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We present a recently introduced real space renormalization group (RG) approach to the study of surface growth. The method permits us to obtain the properties of the KPZ strong coupling fixed point, which is not accessible to standard perturbative field theory approaches. Using this method, and with the aid of small Monte Carlo calculations for systems of linear size 2 and 4, we calculate the roughness exponent in dimensions up to d=8. The results agree with the known numerical values with good accuracy. Furthermore, the method permits us to predict the absence of an upper critical dimension for KPZ contrarily to recent claims. The RG scheme is applied to other growth models in different universality classes and reproduces very well all the observed phenomenology and numerical results. Intended as a sort of finite size scaling method, the new scheme may simplify in some cases from a computational point of view the calculation of scaling exponents of growth processes., Comment: Invited talk presented at the CCP1998 (Granada)

We analyze the behavior of spatially anisotropic Bak-Sneppen model. We demonstrate that a nontrivial relation between critical exponents tau and mu=d/D, recently derived for the isotropic Bak-Sneppen model, holds for its anisotropic version as well. For one-dimensional anisotropic Bak-Sneppen model we derive a novel exact equation for the distribution of avalanche spatial sizes, and extract the value gamma=2 for one of the critical exponents of the model. Other critical exponents are then determined from previously known exponent relations. Our results are in excellent agreement with Monte Carlo simulations of the model as well as with direct numerical integration of the new equation., 8 pages, three figures included with psfig, some rewriting, + extra figure and table of exponents

We propose and study a simple model of dynamical redistribution of capital in a diversified portfolio. We consider a hypothetical situation of a portfolio composed of N uncorrelated stocks. Each stock price follows a multiplicative random walk with identical drift and dispersion. The rules of our model naturally give rise to power law tails in the distribution of capital fractions invested in different stocks. The exponent of this scale free distribution is calculated in both discrete and continuous time formalism. It is demonstrated that the dynamical redistribution strategy results in a larger typical growth rate of the capital than a static ``buy-and-hold'' strategy. In the large N limit the typical growth rate is shown to asymptotically approach that of the expectation value of the stock price. The finite dimensional variant of the model is shown to describe the partition function of directed polymers in random media., 9 pages, 2 figures, accepted for publication in Physica A; Figure captions and PS-files of two figues are added

We introduce a simple model which shows non-trivial self organized critical properties. The model describes a system of interacting units, modelled by Polya urns, subject to perturbations and which occasionally break down. Three equivalent formulations - stochastic, quenched and deterministic - are shown to reproduce the same dynamics. Among the novel features of the model are a non-homogeneous stationary state, the presence of a non-stationary critical phase and non-trivial exponents even in mean field. We discuss simple interpretations in term of biological evolution and earthquake dynamics and we report on extensive numerical simulations in dimensions $d=1,2$ as well as in the random neighbors limit., Comment: 4 pages 1 figure

In this paper we discuss a general theoretical scheme, that we have recently proposed, for a class of phenomena characterized by extremal dynamics with quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochastic dynamics with cognitive memory. This transformation, together with other concepts, permits a mathematical characterization of the self-organized nature of the avalanche type dynamics. By combining the mapping with real space methods, like the fixed scale transformation (FST), it is also possible to compute the relevant critical exponents directly from the microscopic model. A specific application to Invasion Percolation is presented but the approach can be easily extended to various other problems with quenched disorder.

