International Journal of Modern Physics C

Published by World Scientific Publishing
The side and top views of the supercells used in the study of Au atoms on the Al(001) surface. The black and grey balls represent the Au and Al atoms, respectively. The supercells from left to right correspond to the coverages Θ=0.11, 0.25, 0.50, 0.75, and 1.00 ML, respectively. Only the half of the Al substrate including the central layers are shown. The Al atoms labeled by ”C” and ”D”, and the Au atoms labeled by ”1” and ”2” show different bucklings. The Al atoms labeled by ”A” and ”B” are used to define the plane for plots of density profiles as explained in the text. 
Contour plots of the difference electron densities in the (100) plane normal to the Al(001) surface which passes through the Au atom and its two nearest Al(A) and Al(B) atoms (see Fig. 1). (a), (b), and (c) correspond to Θ=0.11, 0.25, and 0.50 ML, respectively. Contour levels in (a) 
In this work, we have studied theoretically the effects of gold adsorption on the Al(001) surface, using {\it ab initio} pseudo-potential method in the framework of the density functional theory. Having found the hollow sites at the Al(001) surface as the most preferred adsorption sites, we have investigated the effects of the Au adsorption with different coverages ($\Theta$=0.11, 0.25, 0.50, 0.75, 1.00 ML) on the geometry, adsorption energy, surface dipole moment, and the work-function of the Al(001) surface. The results show that, even though the work-function of the Al substrate increases with the Au coverage, the surface dipole moment decreases with the changes in coverage from $\Theta=0.11$ ML to $\Theta=0.25$ ML. We have explained this behavior by analyzing the electronic and ionic charge distributions. Furthermore, by studying the diffusion of Au atoms in to the substrate, we have shown that at room temperature the diffusion rate of Au atoms in to the substrate is negligible but, increasing the temperature to about 200$^\circ$ C the Au atoms significantly diffuse in to the substrate, in agreement with the experiment. Comment: 19 pages, 9 eps figures
Concentration of mRNA molecules [mRNA] in arbitrary units as a function of time t. The parameter values are p1 = 0.5, p2 = 0.5, p3 = 0.3, p4 = 0.85, p5 =0.05 and µ=0.4.
Distribution of no. N(m) of cells expressing fraction m of maximal number of mRNA after 10,000 time steps. The total number of cells is 3000. The parameter values are p1 = p2=0.5, p3=0.3, p4=0.85, p5=0.05 and µ=0.4.
Distribution of no. N(m) of cells expressing fraction m of maximal number of mRNA after 10,000 time steps. The total number of cells is 3000. The parameter values are p1=0.7, p2=0.2, p3=0.7, p4=0.85, p5=0.05 and µ=0.5.
Recent experiments at the level of a single cell have shown that gene expression occurs in abrupt stochastic bursts. Further, in an ensemble of cells, the levels of proteins produced have a bimodal distribution. In a large fraction of cells, the gene expression is either off or has a high value. We propose a stochastic model of gene expression the essential features of which are stochasticity and cooperative binding of RNA polymerase. The model can reproduce the bimodal behaviour seen in experiments. Comment: 4 pages (Revtex), 3 eps figures (included), to be published in IJMPC
The restructuring process of diagenesis in the sedimentary rocks is studied using a percolation type model. The cementation and dissolution processes are modeled by the culling of occupied sites in rarefied and growth of vacant sites in dense environments. Starting from sub-critical states of ordinary percolation the system evolves under the diagenetic rules to critical percolation configurations. Our numerical simulation results in two dimensions indicate that the stable configuration has the same critical behaviour as the ordinary percolation. Comment: 7 pages, Revtex, 10 Figures
Average distance < r > versus 1/time 1/6 ; asymptotically a straight line is expected leading to a finite intercept.
Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven dimensions, at the percolation threshold with L^7 sites and L < 420, we confirm the expected time-dependence of the end-to-end distance (including the corrections to the asymptotic behavior). Comment: 8 pages including figures, presentation improved, for Int.J.Mod.Phys.C
The Richardson cascade of turbulent eddies. The fluctuating quantity is the velocity fluctuation across the eddy (solid arrows). For simplicity, this is shown for the mother eddy only. 
The spreading exponent of the quantum wavefunction, α , as a function of the dynamic exponent z for the case of three spatial dimensions D = 3. To be noted that, for z > 3 / 2, the spreading exponent becomes negative, pointing to the development of a finite-time singularity in the quantum wavefunction carrying the propagating signal. 
