Scale-free Behaviors Research Articles

Noncooperative Population-Based Search Relying on Spatial and/or Temporal Scale-Free Behaviors of Individuals

Although individuals of species engaging in cooperative foraging behaviors are often modeled as swarm intelligence optimization algorithms, there are also several species whose individuals take noncooperative foraging behaviors. Some such species exhibit common behaviors, which we call scale-free behaviors in this study. A type of scale-free behavior is spatial scale-free behavior, in which the moving distance of an individual from the present food source follows a power-law distribution. Second, the staying duration of an individual at the current food source follows a power-law distribution, and this behavior is called temporal scale-free behavior. We propose two types of noncooperative population-based search methods, based on the two types of scale-free behaviors. We also conducted simulations to compare the two methods, assuming static and dynamic environments in which the position of the food source did not change and changed, respectively. The simulation results showed that temporal scale-free behavior is suitable for specific problems in which individuals around the global optimum can be eliminated probabilistically, and spatial scale-free behavior is suitable for problems in which such elimination never occurs. In other words, the two types of scale-free behaviors are complementary. Next, we first assume problems for which we cannot know if the probabilistic elimination of individuals occurs in advance, and then propose a search method that selects an appropriate type of scale-free behavior for individuals during the search. The simulation results showed that this method demonstrates a good search performance, on average, for such problems.

Fitting Cumulus Cloud Size Distributions From Idealized Cloud Resolving Model Simulations

AbstractWhereas it is now widely accepted that cumulus cloud sizes are power‐law distributed, characteristic exponents reported in the literature vary greatly, generally taking values between 1 and >3. Although these differences might be explained by variations in environmental conditions or physical processes organizing the cloud ensembles, the use of improper fitting methods may also introduce large biases. To address this issue, we propose to use a combination of maximum likelihood estimation and goodness‐of‐fit tests to provide more robust power‐law fits while systematically identifying the size range over which these fits are valid. The procedure is applied to cloud size distributions extracted from two idealized high‐resolution simulations displaying different organization characteristics. Overall, power‐laws are found to be outperformed by alternative distributions in almost all situations. When clouds are identified based on a condensed water path threshold, using power‐laws with an exponential cutoff yields the best results as it provides superior fits in the tail of the cloud size distributions. For clouds identified using a combination of water content and updraft velocity thresholds in the free troposphere, no substantial improvement over pure power‐laws can be found when considering more complex two‐parameter distributions. In this context however, exponential distributions provide results that are as good as, if not better than power‐laws. Finally, it is demonstrated that the emergence of scale free behaviors in cloud size distributions is related to exponentially distributed cloud cores merging as they are brought closer to each other by underlying organizing mechanisms.

Two-Stage Structural and Slowing-Down Percolation Transitions in the Densifying Cancer Cell Monolayer.

We experimentally demonstrate the two-stage structural and slowing-down percolating transitions, followed by the confluent transition in the densifying cancer cell monolayers from the dilute state, and investigate their impacts on collective cell dynamics. It is found that cells aggregate into clusters at low cell density. With increasing cell number density, the structural percolation through the formation of a large cell cluster percolating through the space precedes the dynamical percolation transition of forming a percolating cluster of slow cell elements. Both percolating transitions exhibit scale-free scaling behaviors of cluster size distributions and fractal structures, similar to those of the universality class of 2D nonequilibrium systems governed by percolation theory. Dynamically, at low cell density, cell aggregation enhances cooperative motion. The structural percolation leads to slower motion, especially with stronger suppression for the high-frequency modes in the turbulent-like velocity power spectra. The following slowing-down percolation associated with the onset of cell crowding in regions occupied by cells further enhances dynamical slowing-down, and suppresses the increasing trend of dynamical heterogeneity and the steepening of the power spectrum of motion, until their reversions after the confluent transition.

