Herd Behaviors in Financial Markets

We investigate the herd behavior of returns for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution $P(R)$ of returns $R$ satisfies the power-law behavior $P(R) \simeq R^{-\beta}$ with the exponents $\beta=3.11$(the time interval $\tau=$ one minute) and 3.36($\tau=$ one day). The informational cascade regime appears in the herding parameter $H\ge 2.33$ at $\tau=$ one minute, while it occurs no herding at $\tau=$ one day. Especially, we find that the distribution of normalized returns shows a crossover to a Gaussian distribution at one time step $\Delta t=1$ day.Comment: 15 pages, 6 figure

Exact Calculation of the Spatio-temporal Correlations in the Takayasu model and in the q-model of Force Fluctuations in Bead Packs

We calculate exactly the two point mass-mass correlations in arbitrary spatial dimensions in the aggregation model of Takayasu. In this model, masses diffuse on a lattice, coalesce upon contact and adsorb unit mass from outside at a constant rate. Our exact calculation of the variance of mass at a given site proves explicitly, without making any assumption of scaling, that the upper critical dimension of the model is 2. We also extend our method to calculate the spatio-temporal correlations in a generalized class of models with aggregation, fragmentation and injection which include, in particular, the $q$-model of force fluctuations in bead packs. We present explicit expressions for the spatio-temporal force-force correlation function in the $q$-model. These can be used to test the applicability of the $q$-model in experiments.Comment: 15 pages, RevTex, 2 figure

Nonequilibrium Phase Transitions in Models of Aggregation, Adsorption, and Dissociation

We study nonequilibrium phase transitions in a mass-aggregation model which allows for diffusion, aggregation on contact, dissociation, adsorption and desorption of unit masses. We analyse two limits explicitly. In the first case mass is locally conserved whereas in the second case local conservation is violated. In both cases the system undergoes a dynamical phase transition in all dimensions. In the first case, the steady state mass distribution decays exponentially for large mass in one phase, and develops an infinite aggregate in addition to a power-law mass decay in the other phase. In the second case, the transition is similar except that the infinite aggregate is missing.Comment: Major revision of tex

Long-term power-law fluctuation in Internet traffic

Power-law fluctuation in observed Internet packet flow are discussed. The data is obtained by a multi router traffic grapher (MRTG) system for 9 months. The internet packet flow is analyzed using the detrended fluctuation analysis. By extracting the average daily trend, the data shows clear power-law fluctuations. The exponents of the fluctuation for the incoming and outgoing flow are almost unity. Internet traffic can be understood as a daily periodic flow with power-law fluctuations.Comment: 10 pages, 8 figure

Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles

We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation and fragmentation. When there is no preferred directionality in the motion of the masses, the model is known to exhibit a nonequilibrium phase transition between two different types of steady states, in all dimensions. We show analytically that introducing a preferred direction in the motion of the masses inhibits the occurrence of the phase transition in one dimension, in the thermodynamic limit. A finite size system, however, continues to show a signature of the original transition, and we characterize the finite size scaling implications of this. Our analysis is supported by numerical simulations. In two dimensions, bias is shown to be irrelevant.Comment: 7 pages, 7 figures, revte

A universal mechanism for long-range cross-correlations

Cross-correlations are thought to emerge through interaction between particles. Here we present a universal dynamical mechanism capable of generating power-law cross-correlations between non-interacting particles exposed to an external potential. This phenomenon can occur as an ensemble property when the external potential induces intermittent dynamics of Pomeau-Manneville type, providing laminar and stochastic phases of motion in a system with a large number of particles. In this case, the ensemble of particle-trajectories forms a random fractal in time. The underlying statistical self-similarity is the origin of the observed power-law cross-correlations. Furthermore, we have strong indications that a sufficient condition for the emergence of these long-range cross-correlations is the divergence of the mean residence time in the laminar phase of the single particle motion (sporadic dynamics). We argue that the proposed mechanism may be relevant for the occurrence of collective behaviour in critical systems

Phase Transition in the Takayasu Model with Desorption

We study a lattice model where particles carrying different masses diffuse, coalesce upon contact, and also unit masses adsorb to a site with rate $q$ or desorb from a site with nonzero mass with rate $p$. In the limit $p=0$ (without desorption), our model reduces to the well studied Takayasu model where the steady-state single site mass distribution has a power law tail $P(m)\sim m^{-\tau}$ for large mass. We show that varying the desorption rate $p$ induces a nonequilibrium phase transition in all dimensions. For fixed $q$, there is a critical $p_c(q)$ such that if $p<p_c(q)$, the steady state mass distribution, $P(m)\sim m^{-\tau}$ for large $m$ as in the Takayasu case. For $p=p_c(q)$, we find $P(m)\sim m^{-\tau_c}$ where $\tau_c$ is a new exponent, while for $p>p_c(q)$, $P(m)\sim \exp(-m/m^*)$ for large $m$. The model is studied analytically within a mean field theory and numerically in one dimension.Comment: RevTex, 11 pages including 5 figures, submitted to Phys. Rev.

Topological Properties of Citation and Metabolic Networks

Topological properties of "scale-free" networks are investigated by determining their spectral dimensions $d_S$, which reflect a diffusion process in the corresponding graphs. Data bases for citation networks and metabolic networks together with simulation results from the growing network model \cite{barab} are probed. For completeness and comparisons lattice, random, small-world models are also investigated. We find that $d_S$ is around 3 for citation and metabolic networks, which is significantly different from the growing network model, for which $d_S$ is approximately 7.5. This signals a substantial difference in network topology despite the observed similarities in vertex order distributions. In addition, the diffusion analysis indicates that whereas the citation networks are tree-like in structure, the metabolic networks contain many loops.Comment: 11 pages, 3 figure

Power law velocity fluctuations due to inelastic collisions in numerically simulated vibrated bed of powder}

Distribution functions of relative velocities among particles in a vibrated bed of powder are studied both numerically and theoretically. In the solid phase where granular particles remain near their local stable states, the probability distribution is Gaussian. On the other hand, in the fluidized phase, where the particles can exchange their positions, the distribution clearly deviates from Gaussian. This is interpreted with two analogies; aggregation processes and soft-to-hard turbulence transition in thermal convection. The non-Gaussian distribution is well-approximated by the t-distribution which is derived theoretically by considering the effect of clustering by inelastic collisions in the former analogy.Comment: 7 pages, using REVTEX (Figures are inculded in text body) %%%Replacement due to rivision (Europhys. Lett., in press)%%