Simple arguments based on the general properties of quantum fluctuations have been recently shown to imply that quantum fluctuations of spacetime obey the same scaling laws of the velocity fluctuations in a homogeneous incompressible turbulent flow, as described by Kolmogorov 1941 (K41) scaling theory. Less noted, however, is the fact that this analogy rules out the possibility of a fractal quantum spacetime, in contradiction with growing evidence in quantum gravity research. In this Note, we show that the notion of a fractal quantum spacetime can be restored by extending the analogy between turbulence and quantum gravity beyond the realm of K41 theory. In particular, it is shown that compatibility of a fractal quantum-space time with the recent Horava-Lifshitz scenario for quantum gravity, implies singular quantum wavefunctions. Finally, we propose an operational procedure, based on Extended Self-Similarity techniques, to inspect the (multi)-scaling properties of quantum gravitational fluctuations.
In January 1999, the authors published a quantitative prediction that the Nikkei index should recover from its 14 year low in January 1999 and reach $\approx 20500$ a year later. The purpose of the present paper is to evaluate the performance of this specific prediction as well as the underlying model: the forecast, performed at a time when the Nikkei was at its lowest (as we can now judge in hindsight), has correctly captured the change of trend as well as the quantitative evolution of the Nikkei index since its inception. As the change of trend from sluggish to recovery was estimated quite unlikely by many observers at that time, a Bayesian analysis shows that a skeptical (resp. neutral) Bayesian sees her prior belief in our model amplified into a posterior belief 19 times larger (resp. reach the 95% level). Comment: 6 pages including 2 figures
The presence of log-periodic structures before and after stock market crashes is considered to be an imprint of an intrinsic discrete scale invariance (DSI) in this complex system. The fractal framework of the theory leaves open the possibility of observing self-similar log-periodic structures at different time scales. In the present work we analyze the daily closures of three of the most important indices worldwide since 2000: the DAX for Germany and the Nasdaq100 and the S&P500 for the United States. The qualitative behaviour of these different markets is similar during the temporal frame studied. Evidence is found for decelerating log-periodic oscillations of duration about two years and starting in September 2000. Moreover, a nested sub-structure starting in May 2002 is revealed, bringing more evidence to support the hypothesis of self-similar, log-periodic behavior. Ongoing log-periodic oscillations are also revealed. A Lomb analysis over the aforementioned periods indicates a preferential scaling factor $\lambda \sim 2$. Higher order harmonics are also present. The spectral pattern of the data has been found to be similar to that of a Weierstrass-type function, used as a prototype of a log-periodic fractal function.
Capital usually leads to income, and income is more accurately and easily measured. Thus we summarize income distributions in USA, Germany, etc.
Sequence of estimates for 1/ν L,sL .
A general numerical method is presented to locate the partition function zeros in the complex beta plane for large lattice sizes. We apply this method to the 2D Ising model and results are reported for square lattice sizes up tp L=64. We also propose an alternative method to evaluate corrections to scaling which relies only on the leading zeros. This method is illustrated with our data. Comment: 9 pages, Latex, 3 figures. To appear in Int. J. Mod. Phys. C
Dependence of the so called magnetization on βJ and q.  
Dependence of the percolation probability p c on βJ for several values of the q parameter.  
Bird eye view of the dependence of the percolation probability on βJ and q.  
The parameter k E in the N s exponential law dependence. The inset shows the same data on a log-log plot.  
A generalized so called magnetically controlled ballistic rain-like deposition (MBD) model of granular piles has been numerically investigated in 2D. The grains are taken to be elongated disks whence characterized by a two-state scalar degree of freedom, called ''nip'', their interaction being described through a Hamiltonian. Results are discussed in order to search for the effect of nip flip (or grain rotation from vertical to horizontal and conversely) probability in building a granular pile. The characteristics of creation of + (or $-$) nip's clusters and clusters of holes (missing nips) are analyzed. Two different cluster-mass regimes have been identified, through the cluster-mass distribution function which can be exponential or have a power law form depending on whether the nip flip (or grain rotation) probability is large or small. Analytical forms of the exponent are empirically found in terms of the Hamiltonian parameters. Comment: submitted to Int.J. Mod. Phys. C; 16 figures; 79 references
Using Mathematica 3.0, the Schroedinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction potential has to be spherically symmetric. The solving procedure is simply defined as some Mathematica function. The output is the energy eigenvalue and the reduced wave function, which is provided as an interpolated function (and can thus be used for the calculation of, e.g., moments by using any Mathematica built-in function) as well as plotted automatically.
We investigate as a member of the Ising universality class the Next-Nearest Neighbour Ising model without external field on a simple cubic lattice by using the Monte Carlo Metropolis Algorithm. The Binder cumulant and the susceptibility ratio, which should be universal quantities at the critical point, were shown to vary for small negative next-nearest neighbour interactions.
The function ∆C T (τ ; tw) as a function of tw/τ obtained in isothermal aging at T = 0.6. In the inset we show {α(τ )} thus extracted at T = 0.5, 0.6, 0.7 and 0.8 from bottom to top. Four symbols at T = 0.6 represents four sets of {α(τ )} which yield significantly different values of κ in eq.(3.3).
