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arXiv2011

Separation Number and Generalized Clustering Coefficient in Small World Networks based on String Formalism

We reformulated the string formalism given by Aoyama, using an adjacent matrix of a network and introduced a series of generalized clustering coefficients based on it. Furthermore we numerically evaluated Milgram condition proposed by their article in order to explore $q$-$th$ degrees of separation in scale free networks. In this article, we apply the reformulation to small world networks and numerically evaluate Milgram condition, especially the separation number of small world networks and its relation to cycle structures are discussed. Considering the number of non-zero elements of an adjacent matrix, the average path length and Milgram condition, we show that the formalism proposed by us is effective to analyze the six degrees of separation, especially effective for analyzing the relation between the separation number and cycle structures in a network. By this analysis of small world networks, it proves that a sort of power low holds between $M_n$, which is a key quantity in Milgram condition, and the generalized clustering coefficients. This property in small world networks stands in contrast to that of scale free networks.

physics.soc-ph↗

arXiv2011

Pricing stocks with yardsticks and sentiments

Human decision making by professionals trading daily in the stock market can be a daunting task. It includes decisions on whether to keep on investing or to exit a market subject to huge price swings, and how to price in news or rumors attributed to a specific stock. The question then arises how professional traders, who specialize in daily buying and selling large amounts of a given stock, know how to properly price a given stock on a given day? Here we introduce the idea that people use heuristics, or "rules of thumb", in terms of "yard sticks" from the performance of the other stocks in a stock index. The under- /over-performance with respect to such a yard stick then signifies a general negative/positive sentiment of the market participants towards a given stock. Using empirical data of the Dow Jones Industrial Average, stocks are shown to have daily performances with a clear tendency to cluster around the measures introduced by the yard sticks. We illustrate how sentiments, most likely due to insider information, can influence the performance of a given stock over period of months, and in one case years.

q-fin.GN↗

arXiv2012

Mathematical aspects of degressive proportionality

We analyze properties of apportionment functions in context of the problem of allocating seats in the European Parliament. Necessary and sufficient conditions for apportionment functions are investigated. Some exemplary families of apportionment functions are specified and the corresponding partitions of the seats in the European Parliament among the Member States of the European Union are presented. Although the choice of the allocation functions is theoretically unlimited, we show that the constraints are so strong that the acceptable functions lead to rather similar solutions.

physics.soc-ph↗

arXiv2012

World Shares of Publications of the USA, EU-27, and China Compared and Predicted using the New Interface of the Web-of-Science versus Scopus

The new interface of the Web of Science (of Thomson Reuters) enables users to retrieve sets larger than 100,000 documents in a single search. This makes it possible to compare publication trends for China, the USA, EU-27, and a number of smaller countries. China no longer grew exponentially during the 2000s, but linearly. Contrary to previous predictions on the basis of exponential growth or Scopus data, the cross-over of the lines for China and the USA is postponed to the next decade (after 2020) according to this data. These long extrapolations, however, should be used only as indicators and not as predictions. Along with the dynamics in the publication trends, one also has to take into account the dynamics of the databases used for the measurement.

cs.DL↗

arXiv2011

An evolving network model with modular growth

In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected nodes, and the nodes between the modules are linked by preferential attachment on degree of nodes. We study the modularity measure of the proposed model, which can be adjusted by changing ratio of the number of inner-module edges and the number of inter-module edges. Based on the mean field theory, we develop an analytical function of the degree distribution, which is verified by a numerical example and indicates that the degree distribution shows characteristics of the small-world network and the scale-free network distinctly at different segments. The clustering coefficient and the average path length of the network are simulated numerically, indicating that the network shows the small-world property and is affected little by the randomness of the new module.

physics.soc-ph↗

arXiv2013

Normalized Mutual Information to evaluate overlapping community finding algorithms

Given the increasing popularity of algorithms for overlapping clustering, in particular in social network analysis, quantitative measures are needed to measure the accuracy of a method. Given a set of true clusters, and the set of clusters found by an algorithm, these sets of clusters must be compared to see how similar or different the sets are. A normalized measure is desirable in many contexts, for example assigning a value of 0 where the two sets are totally dissimilar, and 1 where they are identical. A measure based on normalized mutual information, [1], has recently become popular. We demonstrate unintuitive behaviour of this measure, and show how this can be corrected by using a more conventional normalization. We compare the results to that of other measures, such as the Omega index [2].

physics.soc-ph↗

arXiv2013

Towards Quantifying Vertex Similarity in Networks

Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices (graph matching). With respect to the former problem, we propose to optimize a geometric objective which allows us to express each vertex uniquely as a convex combination of a few extreme types of vertices. Our method has the important advantage of supporting efficiently several types of queries such as "which other vertices are most similar to this vertex?" by the use of the appropriate data structures and of mining interesting patterns in the network. With respect to the latter problem (graph matching), we propose the generalized condition number --a quantity widely used in numerical analysis-- $κ(L_G,L_H)$ of the Laplacian matrix representations of $G,H$ as a measure of graph similarity, where $G,H$ are the graphs of interest. We show that this objective has a solid theoretical basis and propose a deterministic and a randomized graph alignment algorithm. We evaluate our algorithms on both synthetic and real data. We observe that our proposed methods achieve high-quality results and provide us with significant insights into the network structure.

