Tree size distribution as the stationary limit of an evolutionary master equation.

The diameter distribution of a given species of deciduous trees is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data in mature semi-natural forest and ancient, traditionally managed wood-pasture from Central Europe. These distribution functions collapse on a universal shape if the tree sizes are normalized to the mean value in the considered sample. A new evolutionary master equation is used to model the observed distribution. The model incorporates four ecological processes: tree growth, mortality, recruitment, and diversification. Utilizing simple and realistic kernel functions describing the first three, along with an assumed multiplicative dilution due to diversification, the stationary solution of the master equation yields the experimentally observed Gamma distribution. The model as it is formulated allows an analytically compact solution and has only two fitting parameters whose values are consistent with the experimental data related to these processes. We found that the equilibrium size distribution of tree species with different ecology, originating from two contrastingly different semi-natural ecosystem types can be accurately described by a single dynamical mean-field model.

f-Gintropy: An Entropic Distance Ranking Based on the Gini Index.

We consider an entropic distance analog quantity based on the density of the Gini index in the Lorenz map, i.e., gintropy. Such a quantity might be used for pairwise mapping and ranking between various countries and regions based on income and wealth inequality. Its generalization to f-gintropy, using a function of the income or wealth value, distinguishes between regional inequalities more sensitively than the original construction.

Transient Dynamics in the Random Growth and Reset Model.

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.

Gintropy: Gini Index Based Generalization of Entropy.

Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index, on the other hand, is an established measure for social and economical inequalities in a society. In this paper, we explore the mathematical similarities and connections in these two quantities and introduce a new measure that is capable of connecting these two at an interesting analogy level. This supports the idea that a generalization of the Gibbs-Boltzmann-Shannon entropy, based on a transformation of the Lorenz curve, can properly serve in quantifying different aspects of complexity in socio- and econo-physics.

Flickering candle flames and their collective behavior.

Oscillation and collective behavior of diffusion flames is a fascinating phenomena. Considering candle bundles with different sizes in variable oxygen concentration, the flickering dynamics of the flames are experimentally and theoretically investigated. Trends for the flickering frequency as a function of the candle number in the bundle and oxygen concentration is revealed for various topologies of the candles packing. The collective behavior of the flames as a function of their separation distance is studied by measuring an appropriate synchronization order parameter and through the common oscillation frequency. In agreement with previous results we find a discontinuous phase transition between an in-phase synchronized state at small separation distance and a counter-phase synchronized state at larger separation distances. A previously used dynamical model is modified in order to accommodate our experimental findings.

Scaling in the space-time of the Internet.

The Internet on the router level, is a complex network embedded in a geographical space. We provide experimental evidences suggesting that the average travel time for a message, with fixed length, increases roughly as the square root of the geographical distance. To understand this scaling law and other measurable topological properties of the Internet as a graph, we introduce and study a simple network model. The model is based on a few realistic socio-economic facts/assumptions and qualitatively reproduces the experimentally observed stylized facts.

Science and Facebook: The same popularity law!

The distribution of scientific citations for publications selected with different rules (author, topic, institution, country, journal, etc…) collapse on a single curve if one plots the citations relative to their mean value. We find that the distribution of "shares" for the Facebook posts rescale in the same manner to the very same curve with scientific citations. This finding suggests that citations are subjected to the same growth mechanism with Facebook popularity measures, being influenced by a statistically similar social environment and selection mechanism. In a simple master-equation approach the exponential growth of the number of publications and a preferential selection mechanism leads to a Tsallis-Pareto distribution offering an excellent description for the observed statistics. Based on our model and on the data derived from PubMed we predict that according to the present trend the average citations per scientific publications exponentially relaxes to about 4.

Dynamical stationarity as a result of sustained random growth.

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast-growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master equation. The derivation of elementary rates from known stationary distributions is a generalization of the fluctuation-dissipation theorem. Entropic distance evolution is given for such systems. We reconstruct distributions obtained for growing networks, particle production, scientific citations, and income distribution.

Cell-size distribution and scaling in a one-dimensional Kolmogorov-Johnson-Mehl-Avrami lattice model with continuous nucleation.

The Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth model is considered on a one-dimensional (1D) lattice. Cells can grow with constant speed and continuously nucleate on the empty sites. We offer an alternative mean-field-like approach for describing theoretically the dynamics and derive an analytical cell-size distribution function. Our method reproduces the same scaling laws as the KJMA theory and has the advantage that it leads to a simple closed form for the cell-size distribution function. It is shown that a Weibull distribution is appropriate for describing the final cell-size distribution. The results are discussed in comparison with Monte Carlo simulation data.

Time-scale effects on the gain-loss asymmetry in stock indices.

The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over 2%, and it is the result of the non-Pearson-type autocorrelations in the index. These non-Pearson-type correlations can be viewed also as functionally dependent daily volatilities, extending for a finite time interval. A generalized time-window shuffling method is used to show the existence of such autocorrelations. Their characteristic time scale proves to be smaller (less than 25 trading days) than what was previously believed. It is also found that this characteristic time scale has decreased with the appearance of program trading in the stock market transactions. Connections with the leverage effect are also established.

Further We Travel the Faster We Go.

The average travelling speed increases in a nontrivial manner with the travel distance. This leads to scaling-like relations on quite extended spatial scales, for all mobility modes taken together and also for a given mobility mode in part. We offer a wide range of experimental results, investigating and quantifying this universal effect and its measurable causes. The increasing travelling speed with the travel distance arises from the combined effects of: choosing the most appropriate travelling mode; the structure of the travel networks; the travel times lost in the main hubs, starting or target cities; and the speed limit of roads and vehicles.

Chaos on the conveyor belt.

The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by a spring to an external static point and, due to the dragging effect of the belt, the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can be achieved only by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic, dynamics and phase transition-like behavior. Noise-induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks (around five).

Human mobility in a continuum approach.

Human mobility is investigated using a continuum approach that allows to calculate the probability to observe a trip to any arbitrary region, and the fluxes between any two regions. The considered description offers a general and unified framework, in which previously proposed mobility models like the gravity model, the intervening opportunities model, and the recently introduced radiation model are naturally resulting as special cases. A new form of radiation model is derived and its validity is investigated using observational data offered by commuting trips obtained from the United States census data set, and the mobility fluxes extracted from mobile phone data collected in a western European country. The new modeling paradigm offered by this description suggests that the complex topological features observed in large mobility and transportation networks may be the result of a simple stochastic process taking place on an inhomogeneous landscape.

Spring-block model reveals region-like structures.

A mechanical spring-block model is used for realizing an objective space partition of settlements from a geographic territory in region-like structures. The method is based on the relaxation-dynamics of the spring-block system and reveals in a hierarchical manner region-like entities at different spatial scales. It takes into account in an elegant manner both the spatiality of the elements and the connectivity relations among them. Spatiality is taken into account by using the geographic coordinates of the settlements, and by detecting the neighbors with the help of a Delaunay triangulation. Connectivity between neighboring settlements are quantified using a Pearson-like correlation for the relative variation of a relevant socio-economic parameter (population size, GDP, tax payed per inhabitant, etc.). The method is implemented in an interactive JAVA application and it is applied with success for an artificially generated society and for the case of USA, Hungary and Transylvania.

Criticality and pattern formation in fracture by residual stresses.

We address the slow generation of crack networks as a problem of pattern formation. Issues of pattern selection and the associated statistical properties were considered by means of a detailed theoretical analysis and simulations of a discrete spring-block model. Developed after observations in desiccation experiments, the model describes the nucleation and propagation of cracks in a layer in contact with a frictional substrate. Competition between stress concentration at crack tips and pinning effect by friction leads to a cellular pattern. We characterized the events prior to cracking by a growth of correlation in the stress field, and those during cracking by progressive damages manifested in the number of broken bonds and energy releases. Qualitatively distinct regimes were shown to correspond to different stages of development. A host of scaling behaviors in measurable quantities were derived and verified. In particular, consistent with experiments, fragment area was found to be quadratic in the layer thickness and be smaller with increasing friction, which explains why morphologically similar patterns may occur over a diverse length scales.

Persistent collective trend in stock markets.

Empirical evidence is given for a significant difference in the collective trend of the share prices during the stock index rising and falling periods. Data on the Dow Jones Industrial Average and its stock components are studied between 1991 and 2008. Pearson-type correlations are computed between the stocks and averaged over stock pairs and time. The results indicate a general trend: whenever the stock index is falling the stock prices are changing in a more correlated manner than in case the stock index is ascending. A thorough statistical analysis of the data shows that the observed difference is significant, suggesting a constant fear factor among stockholders.