The double logarithmic plot of ∆C T 2 ,T 1 (τ ; t w1 ) versus L T 2 (τ )/R T 1 (t w1 ) of the T-shift process for different τ 's are plotted by the different symbols (with T 1 = 0.8 and T 2 = 0.6). For comparison ∆C T (τ ; tw) versus L T (τ )/R T (tw ) of the isothermal aging for different τ 's are plotted by the different curves (at T = 0.6). The slope of the dotted line is 3.0.
Using Monte Carlo simulations, we have studied aging phenomena in three-dimensional Gaussian Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation functions. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of effective stiffness for droplet excitations in the presence of domain walls. The simulated results in not only isothermal but also $T$-shift aging processes exhibit the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls in spite of the fact that the growth law for these length scales still shows a pre-asymptotic behavior compared with the asymptotic form proposed by the droplet theory. Implications of our simulational results are also discussed in relation to experimental observations.
Corrections to scaling in the 3D Ising model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L. Analytical arguments show the existence of corrections with the exponent (gamma-1)/nu (approximately 0.38), the leading correction-to-scaling exponent being omega =< (gamma-1)/nu. A numerical estimation of omega from the susceptibility data within 40 =< L =< 2048 yields omega=0.25(33). It is consistent with the statement omega =< (gamma-1)/nu, as well as with the value omega = 1/8 of the GFD theory. We reconsider the MC estimation of omega from smaller lattice sizes to show that it does not lead to conclusive results, since the obtained values of omega depend on the particular method chosen. In particular, estimates ranging from omega =1.274(72) to omega=0.18(37) are obtained by four different finite-size scaling methods, using MC data for thermodynamic average quantities, as well as for partition function zeros. We discuss the influence of omega on the estimation of exponents eta and nu.
Using 20 months of CPU time on our special purpose computer ``Percola'' we determined the exponent for the normal conductivity at the threshold of three-dimensional site and bond percolation. The extrapolation analysis taking into account the first correction to scaling gives a value of $t/\nu = 2.26\pm 0.04$ and a correction exponent $\omega$ around 1.4.
In quantum theory, the so-called "spinless Salpeter equation," the relativistic generalization of the nonrelativistic Schroedinger equation, is used to describe both bound states of scalar particles and the spin-averaged spectra of bound states of fermions. A numerical procedure solves the spinless Salpeter equation by approximating this eigenvalue equation by a matrix eigenvalue problem with explicitly known matrices. Comment: 7 pages, LaTeX
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized elementary variables. In terms of the original variables this gives a power-law distribution. This mechanism implies certain relations between the constraints of the system, the power of the distribution and the dispersion law of the fluctuations. These predictions are validated by Monte Carlo simulations and experimental data. We speculate that stochastic multiplicative dynamics might be the natural origin for the emergence of criticality and scale hierarchies without fine-tuning. Comment: latex, 9 pages with 3 figures
By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the log-periodic power law (LPPL) model has been developed as a flexible tool to detect bubbles. The LPPL model considers the faster-than-exponential (power law with finite-time singularity) increase in asset prices decorated by accelerating oscillations as the main diagnostic of bubbles. It embodies a positive feedback loop of higher return anticipations competing with negative feedback spirals of crash expectations. We use the LPPL model in one of its incarnations to analyze two bubbles and subsequent market crashes in two important indexes in the Chinese stock markets between May 2005 and July 2009. Both the Shanghai Stock Exchange Composite index (US ticker symbol SSEC) and Shenzhen Stock Exchange Component index (SZSC) exhibited such behavior in two distinct time periods: 1) from mid-2005, bursting in October 2007 and 2) from November 2008, bursting in the beginning of August 2009. We successfully predicted time windows for both crashes in advance (Sornette, 2007; Bastiaensen et al., 2009) with the same methods used to successfully predict the peak in mid-2006 of the US housing bubble (Zhou and Sornette, 2006b) and the peak in July 2008 of the global oil bubble (Sornette et al., 2009). The more recent bubble in the Chinese indexes was detected and its end or change of regime was predicted independently by two groups with similar results, showing that the model has been well-documented and can be replicated by industrial practitioners. Here we present more detailed analysis of the individual Chinese index predictions and of the methods used to make and test them. We complement the detection of log-periodic behavior with Lomb spectral analysis of detrended residuals and $(H, q)$-derivative of logarithmic indexes for both bubbles. We