cs.SI↗

arXiv2012

Mapping (USPTO) Patent Data using Overlays to Google Maps

A technique is developed using patent information available online (at the US Patent and Trademark Office) for the generation of Google Maps. The overlays indicate both the quantity and quality of patents at the city level. This information is relevant for research questions in technology analysis, innovation studies and evolutionary economics, as well as economic geography. The resulting maps can also be relevant for technological innovation policies and R&D management, because the US market can be considered the leading market for patenting and patent competition. In addition to the maps, the routines provide quantitative data about the patents for statistical analysis. The cities on the map are colored according to the results of significance tests. The overlays are explored for the Netherlands as a "national system of innovations," and further elaborated in two cases of emerging technologies: "RNA interference" and "nanotechnology."

cs.CY↗

arXiv2012

The Decentralized Structure of Collective Attention on the Web

Background: The collective browsing behavior of users gives rise to a flow network transporting attention between websites. By analyzing the structure of this network we uncovered a nontrivial scaling regularity concerning the impact of websites. Methodology: We constructed three clickstreams networks, whose nodes were websites and edges were formed by the users switching between sites. We developed an indicator Ci as a measure of the impact of site i and investigated its correlation with the traffic of the site Ai both on the three networks and across the language communities within the networks. Conclusions: We found that the impact of websites increased slower than their traffic. Specifically, there existed a scaling relationship between Ci and Ai with an exponent gamma smaller than 1. We suggested that this scaling relationship characterized the decentralized structure of the clickstream circulation: the World Wide Web is a system that favors small sites in reassigning the collective attention of users.

cs.IR↗

arXiv2011

Geometric protean graphs

We study the link structure of on-line social networks (OSNs), and introduce a new model for such networks which may help infer their hidden underlying reality. In the geo-protean (GEO-P) model for OSNs nodes are identified with points in Euclidean space, and edges are stochastically generated by a mixture of the relative distance of nodes and a ranking function. With high probability, the GEO-P model generates graphs satisfying many observed properties of OSNs, such as power law degree distributions, the small world property, densification power law, and bad spectral expansion. We introduce the dimension of an OSN based on our model, and examine this new parameter using actual OSN data. We discuss how the geo-protean model may eventually be used as a tool to group users with similar attributes using only the link structure of the network.

physics.soc-ph↗

arXiv2011

Swayed by Friends or by the Crowd?

We have conducted three empirical studies of the effects of friend recommendations and general ratings on how online users make choices. These two components of social influence were investigated through user studies on Mechanical Turk. We find that for a user deciding between two choices an additional rating star has a much larger effect than an additional friend's recommendation on the probability of selecting an item. Equally important, negative opinions from friends are more influential than positive opinions, and people exhibit more random behavior in their choices when the decision involves less cost and risk. Our results can be generalized across different demographics, implying that individuals trade off recommendations from friends and ratings in a similar fashion.

cs.SI↗

arXiv2012

Dynamical Classes of Collective Attention in Twitter

Micro-blogging systems such as Twitter expose digital traces of social discourse with an unprecedented degree of resolution of individual behaviors. They offer an opportunity to investigate how a large-scale social system responds to exogenous or endogenous stimuli, and to disentangle the temporal, spatial and topical aspects of users' activity. Here we focus on spikes of collective attention in Twitter, and specifically on peaks in the popularity of hashtags. Users employ hashtags as a form of social annotation, to define a shared context for a specific event, topic, or meme. We analyze a large-scale record of Twitter activity and find that the evolution of hastag popularity over time defines discrete classes of hashtags. We link these dynamical classes to the events the hashtags represent and use text mining techniques to provide a semantic characterization of the hastag classes. Moreover, we track the propagation of hashtags in the Twitter social network and find that epidemic spreading plays a minor role in hastag popularity, which is mostly driven by exogenous factors.

cs.SI↗

arXiv2012

Cooperation and its emergence in growing systems with cultural reproduction

We explore the emergence of cooperation in the framework of evolutionary game theory. First we introduce the cooperation problem in a novel way that we believe it have important consequences in how problem is addressed. Then we present a minimal model for the emergence of cooperation in growing systems with cultural reproduction where topological structure and the evolution of strategies are decoupled instead a coevolution dynamic. We show that when system grows, there exists cultural reproduction and a nonzero probability that individuals take cooperation as first strategy; there are conditions to build up a cooperative system with real topological structures for any natural selection intensity. When the system is small cooperation is unstable but become stable as soon as the system reaches an enough well defined topological structure which size mainly depends on the intensity of natural selection. In this way, we reduce the emergence of cooperation problem for systems with cultural reproduction to justify a small initial cooperative structure, what we call cooperative seed. Otherwise, given that the system grows principally as cooperator whose cooperators inhabit the most linked parts of the system, the condition required to cooperation prevails into the systems are drastically reduced compared to those found in statics networks.

