On possible origins of trends in financial market price changes

We investigate possible origins of trends using a deterministic threshold model, where we refer to long-term variabilities of price changes (price movements) in financial markets as trends. From the investigation we find two phenomena. One is that the trend of monotonic increase and decrease can be generated by dealers' minuscule change in mood, which corresponds to the possible fundamentals. The other is that the emergence of trends is all but inevitable in the realistic situation because of the fact that dealers cannot always obtain accurate information about deals, even if there is no influence from fundamentals and technical analyses.Comment: 23 pages, 9 figure

Optimization of Robustness of Complex Networks

Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random failure and intentional attack while keeping the cost of the network (which we take to be the average number of links per node) constant. We find optimal parameters for: (i) scale free networks having degree distributions with a single power-law regime, (ii) networks having degree distributions with two power-law regimes, and (iii) networks described by degree distributions containing two peaks. Of these various kinds of distributions we find that the optimal network design is one in which all but one of the nodes have the same degree, $k_1$ (close to the average number of links per node), and one node is of very large degree, $k_2 \sim N^{2/3}$, where $N$ is the number of nodes in the network.Comment: Accepted for publication in European Physical Journal

Optimization of Network Robustness to Waves of Targeted and Random Attack

We study the robustness of complex networks to multiple waves of simultaneous (i) targeted attacks in which the highest degree nodes are removed and (ii) random attacks (or failures) in which fractions $p_t$ and $p_r$ respectively of the nodes are removed until the network collapses. We find that the network design which optimizes network robustness has a bimodal degree distribution, with a fraction $r$ of the nodes having degree k_2= (\kav - 1 +r)/r and the remainder of the nodes having degree $k_1=1$, where \kav is the average degree of all the nodes. We find that the optimal value of $r$ is of the order of $p_t/p_r$ for $p_t/p_r\ll 1$

Entropy Optimization of Scale-Free Networks Robustness to Random Failures

Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random failures from the character of their heterogeneity. Entropy of the degree distribution can be an average measure of a network's heterogeneity. Optimization of scale-free network robustness to random failures with average connectivity constant is equivalent to maximize the entropy of the degree distribution. By examining the relationship of entropy of the degree distribution, scaling exponent and the minimal connectivity, we get the optimal design of scale-free network to random failures. We conclude that entropy of the degree distribution is an effective measure of network's resilience to random failures.Comment: 9 pages, 5 figures, accepted by Physica