In this paper, we give an analytical treatment to study the behavior of the collapse and the revival of the Rabi oscillations in the Jaynes-Cummings model (JCM). The JCM is an exactly soluble quantum mechanical model, which describes the interaction between a two-level atom and a single cavity mode of the electromagnetic field. If we prepare the atom in the ground state and the cavity mode in a coherent state initially, the JCM causes the collapse and the revival of the Rabi oscillations many times in a complicated pattern in its time-evolution. In this phenomenon, the atomic population inversion is described with an intractable infinite series. (When the electromagnetic field is resonant with the atom, the $n$th term of this infinite series is given by a trigonometric function for $\sqrt{n}t$, where $t$ is a variable of the time.) According to Klimov and Chumakov's method, using the Abel-Plana formula, we rewrite this infinite series as a sum of two integrals. We examine the physical meanings of these two integrals and find that the first one represents the initial collapse (the semi-classical limit) and the second one represents the revival (the quantum correction) in the JCM. Furthermore, we evaluate the first and second-order perturbations for the time-evolution of the JCM with an initial thermal coherent state for the cavity mode at low temperature, and write down their correction terms as sums of integrals by making use of the Abel-Plana formula. Comment: 14 pages, 12 eps figures, latex2e; v2: analyses concerned with the off-resonant cases added; v3: discussion about the time-evolution of the JCM with an initial thermal coherent state is added
We present a perturbative calculation of finite-size effects near $T_c$ of the $\phi^4$ lattice model in a $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions for $d > 4$. The structural differences between the $\phi^4$ lattice theory and the $\phi^4$ field theory found previously in the spherical limit are shown to exist also for a finite number of components of the order parameter. The two-variable finite-size scaling functions of the field theory are nonuniversal whereas those of the lattice theory are independent of the nonuniversal model parameters.One-loop results for finite-size scaling functions are derived. Their structure disagrees with the single-variable scaling form of the lowest-mode approximation for any finite $\xi/L$ where $\xi$ is the bulk correlation length. At $T_c$, the large-$L$ behavior becomes lowest-mode like for the lattice model but not for the field-theoretic model. Characteristic temperatures close to $T_c$ of the lattice model, such as $T_{max}(L)$ of the maximum of the susceptibility $\chi$, are found to scale asymptotically as $T_c - T_{max}(L) \sim L^{-d/2}$, in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising model. We also predict $\chi_{max} \sim L^{d/2}$ asymptotically. On a quantitative level, the asymptotic amplitudes of this large -$L$ behavior close to $T_c$ have not been observed in previous MC simulations at $d = 5$ because of nonnegligible finite-size terms $\sim L^{(4-d)/2}$ caused by the inhomogeneous modes. These terms identify the possible origin of a significant discrepancy between the lowest-mode approximation and previous MC data. MC data of larger systems would be desirable for testing the magnitude of the $L^{(4-d)/2}$ and $L^{4-d}$ terms predicted by our theory.
A sampling procedure for the transition matrix Monte Carlo method is introduced that generates the density of states function over a wide parameter range with minimal coding effort.
The stabilized biconjugate gradient algorithm BiCGStab recently presented by van der Vorst is applied to the inversion of the lattice fermion operator in the Wilson formulation of lattice Quantum Chromodynamics. Its computational efficiency is tested in a comparative study against the conjugate gradient and minimal residual methods. Both for quenched gauge configurations at beta= 6.0 and gauge configurations with dynamical fermions at beta=5.4, we find BiCGStab to be superior to the other methods. BiCGStab turns out to be particularly useful in the chiral regime of small quark masses.
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be modeled in this context since they turn out to be explicit solutions. From the numerical viewpoint, the interaction of these waves with a material body is examined. Computations are carried out via a parallel high-order finite-differences code. Due to the presence of a gradient of pressure in the model equations, waves hitting the obstacle may impart acceleration to it. Some explicative 2D dynamical configurations are then studied, enabling the study of photon-particle iterations through classical arguments.
(a) A plot of the frequency distribution vs. the fatalities, x, in a plane accident during the period 1978-2007. The lognormal and power-law fits are also drawn for the comparison. (b) Cumulative counts of plane accidents vs. time interval, ?t, between consecutive plane accidents during the same period. The exponential fit gives a time constant, ? , equal to 5.12 days.  
Human activities can play a crucial role in the statistical properties of observables in many complex systems such as social, technological and economic systems. We demonstrate this by looking into the heavy-tailed distributions of observables in fatal plane and car accidents. Their origin is examined and can be understood as stochastic processes that are related to human activities. Simple mathematical models are proposed to illustrate such processes and compared with empirical results obtained from existing databanks. Comment: 10 pages, 5 figures
Conditions for the occurrence of bidirectional collisions are developed based on the Simon-Gutowitz bidirectional traffic model. Three types of dangerous situations can occur in this model. We analyze those corresponding to head-on collision, rear-end collision and lane-changing collision. Using Monte Carlo simulations, we compute the probability of the occurrence of these collisions for different values of the oncoming cars density. It is found that the risk of collisions is important when the density of cars in one lane is small and that of the other lane is high enough. The influence of different proportions of heavy vehicles is also studied. We found that heavy vehicles cause an important reduction of traffic flow on the home lane and provoke an increase of the risk of car accident.
