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Google matrix of the world trade network

Using the United Nations Commodity Trade Statistics Database [http://comtrade.un.org/db/] we construct the Google matrix of the world trade network and analyze its properties for various trade commodities for all countries and all available years from 1962 to 2009. The trade flows on this network are classified with the help of PageRank and CheiRank algorithms developed for the World Wide Web and other large scale directed networks. For the world trade this ranking treats all countries on equal democratic grounds independent of country richness. Still this method puts at the top a group of industrially developed countries for trade in {\it all commodities}. Our study establishes the existence of two solid state like domains of rich and poor countries which remain stable in time, while the majority of countries are shown to be in a gas like phase with strong rank fluctuations. A simple random matrix model provides a good description of statistical distribution of countries in two-dimensional rank plane. The comparison with usual ranking by export and import highlights new features and possibilities of our approach.

q-fin.GN↗

Integrated Impact Indicators (I3) compared with Impact Factors (IFs): An alternative research design with policy implications

In bibliometrics, the association of "impact" with central-tendency statistics is mistaken. Impacts add up, and citation curves should therefore be integrated instead of averaged. For example, the journals MIS Quarterly and JASIST differ by a factor of two in terms of their respective impact factors (IF), but the journal with the lower IF has the higher impact. Using percentile ranks (e.g., top-1%, top-10%, etc.), an integrated impact indicator (I3) can be based on integration of the citation curves, but after normalization of the citation curves to the same scale. The results across document sets can be compared as percentages of the total impact of a reference set. Total number of citations, however, should not be used instead because the shape of the citation curves is then not appreciated. I3 can be applied to any document set and any citation window. The results of the integration (summation) are fully decomposable in terms of journals or instititutional units such as nations, universities, etc., because percentile ranks are determined at the paper level. In this study, we first compare I3 with IFs for the journals in two ISI Subject Categories ("Information Science & Library Science" and "Multidisciplinary Sciences"). The LIS set is additionally decomposed in terms of nations. Policy implications of this possible paradigm shift in citation impact analysis are specified.

cs.DL↗

Verhulst-Lotka-Volterra (VLV) model of ideological struggles

Let the population of e.g. a country where some opinion struggle occurs be varying in time, according to Verhulst equation. Consider next some competition between opinions such as the dynamics be described by Lotka and Volterra equations. Two kinds of influences can be used, in such a model, for describing the dynamics of an agent opinion conversion: this can occur (i) either by means of mass communication tools, under some external field influence, or (ii) by means of direct interactions between agents. It results, among other features, that change(s) in environmental conditions can prevent the extinction of populations of followers of some ideology due to different kinds of resurrection effects. The tension arising in the country population is proposed to be measured by an appropriately defined scale index.

physics.soc-ph↗

On religion and language evolutions seen through mathematical and agent based models

(shortened version) Religions and languages are social variables, like age, sex, wealth or political opinions, to be studied like any other organizational parameter. In fact, religiosity is one of the most important sociological aspects of populations. Languages are also a characteristics of the human kind. New religions, new languages appear though others disappear. All religions and languages evolve when they adapt to the society developments. On the other hand, the number of adherents of a given religion, the number of persons speaking a language is not fixed. Several questions can be raised. E.g. from a macroscopic point of view : How many religions/languages exist at a given time? What is their distribution? What is their life time? How do they evolve?. From a microscopic view point: can one invent agent based models to describe macroscopic aspects? Does it exist simple evolution equations? It is intuitively accepted, but also found through from statistical analysis of the frequency distribution that an attachment process is the primary cause of the distribution evolution : usually the initial religion/language is that of the mother. Later on, changes can occur either due to heterogeneous agent interaction processes or due to external field constraints, - or both. Such cases can be illustrated with historical facts and data. It is stressed that characteristic time scales are different, and recalled that external fields are very relevant in the case of religions, rending the study more interesting within a mechanistic approach

physics.soc-ph↗

Political protest Italian-style: The dissonance between the blogosphere and mainstream media in the promotion and coverage of Beppe Grillo's V-day

