The scale-free topology of market investments

We propose a network description of large market investments, where both stocks and shareholders are represented as vertices connected by weighted links corresponding to shareholdings. In this framework, the in-degree ($k_{in}$) and the sum of incoming link weights ($v$) of an investor correspond to the number of assets held (\emph{portfolio diversification}) and to the invested wealth (\emph{portfolio volume}) respectively. An empirical analysis of three different real markets reveals that the distributions of both $k_{in}$ and $v$ display power-law tails with exponents $\gamma$ and $\alpha$. Moreover, we find that $k_{in}$ scales as a power-law function of $v$ with an exponent $\beta$. Remarkably, despite the values of $\alpha$, $\beta$ and $\gamma$ differ across the three markets, they are always governed by the scaling relation $\beta=(1-\alpha)/(1-\gamma)$. We show that these empirical findings can be reproduced by a recent model relating the emergence of scale-free networks to an underlying Paretian distribution of `hidden' vertex properties.Comment: Final version accepted for publication on Physica

efficiency and evolution of R&D Networks.

This work introduces a new model to investigate the efficiency and evolution of networks of firms exchanging knowledge in R&D partnerships. We first examine the efficiency of a given network structure from the point of view of maximizing total profits in the industry. We show that the efficient network structure depends on the marginal cost of collaboration. When the marginal cost is low, the complete graph is efficient. However, a high marginal cost implies that the efficient network is sparser and has a core-periphery structure. Next, we examine the evolution of the network structure when the decision on collaborating partners is decentralized. We show the existence of multiple equilibrium structures which are in general inefficient. This is due to (i) the path dependent character of the partner selection process, (ii) the presence of knowledge externalities and (iii) the presence of severance costs involved in link deletion. Finally, we study the properties of the emerging equilibrium networks and we show that they are coherent with the stylized facts on R&D networks.R&D networks;technology spillovers;network efficiency;network formation;

The Efficiency and Evolution of R&D Networks

This work introduces a new model to investigate the efficiency and evolution of networks of firms exchanging knowledge in R&D partnerships. We first examine the efficiency of a given network structure in terms of the maximization of total profits in the industry. We show that the efficient network structure depends on the marginal cost of collaboration. When the marginal cost is low, the complete graph is efficient. However, a high marginal cost implies that the efficient network is sparser and has a core-periphery structure. Next, we examine the evolution of the network struc- ture when the decision on collaborating partners is decentralized. We show the existence of mul- tiple equilibrium structures which are in general inefficient. This is due to (i) the path dependent character of the partner selection process, (ii) the presence of knowledge externalities and (iii) the presence of severance costs involved in link deletion. Finally, we study the properties of the emerg- ing equilibrium networks and we show that they are coherent with the stylized facts of R&D net- works.R&D networks, technology spillovers, network efficiency, network formation

Evolution equations for slowly rotating stars

We present a hyperbolic formulation of the evolution equations describing non-radial perturbations of slowly rotating relativistic stars in the Regge--Wheeler gauge. We demonstrate the stability preperties of the new evolution set of equations and compute the polar w-modes for slowly rotating stars.Comment: 27 pages, 2 figure

An economic and financial exploratory

This paper describes the vision of a European Exploratory for economics and finance using an interdisciplinary consortium of economists, natural scientists, computer scientists and engineers, who will combine their expertise to address the enormous challenges of the 21st century. This Academic Public facility is intended for economic modelling, investigating all aspects of risk and stability, improving financial technology, and evaluating proposed regulatory and taxation changes. The European Exploratory for economics and finance will be constituted as a network of infrastructure, observatories, data repositories, services and facilities and will foster the creation of a new cross-disciplinary research community of social scientists, complexity scientists and computing (ICT) scientists to collaborate in investigating major issues in economics and finance. It is also considered a cradle for training and collaboration with the private sector to spur spin-offs and job creations in Europe in the finance and economic sectors. The Exploratory will allow Social Scientists and Regulators as well as Policy Makers and the private sector to conduct realistic investigations with real economic, financial and social data. The Exploratory will (i) continuously monitor and evaluate the status of the economies of countries in their various components, (ii) use, extend and develop a large variety of methods including data mining, process mining, computational and artificial intelligence and every other computer and complex science techniques coupled with economic theory and econometric, and (iii) provide the framework and infrastructure to perform what-if analysis, scenario evaluations and computational, laboratory, field and web experiments to inform decision makers and help develop innovative policy, market and regulation designs. Graphical abstrac

How big is too big? Critical Shocks for Systemic Failure Cascades

External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical constellations determine whether this cascade remains finite or reaches the size of the system, i.e. leads to systemic risk. We investigate the critical parameters for such cascades in a simple model, where agents are characterized by an individual threshold \theta_i determining their capacity to handle a load \alpha\theta_i with 1-\alpha being their safety margin. If agents fail, they redistribute their load equally to K neighboring agents in a regular network. For three different threshold distributions P(\theta), we derive analytical results for the size of the cascade, X(t), which is regarded as a measure of systemic risk, and the time when it stops. We focus on two different regimes, (i) EEE, an external extreme event where the size of the shock is of the order of the total capacity of the network, and (ii) RIE, a random internal event where the size of the shock is of the order of the capacity of an agent. We find that even for large extreme events that exceed the capacity of the network finite cascades are still possible, if a power-law threshold distribution is assumed. On the other hand, even small random fluctuations may lead to full cascades if critical conditions are met. Most importantly, we demonstrate that the size of the "big" shock is not the problem, as the systemic risk only varies slightly for changes of 10 to 50 percent of the external shock. Systemic risk depends much more on ingredients such as the network topology, the safety margin and the threshold distribution, which gives hints on how to reduce systemic risk.Comment: 23 pages, 7 Figure

Rare Kaon Decays

The current status of rare kaon decay experiments is reviewed. New limits in the search for Lepton Flavor Violation are discussed, as are new measurements of the CKM matrix.Comment: 8 pages, 3 figures, LaTeX, presented at the 3rd International Conference on B Phyiscs and CP Violation, Taipei December 3-7, 199

Systemic Risk in a Unifying Framework for Cascading Processes on Networks

We introduce a general framework for models of cascade and contagion processes on networks, to identify their commonalities and differences. In particular, models of social and financial cascades, as well as the fiber bundle model, the voter model, and models of epidemic spreading are recovered as special cases. To unify their description, we define the net fragility of a node, which is the difference between its fragility and the threshold that determines its failure. Nodes fail if their net fragility grows above zero and their failure increases the fragility of neighbouring nodes, thus possibly triggering a cascade. In this framework, we identify three classes depending on the way the fragility of a node is increased by the failure of a neighbour. At the microscopic level, we illustrate with specific examples how the failure spreading pattern varies with the node triggering the cascade, depending on its position in the network and its degree. At the macroscopic level, systemic risk is measured as the final fraction of failed nodes, $X^\ast$, and for each of the three classes we derive a recursive equation to compute its value. The phase diagram of $X^\ast$ as a function of the initial conditions, thus allows for a prediction of the systemic risk as well as a comparison of the three different model classes. We could identify which model class lead to a first-order phase transition in systemic risk, i.e. situations where small changes in the initial conditions may lead to a global failure. Eventually, we generalize our framework to encompass stochastic contagion models. This indicates the potential for further generalizations.Comment: 43 pages, 16 multipart figure