Histogram of ages for genetic death; mutation probability 20(+), 5(x) and 1(⋆) percent  
We derive catastrophic senescence of the Pacific salmon from an aging model which was recently proposed by Stauffer. The model is based on the postulates of a minimum reproduction age and a maximal genetic lifespan. It allows for self-organization of a typical age of first reproduction and a typical age of death. Our Monte Carlo simulations of the population dynamics show that the model leads to catastrophic senescence for semelparous reproduction as it occurs in the case of salmon, but to a more gradually increase of senescence for iteroparous reproduction. Comment: 7 pages, latex2e, 2 postscript figures, to be published in Int. J. Mod. Phys. C12(3) 2001
The box-counting (BC) algorithm is applied to calculate fractal dimensions of four fractal sets. The sets are contaminated with an additive noise with amplitude $\gamma = 10^{-5} \div 10^{-1}$. The accuracy of calculated numerical values of the fractal dimensions is analyzed as a function of $\gamma$ for different sizes of the data sample ($n_{tot}$). In particular, it has been found that a tiny ($10^{-5}$) addition of noise generates much larger (three orders of magnitude) error of the calculated fractal exponents. Natural saturation of the error for larger noise values prohibits the power-like scaling. Moreover, the noise effect cannot be cured by taking larger data samples.
Density of states for two values λ c
The integrand of Z for λ c = 4π
The integrand of Z for λ c = 2π  
Scan of Z near a zero for λ c = 4π. The zero occurs at k ≃ 1.08.
Scan of Z near a zero for λ c = 2π. The zero occurs at k ≃ 1.89.
We present the main results of our microcanonical simulation of the Wess Zumino Witten action functional. This action, being highly non-trivial and capable of exhibiting many different phase transitions, is chosen to be representative of general complex actions. We verify the applicability of microcanonical simulation by successfully obtaining two of the many critical points of the Wess Zumino Witten action. The microcanonical algorithm has the additional advantage of exhibiting critical behaviour for a small $8\times 8$ lattice. We also briefly discuss the subtleties that, in general, arise in simulating a complex action. Our algorithm for complex actions can be extended to the study of D-branes in the Wess Zumino Witten action. Comment: 5 figures
The evolution of the opinions of agents on a 50 × 50 square lattice for voter interactions. The number of interactions shown for each configuration is the number of times one single agent was drawn and updated.
The evolution of the opinions of agents on a 50 × 50 square lattice for Sznajd interactions. The number of interactions shown for each configuration is the number of times one single agent was drawn and updated.
A model where agents show discrete behavior regarding their actions, but have continuous opinions that are updated by interacting with other agents is presented. This new updating rule is applied to both the voter and Sznajd models for interaction between neighbors and its consequences are discussed. The appearance of extremists is naturally observed and it seems to be a characteristic of this model.
This paper presents a day-to-day re-routing relaxation approach for traffic simulations. Starting from an initial planset for the routes, the route-based microsimulation is exxecuted. The result of the microsimulation is fed into a re-router, which re-routes a certain percentage of all trips. This approach makes the traffic patterns in the microsimulation much more reasonable. Further, it is shown that the method described in this paper can lead to strong oscillations in the solutions.
Assortativity r of fermionic networks (with 2000 nodes) over time, varying the tempera- 
Clustering coefficient of the whole fermionic networks (with 2000 nodes) over time, varying 
Magnetization of the system over time in fermionic networks with 2000 nodes, during a 
We study the structure of Fermionic networks, i.e., a model of networks based on the behavior of fermionic gases, and we analyze dynamical processes over them. In this model, particle dynamics have been mapped to the domain of networks, hence a parameter representing the temperature controls the evolution of the system. In doing so, it is possible to generate adaptive networks, i.e., networks whose structure varies over time. As shown in previous works, networks generated by quantum statistics can undergo critical phenomena as phase transitions and, moreover, they can be considered as thermodynamic systems. In this study, we analyze Fermionic networks and opinion dynamics processes over them, framing this network model as a computational model useful to represent complex and adaptive systems. Results highlight that a strong relation holds between the gas temperature and the structure of the achieved networks. Notably, both the degree distribution and the assortativity vary as the temperature varies, hence we can state that fermionic networks behave as adaptive networks. On the other hand, it is worth to highlight that we did not find relation between outcomes of opinion dynamics processes and the gas temperature. Therefore, although the latter plays a fundamental role in gas dynamics, on the network domain its importance is related only to structural properties of fermionic networks.