Understanding spatial-temporal travel demand of free-floating bike sharing connecting with metro stations

Free-floating bike sharing usage for metro access provides a decent solution to the first- and last-mile problem. A fundamental and still open problem is the spatial and temporal regularities of bike sharing usage integrated with metro stations, which are crucial to achieve a seamless connection and provide an efficient transport system. In this paper, we conduct the usage of bike-and-ride in Beijing as an example to address this issue from macro-level and micro-level perspectives. First, the macroscopic usages, including distinct characteristics of time-varying trips and scaling relationships of spatial distribution, are explored in urban and suburban areas. Then, by adequately deconstructing temporal-spatial trips of bike-and-ride, the bike sharing usage is revealed to follow a power-law distribution with different exponents on weekdays and weekends. Our results suggest that scale-free behaviors for microcosmic travel demand exist across the city. These vital phenomena switch within the same region on different time ranges such as morning and evening peaks but similar scaling relations on different days. The findings improve our understanding of usage patterns and demand distribution of this emerging transport mode and supply an indication of the dynamic deployment of the free-floating bike sharing integrating with the mass transit system.

Supporting sustainable system adoption: Socio-semantic analysis of transit rider debates on social media

Online social media platforms provide a bi-directional communication channel between transit agencies and their customers. It can also be an effective venue for profiling users and their needs as a step towards customizing service and communication policies. This study analyzed online Twitter discussions for three major transit agencies in Canada. In our work, we integrate the analysis of the participants’ social networks with the contents of their discussion. We also conduct the semantic analysis in a manner that parallels the structure and contents of customer satisfaction surveys—allowing for insightful comparisons between the results of both methods Analysis of the structure of the social networks of the Twitter accounts under study, including investigation of the formation of sub-communities and their interrelationship to the overall network. It was found that networks of the three cases portray a scale free and small world behaviors. This means that they are maturing networks; and that they represent viable communities—not just a randomly connected graph. This is important for future studies in relation to information diffusion and opinion dynamics: how people share information and how does this help shape their views. On the semantic front, a lexicon was developed based on existing thesauri for customer satisfaction analysis. Keywords form each tweet were extracted and the topic(s) of each tweet was defined based on the lexicon. It was found that, based on the sample investigated, the behavior of 100-follower networks (networks with nodes having at least 100 followers) closely mimics the behavior of the overall network. Studying these networks (of influential users) can make analysis faster and may not impact accuracy. We also clustered each network into sub-networks: small, medium, and large. Topics discussed in medium-size networks tended to be unique. This seems to be the level where active discussions of specific topics take place. Focusing on detecting these and analyzing their contents can provide better chance for capturing the evolution of community opinions.

Foreword

Most of the distribution functions in the universe, including those for mass, energy, and structure of components like dark matter, galaxy clusters, galaxies, magnetic fields, cosmic rays, star clusters, and stars, have power-law shapes suggesting a lack of definite scales in their formation processes. As these scale-free behaviors are obtained without fine-tuning, they are by definition self-organized, which raises fascinating questions regarding the respective roles of long-range (gravity) and short-range (collisional) interactions. These questions touch on the interaction between dark matter, baryons, cosmic rays and magnetic fields, the importance of scales where the power-laws break down, the observed deviations from power-laws, and the range of scales that are truly coupled. Computer simulations now include a large enough range of scales to reproduce some of these power-laws, and recent theoretical analyses attempt to unify them.

Topological Structure and Spanning Trees of Rectangular Growing Network Models

Fractals in building network models are objects which appear similar (at least in some statistical sense) at every lengthscale. We focus on produce the rectangular growing network models by constructive operations based on fractals, and show the scale-free behaviors of our models. We, also, try to find those nodes like “hubs” in the models by spanning trees having maximal leaves.

On Relationships Between Fixation Identification Algorithms and Fractal Box Counting Methods.

Fixation identification algorithms facilitate data comprehension and provide analytical convenience in eye-tracking analysis. However, current fixation algorithms for eye-tracking analysis are heavily dependent on parameter choices, leading to instabilities in results and incompleteness in reporting. This work examines the nature of human scanning patterns during complex scene viewing. We show that standard implementations of the commonly used distance-dispersion algorithm for fixation identification are functionally equivalent to greedy spatiotemporal tiling. We show that modeling the number of fixations as a function of tiling size leads to a measure of fractal dimensionality through box counting. We apply this technique to examine scale-free gaze behaviors in toddlers and adults looking at images of faces and blocks, as well as large number of adults looking at movies or static images. The distributional aspects of the number of fixations may suggest a fractal structure to gaze patterns in free scanning and imply that the incompleteness of standard algorithms may be due to the scale-free behaviors of the underlying scanning distributions. We discuss the nature of this hypothesis, its limitations, and offer directions for future work.

