On the interaction of adaptive timescales on networks

The dynamics of real-world systems often involve multiple processes that influence system state. The timescales that these processes operate on may be separated by orders of magnitude or may coincide closely. Where timescales are not separable, the way that they relate to each other will be important for understanding system dynamics. In this paper, we present a short overview of how modellers have dealt with multiple timescales and introduce a definition to formalise conditions under which timescales are separable. We investigate timescale separation in a simple model, consisting of a network of nodes on which two processes act. The first process updates the values taken by the network’s nodes, tending to move a node’s value towards that of its neighbours. The second process influences the topology of the network, by rewiring edges such that they tend to more often lie between similar individuals. We show that the behaviour of the system when timescales are separated is very different from the case where they are mixed. When the timescales of the two processes are mixed, the ratio of the rates of the two processes determines the systems equilibrium state. We go on to explore the impact of heterogeneity in the system’s timescales, i.e., where some nodes may update their value and/or neighbourhood faster than others, demonstrating that it can have a significant impact on the equilibrium behaviour of the model

Timescales of Turbulent Relative Dispersion

Tracers in a turbulent flow separate according to the celebrated $t^{3/2}$ Richardson--Obukhov law, which is usually explained by a scale-dependent effective diffusivity. Here, supported by state-of-the-art numerics, we revisit this argument. The Lagrangian correlation time of velocity differences is found to increase too quickly for validating this approach, but acceleration differences decorrelate on dissipative timescales. This results in an asymptotic diffusion $\propto t^{1/2}$ of velocity differences, so that the long-time behavior of distances is that of the integral of Brownian motion. The time of convergence to this regime is shown to be that of deviations from Batchelor's initial ballistic regime, given by a scale-dependent energy dissipation time rather than the usual turnover time. It is finally argued that the fluid flow intermittency should not affect this long-time behavior of relativeComment: 4 pages, 3 figure

Timescales of Massive Human Entrainment

The past two decades have seen an upsurge of interest in the collective behaviors of complex systems composed of many agents entrained to each other and to external events. In this paper, we extend concepts of entrainment to the dynamics of human collective attention. We conducted a detailed investigation of the unfolding of human entrainment - as expressed by the content and patterns of hundreds of thousands of messages on Twitter - during the 2012 US presidential debates. By time locking these data sources, we quantify the impact of the unfolding debate on human attention. We show that collective social behavior covaries second-by-second to the interactional dynamics of the debates: A candidate speaking induces rapid increases in mentions of his name on social media and decreases in mentions of the other candidate. Moreover, interruptions by an interlocutor increase the attention received. We also highlight a distinct time scale for the impact of salient moments in the debate: Mentions in social media start within 5-10 seconds after the moment; peak at approximately one minute; and slowly decay in a consistent fashion across well-known events during the debates. Finally, we show that public attention after an initial burst slowly decays through the course of the debates. Thus we demonstrate that large-scale human entrainment may hold across a number of distinct scales, in an exquisitely time-locked fashion. The methods and results pave the way for careful study of the dynamics and mechanisms of large-scale human entrainment.Comment: 20 pages, 7 figures, 6 tables, 4 supplementary figures. 2nd version revised according to peer reviewers' comments: more detailed explanation of the methods, and grounding of the hypothese

Chemical Timescales in the Atmospheres of Highly Eccentric Exoplanets

Close-in exoplanets with highly eccentric orbits are subject to large variations in incoming stellar flux between periapse and apoapse. These variations may lead to large swings in atmospheric temperature, which in turn may cause changes in the chemistry of the atmosphere from higher CO abundances at periapse to higher CH4 abundances at apoapse. Here we examine chemical timescales for COCH4 interconversion compared to orbital timescales and vertical mixing timescales for the highly eccentric exoplanets HAT-P-2b and CoRoT-10b. As exoplanet atmospheres cool, the chemical timescales for COCH4 tend to exceed orbital and/or vertical mixing timescales, leading to quenching. The relative roles of orbit-induced thermal quenching and vertical quenching depend upon mixing timescales relative to orbital timescales. For both HAT-P-2b and CoRoT-10b, vertical quenching will determine disequilibrium COCH4 chemistry at faster vertical mixing rates (Kzz > 10^7 cm^2 s^-1), whereas orbit-induced thermal quenching may play a significant role at slower mixing rates (Kzz < 10^7 cm^2 s^-1). The general abundance and chemical timescale results - calculated as a function of pressure, temperature, and metallicity - can be applied for different atmospheric profiles in order to estimate the quench level and disequilibrium abundances of CO and CH4 on hydrogen-dominated exoplanets. Observations of CO and CH4 on highly eccentric exoplanets may yield important clues to the chemical and dynamical properties of their atmospheres.Comment: 9 pages, 4 figures, accepted for publication in the Astrophysical Journal; v2 corrects typos and figure resolution issue

Timescales of spike-train correlation for neural oscillators with common drive

We examine the effect of the phase-resetting curve (PRC) on the transfer of correlated input signals into correlated output spikes in a class of neural models receiving noisy, super-threshold stimulation. We use linear response theory to approximate the spike correlation coefficient in terms of moments of the associated exit time problem, and contrast the results for Type I vs. Type II models and across the different timescales over which spike correlations can be assessed. We find that, on long timescales, Type I oscillators transfer correlations much more efficiently than Type II oscillators. On short timescales this trend reverses, with the relative efficiency switching at a timescale that depends on the mean and standard deviation of input currents. This switch occurs over timescales that could be exploited by downstream circuits