Complexity threshold for different parameters and criteria 
We describe systems using Kauffman and similar networks. They are directed funct ioning networks consisting of finite number of nodes with finite number of discr ete states evaluated in synchronous mode of discrete time. In this paper we introduce the notion and phenomenon of `structural tendencies'. Along the way we expand Kauffman networks, which were a synonym of Boolean netw orks, to more than two signal variants and we find a phenomenon during network g rowth which we interpret as `complexity threshold'. For simulation we define a simplified algorithm which allows us to omit the problem of periodic attractors. We estimate that living and human designed systems are chaotic (in Kauffman sens e) which can be named - complex. Such systems grow in adaptive evolution. These two simple assumptions lead to certain statistical effects i.e. structural tendencies observed in classic biology but still not explained and not investigated on theoretical way. E.g. terminal modifications or terminal predominance of additions where terminal means: near system outputs. We introduce more than two equally probable variants of signal, therefore our networks generally are not Boolean networks. T hey grow randomly by additions and removals of nodes imposed on Darwinian elimination. Fitness is defined on external outputs of system. During growth of the system we observe a phase transition to chaos (threshold of complexity) in damage spreading. Above this threshold we identify mechanisms of structural tendencies which we investigate in simulation for a few different networks types, including scale-free BA networks. Comment: 20 pages with fugures, to be published in Int. J. Mod. Phys. C
We have translated fractional Brownian motion (FBM) signals into a text based on two ''letters'', as if the signal fluctuations correspond to a constant stepsize random walk. We have applied the Zipf method to extract the $\zeta '$ exponent relating the word frequency and its rank on a log-log plot. We have studied the variation of the Zipf exponent(s) giving the relationship between the frequency of occurrence of words of length $m<8$ made of such two letters: $\zeta '$ is varying as a power law in terms of $m$. We have also searched how the $\zeta '$ exponent of the Zipf law is influenced by a linear trend and the resulting effect of its slope. We can distinguish finite size effects, and results depending whether the starting FBM is persistent or not, i.e. depending on the FBM Hurst exponent $H$. It seems then numerically proven that the Zipf exponent of a persistent signal is more influenced by the trend than that of an antipersistent signal. It appears that the conjectured law $\zeta ' = |2H-1|$ only holds near $H=0.5$. We have also introduced considerations based on the notion of a {\it time dependent Zipf law} along the signal. Comment: 24 pages, 12 figures; to appear in Int. J. Modern Phys C
Semilog plot of the pdf for first escape times in the system. The differences between lines fitted to the slopes reflect various τ − values for a given type of barrier switching: (+) for H + = 8T, H − = −8T ; (×) for H + = 8T, H − = 0 and ( * ) for H + = 8T, H − = 4T (cf. Table 1). 
The problem of escape of a Brownian particle in a cusp-shaped metastable potential is of special importance in nonadiabatic and weakly-adiabatic rate theory for electron transfer (ET) reactions. Especially, for the weakly-adiabatic reactions, the reaction follows an adiabaticity criterion in the presence of a sharp barrier. In contrast to the non-adiabatic case, the ET kinetics can be, however considerably influenced by the medium dynamics. In this paper, the problem of the escape time over a dichotomously fluctuating cusp barrier is discussed with its relevance to the high temperature ET reactions in condensed media. Comment: RevTeX 4, 14 pages, 3 figures. To be printed in IJMP C. References corrected and updated
We propose a new version of the spatial model of voting. Platforms of five parties are evolving in a two-dimensional landscape of political issues so as to get maximal numbers of voters. For a Gaussian landscape the evolution leads to a spatially symmetric state, where the platform centers form a pentagon around the Gaussian peak. For a bimodal landscape the platforms located at different peaks get different numbers of voters. Comment: 8 pages, 3 figures. Accepted in Int. J. Modern Phys. C
We investigate transport properties of percolating clusters generated by irreversible cooperative sequential adsorption (CSA) on square lattices with Arrhenius rates given by ki= q^(ni), where ni is the number of occupied neighbors of the site i, and q a controlling parameter. Our results show a dependence of the prefactors on q and a strong finite size effect for small values of this parameter, both impacting the size of the backbone and the global conductance of the system. These results might be pertinent to practical applications in processes involving adsorption of particles.
An efficient algorithm for random sequential adsorption of hard discs in two dimensions is implemented. A precise value for the coverage is obtained: theta(infty) = 0.547069. The asymptotic law theta(t) = theta(infty) - ct^{-1/2} is verified to a high accuracy. Pair correlation function is analyzed.
Irreversible opinion spreading phenomena are studied on small-world and scale-free networks by means of the magnetic Eden model, a nonequilibrium kinetic model for the growth of binary mixtures in contact with a thermal bath. In this model, the opinion of an individual is affected by those of their acquaintances, but opinion changes (analogous to spin flips in an Ising-like model) are not allowed. We focus on the influence of advertising, which is represented by external magnetic fields. The interplay and competition between temperature and fields lead to order-disorder transitions, which are found to also depend on the link density and the topology of the complex network substrate. The effects of advertising campaigns with variable duration, as well as the best cost-effective strategies to achieve consensus within different scenarios, are also discussed.
The standard Penna ageing model with sexual reproduction is enlarged by adding additional bit-strings for love: Marriage happens only if the male love strings are sufficiently different from the female ones. We simulate at what level of required difference the population dies out.
