Miguel A. Fuentes

Vegetation pattern formation in a fog-dependent ecosystem

Vegetation pattern formation is a striking characteristic of several water-limited ecosystems around the world. Typically, they have been described on runoff-based ecosystems emphasizing local interactions between water, biomass interception, growth and dispersal. Here, we show that this situation is by no means general, as banded patterns in vegetation can emerge in areas without rainfall and in plants without functional root (the Bromeliad Tillandsia landbeckii) and where fog is the principal source of moisture. We show that a simple model based on the advection of fog-water by wind and its interception by the vegetation can reproduce banded patterns which agree with empirical patterns observed in the Coastal Atacama Desert. Our model predicts how the parameters may affect the conditions to form the banded pattern, showing a transition from a uniform vegetated state, at high water input or terrain slope to a desert state throughout intermediate banded states. Moreover, the model predicts that the pattern wavelength is a decreasing non-linear function of fog-water input and slope, and an increasing function of plant loss and fog-water flow speed. Finally, we show that the vegetation density is increased by the formation of the regular pattern compared to the density expected by the spatially homogeneous model emphasizing the importance of self-organization in arid ecosystems.

Model for non-Gaussian intraday stock returns

Stock prices are known to exhibit non-Gaussian dynamics, and there is much interest in understanding the origin of this behavior. Here, we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations (called intraday returns) and verify the model using a large database for several stocks traded on the London Stock Exchange. We provide evidence that the return distribution for these stocks is non-Gaussian and similar in shape and that the distribution appears stable over intraday time scales. We explain these results by assuming the volatility of returns is constant intraday but varies over longer periods such that its inverse square follows a gamma distribution. This produces returns that are Student distributed for intraday time scales. The predicted results show excellent agreement with the data for all stocks in our study and over all regions of the return distribution.

Influence of global correlations on central limit theorems and entropic extensivity

We consider probabilistic models of N identical distinguishable, binary random variables. If these variables are strictly or asymptotically independent, then, for N→∞, (i) the attractor in distribution space is, according to the standard central limit theorem, a Gaussian, and (ii) the Boltzmann-Gibbs-Shannon entropy SBGS≡-∑i=1Wpilnpi (where W=2N) is extensive, meaning that SBGS(N)∼N. If these variables have any nonvanishing global (i.e., not asymptotically independent) correlations, then the attractor deviates from the Gaussian. The entropy appears to be more robust, in the sense that, in some cases, SBGS remains extensive even in the presence of strong global correlations. In other cases, however, even weak global correlations make the entropy deviate from the normal behavior. More precisely, in such cases the entropic form Sq≡1q-1(1-∑i=1Wpiq) (with S1SBGS) can become extensive for some value of q≠1. This scenario is illustrated with several new as well as previously described models. The discussion illuminates recent progress into q-describable nonextensive probabilistic systems, and the conjectured q-Central Limit Theorem (q-CLT) which posses a q-Gaussian attractor.

Beneficial effects of human altruism.

In this work we review converging evidence from several lines of research which suggests that altruism in humans can be intrinsically rewarding. Various investigations illustrate how human altruism can have beneficial effects on health and wellbeing. In this contribution we propose a model that includes positive effects of altruism. These beneficial effects lead to significant changes in the dynamics of the system, favouring higher levels of altruism and facilitating abrupt changes towards cooperation. In the present model, social modulation occurs at both individual and collective levels. The potential beneficial role of altruism proposed here may account for its occurrence among non-kin and beyond reciprocity.

Renormalization group structure for sums of variables generated by incipiently chaotic maps

We look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group (RG) structure associated with the operation of increment of summands and rescaling. In this structure—where the only relevant variable is the difference in control parameter from its value at the transition to chaos—the trivial fixed point is the Gaussian distribution and a novel nontrivial fixed point is a multifractal distribution that emulates the Feigenbaum attractor, and is universal in the sense of the latter. The crossover between the two fixed points is explained and the flow toward the trivial fixed point is seen to be comparable to the chaotic band merging sequence. We discuss the nature of the central limit theorem for deterministic variables.

Living in an irrational society: Wealth distribution with correlations between risk and expected profits

Different models to study the wealth distribution in an artificial society have considered a transactional dynamics as the driving force. Those models include a risk aversion factor, but also a finite probability of favoring the poorer agent in a transaction. Here, we study the case where the partners in the transaction have a previous knowledge of the winning probability and adjust their risk aversion taking this information into consideration. The results indicate that a relatively equalitarian society is obtained when the agents risk in direct proportion to their winning probabilities. However, it is the opposite case that delivers wealth distribution curves and Gini indices closer to empirical data. This indicates that, at least for this very simple model, either agents have no knowledge of their winning probabilities, either they exhibit an “irrational” behavior risking more than reasonable.

Universal behavior of extreme price movements in stock markets.

Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evidence that a modification to the random model—adding a slow, but significant, fluctuation to the standard deviation of the process—accurately explains the probability of different-sized price changes, including the relative high frequency of extreme movements. Furthermore, we show that this process is similar across stocks so that their price fluctuations can be characterized by a single curve. Because the behavior of price fluctuations is rooted in the characteristics of volatility, we expect our results to bring increased interest to stochastic volatility models, and especially to those that can produce the properties of volatility reported here.

Sums of variables at the onset of chaos

We explain how specific dynamical properties give rise to the limit distribution of sums of deterministic variables at the transition to chaos via the period-doubling route. We study the sums of successive positions generated by an ensemble of initial conditions uniformly distributed in the entire phase space of a unimodal map as represented by the logistic map. We find that these sums acquire their salient, multiscale, features from the repellor preimage structure that dominates the dynamics toward the attractors along the period-doubling cascade. And we explain how these properties transmit from the sums to their distribution. Specifically, we show how the stationary distribution of sums of positions at the Feigebaum point is built up from those associated with the supercycle attractors forming a hierarchical structure with multifractal and discrete scale invariance properties.

Stationary distributions of sums of marginally chaotic variables as renormalization group fixed points

We determine the limit distributions of sums of deterministic chaotic variables in unimodal maps assisted by a novel renormalization group (RG) framework associated to the operation of increment of summands and rescaling. In this framework the difference in control parameter from its value at the transition to chaos is the only relevant variable, the trivial fixed point is the Gaussian distribution and a nontrivial fixed point is a multifractal distribution with features similar to those of the Feigenbaum attractor. The crossover between the two fixed points is discussed and the flow toward the trivial fixed point is seen to consist of a sequence of chaotic band mergers.

Developmental autonomy and somatic niche construction promotes robust cell fate decisions

During the course of development cells undergo division producing a variety of cell types. Proliferation and differentiation are dependent on both genetic programs, encoded by the cellular genome, and environmental cues produced by the local cellular environment imposing local selection pressures on cells. We explore the role that cellular signals play over a large range of potential parameter regimes, in minimizing developmental error: errors in differentiation where an inappropriate proportion of differentiated daughter cells are generated. We find that trophic factors produced by the population of dividing cells can compensate for increased error rates when signals act through a form of positive feedback--survival signals. We operationalize these signals as the somatic niche and refer to their production as somatic niche construction. We find that tissue development switches to an autonomous state, independent of cellular signals, when errors are unmanageably high or density regulation is very strong. A signal-selective regime--strong niche dependence--is favored at low to intermediate error, assuming compartmentalized density dependence.