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arXiv2010

Modeling correlated human dynamics

We empirically study the activity patterns of individual blog-posting and find significant memory effects. The memory coefficient first decays in a power law and then turns to an exponential form. Moreover, the inter-event time distribution displays a heavy-tailed nature with power-law exponent dependent on the activity. Our findings challenge the priority-queue model that can not reproduce the memory effects or the activity-dependent distributions. We think there is another kind of human activity patterns driven by personal interests and characterized by strong memory effects. Accordingly, we propose a simple model based on temporal preference, which can well reproduce both the heavy-tailed nature and the strong memory effects. This work helps in understanding both the temporal regularities and the predictability of human behaviors.

physics.soc-ph↗

arXiv2010

How fractional counting affects the Impact Factor: Normalization in terms of differences in citation potentials among fields of science

The ISI-Impact Factors suffer from a number of drawbacks, among them the statistics-why should one use the mean and not the median?-and the incomparability among fields of science because of systematic differences in citation behavior among fields. Can these drawbacks be counteracted by counting citation weights fractionally instead of using whole numbers in the numerators? (i) Fractional citation counts are normalized in terms of the citing sources and thus would take into account differences in citation behavior among fields of science. (ii) Differences in the resulting distributions can be tested statistically for their significance at different levels of aggregation. (iii) Fractional counting can be generalized to any document set including journals or groups of journals, and thus the significance of differences among both small and large sets can be tested. A list of fractionally counted Impact Factors for 2008 is available online at http://www.leydesdorff.net/weighted_if/weighted_if.xls. The in-between group variance among the thirteen fields of science identified in the U.S. Science and Engineering Indicators is not statistically significant after this normalization. Although citation behavior differs largely between disciplines, the reflection of these differences in fractionally counted citation distributions could not be used as a reliable instrument for the classification.

cs.DL↗

arXiv2010

Probabilistic spreading of information in a spatial network

Spread of information in crowd is analysed in terms of directed percolation in two-dimensional spatial network. We investigate the case when the information transmitted can be incomplete or damaged. The results indicate that for small or moderate probability of errors, it is only the critical connectivity that varies with this probability, but the shape of the transmission velocity curve remains unchanged in a wide range of the probability. The shape of the boundary between those already informed and those yet uninformed becomes complex when the connectivity of agents is small.

physics.soc-ph↗

arXiv2010

Degree of Separation in Social Networks

According to the small-world concept, the entire world is connected through short chains of acquaintances. In popular imagination this is captured in the phrase six degrees of separation, implying that any two individuals are, at most, six handshakes away. Social network analysis is the understanding of concepts and information on relationships among interacting units in an ecological system. In this analysis the properties of the actors are explained in terms of the structures of links amongst them. In general, the relational links between the actors are primary and the properties of the actors are secondary. This paper presents two methods to calculate the average degree of separation between the actors or nodes in a graph. We apply this approach to other random graphs depicting social networks and then compare the characteristics of these graphs with the average degree of separation.

cs.SI↗

arXiv2011

Convergence to global consensus in opinion dynamics under a nonlinear voter model

We propose a nonlinear voter model to study the emergence of global consensus in opinion dynamics. In our model, agent $i$ agrees with one of binary opinions with the probability that is a power function of the number of agents holding this opinion among agent $i$ and its nearest neighbors, where an adjustable parameter $α$ controls the effect of herd behavior on consensus. We find that there exists an optimal value of $α$ leading to the fastest consensus for lattices, random graphs, small-world networks and scale-free networks. Qualitative insights are obtained by examining the spatiotemporal evolution of the opinion clusters.

stat.AP↗

arXiv2010

Identification of Overlapping Communities by Locally Calculating Community-Changing Resolution Levels

An algorithm for the detection of overlapping natural communities in networks was proposed by Lancichinetti, Fortunato, and Kertesz (LFK) last year. The LFK algorithm constructs natural communities of (in principle) all nodes of a graph by maximising the local fitness of communities. The resulting modules can overlap. The generation of communities can easily be repeated for many values of resolution; thus allowing different views on the network at different resolutions. We implemented the main idea of the LFK algorithm---to generate natural communities of each node of a network---in a different way. We start with a value of the resolution parameter that is high enough for each node to be its own natural community. As soon as the resolution is reduced, each node acquires other nodes as members of its community, i.e. natural communities grow. For each community found at a certain resolution level we calculate the next lower resolution where a node is added. After adding a node to a community of a seed node we check whether it is also the natural community of a node that we have already analysed. In this case, we can stop expanding the seed node's community. We tested our algorithm on a small benchmark graph and on a network of about 500 papers in information science (weighted with the Salton index of bibliographic coupling). In our tests, this approach results in characteristic ranges of resolution where a large resolution change does not lead to a growth of the natural community. Such stable modules were also obtained by applying the LFK algorithm but since we determine communities for all resolution values in one run, our approach is faster than the LFK reference. And our algorithm reveals the hierarchical structure of the graph more easily.