In simulations of sexual reproduction with diploid individuals, we introduce that female haploid gametes recognize one specific allele of the genomes as a marker of the male haploid gametes. They fuse to zygotes preferrably with male gametes having a different marker than their own. This gamete recognition enhances the advantage of complementary bit-strings in the simulated diploid individuals, at low recombination rates. Thus with rare recombinations the bit-string evolve to be complementary; with recombination rate above about 0.1 instead they evolve under Darwinian purification selection, with few bits mutated. Comment: 9 pages including many figures
Number of individuals as a function of time for cases: a (circles), b (triangles) and c (squares).  
Distribution of minimum age of reproduction (circles) and of genetic death age (triangles) after a stationary state has been reached for the sexual population. Parameters: initial population = 25,000 males plus 25,000 females; maximum population size N max = 500, 000, initial a m = 1 and initial a d = 16.  
Mortality function µ versus age (in iterations) giving rough agreement with the Gompertz law; β = 0.7 with and without Verhulst deaths using 9 million individuals.  
We use a simple model for biological ageing to study the mortality of the population, obtaining a good agreement with the Gompertz law. We also simulate the same model on a square lattice, considering different strategies of parental care. The results are in agreement with those obtained earlier with the more complicated Penna model for biological ageing. Finally, we present the sexual version of this simple model. Comment: For Int.J.Mod.Phys.C Dec. 2001; 11 pages including 6 figs
We embed the behaviour of tax evasion into the standard two-dimensional Ising model. In the presence of an external magnetic field, the Ising model is able to generate the empirically observed effect of tax morale, i.e. the phenomenon that in some countries tax evasion is either rather high or low. The external magnetic field captures the agents' trust in governmental institutions. We also find that tax authorities may curb tax evasion via appropriate enforcement mechanisms. Our results are robust for the Barab\'asi-Albert and Voronoi-Delaunay networks.
We study a nonequilibrium model with up-down symmetry and a noise parameter $q$ known as majority-vote model of M.J. Oliveira 1992 with heterogeneous agents on square lattice. By Monte Carlo simulations and finite-size scaling relations the critical exponents $\beta/\nu$, $\gamma/\nu$, and $1/\nu$ and points $q_{c}$ and $U^*$ are obtained. After extensive simulations, we obtain $\beta/\nu=0.35(1)$, $\gamma/\nu=1.23(8)$, and $1/\nu=1.05(5)$. The calculated values of the critical noise parameter and Binder cumulant are $q_{c}=0.1589(4)$ and $U^*=0.604(7)$. Within the error bars, the exponents obey the relation $2\beta/\nu+\gamma/\nu=2$ and the results presented here demonstrate that the majority-vote model heterogeneous agents belongs to a different universality class than the nonequilibrium majority-vote models with homogeneous agents on square lattice.
Time-averaged correlation s (triangles) and "mount probability" P (black circles-see text for details) as a function of M for 12 bits. Inset: s as a function of the initial concentration for M = 10 −3 (upper curve) and 10 −1 (lower curve). The results correspond to an average over 50 runs.
Complementarity is one of the main features underlying the interactions in biological and biochemical systems. Inspired by those systems we propose a model for the dynamical evolution of a system composed by agents that interact due to their complementary attributes rather than their similarities. Each agent is represented by a bit-string and has an activity associated to it; the coupling among complementary peers depends on their activity. The connectivity of the system changes in time respecting the constraint of complementarity. We observe the formation of a network of active agents whose stability depends on the rate at which activity diffuses in the system. The model exhibits a non-equilibrium phase transition between the ordered phase, where a stable network is generated, and a disordered phase characterized by the absence of correlation among the agents. The ordered phase exhibits multi-modal distributions of connectivity and activity, indicating a hierarchy of interaction among different populations characterized by different degrees of activity. This model may be used to study the hierarchy observed in social organizations as well as in business and other networks. Comment: 13 pages, 4 figures, submitted
There are numerous examples of societies with extremely stable mix of contrasting opinions. We argue that this stability is a result of an interplay between society network topology adjustment and opinion changing processes. To support this position we present a computer model of opinion formation based on some novel assumptions, designed to bring the model closer to social reality. In our model, the agents, in addition to changing their opinions due to influence of the rest of society and external propaganda, have the ability to modify their social network, forming links with agents sharing the same opinions and cutting the links with those they disagree with. To improve the model further we divide the agents into `fanatics' and `opportunists', depending on how easy is to change their opinions. The simulations show significant differences compared to traditional models, where network links are static. In particular, for the dynamical model where inter-agent links are adjustable, the final network structure and opinion distribution is shown to resemble real world observations, such as social structures and persistence of minority groups even when most of the society is against them and the propaganda is strong. Comment: Revised version accepted by International Journal of Modern Physics C Added analysis, references and a new figure
A directed graph consisting of 4 nodes (species) and 5 links (interactions). Left: the corresponding interaction matrix
Network structure in the random phase (n = 800): several chains and trees exist, but no supporting structure (i.e. autocatalytic set) has yet emerged. Parameters: N = 100, m = 0.25.
