Visualization of chiral condensate at finite temperature on the lattice

We perform an analysis of the topological and chiral vacuum structure of four-dimensional QCD on the lattice at finite temperature. From correlation functions we show the existence of local correlations between the topological charge density and the quark condensate on gauge average. We comment on sizes of clusters of nontrivial chiral condensate and of instantons in full QCD. By analysis of individual gauge configurations, we demonstrate that at the places in Euclidian space-time, where instantons are present, amplified production of quark condensate occurs.Comment: 5 pages, 3 EPS figures, Talk presented at ``QCD97'', to appear in Nucl. Phys. B (Proc. Suppl.

A Dynamical Thermostat Approach To Financial Asset Price Dynamics

A dynamical price formation model for financial assets is presented. It aims to capture the essence of speculative trading where mispricings of assets are used to make profits. It is shown that together with the incorporation of the concept of risk aversion of agents the model is able to reproduce several key characteristics of financial price series. The approach is contrasted to the conventional view of price formation in financial economics.Comment: contribution to the 6th Granada Seminar 2000: Modeling Complex Systems, 10 pages, eps figure

Hierarchical and mixing properties of static complex networks emerging from the fluctuating classical random graphs

The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to lead to a static complex network with an arbitrary connectivity distribution. In particular, a scale-free network with the hierarchical organization is constructed without assuming any knowledge about the global linking structure, in contrast to the preferential attachment rule for a growing network. The hierarchical and mixing properties of the static scale-free network thus constructed are studied. The present approach establishes a bridge between a scalar characterization of individual vertices and topology of an emerging complex network. The result may offer a clue for understanding the origin of a few abundance of connectivity distributions in a wide variety of static real-world networks.Comment: 15 pages and 3 figure

DebtRank-transparency: Controlling systemic risk in financial networks

Banks in the interbank network can not assess the true risks associated with lending to other banks in the network, unless they have full information on the riskiness of all the other banks. These risks can be estimated by using network metrics (for example DebtRank) of the interbank liability network which is available to Central Banks. With a simple agent based model we show that by increasing transparency by making the DebtRank of individual nodes (banks) visible to all nodes, and by imposing a simple incentive scheme, that reduces interbank borrowing from systemically risky nodes, the systemic risk in the financial network can be drastically reduced. This incentive scheme is an effective regulation mechanism, that does not reduce the efficiency of the financial network, but fosters a more homogeneous distribution of risk within the system in a self-organized critical way. We show that the reduction of systemic risk is to a large extent due to the massive reduction of cascading failures in the transparent system. An implementation of this minimal regulation scheme in real financial networks should be feasible from a technical point of view.Comment: 8 pages, 5 figure

Generalized (c,d)-entropy and aging random walks

Complex systems are often inherently non-ergodic and non-Markovian for which Shannon entropy loses its applicability. In particular accelerating, path-dependent, and aging random walks offer an intuitive picture for these non-ergodic and non-Markovian systems. It was shown that the entropy of non-ergodic systems can still be derived from three of the Shannon-Khinchin axioms, and by violating the fourth -- the so-called composition axiom. The corresponding entropy is of the form $S_{c,d} \sim \sum_i \Gamma(1+d,1-c\ln p_i)$ and depends on two system-specific scaling exponents, $c$ and $d$. This entropy contains many recently proposed entropy functionals as special cases, including Shannon and Tsallis entropy. It was shown that this entropy is relevant for a special class of non-Markovian random walks. In this work we generalize these walks to a much wider class of stochastic systems that can be characterized as `aging' systems. These are systems whose transition rates between states are path- and time-dependent. We show that for particular aging walks $S_{c,d}$ is again the correct extensive entropy. Before the central part of the paper we review the concept of $(c,d)$-entropy in a self-contained way.Comment: 8 pages, 5 eps figures. arXiv admin note: substantial text overlap with arXiv:1104.207

Behavioral and Network Origins of Wealth Inequality: Insights from a Virtual World

Almost universally, wealth is not distributed uniformly within societies or economies. Even though wealth data have been collected in various forms for centuries, the origins for the observed wealth-disparity and social inequality are not yet fully understood. Especially the impact and connections of human behavior on wealth could so far not be inferred from data. Here we study wealth data from the virtual economy of the massive multiplayer online game (MMOG) Pardus. This data not only contains every player's wealth at every point in time, but also all actions of every player over a timespan of almost a decade. We find that wealth distributions in the virtual world are very similar to those in western countries. In particular we find an approximate exponential for low wealth and a power-law tail. The Gini index is found to be $g=0.65$, which is close to the indices of many Western countries. We find that wealth-increase rates depend on the time when players entered the game. Players that entered the game early on tend to have remarkably higher wealth-increase rates than those who joined later. Studying the players' positions within their social networks, we find that the local position in the trade network is most relevant for wealth. Wealthy people have high in- and out-degree in the trade network, relatively low nearest-neighbor degree and a low clustering coefficient. Wealthy players have many mutual friendships and are socially well respected by others, but spend more time on business than on socializing. We find that players that are not organized within social groups with at least three members are significantly poorer on average. We observe that high `political' status and high wealth go hand in hand. Wealthy players have few personal enemies, but show animosity towards players that behave as public enemies.Comment: 22 pages, 8 figures, 8 pages S