physics.data-an↗

arXiv2010

A complex network approach to robustness and vulnerability of spatially organized water distribution networks

In this work, water distribution systems are regarded as large sparse planar graphs with complex network characteristics and the relationship between important topological features of the network (i.e. structural robustness and loop redundancy) and system resilience, viewed as the antonym to structural vulnerability, are assessed. Deterministic techniques from complex networks and spectral graph theory are utilized to quantify well-connectedness and estimate loop redundancy in the studied benchmark networks. By using graph connectivity and expansion properties, system robustness against node/link failures and isolation of the demand nodes from the source(s) are assessed and network tolerance against random failures and targeted attacks on their bridges and cut sets are analyzed. Among other measurements, two metrics of meshed-ness and algebraic connectivity are proposed as candidates for quantification of redundancy and robustness, respectively, in optimization design models. A brief discussion on the scope and limitations of the provided measurements in the analysis of operational reliability of water distribution systems is presented.

physics.soc-ph↗

arXiv2010

A unified model for informetrics based on the wave and heat equations

The function g(r,t) = p(r+q)^(-β). e^(kt) is introduced as a basic informetric function describing the classical informetric laws (through its Mandelbrot part) and a time evolution. It is shown that this function is a solution of a wave-type and of a heat-type partial differential equation. It is suggested that our approach may lead to a description of informetrics in a partial differential equation setting, formally similar to that for well-known physical laws.

physics.soc-ph↗

arXiv2011

Dynamics on networks I. Combinatorial categories of modular continuous-time systems

We develop a new framework for the study of complex continuous time dynamical systems based on viewing them as collections of interacting control modules. This framework is inspired by and builds upon the groupoid formalism of Golubitsky, Stewart and their collaborators. Our approach uses the tools and --- more importantly ---the stance of category theory. This enables us to put the groupoid formalism in a coordinate-free setting and to extend it from ordinary differential equations to vector fields on manifolds. In particular, we construct combinatorial models for categories of modular continuous time dynamical systems. Each such model, as a category, is a fibration over an appropriate category of labeled directed graphs. This makes precise the relation between dynamical systems living on networks and the combinatorial structure of the underlying directed graphs, allowing us to exploit the relation in new and interesting ways.

math.DS↗

arXiv2012

Modeling Dynamical Influence in Human Interaction Patterns

How can we model influence between individuals in a social system, even when the network of interactions is unknown? In this article, we review the literature on the "influence model," which utilizes independent time series to estimate how much the state of one actor affects the state of another actor in the system. We extend this model to incorporate dynamical parameters that allow us to infer how influence changes over time, and we provide three examples of how this model can be applied to simulated and real data. The results show that the model can recover known estimates of influence, it generates results that are consistent with other measures of social networks, and it allows us to uncover important shifts in the way states may be transmitted between actors at different points in time.

cs.SI↗

arXiv2010

Empirical study and modeling of human behaviour dynamics of comments on Blog posts

On-line communities offer a great opportunity to investigate human dynamics, because much information about individuals is registered in databases. In this paper, based on data statistics of online comments on Blog posts, we first present an empirical study of a comment arrival-time interval distribution. We find that people interested in some subjects gradually disappear and the interval distribution is a power law. According to this feature, we propose a model with gradually decaying interest. We give a rigorous analysis on the model by non-homogeneous Poisson processes and obtain an analytic expression of the interval distribution. Our analysis indicates that the time interval between two consecutive events follows the power-law distribution with a tunable exponent, which can be controlled by the model parameters and is in interval (1,+{\infty}). The analytical result agrees with the empirical results well, obeying an approximately power-law form. Our model provides a theoretical basis for human behaviour dynamics of comments on Blog posts.

cs.SI↗

arXiv2010

Are large complex economic systems unstable ?

