arXiv subjects

Miguel A. Fuentes

Publications and source records attributed to Miguel A. Fuentes.

7 recordsLinked to original sources

arXiv2019

Non-equilibrium evolution of volatility in origination and extinction explains fat-tailed fluctuations in Phanerozoic biodiversity

Fluctuations in biodiversity, large and small, are pervasive in the fossil record, yet we do not understand the processes generating them. Here we extend theory from non-equilibrium statistical physics to describe the previously unaccounted for fat-tailed form of fluctuations in marine invertebrate richness through the Phanerozoic. Using this theory, known as superstatistics, we show that the simple fact of heterogeneous origination and extinction rates between clades and conserved rates within clades is sufficient to account for this fat-tailed form. We identify orders and the families they subsume as the taxonomic level at which clades experience inter-clade heterogeneity and within clade homogeneity of rates. Following superstatistics we would posit that orders and families are subsystems in local statistical equilibrium while the entire system is not in equilibrium. The separation of timescales between background origination and extinction within clades compared to the origin of major ecological and evolutionary innovations leading to new clades allows within-clade dynamics to reach equilibrium, while between-clade diversification is non-equilibrial. This between clade non-equilibrium accounts for the fat-tailed nature of the system as a whole. The distribution of shifts in diversification dynamics across orders and families is consistent with niche conservatism and pulsed exploration of adaptive landscapes by higher taxa. Compared to other approaches that have used simple birth-death processes, simple equilibrial dynamics, or non-linear theories from complexity science, superstatistics is superior in its ability to account for both small and extreme fluctuations in the richness of fossil taxa. Its success opens up new research directions to better understand the evolutionary processes leading to stasis in an adaptive landscape interrupted by innovations that lead to novel forms.

q-bio.PE↗

arXiv2009

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.

q-fin.ST↗

arXiv2009

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.

q-fin.ST↗

arXiv2009

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.

cond-mat.stat-mech↗

arXiv2007

Noise-induced phase transitions: Effects of the noises' statistics and spectrum

The local, uncorrelated multiplicative noises driving a second-order, purely noise-induced, ordering phase transition (NIPT) were assumed to be Gaussian and white in the model of [Phys. Rev. Lett. \textbf{73}, 3395 (1994)]. The potential scientific and technological interest of this phenomenon calls for a study of the effects of the noises' statistics and spectrum. This task is facilitated if these noises are dynamically generated by means of stochastic differential equations (SDE) driven by white noises. One such case is that of Ornstein--Uhlenbeck noises which are stationary, with Gaussian pdf and a variance reduced by the self-correlation time (τ), and whose effect on the NIPT phase diagram has been studied some time ago. Another such case is when the stationary pdf is a (colored) Tsallis' (q)--\emph{Gaussian} which, being a \emph{fat-tail} distribution for (q>1) and a \emph{compact-support} one for (q<1), allows for a controlled exploration of the effects of the departure from Gaussian statistics. As done before with stochastic resonance and other phenomena, we now exploit this tool to study--within a simple mean-field approximation and with an emphasis on the \emph{order parameter} and the ``\emph{susceptibility}''--the combined effect on NIPT of the noises' statistics and spectrum. Even for relatively small (τ), it is shown that whereas fat-tail noise distributions ((q>1)) counteract the effect of self-correlation, compact-support ones ((q<1)) enhance it. Also, an interesting effect on the susceptibility is seen in the last case.

cond-mat.stat-mech↗

arXiv2006

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>>1, (i) the attractor in distribution space is, according to the standard central limit theorem, a Gaussian, and (ii) the Boltzmann-Gibbs-Shannon entropy is extensive, meaning that S_BGS(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, S_BGS 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 can become extensive for some value of q different from unity . 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.

cond-mat.stat-mech↗

arXiv2006

Stochastic Resonance: influence of a $f^{-κ}$ noise spectrum

Here, in order to study \textit{stochastic resonance} (SR) in a double-well potential when the noise source has a spectral density of the form $f^{-κ}$ with varying $κ$, we have extended a procedure, introduced by Kaulakys et al (Phys. Rev. E \textbf{70}, 020101 (2004)). In order to have an analytical understanding of the results, we have obtained an effective Markovian approximation, that allows us to make a systematic study of the effect of such kind of noises on the SR phenomenon. The comparison of numerical and analytical results shows an excellent qualitative agreement indicating that the effective Markovian approximation is able to correctly describe the general trends.

cond-mat.stat-mech↗