We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statistics, Comment: 4 pages 2 figures

We investigate the fluctuations induced by irrationality in simple games with a large number of competing players. We show that Nash equilibria in such games are ``weakly'' stable: irrationality propagates and amplifies through players' interactions so that huge fluctuations can results from a small amount of irrationality. In the presence of multiple Nash equilibria, our statistical approach allows to establish which is the globally stable equilibrium. However characteristic times to reach this state can be very large., 5 pages, Revtex, to appear in Physica A

We introduce a general theoretical scheme for a class of phenomena characterized by an extremal dynamics and quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochastic one with cognitive memory and on other concepts which permit a mathematical characterization of the self-organized nature of the avalanche type dynamics. In addition it is possible to compute the relevant critical exponents directly from the microscopic model. A specific application to Invasion Percolation is presented but the approach can be easily extended to various other problems., 11 pages Latex (revtex), 3 postscript figures included. Submitted to Europhys. Lett

We analyze the combined effect of a Laplacian field and quenched disorder for the generation of fractal structures with a study, both numerical and theoretical, of the quenched dielectric breakdown model (QDBM). The growth dynamics is shown to evolve from the avalanches of invasion percolation (IP) to the smooth growth of Laplacian fractals, i. e. diffusion limited aggregation (DLA) and the dielectric breakdown model (DBM). The fractal dimension is strongly reduced with respect to both DBM and IP, due to the combined effect of memory and field screening. This implies a specific relation between the fractal dimension of the breakdown structures (dielectric or mechanical) and the microscopic properties of disordered materials., 11 pages Latex (revtex), 3 postscript figures included. Submitted to PRL

A prototype model of stock market is introduced and studied numerically. In this self-organized system, we consider only the interaction among traders without external influences. Agents trade according to their own strategy, to accumulate his assets by speculating on the price's fluctuations which are produced by themselves. The model reproduced rather realistic price histories whose statistical properties are also similar to those observed in real markets., LaTex, 4 pages, 4 Encapsulated Postscript figures, uses psfig

We study a recently proposed equation for the avalanche distribution in the Bak-Sneppen model. We demonstrate that this equation indirectly relates $\tau$,the exponent for the power law distribution of avalanche sizes, to $D$, the fractal dimension of an avalanche cluster.We compute this relation numerically and approximate it analytically up to the second order of expansion around the mean field exponents. Our results are consistent with Monte Carlo simulations of Bak-Sneppen model in one and two dimensions., Comment: 5 pages, 2 ps-figures icluded

There has been considerable recent interest on large scale evolution biology. In the physics community this was triggered by the scenario of punctuated equilibrium, proposed by Gould and Eldredge [1], and by the work of Bak and co-workers stressing the similarities between this framework and the paradigm of Self Organized Criticality[2, 3]. Analyzing the fossil record[3, 4, 5], it has been realized that evolution might not take place smoothly, with small variations occurring at a more or less constant rate. Rather it occurred in bursts of very high activity, characterized by mass extinction, separated by periods of apparent stasis. More precisely, one can measure the number s t of species (or of families) which went extinct in an interval dt (typically of the order of one million years) around time t. The signal s t is intermittent, with quiet periods separated by large peaks on any size. The distribution P(s) of s t behaves as a power law P(s) ~ s −τ with τ ≈ 2. As discussed at length in ref. [3, 4, 5, 6], the main issue is whether the ecosystem as a whole has to be regarded as being in a “normal” state, characterized by linear response to external perturbations, or whether it is in a “critical” state, where external perturbations can trigger fluctuations of any size. In the former case, one has to assume that mass extinction have been provoked by extreme external events, such as meteor impacts, volcano eruptions and the like. This assumption suggests that the statistics of mass extinction events should be related to that of extreme catastrophic events. The second scenario, on the other hand, describes ecology as a system which is poised in a critical state by its dynamics itself. Even small perturbations can propagate and amplify in such a state, and produce in the end a macroscopic change.

We study the scaling behavior in currency exchange rates. Our results suggest that they satisfy scaling with an exponent close to 0.5, but that it differs qualitatively from that of a simple random walk. Indeed price variations cannot be considered as independent variables and subtle correlations are present. Furthermore, we introduce a novel statistical analysis for economic data which makes the physical properties of a signal more evident and eliminates the systematic effects of time periodicity.

