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arXiv2011

A Contextual Risk Model for the Ellsberg Paradox

The Allais and Ellsberg paradoxes show that the expected utility hypothesis and Savage's Sure-Thing Principle are violated in real life decisions. The popular explanation in terms of 'ambiguity aversion' is not completely accepted. On the other hand, we have recently introduced a notion of 'contextual risk' to mathematically capture what is known as 'ambiguity' in the economics literature. Situations in which contextual risk occurs cannot be modeled by Kolmogorovian classical probabilistic structures, but a non-Kolmogorovian framework with a quantum-like structure is needed. We prove in this paper that the contextual risk approach can be applied to the Ellsberg paradox, and elaborate a 'sphere model' within our 'hidden measurement formalism' which reveals that it is the overall conceptual landscape that is responsible of the disagreement between actual human decisions and the predictions of expected utility theory, which generates the paradox. This result points to the presence of a 'quantum conceptual layer' in human thought which is superposed to the usually assumed 'classical logical layer'.

physics.soc-ph↗

arXiv2012

Diffusion in Social Networks with Competing Products

We introduce a new threshold model of social networks, in which the nodes influenced by their neighbours can adopt one out of several alternatives. We characterize the graphs for which adoption of a product by the whole network is possible (respectively necessary) and the ones for which a unique outcome is guaranteed. These characterizations directly yield polynomial time algorithms that allow us to determine whether a given social network satisfies one of the above properties. We also study algorithmic questions for networks without unique outcomes. We show that the problem of computing the minimum possible spread of a product is NP-hard to approximate with an approximation ratio better than $Ω(n)$, in contrast to the maximum spread, which is efficiently computable. We then move on to questions regarding the behavior of a node with respect to adopting some (resp. a given) product. We show that the problem of determining whether a given node has to adopt some (resp. a given) product in all final networks is co-NP-complete.

cs.SI↗

arXiv2011

Universality of citation distributions revisited

Radicchi, Fortunato, and Castellano [arXiv:0806.0974, PNAS 105(45), 17268] claim that, apart from a scaling factor, all fields of science are characterized by the same citation distribution. We present a large-scale validation study of this universality-of-citation-distributions claim. Our analysis shows that claiming citation distributions to be universal for all fields of science is not warranted. Although many fields indeed seem to have fairly similar citation distributions, there are quite some exceptions as well. We also briefly discuss the consequences of our findings for the measurement of scientific impact using citation-based bibliometric indicators.

cs.DL↗

arXiv2011

Generating Scale-free Networks with Adjustable Clustering Coefficient Via Random Walks

This paper presents an algorithm for generating scale-free networks with adjustable clustering coefficient. The algorithm is based on a random walk procedure combined with a triangle generation scheme which takes into account genetic factors; this way, preferential attachment and clustering control are implemented using only local information. Simulations are presented which support the validity of the scheme, characterizing its tuning capabilities.

physics.soc-ph↗

arXiv2011

How the competitive altruism leads to bistable homogeneous states of cooperation or defection

Our recent minimal model of cooperation (P. Gawronski et al, Physica A 388 (2009) 3581) is modified as to allow for time-dependent altruism. This evolution is based on reputation of other agents, which in turn depends on history. We show that this modification leads to two absorbing states of the whole system, where the cooperation flourishes in one state and is absent in another one. The effect is compared with the results obtained with the model of indirect reciprocity, where the altruism of agents is constant.

physics.soc-ph↗

arXiv2011

Return probability and k-step measures

The notion of return probability -- explored most famously by George Pólya on d-dimensional lattices -- has potential as a measure for the analysis of networks. We present an efficient method for finding return probability distributions for connected undirected graphs. We argue that return probability has the same discriminatory power as existing k-step measures -- in particular, beta centrality (with negative beta), the graph-theoretical power index (GPI), and subgraph centrality. We compare the running time of our algorithm to beta centrality and subgraph centrality and find that it is significantly faster. When return probability is used to measure the same phenomena as beta centrality, it runs in linear time -- O(n+m), where n and m are the number of nodes and edges, respectively -- which takes much less time than either the matrix inversion or the sequence of matrix multiplications required for calculating the exact or approximate forms of beta centrality, respectively. We call this form of return probability the Pólya power index (PPI). Computing subgraph centrality requires an expensive eigendecomposition of the adjacency matrix; return probability runs in half the time of the eigendecomposition on a 2000-node network. These performance improvements are important because computationally efficient measures are necessary in order to analyze large networks.

physics.soc-ph↗

arXiv2012

Partitioning Breaks Communities

Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping communities. We show that on a wide range of empirical networks, from different domains, significant numbers of cliques are split across the separate partitions produced by these algorithms. We then examine the largest connected component of the subgraph formed by retaining only edges in cliques, and apply partitioning strategies that explicitly minimise the number of cliques split. We further examine several modern overlapping community finding algorithms, in terms of the interaction between cliques and the communities they find, and in terms of the global overlap of the sets of communities they find. We conclude that, due to the connectedness of many networks, any community finding algorithm that produces partitions must fail to find at least some significant structures. Moreover, contrary to traditional intuition, in some empirical networks, strong ties and cliques frequently do cross community boundaries; much community structure is fundamentally overlapping and unpartitionable in nature.