We analyze the organization, promotion and public perception of V-day, a political rally that took place on September 8, 2007, to protest against corruption in the Italian Parliament. Launched by blogger Beppe Grillo, and promoted via a word of mouth mobilization on the Italian blogosphere, V-day brought close to one million Italians in the streets on a single day, but was mostly ignored by mainstream media. This article is divided into two parts. In the first part, we analyze the volume and content of online articles published by both bloggers and mainstream news sources from June 14 (the day V-day was announced) until September 15, 2007 (one week after it took place) . We find that the success of V-day can be attributed to the coverage of bloggers and small-scale local news outlets only, suggesting a strong grassroots component in the organization of the rally. We also find a dissonant thematic relationship between content published by blogs and mainstream media: while the majority of blogs analyzed promote V-day, major mainstream media sources critique the methods of information production and dissemination employed by Grillo. Based on this finding, in the second part of the study, we explore the role of Grillo in the organization of the rally from a network analysis perspective. We study the interlinking structure of the V-day blogosphere network, to determine its structure, its levels of heterogeneity, and resilience. Our analysis contradicts the hypothesis that Grillo served as a top-down, broadcast-like source of information. Rather, we find that information about V-day was transferred across heterogeneous nodes in a moderately robust and resilient core network of blogs. We speculate that the organization of V-day represents the very first case, in Italian history, of a political demonstration developed and promoted primarily via the use of social media on the web.

cs.SI↗

Peer Effects and Stability in Matching Markets

Many-to-one matching markets exist in numerous different forms, such as college admissions, matching medical interns to hospitals for residencies, assigning housing to college students, and the classic firms and workers market. In all these markets, externalities such as complementarities and peer effects severely complicate the preference ordering of each agent. Further, research has shown that externalities lead to serious problems for market stability and for developing efficient algorithms to find stable matchings. In this paper we make the observation that peer effects are often the result of underlying social connections, and we explore a formulation of the many-to-one matching market where peer effects are derived from an underlying social network. The key feature of our model is that it captures peer effects and complementarities using utility functions, rather than traditional preference ordering. With this model and considering a weaker notion of stability, namely two-sided exchange stability, we prove that stable matchings always exist and characterize the set of stable matchings in terms of social welfare. We also give distributed algorithms that are guaranteed to converge to a two-sided exchange stable matching. To assess the competitive ratio of these algorithms and to more generally characterize the efficiency of matching markets with externalities, we provide general bounds on how far the welfare of the worst-case stable matching can be from the welfare of the optimal matching, and find that the structure of the social network (e.g. how well clustered the network is) plays a large role.

cs.SI↗

The Anna Karenina principle: A concept for the explanation of success in science

The first sentence of Leo Tolstoy's novel Anna Karenina is: "Happy families are all alike; every unhappy family is unhappy in its own way." Here Tolstoy means that for a family to be happy, several key aspects must be given (such as good health of all family members, acceptable financial security, and mutual affection). If there is a deficiency in any one or more of these key aspects, the family will be unhappy. In this paper we introduce the Anna Karenina principle as a concept that can explain success in science. Here we will refer to three central areas in modern science in which scarce resources will most usually lead to failure: (1) peer review of research grant proposals and manuscripts (money and journal space as scarce resources), (2) citation of publications (reception as a scarce resource), and (3) new scientific discoveries (recognition as a scarce resource). If resources are scarce (journal space, funds, reception, and recognition), there can be success only when several key prerequisites for the allocation of the resources are fulfilled. If any one of these prerequisites is not fulfilled, the grant proposal, manuscript submission, the published paper, or the discovery will not be successful.

cs.DL↗

Allocation of seats in the European Parliament and a degressive proportionality

Distribution of seats in The European Parliament postulated by Treaty of Lisbon should be degressively proportional. The meaning of degressively proportional concept can be found in two principles annexed to the draft of European Parliament resolution. The first, referred as the principle of fair division, states that "the larger the population of a Member State, the greater is entitlement to a large number of seats". The other condition, referred to as the principle of relative proportionality, holds that "the larger the population of a country, the more inhabitants are represented by each of its Members of the EU". We postulate a clear and fair method which determines uniquely a distribution of seats in the European Parliament which fulfil the requirements of degressive proportionality. More generally, let $l_i$ be any non-increasing sequence of real positive numbers. We say that a sequence of natural numbers $m_{i}$ is degressively proportional with respect to the sequence $l_{i}$, if $m_{i}$ and $l_{i}/m_{i}$ are non-increasing sequences. Our method can be instrumental in uniquely determining a degressively proportional sequence $m_{i}$ with respect to $l_{i}$ which fulfils given conditions.