The genetic code is redundant, as there are about three times more codons than amino acids. Because of this redundancy, a given amino acid can be specified by different codons, which are therefore considered synonymous. Despite being synonymous, however, such codons are used with different frequencies, a phenomenon known as codon bias. The origin and roles of the codon bias have not yet been fully clarified, although it is clear that it can affect the efficiency, accuracy and regulation of the translation process. In order to provide a tool to address these issues, we introduce here the codon information index (CII), which represents a measure of the amount of information stored in mRNA sequences through the codon bias. The calculation of the CII requires solely the knowledge of the mRNA sequences, without any other additional information. We found that the CII is highly correlated with the tRNA adaptation index (tAI), even if the latter requires the knowledge of the tRNA pool of an organism. We anticipate that the CII will represent a useful tool to study quantitatively the relationship between the information provided by the codon bias and various aspects of the translation process, thus identifying those aspects that are most influenced by it.

Neurons subject to a common non-stationary input may exhibit a correlated firing behavior. Correlations in the statistics of neural spike trains also arise as the effect of interaction between neurons. Here we show that these two situations can be distinguished, with machine learning techniques, provided the data are rich enough. In order to do this, we study the problem of inferring a kinetic Ising model, stationary or nonstationary, from the available data. We apply the inference procedure to two data sets: one from salamander retinal ganglion cells and the other from a realistic computational cortical network model. We show that many aspects of the concerted activity of the salamander retinal neurons can be traced simply to the external input. A model of non-interacting neurons subject to a non-stationary external field outperforms a model with stationary input with couplings between neurons, even accounting for the differences in the number of model parameters. When couplings are added to the non-stationary model, for the retinal data, little is gained: the inferred couplings are generally not significant. Likewise, the distribution of the sizes of sets of neurons that spike simultaneously and the frequency of spike patterns as function of their rank (Zipf plots) are well-explained by an independent-neuron model with time-dependent external input, and adding connections to such a model does not offer significant improvement. For the cortical model data, robust couplings, well correlated with the real connections, can be inferred using the non-stationary model. Adding connections to this model slightly improves the agreement with the data for the probability of synchronous spikes but hardly affects the Zipf plot., Comment: version in press in J Stat Mech

Using the cross-correlation of the wavelet transformation, we propose a general method of studying the scale dependence of the direction of coupling for coupled time series. The method is first demonstrated by applying it to coupled van der Pol forced oscillators and coupled nonlinear stochastic equations. We then apply the method to the analysis of the log-return time series of the stock values of the IBM and General Electric (GE) companies. Our analysis indicates that, on average, IBM stocks react earlier to possible common sector price movements than those of GE.

It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach provides a particularly transparent way to obtain continuum growth equations for interfaces. It is straightforward to derive equations which describe the coarse grained evolution of discrete lattice models and analyze their small gradient expansion. In this way, the authors identify the basic mechanisms which lead to the most commonly used growth equations. The advantages of this formulation of growth processes is that it allows one to go beyond the frequently used no-overhang approximation. The reparametrization invariant form also displays explicitly the conservation laws for the specific process and all the symmetries with respect to space-time transformations which are usually lost in the small gradient expansion. Finally, it is observed, that the knowledge of the full equation of motion, beyond the lowest order gradient expansion, might be relevant in problems where the usual perturbative renormalization methods fail., 42 pages, Revtex, no figures. To appear in Rev. of Mod. Phys

A renormalization group analysis of interfacial growth processes with an oblique incident flux and surface tension is carried out in (6 − ) dimensions. A rich behavior characterized by a crossover from a novel growth regime to the familiar Edwards-Wilkinson universality class is predicted. The exponents are calculated in the intermediate regime.

We use a stochastic description of models with a dynamic in quenched disorder to analyze the mechanism of their self-organization to a critical state in terms of memory effects. We introduce a framework to characterize both memory effects and avalanche events which suggests that self-organization can result in general from memory. This issue is settled by the introduction and the analysis of a model that contains explicitly memory and generalizes the corresponding dynamics in quenched disorder. The model displays a rich behavior and self-organized critical properties for a whole range of the exponent that tunes the strength of memory.