Average number of links, l evolving over network time, n, for three values of the parameter m. System size N = 100
Saturated average connectivity per node l s dependent on average incoming connectivity m. System sizes are the same as in Fig. 6. The plots are fitted by the logarithmic scaling of Eq. (10).
We analyze a model of interacting agents (e.g. prebiotic chemical species) which are represended by nodes of a network, whereas their interactions are mapped onto directed links between these nodes. On a fast time scale, each agent follows an eigendynamics based on catalytic support from other nodes, whereas on a much slower time scale the network evolves through selection and mutation of its nodes-agent. In the first part of the paper, we explain the dynamics of the model by means of characteristic snapshots of the network evolution and confirm earlier findings on crashes an recoveries in the network structure. In the second part, we focus on the aggregate behavior of the network dynamics. We show that the disruptions in the network structure are smoothed out, so that the average evolution can be described by a growth regime followed by a saturation regime, without an initial random regime. For the saturation regime, we obtain a logarithmic scaling between the average connectivity per node $\mean{l}_{s}$ and a parameter $m$, describing the average incoming connectivity, which is independent of the system size $N$.
Plots of (a) maximum life span and (b) total population as functions of fecundity b for different values of mutation probability p. The maximum life span decreases with increasing p and decreasing b. Observe that here x can be greater than one, since we are considering the orthodox time evolution. 
Plots of x(0, m)/x(0, R) for sets of R, p and b respecting the scaling conditions, as given in the inset, for both T = 1 and 2. This behaviour refers to the orthodox evolution with Poisson mutation protocol. 
Survival rate S(a) versus b for mutation rate p = 0.001 for the orthodox evolution with Poisson mutation protocol. Observe that smaller T imply higher S(a) for the same a. 
Survival rate S(a) versus p for birth rate b = 4 for the orthodox evolution with Poisson mutation protocol. 
Plots of (a) maximum life span and (b) total population as functions of fecundity b for different values of mutation probability p. The maximum life span decreases with increasing p and decreasing b. Observe that here x can be greater than one, since we are considering the orthodox time evolution. 
In this paper we consider a generalization to the asexual version of the Penna model for biological aging, where we take a continuous time limit. The genotype associated to each individual is an interval of real numbers over which Dirac $\delta$--functions are defined, representing genetically programmed diseases to be switched on at defined ages of the individual life. We discuss two different continuous limits for the evolution equation and two different mutation protocols, to be implemented during reproduction. Exact stationary solutions are obtained and scaling properties are discussed. Comment: 10 pages, 6 figures
Decays of population and survival rate with age t. In a stationary state like here, the survival rate is the ratio of the population at age t to that at age t 1. This simulation with 512 million initial babies took about 12 minutes on an Intel Paragon parallel computer using 128 nodes. (Finite size eeects have been observed in the simulation with 200 thousands initial babies).  
As g.2, but without mutations at the beginning and with only negative mutations later. This simulation took about 10 hours on an IBM Powerstation.  
Development of population with the number of computer interations (corresponding to biological generations or years) showing how a stationary state is established.  
shows the changes with the number of iterations (\years") for the simulations of gs.2, using smaller systems. Variation of the above parameters of Figs.2 did not change drastically the qualitative behavior, provided the birth rate was adjusted such that the population did not decay to zero nor increased too rapidly towards the limit imposed by N max .
A bit-string model of biological life-histories is parallelized, with hundreds of millions of individuals. It gives the desired drastic decay of survival probabilities with increasing age for 32 age intervals.
It is shown that if the computer model of biological ageing proposed by Stauffer is modified such that the late reproduction is privileged then the Gompertz law of exponential increase of mortality can be retrieved. Comment: 5 pages, 6 figures
In this article, we propose a network spread model for HIV epidemics, wherein each individual is represented by a node of the transmission network and the edges are the connections between individuals along which the infection may spread. The sexual activity of each individual, measured by its degree, is not homogeneous but obeys a power-law distribution. Due to the heterogeneity of activity, the infection can persistently exist at a very low prevalence, which has been observed in real data but can not be illuminated by previous models with homogeneous mixing hypothesis. Furthermore, the model displays a clear picture of hierarchical spread: In the early stage the infection is adhered to these high-risk persons, and then, diffuses toward low-risk population. The prediction results show that the development of epidemics can be roughly categorized into three patterns for different countries, and the pattern of a given country is mainly determined by the average sex-activity and transmission probability per sexual partner. In most cases, the effect of HIV epidemics on demographic structure is very small. However, for some extremely countries, like Botswana, the number of sex-active people can be depressed to nearly a half by AIDS.
Top-cited authors
Katarzyna Sznajd-Weron
  • Wroclaw University of Science and Technology
Hudong Chen
  • Dassault Systèmes
Didier Sornette
  • ETH Zurich
Jan Lorenz
  • Constructor University Bremen gGmbH
Sauro Succi
  • INFN - Istituto Nazionale di Fisica Nucleare