Dynamical process of complex systems and fractional differential equations

Abstract Behavior of dynamical process of complex systems is investigated. Specifically we analyse two types of ideal complex systems. For analysing the ideal complex systems, we define the response functions describing the internal states to an external force. The internal states are obtained as a relaxation process showing a “power law” distribution, such as scale free behaviors observed in actual measurements. By introducing a hybrid system, the logarithmic time, and double logarithmic time, we show how the “slow relaxation” (SR) process and “super slow relaxation” (SSR) process occur. Regarding the irregular variations of the internal states as an activation process, we calculate the response function to the external force. The behaviors are classified into “power”, “exponential”, and “stretched exponential” type. Finally we construct a fractional differential equation (FDE) describing the time evolution of these complex systems. In our theory, the exponent of the FDE or that of the power law distribution is expressed in terms of the parameters characterizing the structure of the system.

A Weighted Scale-Free Network with Triad Formation

We propose an evolutionary model for weighted network according to characteristics of real-life network, and the weighted model integrates the triad formation and the preferential mechanism. The two mechanisms provide a wide variety of scale-free behaviors depending on the parameter that govern the new nodes and new links growth. The model gives power-law distributions of degree, weight, and strength. In particular, the average strength displays scale-free property , , as confirmed in many real networks. While in BBV weighted model, the scaling exponent . This implies that the strength of nodes grows faster than their degree. This denotes a strong correlation between the weight and the topological properties in the model, which can be considered as a meaningful development of weighted network model.

On scale-free and poly-scale behaviors of random hierarchical networks

In this paper the question of statistical properties of block-hierarchical randommatrices is raised for the first time in connection with structural characteristicsof random hierarchical networks obtained by a ‘mipmapping’ procedure. Inparticular, we compute numerically the spectral density of large randomadjacency matrices defined via a hierarchy of the Bernoulli distributions{q1,q2,...} on matrix elements,where qγ depends onthe hierarchy level γ as qγ = p−μγ (μ>0). For the spectral density we clearly see scale-free behavior. We show also that forthe Gaussian distributions on matrix elements with zero mean and variancesσγ = p−νγ, the tail of thespectral density, ρG(λ), behaves as ρG(λ)∼|λ|−(2−ν)/(1−ν) for and 0<ν<1,while for ν≥1 the power-law behavior is terminated. We also find that the vertex degree distribution ofsuch hierarchical networks has a poly-scale fractal behavior extended over a very broadrange of scales.

Network topology of an experimental futures exchange

Many systems of different nature exhibit scale free behaviors. Economic systems with power law distribution in the wealth is one of the examples. To better understand the working behind the complexity, we undertook an empirical study measuring the interactions between market participants. A Web server was setup to administer the exchange of futures contracts whose liquidation prices were coupled to event outcomes. After free registration, participants started trading to compete for the money prizes upon maturity of the futures contracts at the end of the experiment. The evolving `cash' flow network was reconstructed from the transactions between players. We show that the network topology is hierarchical, disassortative and scale-free with a power law exponent of 1.02+-0.09 in the degree distribution. The small-world property emerged early in the experiment while the number of participants was still small. We also show power law distributions of the net incomes and inter-transaction time intervals. Big winners and losers are associated with high degree, high betweenness centrality, low clustering coefficient and low degree-correlation. We identify communities in the network as groups of the like-minded. The distribution of the community sizes is shown to be power-law distributed with an exponent of 1.19+-0.16.

Scaling in weighted networks and complex systems

Network systems evolving by preferential attachment of new vertices and by link loading are considered. The probability of node attaching is assumed to depend linearly on degrees of existing nodes to which new ones are connected. The rule of the network loading allows both deterministic and random processes of distributing weights among links. Specifically, the rule is determined by assigning to each link a weight dependent on randomly modified intervals between times at which linked vertices are connected to the system. This enables the investigation of the influence of local and global loading processes on statistical properties of weighted networks. It is demonstrated that, for different values of parameters controlling these processes, the distribution of weights concentrated at vertices of such networks displays a large variety of scale-free and truncated scale-free behaviors. It is also shown that statistical properties of the studied weighted networks and statistical properties of some complex evolving spatial systems exhibit a close relationship.