We point out an error in the equations for the evolution of the run time statistics given in a paper by Marsili and give the correct expression. Moreover, we discuss the annealing approximation which is implicit in the transformation.

It is shown that the mode-coupling equations for the strong-coupling limit of the KPZ equation have a solution for d>4 such that the dynamic exponent z is 2 (with possible logarithmic corrections) and that there is a delta function term in the height correlation function = (A/k^{d+4-z}) \delta(w/k^z) where the amplitude A vanishes as d -> 4. The delta function term implies that some features of the growing surface h(x,t) will persist to all times, as in a glassy state., Comment: 11 pages, Revtex, 1 figure available upon request (same as figure 1 in ref [10]) Important corrections have been made which yield a much simpler picture of what is happening. We still find "glassy" solutions for d>4 where z is 2 (with possible logarithmic corrections). However, we now find no glassy solutions below d=4. A (linear) stability analysis (for d>4) has been included. Also one Author has been added

Irreversible dynamics in media with quenched disorder seems to be the essential mechanism for a variety of phenomena like fracture propagation or displacement of immiscible fluids in disordered porous media. This problem does not seem to be treatable along the standard theoretical schemes. Recently a new approach has been introduced that allows mapping of a deterministic dynamics with quenched disorder like that of Invasion Percolation into a stochastic dynamics with memory. This memory consists essentially in a cognitive process that modifies the probability distribution of quenched variables conditionally to all previous events. This approach, together with the FST and the corresponding analysis of the scale invariant dynamics, provides a new framework to understand the self organization and to compute the critical exponents of problems like Invasion Percolation and Bak and Sneppen.

Inverse phase transitions are striking phenomena in which an apparently more ordered state disorders under cooling. This behavior can naturally emerge in tricritical systems on heterogeneous networks and it is strongly enhanced by the presence of disassortative degree correlations. We show it both analytically and numerically, providing also a microscopic interpretation of inverse transitions in terms of freezing of sparse subgraphs and coupling renormalization., 4 pages, 4 figures

We consider the coarsening properties of a kinetic Ising model with a memory field. The probability of a spin-flip depends on the persistence time of the spin in a state. The more a spin has been in a given state, the less the spin-flip probability is. We numerically studied the growth and persistence properties of such a system on a two dimensional square lattice. The memory introduces energy barriers which freeze the system at zero temperature. At finite temperature we can observe an apparent arrest of coarsening for low temperature and long memory length. However, since the energy barriers introduced by memory are due to local effects, there exists a timescale on which coarsening takes place as for the Ising model. Moreover the two point correlation functions of the Ising model with and without memory are the same, indicating that they belong to the same universality class., Comment: 10 pages, 7 figures; some figures and some comments added

Since the introduction of the concept of multifractality there has been a large amount of activity aimed at the characterization of the growth probability distribution (GPD) of Diffusion Limited Aggregation (DLA), and of the Dielectric Breakdown Model (DBM), in terms of a multifractal spectrum.1 This formalism seems to be appropriate for this problem because of the scale invariant properties both of the DLA cluster and of Laplace equation. However it has recently become clear that the properties of the GPD seem to be more complex then those of a simple multiplicative multifractal, in the same sense as the fractal properties of the cluster are more complex than those of a simple homogeneous fractal. Most of the studies, up to now, have been performed for the case of radial geometry.

The relevance of spatial correlations set up in the quenched disorder by extremal dynamics is studied both analytically and by numerical simulations. We find that these correlations, although present in systems of small size L, vanish in the thermodynamic limit.

