We provide direct evidence of market manipulation at the beginning of the financial crisis in November 2007. The type of manipulation, a "bear raid," would have been prevented by a regulation that was repealed by the Securities and Exchange Commission in July 2007. The regulation, the uptick rule, was designed to prevent manipulation and promote stability and was in force from 1938 as a key part of the government response to the 1929 market crash and its aftermath. On November 1, 2007, Citigroup experienced an unusual increase in trading volume and decrease in price. Our analysis of financial industry data shows that this decline coincided with an anomalous increase in borrowed shares, the selling of which would be a large fraction of the total trading volume. The selling of borrowed shares cannot be explained by news events as there is no corresponding increase in selling by share owners. A similar number of shares were returned on a single day six days later. The magnitude and coincidence of borrowing and returning of shares is evidence of a concerted effort to drive down Citigroup's stock price and achieve a profit, i.e., a bear raid. Interpretations and analyses of financial markets should consider the possibility that the intentional actions of individual actors or coordinated groups can impact market behavior. Markets are not sufficiently transparent to reveal even major market manipulation events. Our results point to the need for regulations that prevent intentional actions that cause markets to deviate from equilibrium and contribute to crashes. Enforcement actions cannot reverse severe damage to the economic system. The current "alternative" uptick rule which is only in effect for stocks dropping by over 10% in a single day is insufficient. Prevention may be achieved through improved availability of market data and the original uptick rule or other transaction limitations.

The structure of a social network contains information useful for predicting its evolution. Nodes that are "close" in some sense are more likely to become linked in the future than more distant nodes. We show that structural information can also help predict node activity. We use proximity to capture the degree to which two nodes are "close" to each other in the network. In addition to standard proximity metrics used in the link prediction task, such as neighborhood overlap, we introduce new metrics that model different types of interactions that can occur between network nodes. We argue that the "closer" nodes are in a social network, the more similar will be their activity. We study this claim using data about URL recommendation on social media sites Digg and Twitter. We show that structural proximity of two users in the follower graph is related to similarity of their activity, i.e., how many URLs they both recommend. We also show that given friends' activity, knowing their proximity to the user can help better predict which URLs the user will recommend. We compare the performance of different proximity metrics on the activity prediction task and find that some metrics lead to substantial performance improvements.

We show that world trade network datasets contain empirical evidence that the dynamics of innovation in the world economy follows indeed the concept of creative destruction, as proposed by J.A. Schumpeter more than half a century ago. National economies can be viewed as complex, evolving systems, driven by a stream of appearance and disappearance of goods and services. Products appear in bursts of creative cascades. We find that products systematically tend to co-appear, and that product appearances lead to massive disappearance events of existing products in the following years. The opposite - disappearances followed by periods of appearances - is not observed. This is an empirical validation of the dominance of cascading competitive replacement events on the scale of national economies, i.e. creative destruction. We find a tendency that more complex products drive out less complex ones, i.e. progress has a direction. Finally we show that the growth trajectory of a country's product output diversity can be understood by a recently proposed evolutionary model of Schumpeterian economic dynamics.

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely considered to which degree the results obtained for one particular network class can be extrapolated to real-world networks. We address this issue by comparing different classical and more recently developed network models with respect to their generalisation power, which we identify with large structural variability and absence of constraints imposed by the construction scheme. After having identified the most variable networks, we address the issue of which constraints are common to all network classes and are thus suitable candidates for being generic statistical laws of complex networks. In fact, we find that generic, not model-related dependencies between different network characteristics do exist. This allows, for instance, to infer global features from local ones using regression models trained on networks with high generalisation power. Our results confirm and extend previous findings regarding the synchronisation properties of neural networks. Our method seems especially relevant for large networks, which are difficult to map completely, like the neural networks in the brain. The structure of such large networks cannot be fully sampled with the present technology. Our approach provides a method to estimate global properties of under-sampled networks with good approximation. Finally, we demonstrate on three different data sets (C. elegans' neuronal network, R. prowazekii's metabolic network, and a network of synonyms extracted from Roget's Thesaurus) that real-world networks have statistical relations compatible with those obtained using regression models.

