Ising model on two connected Barabasi-Albert networks

We investigate analytically the behavior of Ising model on two connected Barabasi-Albert networks. Depending on relative ordering of both networks there are two possible phases corresponding to parallel or antiparallel alingment of spins in both networks. A difference between critical temperatures of both phases disappears in the limit of vanishing inter-network coupling for identical networks. The analytic predictions are confirmed by numerical simulations.Comment: 6 pages including 6 figure

Conservation laws for the voter model in complex networks

We consider the voter model dynamics in random networks with an arbitrary distribution of the degree of the nodes. We find that for the usual node-update dynamics the average magnetization is not conserved, while an average magnetization weighted by the degree of the node is conserved. However, for a link-update dynamics the average magnetization is still conserved. For the particular case of a Barabasi-Albert scale-free network the voter model dynamics leads to a partially ordered metastable state with a finite size survival time. This characteristic time scales linearly with system size only when the updating rule respects the conservation law of the average magnetization. This scaling identifies a universal or generic property of the voter model dynamics associated with the conservation law of the magnetization.Comment: 5 pages, 4 figures; for related material please visit http://www.imedea.uib.e

Social stress and glucocorticoids alter PERIOD2 rhythmicity in the liver, but not in the suprachiasmatic nucleus

Circadian (~24 h) rhythms in behavior and physiological functions are under control of an endogenous circadian pacemaker in the suprachiasmatic nucleus (SCN) of the hypothalamus. The SCN directly drives some of these rhythms or serves as a coordinator of peripheral oscillators residing in other tissues and organs. Disruption of the circadian organization may contribute to disease, including stress-related disorders. Previous research indicates that the master clock in the SCN is resistant to stress, although it is unclear whether stress affects rhythmicity in other tissues, possibly mediated by glucocorticoids, released in stressful situations. In the present study, we examined the effect of uncontrollable social defeat stress and glucocorticoid hormones on the central and peripheral clocks, respectively in the SCN and liver. Transgenic PERIOD2::LUCIFERASE knock-in mice were used to assess the rhythm of the clock protein PERIOD2 (PER2) in SCN slices and liver tissue collected after 10 consecutive days of social defeat stress. The rhythmicity of PER2 expression in the SCN was not affected by stress exposure, whereas in the liver the expression showed a delayed phase in defeated compared to non-defeated control mice. In a second experiment, brain slices and liver samples were collected from transgenic mice and exposed to different doses of corticosterone. Corticosterone did not affect PER2 rhythm of the SCN samples, but caused a phase shift in PER2 expression in liver samples. This study confirms earlier findings that the SCN is resistant to stress and shows that clocks in the liver are affected by social stress, which might be due to the direct influence of glucocorticoids released from the adrenal gland

Consensus formation on coevolving networks: groups' formation and structure

We study the effect of adaptivity on a social model of opinion dynamics and consensus formation. We analyze how the adaptivity of the network of contacts between agents to the underlying social dynamics affects the size and topological properties of groups and the convergence time to the stable final state. We find that, while on static networks these properties are determined by percolation phenomena, on adaptive networks the rewiring process leads to different behaviors: Adaptive rewiring fosters group formation by enhancing communication between agents of similar opinion, though it also makes possible the division of clusters. We show how the convergence time is determined by the characteristic time of link rearrangement. We finally investigate how the adaptivity yields nontrivial correlations between the internal topology and the size of the groups of agreeing agents.Comment: 10 pages, 3 figures,to appear in a special proceedings issue of J. Phys. A covering the "Complex Networks: from Biology to Information Technology" conference (Pula, Italy, 2007

Analytical Solution of the Voter Model on Disordered Networks

We present a mathematical description of the voter model dynamics on heterogeneous networks. When the average degree of the graph is $\mu \leq 2$ the system reaches complete order exponentially fast. For $\mu >2$, a finite system falls, before it fully orders, in a quasistationary state in which the average density of active links (links between opposite-state nodes) in surviving runs is constant and equal to $\frac{(\mu-2)}{3(\mu-1)}$, while an infinite large system stays ad infinitum in a partially ordered stationary active state. The mean life time of the quasistationary state is proportional to the mean time to reach the fully ordered state $T$, which scales as $T \sim \frac{(\mu-1) \mu^2 N}{(\mu-2) \mu_2}$, where $N$ is the number of nodes of the network, and $\mu_2$ is the second moment of the degree distribution. We find good agreement between these analytical results and numerical simulations on random networks with various degree distributions.Comment: 20 pages, 8 figure

A simple mean field model for social interactions: dynamics, fluctuations, criticality

We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in the limit of infinitely many interacting individuals, and show that phase transition occurs. Then, after having obtained the dynamics of normal fluctuations around this limit, we analize long time fluctuations for critical values of the parameters. We show that random inhomogeneities produce critical fluctuations at a shorter time scale compared to the homogeneous system.Comment: 37 pages, 2 figure

Timing interactions in social simulations: The voter model

The recent availability of huge high resolution datasets on human activities has revealed the heavy-tailed nature of the interevent time distributions. In social simulations of interacting agents the standard approach has been to use Poisson processes to update the state of the agents, which gives rise to very homogeneous activity patterns with a well defined characteristic interevent time. As a paradigmatic opinion model we investigate the voter model and review the standard update rules and propose two new update rules which are able to account for heterogeneous activity patterns. For the new update rules each node gets updated with a probability that depends on the time since the last event of the node, where an event can be an update attempt (exogenous update) or a change of state (endogenous update). We find that both update rules can give rise to power law interevent time distributions, although the endogenous one more robustly. Apart from that for the exogenous update rule and the standard update rules the voter model does not reach consensus in the infinite size limit, while for the endogenous update there exist a coarsening process that drives the system toward consensus configurations.Comment: Book Chapter, 23 pages, 9 figures, 5 table

High resolution mapping of traits related to whole-plant transpiration under increasing evaporative demand in wheat

First published online: March 20, 2016Atmospheric vapor pressure deficit (VPD) is a key component of drought and has a strong influence on yields. Whole-plant transpiration rate (TR) response to increasing VPD has been linked to drought tolerance in wheat, but because of its challenging phenotyping, its genetic basis remains unexplored. Further, the genetic control of other key traits linked to daytime TR such as leaf area, stomata densities and - more recently - nocturnal transpiration remains unknown. Considering the presence of wheat phenology genes that can interfere with drought tolerance, the aim of this investigation was to identify at an enhanced resolution the genetic basis of the above traits while investigating the effects of phenology genes Ppd-D1 and Ppd-B1 Virtually all traits were highly heritable (heritabilities from 0.61 to 0.91) and a total of mostly trait-specific 68 QTL were detected. Six QTL were identified for TR response to VPD, with one QTL (QSLP.ucl-5A) individually explaining 25.4% of the genetic variance. This QTL harbored several genes previously reported to be involved in ABA signaling, interaction with DREB2A and root hydraulics. Surprisingly, nocturnal TR and stomata densities on both leaf sides were characterized by highly specific and robust QTL. In addition, negative correlations were found between TR and leaf area suggesting trade-offs between these traits. Further, Ppd-D1 had strong but opposite effects on these traits, suggesting an involvement in this trade-off. Overall, these findings revealed novel genetic resources while suggesting a more direct role of phenology genes in enhancing wheat drought tolerance.Rémy Schoppach, Julian D Taylor, Elisabeth Majerus, Elodie Claverie, Ute Baumann, Radoslaw Suchecki, Delphine Fleury and Walid Sado