After the remarkable discoveries in equilibrium critical phenomena and the development of the Renormalization Group (RG) a branch of Statistical Physics has evolved towards the study of fractal growth and self-organization. The main models in this area are Diffusion Limited Aggregation, the Sandpile model. Invasion Percolation and the Kardar-Parisi-Zhang dynamics of rough surfaces. For these models the usual theoretical methods of equilibrium critical phenomena cannot be applied and new theoretical concepts are necessary. In the past years we have developed a new theoretical framework for non-ergodic dynamics and self-organization. A novel and essential concept consists in the Scale Invariant Dynamics, which is the dynamics that corresponds to coarse grained variables. In this lecture we describe the development and the properties of this concept in relation to the usual RG ideas and methods. We also discuss briefly its specific applications for each of the above mentioned models.

We propose a generalized version of the Dielectric Breakdown Model (DBM) for generic breakdown processes. It interpolates between the standard DBM and its analog with quenched disorder, as a temperature like parameter is varied. The physics of other well known fractal growth phenomena as Invasion Percolation and the Eden model are also recovered for some particular parameter values. The competition between different growing mechanisms leads to new non-trivial effects and allows us to better describe real growth phenomena. Detailed numerical and theoretical analysis are performed to study the interplay between the elementary mechanisms. In particular, we observe a continuously changing fractal dimension as temperature is varied, and report an evidence of a novel phase transition at zero temperature in absence of an external driving field; the temperature acts as a relevant parameter for the ``self-organized'' invasion percolation fixed point. This permits us to obtain new insight into the connections between self-organization and standard phase transitions., Submitted to PRL

We introduce a simple continuous model for nonequilibrium surface growth. The dynamics of the system is defined by the KPZ equation with a Morse-like potential representing a short range interaction between the surface and the substrate. The mean field solution displays a non trivial phase diagram with a first order transition between a growing and a bound surface, associated with a region of coexisting phases, and a tricritical point where the transition becomes second order. Numerical simulations in 3 dimensions show quantitative agreement with mean field results, and the features of the phase space are preserved even in 2 dimensions., Comment: 7 figures, revtex, submitted to Phys. Rev. E

The problem of a random walk in a disordered media is mapped into a model of a random walk with memory. The latter model, as opposed to the former one, does not make reference to a particular realization of the disorder. The equivalence of the two models implies that the new model retrieves dynamically a realization of disorder; the only one which is consistent with its dynamics. In this new approach to the dynamics in disordered media, effects of memory, aging and the peculiar localization properties of the random walker, appear quite natural., Comment: 4 pages, RevTex file, 1 Postscript figure

The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a particular Hopfield like hamiltonian. On the basis of a replica symmetric calculations, we draw the phase diagram, which contains the analog of a retrieval phase. The number of metastable states is estimated using the annealed approximation. The results are confronted with extensive numerical simulations., Comment: 14 pages, 9 figures, jpa style

We study analytically and by computer simulations a complex system of adaptive agents with finite memory. Borrowing the framework of the Minority Game and using the replica formalism we show the existence of an equilibrium phase transition as a function of the ratio between the memory $\lambda$ and the learning rates $\Gamma$ of the agents. We show that, starting from a random configuration, a dynamic phase transition also exists, which prevents the system from reaching any Nash equilibria. Furthermore, in a non-stationary environment, we show by numerical simulations that agents with infinite memory play worst than others with less memory and that the dynamic transition naturally arises independently from the initial conditions., Comment: 4 pages, 3 figures

The study of phenomena such as capillary displacement in porous media, fracture propagation, and interface dynamics in quenched random media has attracted a great deal of interest in the last few years. This class of problems does not seem to be treatable with the standard theoretical methods, and the only analytical results come from scaling theory or mapping, for some of their properties, to other solvable models. In this paper a recently proposed approach to problems with extremal dynamics in quenched disordered media, named run time statistics (RTS) or quenched-stochastic transformation, is described in detail. This method allows is to map a quenched dynamics such as invasion percolation onto a stochastic annealed process with cognitive memory. By combining RTS with the fixed scale transformation approach, we develop a general and systematic theoretical method to compute analytically the critical exponents of invasion percolation, with and without trapping, and directed invasion percolation. In addition we can also understand and describe quantitatively the self-organized nature of the process.