Although classical economic theory is based on the concept of stable equilibrium, real economic systems appear to be always out of equilibrium. Indeed, they share many of the dynamical features of other complex systems, e.g., ecological food-webs. We focus on the relation between increasing complexity of the economic network and its stability with respect to small perturbations in the dynamical variables associated with the constituent nodes. Inherent delays and multiple time-scales suggest that economic systems will be more likely to exhibit instabilities as their complexity is increased even though the speed at which transactions are conducted has increased many-fold through technological developments. Analogous to the birth of nonlinear dynamics from Poincare's work on the question of whether the solar system is stable, we suggest that similar theoretical developments may arise from efforts by econophysicists to understand the mechanisms by which instabilities arise in the economy.

physics.soc-ph↗

arXiv2013

A mathematical model of the Mafia game

Mafia (also called Werewolf) is a party game. The participants are divided into two competing groups: citizens and a mafia. The objective is to eliminate the opponent group. The game consists of two consecutive phases (day and night) and a certain set of actions (e.g. lynching during day). The mafia members have additional powers (knowing each other, killing during night) whereas the citizens are more numerous. We propose a simple mathematical model of the game, which is essentially a pure death process with discrete time. We find the closed-form solutions for the mafia winning-chance, w(n,m), as well as for the evolution of the game. Moreover, we investigate the discrete properties of results, as well as their continuous-time approximations. It turns out that a relatively small number of the mafia members, i.e. proportional to the square root of the total number of players, gives equal winning-chance for both groups. Furthermore, the game strongly depends on the parity of the total number of players.

math.PR↗

arXiv2010

Statistical Behavior of Embeddedness and Communities of Overlapping Cliques in Online Social Networks

Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order structure of a network. Higher-order structures such as the edge embeddedness and the size of communities may play more important roles in many online social networks. In this paper, we provide empirical evidence on the existence of rich higherorder structural characteristics in online social networks, develop mathematical models to interpret and model these characteristics, and discuss their various applications in practice. In particular, 1) We show that the embeddedness distribution of social links in many social networks has interesting and rich behavior that cannot be captured by well-known network models. We also provide empirical results showing a clear correlation between the embeddedness distribution and the average number of messages communicated between pairs of social network nodes. 2) We formally prove that random k-tree, a recent model for complex networks, has a power law embeddedness distribution, and show empirically that the random k-tree model can be used to capture the rich behavior of higherorder structures we observed in real-world social networks. 3) Going beyond the embeddedness, we show that a variant of the random k-tree model can be used to capture the power law distribution of the size of communities of overlapping cliques discovered recently.

cs.SI↗

arXiv2010

Efficient Bayesian Community Detection using Non-negative Matrix Factorisation

Identifying overlapping communities in networks is a challenging task. In this work we present a novel approach to community detection that utilises the Bayesian non-negative matrix factorisation (NMF) model to produce a probabilistic output for node memberships. The scheme has the advantage of computational efficiency, soft community membership and an intuitive foundation. We present the performance of the method against a variety of benchmark problems and compare and contrast it to several other algorithms for community detection. Our approach performs favourably compared to other methods at a fraction of the computational costs.

stat.ML↗

arXiv2010

Fokker-Planck Asymptotics for Traffic Flow Models

Starting from microscopic interaction rules we derive kinetic models of Fokker--Planck type for vehicular traffic flow. The derivation is based on taking a suitable asymptotic limit of the corresponding Boltzmann model. As particular cases, the derived models comprise existing models. New Fokker--Planck models are also given and their differences to existing models are highlighted. Finally, we report on numerical experiments.

math-ph↗

arXiv2010

Gamma Radiation Measurements and Dose Rates in Commonly Used Building Materials in Cyprus

A first comprehensive study is presented on radioactivity concentrations and dose rates in 87 commonly used materials, manufactured or imported in Cyprus, for building purposes. The natural radioactivity of K-40, Th-232, U-238 and Ra-226 is determined using high-resolution gamma ray spectroscopy. The respective dose rates and the associated radiological effect indices are also calculated. A comparison of the measured specific activity values with the corresponding world average values shows that most of them are below the world average activity values. The annual indoor effective dose rates received by an individual from three measured imported granites and four measured imported ceramics are found to be higher than the world upper limit value of 1 mSv y-1. Hence, these materials should have a restricted use according to their corresponding calculated activity concentration index values and the related EC 1999 guidelines.

physics.med-ph↗

arXiv2011

Expansion and Search in Networks

Borrowing from concepts in expander graphs, we study the expansion properties of real-world, complex networks (e.g. social networks, unstructured peer-to-peer or P2P networks) and the extent to which these properties can be exploited to understand and address the problem of decentralized search. We first produce samples that concisely capture the overall expansion properties of an entire network, which we collectively refer to as the expansion signature. Using these signatures, we find a correspondence between the magnitude of maximum expansion and the extent to which a network can be efficiently searched. We further find evidence that standard graph-theoretic measures, such as average path length, fail to fully explain the level of "searchability" or ease of information diffusion and dissemination in a network. Finally, we demonstrate that this high expansion can be leveraged to facilitate decentralized search in networks and show that an expansion-based search strategy outperforms typical search methods.

cs.SI↗