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Open Access. Attribution 4.0 International (CC BY 4.0), This paper aims at being a provocative guide to the future of asteroseismology from the perspective of the analysis of time series, where the fundamentals of harmonic analysis are subjected to stress tests. In this context, we give an annotated summary of our research over the last decades on harmonic analysis of A-F stars. We discuss and explore the consequences of our findings, which may extend to any kind of pulsators. As well, we analyse the impact of this reconsideration on future asteroseismic studies, which would entail a paradigm shift. This includes a discussion on the presence of fractal behavior in delta Sct stars, and how this can be used to develop a stopping criterion of the pre-whitening process, as an alternative to SNR (or significance) criterion. Drilling a scientific paradigm has its natural resilience, hence the path described here is being arduous, although fruitful at the same time., SF, JP-G, JR, ML-M, and RG acknowledges financial support from the State Agency for Research of the Spanish MCIU through the Center of Excellence Severo Ochoa award for the Instituto de Astrofisica de Andalucia (SEV-2017-0709) and Spanish public funds for research under projects ESP2015-65712C5-5-R. JS and AG acknowledge funding support from Spanish public funds for research under projects ESP2017-87676-C5-2R. JS also acknowledges funding support from project RYC2012-09913 under the Ramon y Cajal program of the Spanish MINECO. AG acknowledges support from Universidad de Granada under project E-FQM-041-UGR18 from the Programa Operativo FEDER 2014-2020 programme by Junta de Andalucia regional Government.

Gene switching dynamics is a major source of randomness in genetic networks, also in the case of large concentrations of the transcription factors. In this work, we consider a common network motif - the positive feedback of a transcription factor on its own synthesis - and assess its response to extrinsic noises perturbing gene deactivation in a variety of settings where the network might operate. These settings are representative of distinct cellular types, abundance of transcription factors and ratio between gene switching and protein synthesis rates. By investigating noise-induced transitions among the different network operative states, our results suggest that gene switching rates are key parameters to shape network response to external perturbations and that such response depends on the particular biological setting, i.e. the characteristic time scales and protein abundance. These results might have implications on our understanding of irreversible transitions for noise-related phenomena such as cellular differentiation. In addition these evidences suggest to adopt the appropriate mathematical model of the network in order to analyze the system consistently to the reference biological setting.

Cued and un-cued cell polarization is a fundamental mechanism in cell biology. As an alternative to the classical Turing bifurcation, it has been proposed that the cell polarity might onset by means of the well-known phenomenon of wave-pinning (Gamba et al, PNAS, 2005). A particularly simple and elegant model of wave-pinning has been proposed by Edelstein-Keshet and coworkers (Biop. J., 2008). However, biomolecular networks do communicate with other networks as well as with the external world. As such, their dynamics has to be considered as perturbed by extrinsic noises. These noises may have both a spatial and a temporal correlation, but any case they must be bounded to preserve the biological meaningfulness of the perturbed parameters. Here we numerically show that the inclusion of external spatio-temporal bounded perturbations may sometime destroy the polarized state. The polarization loss depends on both the extent of temporal and spatial correlations, and on the kind of adopted noise. Namely, independently of the specific model of noise, an increase of the spatial correlation induces an increase of the probability of polarization. However, if the noise is spatially homogeneous then the polarization is lost in the majority of cases. On the contrary, an increase of the temporal autocorrelation of the noise induces an effect that depends on the noise model., 21 pages, 9 figures

In this work we introduce a spatio-temporal bounded noise derived by the sine-Wiener noise and by the spatially colored unbounded noise proposed by Garcia-Ojalvo, Sancho, and Ramirez-Piscina (GSR noise). We characterize the behavior of the equilibrium distribution of this novel noise by showing its dependence on both the temporal and the spatial autocorrelation lengths. In particular, we show that the distribution experiences a stochastic transition from bimodality to trimodality. Then, we employ the noise here defined to study the emergence of phase transitions in the real Ginzburg–Landau model. Various phenomena are evidenced by means of numerical simulations, among which reentrant transitions, as well as differences in the response of the system to “equivalent” GSR additive noise perturbations.

In this work, we introduce three spatiotemporal colored bounded noises, based on the zero-dimensional Cai–Lin, Tsallis–Borland, and sine-Wiener noises. Then we study and characterize the dependence of the defined stochastic processes on both a temporal correlation parameter τ and a spatial coupling parameter λ. In particular, we found that varying λ may induce a transition of the distribution of the noise from bimodality to unimodality. With the aim to investigate the role played by bounded noises on spatially extended nonlinear dynamical systems, we analyze the behavior of the real Ginzburg–Landau time-varying model additively perturbed by such noises. The observed phase transitions phenomenology is quite different from the one observed when the perturbations are unbounded. In particular, we observed inverse “order-to-disorder” transitions, and reentrant transitions, with dependence on the specific type of bounded noise.

In this work, we introduce two spatio-temporal colored bounded noises, based on the zero-dimensional Cai-Lin and Tsallis-Borland noises. We then study and characterize the dependence of the defined bounded noises on both a temporal correlation parameter $\tau$ and on a spatial coupling parameter $\lambda$. The boundedness of these noises has some consequences on their equilibrium distributions. Indeed in some cases varying $\lambda$ may induce a transition of the distribution of the noise from bimodality to unimodality. With the aim to study the role played by bounded noises on nonlinear dynamical systems, we investigate the behavior of the real Ginzburg-Landau time-varying model additively perturbed by such noises. The observed phase transitions phenomenology is quite different from the one observed when the perturbations are unbounded. In particular, we observed an inverse "order-to-disorder" transition, and a re-entrant transition, with dependence on the specific type of bounded noise., Comment: 12 (main text)+5 (supplementary) pages

Recent experiments on cortical neural networks have revealed the existence of well-defined avalanches of electrical activity. Such avalanches have been claimed to be generically scale-invariant -- i.e. power-law distributed -- with many exciting implications in Neuroscience. Recently, a self-organized model has been proposed by Levina, Herrmann and Geisel to justify such an empirical finding. Given that (i) neural dynamics is dissipative and (ii) there is a loading mechanism "charging" progressively the background synaptic strength, this model/dynamics is very similar in spirit to forest-fire and earthquake models, archetypical examples of non-conserving self-organization, which have been recently shown to lack true criticality. Here we show that cortical neural networks obeying (i) and (ii) are not generically critical; unless parameters are fine tuned, their dynamics is either sub- or super-critical, even if the pseudo-critical region is relatively broad. This conclusion seems to be in agreement with the most recent experimental observations. The main implication of our work is that, if future experimental research on cortical networks were to support that truly critical avalanches are the norm and not the exception, then one should look for more elaborate (adaptive/evolutionary) explanations, beyond simple self-organization, to account for this., 28 pages, 11 figures, regular paper