physics.soc-ph↗

arXiv2011

Intra-City Urban Network and Traffic Flow Analysis from GPS Mobility Trace

We analyse two large-scale intra-city urban networks and traffic flows therein measured by GPS traces of taxis in San Francisco and Shanghai. Our results coincide with previous findings that, based purely on topological means, it is often insufficient to characterise traffic flow. Traditional shortest-path betweenness analysis, where shortest paths are calculated from each pairs of nodes, carries an unrealistic implicit assumption that each node or junction in the urban network generates and attracts an equal amount of traffic. We also argue that weighting edges based only on euclidean distance is inadequate, as primary roads are commonly favoured over secondary roads due to the perceived and actual travel time required. We show that betweenness traffic analysis can be improved by a simple extended framework which incorporates both the notions of node weights and fastest-path betweenness. We demonstrate that the framework is superior to traditional methods based solely on simple topological perspectives.

physics.soc-ph↗

arXiv2011

Deregulating 'the rural'; threatening land management regime. Experiences of space in the Tuscan countryside

In this research the relationships between landownership and the use of rural land are investigated and analyzed through an empirical study, conducted in Tuscany, which was based on interviews with landowners. Through the development of farmers' typologies, the results highlight a general process of decoupling from farming, which appears through 'disinvestments' in farming activity and changing the intended uses of rural land and buildings. The dynamic of liberalization (and urbanization) of rural space arises challenges to the future of land management system, which seems to be going to suffer a process of restructuring.

physics.soc-ph↗

arXiv2011

A Sequence of Relaxations Constraining Hidden Variable Models

Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose violation rules out some latent variable model as a "hidden variable test" for that model. Our main contribution is to introduce a sequence of relaxations which provides progressively tighter hidden variable tests. We demonstrate applicability to mixtures of sequences of i.i.d. variables, Bell inequalities, and homophily models in social networks. For the last, we demonstrate that our method provides a test that is able to rule out latent homophily as the sole explanation for correlations on a real social network that are known to be due to influence.

cs.AI↗

arXiv2011

On the Non-Progressive Spread of Influence through Social Networks

The spread of influence in social networks is studied in two main categories: the progressive model and the non-progressive model (see e.g. the seminal work of Kempe, Kleinberg, and Tardos in KDD 2003). While the progressive models are suitable for modeling the spread of influence in monopolistic settings, non-progressive are more appropriate for modeling non-monopolistic settings, e.g., modeling diffusion of two competing technologies over a social network. Despite the extensive work on the progressive model, non-progressive models have not been studied well. In this paper, we study the spread of influence in the non-progressive model under the strict majority threshold: given a graph $G$ with a set of initially infected nodes, each node gets infected at time $τ$ iff a majority of its neighbors are infected at time $τ-1$. Our goal in the \textit{MinPTS} problem is to find a minimum-cardinality initial set of infected nodes that would eventually converge to a steady state where all nodes of $G$ are infected. We prove that while the MinPTS is NP-hard for a restricted family of graphs, it admits an improved constant-factor approximation algorithm for power-law graphs. We do so by proving lower and upper bounds in terms of the minimum and maximum degree of nodes in the graph. The upper bound is achieved in turn by applying a natural greedy algorithm. Our experimental evaluation of the greedy algorithm also shows its superior performance compared to other algorithms for a set of real-world graphs as well as the random power-law graphs. Finally, we study the convergence properties of these algorithms and show that the non-progressive model converges in at most $O(|E(G)|)$ steps.

cs.SI↗

arXiv2012

Uncovering Evolutionary Ages of Nodes in Complex Networks

In a complex network, different groups of nodes may have existed for different amounts of time. To detect the evolutionary history of a network is of great importance. We present a general method based on spectral analysis to address this fundamental question in network science. In particular, we argue and demonstrate, using model and real-world networks, the existence of positive correlation between the magnitudes of eigenvalues and node ages. In situations where the network topology is unknown but short time series measured from nodes are available, we suggest to uncover the network topology at the present (or any given time of interest) by using compressive sensing and then perform the spectral analysis. Knowledge of ages of various groups of nodes can provide significant insights into the evolutionary process underpinning the network.

physics.soc-ph↗

arXiv2012

Quantum Financial Economics - Risk and Returns

Financial volatility risk and its relation to a business cycle-related intrinsic time is addressed through a multiple round evolutionary quantum game equilibrium leading to turbulence and multifractal signatures in the financial returns and in the risk dynamics. The model is simulated and the results are compared with actual financial volatility data.