physics.soc-ph↗

Heterogeneity and Allometric Growth of Human Collaborative Tagging Behavior

Allometric growth is found in many tagging systems online. That is, the number of new tags (T) is a power law function of the active population (P), or T P^gamma (gamma!=1). According to previous studies, it is the heterogeneity in individual tagging behavior that gives rise to allometric growth. These studies consider the power-law distribution model with an exponent beta, regarding 1/beta as an index for heterogeneity. However, they did not discuss whether power-law is the only distribution that leads to allometric growth, or equivalently, whether the positive correlation between heterogeneity and allometric growth holds in systems of distributions other than power-law. In this paper, the authors systematically examine the growth pattern of systems of six different distributions, and find that both power-law distribution and log-normal distribution lead to allometric growth. Furthermore, by introducing Shannon entropy as an indicator for heterogeneity instead of 1/beta, the authors confirm that the positive relationship between heterogeneity and allometric growth exists in both cases of power-law and log-normal distributions.

cs.IR↗

Internal links and pairs as a new tool for the analysis of bipartite complex networks

Many real-world complex networks are best modeled as bipartite (or 2-mode) graphs, where nodes are divided into two sets with links connecting one side to the other. However, there is currently a lack of methods to analyze properly such graphs as most existing measures and methods are suited to classical graphs. A usual but limited approach consists in deriving 1-mode graphs (called projections) from the underlying bipartite structure, though it causes important loss of information and data storage issues. We introduce here internal links and pairs as a new notion useful for such analysis: it gives insights on the information lost by projecting the bipartite graph. We illustrate the relevance of theses concepts on several real-world instances illustrating how it enables to discriminate behaviors among various cases when we compare them to a benchmark of random networks. Then, we show that we can draw benefit from this concept for both modeling complex networks and storing them in a compact format.

cs.SI↗

Exploring Human Mobility Patterns Based on Location Information of US Flights

A range of early studies have been conducted to illustrate human mobility patterns using different tracking data, such as dollar notes, cell phones and taxicabs. Here, we explore human mobility patterns based on massive tracking data of US flights. Both topological and geometric properties are examined in detail. We found that topological properties, such as traffic volume (between airports) and degree of connectivity (of individual airports), including both in- and outdegrees, follow a power law distribution but not a geometric property like travel lengths. The travel lengths exhibit an exponential distribution rather than a power law with an exponential cutoff as previous studies illustrated. We further simulated human mobility on the established topologies of airports with various moving behaviors and found that the mobility patterns are mainly attributed to the underlying binary topology of airports and have little to do with other factors, such as moving behaviors and geometric distances. Apart from the above findings, this study adopts the head/tail division rule, which is regularity behind any heavy-tailed distribution for extracting individual airports. The adoption of this rule for data processing constitutes another major contribution of this paper. Keywords: scaling of geographic space, head/tail division rule, power law, geographic information, agent-based simulations

physics.data-an↗

High Degree Vertices, Eigenvalues and Diameter of Random Apollonian Networks

In this work we analyze basic properties of Random Apollonian Networks \cite{zhang,zhou}, a popular stochastic model which generates planar graphs with power law properties. Specifically, let $k$ be a constant and $Δ_1 \geq Δ_2 \geq .. \geq Δ_k$ be the degrees of the $k$ highest degree vertices. We prove that at time $t$, for any function $f$ with $f(t) \rightarrow +\infty$ as $t \rightarrow +\infty$, $\frac{t^{1/2}}{f(t)} \leq Δ_1 \leq f(t)t^{1/2}$ and for $i=2,...,k=O(1)$, $\frac{t^{1/2}}{f(t)} \leq Δ_i \leq Δ_{i-1} - \frac{t^{1/2}}{f(t)}$ with high probability (\whp). Then, we show that the $k$ largest eigenvalues of the adjacency matrix of this graph satisfy $λ_k = (1\pm o(1))Δ_k^{1/2}$ \whp. Furthermore, we prove a refined upper bound on the asymptotic growth of the diameter, i.e., that \whp the diameter $d(G_t)$ at time $t$ satisfies $d(G_t) \leq ρ\log{t}$ where $\frac{1}ρ=η$ is the unique solution greater than 1 of the equation $η- 1 - \logη = \log{3}$. Finally, we investigate other properties of the model.

cs.SI↗

Robustness of Complex Networks against Attacks Guided by Damage

Extensive researches have been dedicated to investigating the performance of real networks and synthetic networks against random failures or intentional attack guided by degree (degree attack). Degree is one of straightforward measures to characterize the vitality of a vertex in maintaining the integrity of the network but not the only one. Damage, the decrease of the largest component size that was caused by the removal of a vertex, intuitively is a more destructive guide for intentional attack on networks since the network functionality is usually measured by the largest component size. However, it is surprising to find that little is known about behaviors of real networks or synthetic networks against intentional attack guided by damage (damage attack), in which adversaries always choose the vertex with the largest damage to attack. In this article, we dedicate our efforts to understanding damage attack and behaviors of real networks as well as synthetic networks against this attack. To this end, existing attacking models, statistical properties of damage in complex networks are first revisited. Then, we present the empirical analysis results about behaviors of complex networks against damage attack with the comparisons to degree attack. It is surprising to find a cross-point for diverse networks before which damage attack is more destructive than degree attack. Further investigation shows that the existence of cross-point can be attributed to the fact that: degree attack tends produce networks with more heterogenous damage distribution than damage attack. Results in this article strongly suggest that damage attack is one of most destructive attacks and deserves our research efforts.Our understandings about damage attack may also shed light on efficient solutions to protect real networks against damage attack.

