Power-law relaxation in human violent conflicts

We study relaxation patterns of violent conflicts after bursts of activity. Data were obtained from available catalogs on the conflicts in Iraq, Afghanistan and Northern Ireland. We find several examples in each catalog for which the observed relaxation curves can be well described by an asymptotic power-law decay (the analog of the Omori’s law in geophysics). The power-law exponents are robust, nearly independent of the conflict. We also discuss the exogenous or endogenous nature of the shocks. Our results suggest that violent conflicts share with earthquakes and other natural and social phenomena a common feature in the dynamics of aftershocks.     

Power-law stellar distributions

The density profiles and other quantities of physical interest for spherically symmetric systems are computed by assuming that a collisionless stellar gas may relax to the non-Gaussian power-law distribution suggested by the nonextensive kinetic theory. There are two different classes of solutions. The first class behaves like a subset of the polytropic Lane–Emden spheres, whereas the second one corresponds to a transition between two different potytropic indices. Unlike the isothermal Maxwellian sphere, the total mass and sizes of both classes are finite for a large range of the nonextensive q-parameter.     

Power-law tail distributions and nonergodicity

We establish an explicit correspondence between ergodicity breaking in a system described by power-law tail distributions and the divergence of the moments of these distributions.     

Power-law tails from multiplicative noise

We show that the well-known linear Langevin equation, modeling the Brownian motion and leading to a Gaussian stationary distribution of the corresponding Fokker-Planck equation, is changed by the smallest multiplicative noise. This leads to a power-law tail of the distribution for sufficiently large momenta. At finite ratio of the correlation strength for the multiplicative and the additive noises the stationary energy distribution becomes exactly the Tsallis distribution.     

Power-law inflation with exponential potentials

We investigate some power-law solutions in inflationary cosmology, both by analytic and numerical means, considering first a simple model of a scalar field with an exponential field coupled to gravity. As has been pointed out recently by Yokoyama and Maeda, in power-law inflation viscous forces caused by couplings of the inflation to other particles can be important. We use numerical simulation to examine the effects of this viscosity on the inflation, for both a simple exponential potential and a more realistic potential motivated by particle physics. In general, the viscosity enhances the exponent of the power-law inflation, increasing the efficiency of inflation in power-law models, and we outline a specific inflationary model featuring viscosity.     

Power-law distribution of gene expression fluctuations

Large-scale genomic technologies has opened new possibilities to infer gene regulatory networks from time series data. Here, we investigate the relationship between the dynamic information of gene expression in time series and the underlying network structure. First, our results show that the distribution of gene expression fluctuations (i.e., standard deviation) follows a power-law. This finding indicates that while most genes exhibit a relatively low variation in expression level, a few genes are revealed as highly variable genes. Second, we propose a stochastic model that explains the emergence of this power-law behavior. The model derives a relationship that connects the standard deviation (variance) of each node to its degree. In particular, it allows us to identify a global property of the underlying genetic regulatory network, such as the degree exponent, by only computing dynamic information. This result not only offers an interesting link to explore the topology of real systems without knowing the real structure but also supports earlier findings showing that gene networks may follow a scale-free distribution.     

Power-law time distribution of large earthquakes

We study the statistical properties of time distribution of seismicity in California by means of a new method of analysis, the diffusion entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent mu=2.06+/-0.01. We propose the long-range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes.     

Further regularities in period-doubling bifurcations

The period-doubling bifurcations of the map x → x′ = f(λ, x) is known to be characterized by a generalized renormalization ground expressing simultaneous scaling in λ and x along the central sequence of bifurcation points (i.e. the sequence which converges to the maximum in f). For other sequences (e.g. the sequence with the largest x in each cycle), the generalized RG is valid only in a well defined subclass of functions S. For other cases, only separate scalings in λ and in x are valid. However, every f can be related to a representative f in S by a linear conjugacy, so that the generalized RG nevertheless reflects a universal regularity. Moreover, the spacings of the bifurcation points are found to be characterized by novel subasymptotic eigenvalues related to δ and α.     

Power-law statistics for avalanches in a martensitic transformation

We devise a two-dimensional model that mimics the recently observed power-law distributions for the amplitudes and durations of the acoustic emission signals observed during martensitic transformation [Vives et al., Phys. Rev. Lett. 72, 1694 (1994)]. We include a threshold mechanism, long-range interaction between the transformed domains, inertial effects, and dissipation arising due to the motion of the interface. The model exhibits thermal hysteresis and, more importantly, it shows that the energy is released in the form of avalanches with power-law distributions for their amplitudes and durations. Computer simulations also reveal morphological features similar to those observed in real systems.     