Probabilistic preference models predict that a subject makes different choices with different probabilities when repeatedly faced with the same or similar situation(s). However, they do not explain why choice is probabilistic. This paper provides an explanation. First, we prove that a gamble is a statistical ensemble or sample function of a random field with canonical Luce-Gibbs measure. And we employ entropy measures of uncertainty to characterize the underlying function space. Second, we find that under the Luce-Gibbs measure, maximum entropy for unconstrained unobserved probability distributions predicts that subjects have Von Neuman Morgenstern utility. Therefore, probability weighting is inapplicable to ambiguity aversion. Third, when unobserved probability distributions are constrained by finite moments, maximum entropy predicts that the source of probabilistic preference is a behavioural quantum wave function embedded in probability weighting functionals (MaxEnt-PWF), from which probability amplitudes are computed. The [standing] waves have fixed point probability 1/e, and they subsume the Prelec class of pwfs. Fourth, for application, we show how a simple affine transformation of the MaxEnt-PWF produces a sinusoidal inverted S-shaped probability weighting functional consistent with likelihood insensitivity reported in recent source function theory of uncertainty. However, our model reveals a tautologous fixed point probability puzzle--vizly, the fixed point has maximum entropy even though it is invariant. In fact, we prove that there exist a cluster set of fixed points for MaxEnt probability weighting functionals that include Prelec's generalized pwf's which are not constrained to 1/e.

A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems, ecosystems, stock markets and economies, biological evolution, and indeed the whole of human society. Substantial progress has been made in the quantitative understanding of complex systems, particularly since the 1980s, using a combination of basic theory, much of it derived from physics, and computer simulation. The subject is a broad one, drawing on techniques and ideas from a wide range of areas. Here I give a survey of the main themes and methods of complex systems science and an annotated bibliography of resources, ranging from classic papers to recent books and reviews.

We suggest an empirical model of investment strategy returns which elucidates the importance of non-Gaussian features, such as time-varying volatility, asymmetry and fat tails, in explaining the level of expected returns. Estimating the model on the (former) Lehman Brothers Hedge Fund Index data, we demonstrate that the volatility compensation is a significant component of the expected returns for most strategy styles, suggesting that many of these strategies should be thought of as being `short vol'. We present some fundamental and technical reasons why this should indeed be the case, and suggest explanation for exception cases exhibiting `long vol' characteristics. We conclude by drawing some lessons for hedge fund portfolio construction.

We address the issue of the distribution of firm size. To this end we propose a model of firms in a closed, conserved economy populated with zero-intelligence agents who continuously move from one firm to another. We then analyze the size distribution and related statistics obtained from the model. Our ultimate goal is to reproduce the well known statistical features obtained from the panel study of the firms i.e., the power law in size (in terms of income and/or employment), the Laplace distribution in the growth rates and the slowly declining standard deviation of the growth rates conditional on the firm size. First, we show that the model generalizes the usual kinetic exchange models with binary interaction to interactions between an arbitrary number of agents. When the number of interacting agents is in the order of the system itself, it is possible to decouple the model. We provide some exact results on the distributions. Our model easily reproduces the power law. The fluctuations in the growth rate falls with increasing size following a power law (with an exponent 1 whereas the data suggests that the exponent is around 1/6). However, the distribution of the difference of the firm-size in this model has Laplace distribution whereas the real data suggests that the difference of the log sizes has the same distribution.

Recent research [1] has suggested that coreness, and not degree, constitutes a better topological descriptor to identifying influential spreaders in complex networks. This hypothesis has been verified in the context of disease spreading. Here, we instead focus on rumor spreading models, which are more suited for social contagion and information propagation. To this end, we perform extensive computer simulations on top of several real-world networks and find opposite results. Namely, we show that the spreading capabilities of the nodes do not depend on their $k$-core index, which instead determines whether or not a given node prevents the diffusion of a rumor to a system-wide scale. Our findings are relevant both for sociological studies of contagious dynamics and for the design of efficient commercial viral processes.

Existing centrality measures for social network analysis suggest the im-portance of an actor and give consideration to actor's given structural position in a network. These existing measures suggest specific attribute of an actor (i.e., popularity, accessibility, and brokerage behavior). In this study, we propose new hybrid centrality measures (i.e., Degree-Degree, Degree-Closeness and Degree-Betweenness), by combining existing measures (i.e., degree, closeness and betweenness) with a proposition to better understand the importance of actors in a given network. Generalized set of measures are also proposed for weighted networks. Our analysis of co-authorship networks dataset suggests significant correlation of our proposed new centrality measures (especially weighted networks) than traditional centrality measures with performance of the scholars. Thus, they are useful measures which can be used instead of traditional measures to show prominence of the actors in a network.