We study the cross-correlations in stock price changes between the S&P 500 companies by introducing a weighted random graph, where all vertices (companies) are fully connected, and each edge is weighted. The weight assigned to each edge is given by the normalized covariance of the two modified returns connected, so that it is ranged from -1 to 1. Here the modified return means the deviation of a return from its average over all companies. We define influence-strength at each vertex as the sum of the weights on the edges incident upon that vertex. Then we found that the influence-strength distribution in its absolute magnitude |s| follows a power-law, P (|s|) ∼ |s| −δ , with exponent δ ≈ 1.8(1).PACS numbers: 89.75. Da, 89.65.Gh, Recently complex systems such as biological, economic, physical, and social systems have received considerable attentions as an interdisciplinary subject [1]. Such systems consist of many constituents such as individuals, companies, substrates, spins, etc, exhibiting cooperative and adaptive phenomena through diverse interactions between them. In particular, in economic systems, adaptive behaviors of individuals, companies, or nations, play a crucial role in forming macroscopic patterns such as commodity prices, stock prices, exchange rates, etc, which are formed mostly in a self-organized way [2]. Recently, many attentions and studies have been focused and performed on the fluctuations and the correlations in stock price changes between different companies in physics communities by applying physics concepts and methods [3,4].Stock price changes of individual companies are influenced by others. Thus, one of the most important quantities in understanding the cooperative behavior in stock market is the cross-correlation coefficients between different companies. Since the stock prices changes depend on various economic environments, it is very hard to construct a dynamic equation, and predict the evolution of the stock price change in the future. Recently, there have been some efforts to understand the correlations in stock price changes between different companies using a random matrix theory, where large eigenvalues are located far away from the rest part predicted by the random matrix theory, reflecting the collective behavior of the entire market as well as the subordination among the stock prices [5][6][7].Let Y i (t) be the stock-price of a company i (i = 1, . . . , N ) at time t. Then the return of the stock-price after a time interval ∆t is defined asmeaning the geometrical change of Y i (t) during the interval ∆t. We take ∆t = 1 day for the following analysis in this Letter. The cross-correlations between individual stocks are considered in terms of a matrix C, whose elements are given aswhere the brackets mean a temporal average over the period we studied. Then C i,j can vary between [-1,1], where C i,j = 1 (-1) means that two companies i and j are completely correlated (anti-correlated), while C i,j = 0 means that they are uncorrelated. Since the matrix C is symmetric and real, al...

We argue that the reaction-diffusion process 3A-->4A,3A-->2A exhibits a different type of continuous phase transition from an active into an absorbing phase. Because of the upper critical dimension d(c)> or =4/3 we expect the phase transition in 1+1 dimensions to be characterized by nontrivial fluctuation effects.

Recently there has been a debate concerning the universal properties of the phase transition in the pair contact process with diffusion (PCPD) $2A\to 3A, 2A\to \emptyset$. Although some of the critical exponents seem to coincide with those of the so-called parity-conserving universality class, it was suggested that the PCPD might represent an independent class of phase transitions. This point of view is motivated by the argument that the PCPD does not conserve parity of the particle number. In the present work we pose the question what happens if the parity conservation law is restored. To this end we consider the the reaction-diffusion process $2A\to 4A, 2A\to \emptyset$. Surprisingly this process displays the same type of critical behavior, leading to the conclusion that the most important characteristics of the PCPD is the use of binary reactions for spreading, regardless of whether parity is conserved or not.Comment: RevTex, 4pages, 4 eps figure

Applying the histogram reweighting method, we investigate the critical behavior of the XY model on growing scale-free networks with various degree exponents lambda. For lambda < or = 3 , the critical temperature diverges as it does for the Ising model on scale-free networks. For lambda=8 , on the other hand, we observe a second-order phase transition at finite temperature. We obtain the critical temperature T{c}=3.08(2) and the critical exponents nu=2.62(3) , gammanu=0.127(4) , and betanu=0.442(2) from a finite-size scaling analysis.

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