Power-law spatial correlations in arrays of locally coupled lasers

We investigate correlations of the intensity fluctuations of two-dimensional arrays of nonidentical, locally coupled lasers, numerically and experimentally. We find evidence of a power-law dependence of spatial correlations as a function of laser pair distance (or coupling strength) near the phase-locking threshold.     

Power-law scaling for macroscopic entropy and microscopic complexity: evidence from human movement and posture

We investigated the relationship between macroscopic entropy and microscopic complexity of the dynamics of body rocking and sitting still across adults with stereotyped movement disorder and mental retardation (profound and severe) against controls matched for age, height, and weight. This analysis was performed through the examination of center of pressure (COP) motion on the mediolateral (side-to-side) and anteroposterior (fore-aft) dimensions and the entropy of the relative phase between the two dimensions of motion. Intentional body rocking and stereotypical body rocking possessed similar slopes for their respective frequency spectra, but differences were revealed during maintenance of sitting postures. The dynamics of sitting in the control group produced lower spectral slopes and higher complexity (approximate entropy). In the controls, the higher complexity found on each dimension of motion was related to a weaker coupling between dimensions. Information entropy of the relative phase between the two dimensions of COP motion and irregularity (complexity) of their respective motions fitted a power-law function, revealing a relationship between macroscopic entropy and microscopic complexity across both groups and behaviors. This power-law relation affords the postulation that the organization of movement and posture dynamics occurs as a fractal process.     

Approaching human language with complex networks

The interest in modeling and analyzing human language with complex networks is on the rise in recent years and a considerable body of research in this area has already been accumulated. We survey three major lines of linguistic research from the complex network approach: 1) characterization of human language as a multi-level system with complex network analysis; 2) linguistic typological research with the application of linguistic networks and their quantitative measures; and 3) relationships between the system-level complexity of human language (determined by the topology of linguistic networks) and microscopic linguistic (e.g., syntactic) features (as the traditional concern of linguistics). We show that the models and quantitative tools of complex networks, when exploited properly, can constitute an operational methodology for linguistic inquiry, which contributes to the understanding of human language and the development of linguistics. We conclude our review with suggestions for future linguistic research from the complex network approach: 1) relationships between the system-level complexity of human language and microscopic linguistic features; 2) expansion of research scope from the global properties to other levels of granularity of linguistic networks; and 3) combination of linguistic network analysis with other quantitative studies of language (such as quantitative linguistics).     

Power-law statistics of intermittent photoluminescence in single semiconductor nanocrystals

A physical model is proposed for a single CdSe nanocrystal coated with a ZnS shell which can explain the power-law statistics of its experimentally observed intermittent photoluminescence. If the localized electron-hole pairs (excitons) form in the nanocrystal, this suggestion alone will suffice to explain why the on-time distribution follows the law close to t ^?1.5 found experimentally.     

Power-law electron and ion distributions in a strong magnetic field

The possibility of establishing steady-state power-law distributions with constant fluxes in systems comprised of two kinds of particles is investigated. A local distribution n_e= p _e ^3/2 , which is established in pulsar magnetospheres, is derived for magnetized electrons interacting with ions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenij, Radiofizika, Vol. 21, No. 11, pp. 1549–1557, November, 1978.     

Power-law for axon diameters at branch point

Background

Axon calibers vary widely among different animals, neuron classes, and even within the same neuron. What determines the diameter of axon branches?

Results

We pursue the hypothesis that the axon caliber has evolved to minimize signal propagation delays, while keeping arbor volume to a minimum. For a general cost function, we show that the optimal diameters of mother and daughter branches at a bifurcation satisfy a power law. The derivation relies on the fact that the axon conduction speed scales as a power of axon diameter. Although available data are consistent with the law, there is a large spread in the data. Future experimental tests will determine whether this spread is due to biological variability or measurement error.

Conclusions

Minimization of arbor volume and signal propagation delay may have been an important factor in the evolution of the brain.

     

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.     

Power-law scaling of proton conductivity in amorphous silicate thin films

Amorphous hafnium silicate, a-Hf_0.1Si_0.9O_x, thin film with thickness of 32, 41, 55, 80, 110, 120, 180 and 320 nm was prepared by multiple spin-cast process and the proton conductivity across the films was measured at intermediate temperatures (100-400 °C) in dry atmosphere. The morphologically- and compositionally-uniform films were prepared on a substrate as confirmed by SEM, RBS and XPS measurements. a-Hf_0.1Si_0.9O_x thin film clearly revealed the H/D isotope effect on ionic conductivity, indicating that protonic conduction is dominant in the measured temperature range. The films did not reveal thickness-dependent proton conductivity in dry air and the σ at given temperatures is almost constant at any thickness. No increment of σ in a-Hf_0.1Si_0.9O_x thin films by reduction of thickness might be related to the absence of the highly-conductive acid network with mesoscopically-sized length because of the relatively low concentration of Brønsted acid sites inside films.