cs.GT↗

arXiv2012

From Caesar to Twitter: An Axiomatic Approach to Elites of Social Networks

In many societies there is an elite, a relatively small group of powerful individuals that is well-connected and highly influential. Since the ancient days of Julius Caesar's senate of Rome to the recent days of celebrities on Twitter, the size of the elite is a result of conflicting social forces competing to increase or decrease it. The main contribution of this paper is the answer to the question how large the elite is at equilibrium. We take an axiomatic approach to solve this: assuming that an elite exists and it is influential, stable and either minimal or dense, we prove that its size must be $Θ(\sqrt{m})$ (where $m$ is the number of edges in the network). As an approximation for the elite, we then present an empirical study on nine large real-world networks of the subgraph formed by the highest degree nodes, also known as the rich-club. Our findings indicate that elite properties such as disproportionate influence, stability and density of $Θ(\sqrt{m})$-rich-clubs are universal properties and should join a growing list of common phenomena shared by social networks and complex systems such as "small world," power law degree distributions, high clustering, etc.

cs.SI↗

arXiv2012

Four Degrees of Separation

Frigyes Karinthy, in his 1929 short story "Láancszemek" ("Chains") suggested that any two persons are distanced by at most six friendship links. (The exact wording of the story is slightly ambiguous: "He bet us that, using no more than five individuals, one of whom is a personal acquaintance, he could contact the selected individual [...]". It is not completely clear whether the selected individual is part of the five, so this could actually allude to distance five or six in the language of graph theory, but the "six degrees of separation" phrase stuck after John Guare's 1990 eponymous play. Following Milgram's definition and Guare's interpretation, we will assume that "degrees of separation" is the same as "distance minus one", where "distance" is the usual path length-the number of arcs in the path.) Stanley Milgram in his famous experiment challenged people to route postcards to a fixed recipient by passing them only through direct acquaintances. The average number of intermediaries on the path of the postcards lay between 4.4 and 5.7, depending on the sample of people chosen. We report the results of the first world-scale social-network graph-distance computations, using the entire Facebook network of active users (\approx721 million users, \approx69 billion friendship links). The average distance we observe is 4.74, corresponding to 3.74 intermediaries or "degrees of separation", showing that the world is even smaller than we expected, and prompting the title of this paper. More generally, we study the distance distribution of Facebook and of some interesting geographic subgraphs, looking also at their evolution over time. The networks we are able to explore are almost two orders of magnitude larger than those analysed in the previous literature. We report detailed statistical metadata showing that our measurements (which rely on probabilistic algorithms) are very accurate.

cs.SI↗

arXiv2011

Optimization of brain and life performance: Striving for playing at the top for the long run

In this essay written with my students and collaborators in mind, I share simple recipes that are easy and often fun to put in practice and that make a big difference in one's life. The seven guiding principles are: (1) sleep, (2) love and sex, (3) deep breathing and daily exercises, (4) water and chewing, (5) fruits, unrefined products, food combination, vitamin D and no meat, (6) power foods, (7) play, intrinsic motivation, positive psychology and will. These simple laws are based on an integration of evolutionary thinking, personal experimentation, and evidence from experiments reported in the scientific literature. I develop their rationality, expected consequences and describe briefly how to put them in practice. I hope that professionals and the broader public may also find some use for it, as I have seen already the positive impacts on some of my students.

q-bio.OT↗

arXiv2012

IRIE: Scalable and Robust Influence Maximization in Social Networks

Influence maximization is the problem of selecting top $k$ seed nodes in a social network to maximize their influence coverage under certain influence diffusion models. In this paper, we propose a novel algorithm IRIE that integrates a new message passing based influence ranking (IR), and influence estimation (IE) methods for influence maximization in both the independent cascade (IC) model and its extension IC-N that incorporates negative opinion propagations. Through extensive experiments, we demonstrate that IRIE matches the influence coverage of other algorithms while scales much better than all other algorithms. Moreover IRIE is more robust and stable than other algorithms both in running time and memory usage for various density of networks and cascade size. It runs up to two orders of magnitude faster than other state-of-the-art algorithms such as PMIA for large networks with tens of millions of nodes and edges, while using only a fraction of memory comparing with PMIA.

cs.SI↗

arXiv2011

Prediction Of Arrival Of Nodes In A Scale Free Network

Most of the networks observed in real life obey power-law degree distribution. It is hypothesized that the emergence of such a degree distribution is due to preferential attachment of the nodes. Barabasi-Albert model is a generative procedure that uses preferential attachment based on degree and one can use this model to generate networks with power-law degree distribution. In this model, the network is assumed to grow one node every time step. After the evolution of such a network, it is impossible for one to predict the exact order of node arrivals. We present in this article, a novel strategy to partially predict the order of node arrivals in such an evolved network. We show that our proposed method outperforms other centrality measure based approaches. We bin the nodes and predict the order of node arrivals between the bins with an accuracy of above 80%.

cs.SI↗