We show that the Minority Game, a model of interacting heterogeneous agents, can be described as a spin systems and it displays a phase transition between a symmetric phase and a symmetry broken phase where the games outcome is predicable. As a result a ``spontaneous magnetization'' arises in the spin formalism., Comment: 4 pages, 2 figures, submitted to PRE/Rapid Communications Major revision of the text

We discuss a simple model based on the minority game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit. Stylized facts arise only close to a line of critical points with nontrivial properties, marking the transition to an unpredictable market. We show that the emergence of critical fluctuations close to the phase transition is governed by the interplay between the signal to noise ratio and the system size. These results provide a clear and consistent picture of financial markets, where stylized facts and verge of unpredictability are intimately related aspects of the same critical systems.

The family of six-transmembrane-helices channels shows recognizable sequence homology and a strictly conserved structural architecture; yet these channels are involved in a significantly heterogeneous set of physiological functions, ranging from reporting noxious environmental conditions, to shaping the neuronal action potential, to syncing the beating of the heart. A striking example of this heterogeneity is provided by the comparison between the polymodal transient receptor channels (TRPs), whose activation can be regulated by several stimuli, and the voltage-gated ion channels (VGCs), which are activated by the variations of the transmembrane potential through. By analyzing multiple sequence alignments spanning the first four transmembrane segments (the voltage sensor domain in VGCs) and comparing TRPs and VGCs, we highlight the sequence determinants of voltage-driven activation. To this end we exploit the concept of fractal dimension to characterize the complexity of the two datasets. Moreover, we use a novel feature-selection approach, to identify the so-called maximally informative samples, i.e. set of residues whose distribution is maximally informative about the selection pressure that generated and differentiate the sequence ensembles.

Summary Loss of functional cardiomyocytes is a major determinant of heart failure after myocardial infarction. Previous high throughput screening studies have identified a few microRNAs (miRNAs) that can induce cardiomyocyte proliferation and stimulate cardiac regeneration in mice. Here, we show that all of the most effective of these miRNAs activate nuclear localization of the master transcriptional cofactor Yes-associated protein (YAP) and induce expression of YAP-responsive genes. In particular, miR-199a-3p directly targets two mRNAs coding for proteins impinging on the Hippo pathway, the upstream YAP inhibitory kinase TAOK1, and the E3 ubiquitin ligase β-TrCP, which leads to YAP degradation. Several of the pro-proliferative miRNAs (including miR-199a-3p) also inhibit filamentous actin depolymerization by targeting Cofilin2, a process that by itself activates YAP nuclear translocation. Thus, activation of YAP and modulation of the actin cytoskeleton are major components of the pro-proliferative action of miR-199a-3p and other miRNAs that induce cardiomyocyte proliferation., Graphical Abstract, Highlights • A few microRNAs can stimulate cardiac myocyte proliferation • The most effective of these microRNAs activate YAP • Several pro-proliferative microRNAs also inhibit actin depolymerization • miR-199a-3p directly targets TAOK1, b-TrCP, and Cofilin2 to achieve its effects, Torrini et al. report that several microRNAs that induce cardiomyocyte proliferation act by stimulating activation of the transcriptional cofactor YAP, a master regulator of cell proliferation. Several microRNAs also act on the cardiomyocyte cytoskeleton by promoting actin polymerization. These microRNAs can be considered as potential treatments for cardiac regeneration.

The paper is devoted at analyzing the co-ordination role that markets and organizations are called to play in order to make viable innovation processes. This analysis reveals that the viability of innovation processes cannot be dissociated from the way market structures emerge and evolve, and hence that there is not a ‘new economy’ problem referring to the specific character of certain technologies, namely, the information and communication technologies.