q-fin.RM↗

arXiv2012

An Analysis of Anonymity in the Bitcoin System

Anonymity in Bitcoin, a peer-to-peer electronic currency system, is a complicated issue. Within the system, users are identified by public-keys only. An attacker wishing to de-anonymize its users will attempt to construct the one-to-many mapping between users and public-keys and associate information external to the system with the users. Bitcoin tries to prevent this attack by storing the mapping of a user to his or her public-keys on that user's node only and by allowing each user to generate as many public-keys as required. In this chapter we consider the topological structure of two networks derived from Bitcoin's public transaction history. We show that the two networks have a non-trivial topological structure, provide complementary views of the Bitcoin system and have implications for anonymity. We combine these structures with external information and techniques such as context discovery and flow analysis to investigate an alleged theft of Bitcoins, which, at the time of the theft, had a market value of approximately half a million U.S. dollars.

physics.soc-ph↗

arXiv2011

Collective Attention and the Dynamics of Group Deals

We present a study of the group purchasing behavior of daily deals in Groupon and LivingSocial and introduce a predictive dynamic model of collective attention for group buying behavior. In our model, the aggregate number of purchases at a given time comprises two types of processes: random discovery and social propagation. We find that these processes are very clearly separated by an inflection point. Using large data sets from both Groupon and LivingSocial we show how the model is able to predict the success of group deals as a function of time. We find that Groupon deals are easier to predict accurately earlier in the deal lifecycle than LivingSocial deals due to the final number of deal purchases saturating quicker. One possible explanation for this is that the incentive to socially propagate a deal is based on an individual threshold in LivingSocial, whereas in Groupon it is based on a collective threshold, which is reached very early. Furthermore, the personal benefit of propagating a deal is also greater in LivingSocial.

cs.CY↗

arXiv2011

Revisiting Degree Distribution Models for Social Graph Analysis

Degree distribution models are incredibly important tools for analyzing and understanding the structure and formation of social networks, and can help guide the design of efficient graph algorithms. In particular, the Power-law degree distribution has long been used to model the structure of online social networks, and is the basis for algorithms and heuristics in graph applications such as influence maximization and social search. Along with recent measurement results, our interest in this topic was sparked by our own experimental results on social graphs that deviated significantly from those predicted by a Power-law model. In this work, we seek a deeper understanding of these deviations, and propose an alternative model with significant implications on graph algorithms and applications. We start by quantifying this artifact using a variety of real social graphs, and show that their structures cannot be accurately modeled using elementary distributions including the Power-law. Instead, we propose the Pareto-Lognormal (PLN) model, verify its goodness-of-fit using graphical and statistical methods, and present an analytical study of its asymptotical differences with the Power-law. To demonstrate the quantitative benefits of the PLN model, we compare the results of three wide-ranging graph applications on real social graphs against those on synthetic graphs generated using the PLN and Power-law models. We show that synthetic graphs generated using PLN are much better predictors of degree distributions in real graphs, and produce experimental results with errors that are orders-of-magnitude smaller than those produced by the Power-law model.

cs.SI↗

arXiv2011

Second-Order, Dissipative Tâtonnement: Economic Interpretation and 2-Point Limit Cycles

This paper proposes an alternative to the classical price-adjustment mechanism (called "tâtonnement" after Walras) that is second-order in time. The proposed mechanism, an analogue to the damped harmonic oscillator, provides a dynamic equilibration process that depends only on local information. We show how such a process can result from simple behavioural rules. The discrete-time form of the model can result in two-step limit cycles, but as the distance covered by the cycle depends on the size of the damping, the proposed mechanism can lead to both highly unstable and relatively stable behaviour, as observed in real economies.

q-fin.GN↗

arXiv2011

Diffusive Logistic Model Towards Predicting Information Diffusion in Online Social Networks

Online social networks have recently become an effective and innovative channel for spreading information and influence among hundreds of millions of end users. Many prior work have carried out empirical studies and proposed diffusion models to understand the information diffusion process in online social networks. However, most of these studies focus on the information diffusion in temporal dimension, that is, how the information propagates over time. Little attempt has been given on understanding information diffusion over both temporal and spatial dimensions. In this paper, we propose a Partial Differential Equation (PDE), specifically, a Diffusive Logistic (DL) equation to model the temporal and spatial characteristics of information diffusion in online social networks. To be more specific, we develop a PDE-based theoretical framework to measure and predict the density of influenced users at a given distance from the original information source after a time period. The density of influenced users over time and distance provides valuable insight on the actual information diffusion process. We present the temporal and spatial patterns in a real dataset collected from Digg social news site, and validate the proposed DL equation in terms of predicting the information diffusion process. Our experiment results show that the DL model is indeed able to characterize and predict the process of information propagation in online social networks. For example, for the most popular news with 24,099 votes in Digg, the average prediction accuracy of DL model over all distances during the first 6 hours is 92.08%. To the best of our knowledge, this paper is the first attempt to use PDE-based model to study the information diffusion process in both temporal and spatial dimensions in online social networks.

cs.SI↗