolving model of online bipartite networks

Understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e-commerce services nowadays. Recently, various attempts have been tried to propose different models, resulting in either power-law or exponential degree distributions. However, many empirical results show that the user degree distribution actually follows a shifted power-law distribution, the so-called Mandelbrot’s law, which cannot be fully described by previous models. In this paper, we propose an evolving model, considering two different user behaviors: random and preferential attachment. Extensive empirical results on two real bipartite networks, Delicious and CiteULike  , show that the theoretical model can well characterize the structure of real networks for both user and object degree distributions. In addition, we introduce a structural parameter p$p$, to demonstrate that the hybrid user behavior leads to the shifted power-law degree distribution, and the region of power-law tail will increase with the increment of p$p$. The proposed model might shed some lights in understanding the underlying laws governing the structure of real online bipartite networks.