physics.soc-ph↗

Core-Periphery Segregation in Evolving Prisoner's Dilemma Networks

Dense cooperative networks are an essential element of social capital for a prosperous society. These networks enable individuals to overcome collective action dilemmas by enhancing trust. In many biological and social settings, network structures evolve endogenously as agents exit relationships and build new ones. However, the process by which evolutionary dynamics lead to self-organization of dense cooperative networks has not been explored. Our large group prisoner's dilemma experiments with exit and partner choice options show that core-periphery segregation of cooperators and defectors drives the emergence of cooperation. Cooperators' Quit-for-Tat and defectors' Roving strategy lead to a highly asymmetric core and periphery structure. Densely connected to each other, cooperators successfully isolate defectors and earn larger payoffs than defectors. Our analysis of the topological characteristics of evolving networks illuminates how social capital is generated.

q-bio.PE↗

Explicit Solutions to the Continuous Time Albert-Barabási Scale-Free Model

Presented here is the explicit solution to the continuous time approximation of the Albert-Barabási scale-free network model at any time t. The solution is found by recursively solving the differential equations via integrating factors, identifying a pattern for the coefficients and then proving this observed pattern using induction.

math-ph↗

An Empirical Investigation on Important Subgraphs in Cooperation-Competition networks

Subgraphs are very important for understanding structure and function of complex networks. Dyad and triad are the elementary subgraphs. We focus on the distribution of their act degree defined as the number of activities, events or organizations they join, which indicates the importance of the subgraphs. The empirical studies show that, in a lot of real world systems, the dyad or triad act degree distributions follow "shifted power law" (SPL), where α and γ are constants. We defined a "heterogeneity index", H, to describe how it is uneven and analytically deduced the correlation between H and α and γ. This manuscript, which shows the details of the empirical studies, serves as an online supplement of a paper submitted to a journal.

physics.soc-ph↗

Block Voter Model

We introduce and study the block voter model with noise on two-dimensional square lattices using Monte Carlo simulations and finite-size scaling techniques. The model is defined by an outflow dynamics where a central set of $N_{PCS}$ spins, here denoted by persuasive cluster spins (PCS), tries to influence the opinion of their neighbouring counterparts. We consider the collective behaviour of the entire system with varying PCS size. When $N_{PCS}>2$, the system exhibits an order-disorder phase transition at a critical noise parameter $q_{c}$ which is a monotonically increasing function of the size of the persuasive cluster. We conclude that how large the PCS is more power of persuasion it has. It also seems that the resulting critical behaviour is Ising-like independent of the range of the interactions.

physics.soc-ph↗

Contextual Risk and Its Relevance in Economics

Uncertainty in economics still poses some fundamental problems illustrated, e.g., by the Allais and Ellsberg paradoxes. To overcome these difficulties, economists have introduced an interesting distinction between 'risk' and 'ambiguity' depending on the existence of a (classical Kolmogorovian) probabilistic structure modeling these uncertainty situations. On the other hand, evidence of everyday life suggests that 'context' plays a fundamental role in human decisions under uncertainty. Moreover, it is well known from physics that any probabilistic structure modeling contextual interactions between entities structurally needs a non-Kolmogorovian quantum-like framework. In this paper we introduce the notion of 'contextual risk' with the aim of modeling a substantial part of the situations in which usually only 'ambiguity' is present. More precisely, we firstly introduce the essentials of an operational formalism called 'the hidden measurement approach' in which probability is introduced as a consequence of fluctuations in the interaction between entities and contexts. Within the hidden measurement approach we propose a 'sphere model' as a mathematical tool for situations in which contextual risk occurs. We show that a probabilistic model of this kind is necessarily non-Kolmogorovian, hence it requires either the formalism of quantum mechanics or a generalization of it. This insight is relevant, for it explains the presence of quantum or, better, quantum-like, structures in economics, as suggested by some authors, and can serve to solve the aforementioned paradoxes.

physics.soc-ph↗