Heterogeneous pair approximation for voter models on networks

For models whose evolution takes place on a network it is often necessary to augment the mean-field approach by considering explicitly the degree dependence of average quantities (heterogeneous mean-field). Here we introduce the degree dependence in the pair approximation (heterogeneous pair approximation) for analyzing voter models on uncorrelated networks. This approach gives an essentially exact description of the dynamics, correcting some inaccurate results of previous approaches. The heterogeneous pair approximation introduced here can be applied in full generality to many other processes on complex networks.Comment: 6 pages, 6 figures, published versio

Universal scaling of distances in complex networks

Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k_i and k_j equals to =A-B log(k_i k_j). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree _nn calculated for the nearest neighbors and on network clustering coefficients.Comment: 4 pages, 3 figures, 1 tabl

Voter Model with Time dependent Flip-rates

We introduce time variation in the flip-rates of the Voter Model. This type of generalisation is relevant to models of ageing in language change, allowing the representation of changes in speakers' learning rates over their lifetime and may be applied to any other similar model in which interaction rates at the microscopic level change with time. The mean time taken to reach consensus varies in a nontrivial way with the rate of change of the flip-rates, varying between bounds given by the mean consensus times for static homogeneous (the original Voter Model) and static heterogeneous flip-rates. By considering the mean time between interactions for each agent, we derive excellent estimates of the mean consensus times and exit probabilities for any time scale of flip-rate variation. The scaling of consensus times with population size on complex networks is correctly predicted, and is as would be expected for the ordinary voter model. Heterogeneity in the initial distribution of opinions has a strong effect, considerably reducing the mean time to consensus, while increasing the probability of survival of the opinion which initially occupies the most slowly changing agents. The mean times to reach consensus for different states are very different. An opinion originally held by the fastest changing agents has a smaller chance to succeed, and takes much longer to do so than an evenly distributed opinion.Comment: 16 pages, 6 figure

Anomalous lifetime distributions and topological traps in ordering dynamics

We address the role of community structure of an interaction network in ordering dynamics, as well as associated forms of metastability. We consider the voter and AB model dynamics in a network model which mimics social interactions. The AB model includes an intermediate state between the two excluding options of the voter model. For the voter model we find dynamical metastable disordered states with a characteristic mean lifetime. However, for the AB dynamics we find a power law distribution of the lifetime of metastable states, so that the mean lifetime is not representative of the dynamics. These trapped metastable states, which can order at all time scales, originate in the mesoscopic network structure.Comment: 7 pages; 6 figure

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

Lack of consensus in social systems

We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model, as the connections in the network evolve with the dynamics of the voters. In the infinite time limit, an exact solution predicts the emergence of consensus, for arbitrary initial conditions. However, before consensus is reached, two different metastable states can persist for exponentially long times. One state reflects a perfect balancing of opinions, the other reflects a completely static situation. An estimate of the associated lifetimes suggests that lack of consensus is typical for large systems.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let

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

Ordering in voter models on networks: Exact reduction to a single-coordinate diffusion

We study the voter model and related random-copying processes on arbitrarily complex network structures. Through a representation of the dynamics as a particle reaction process, we show that a quantity measuring the degree of order in a finite system is, under certain conditions, exactly governed by a universal diffusion equation. Whenever this reduction occurs, the details of the network structure and random-copying process affect only a single parameter in the diffusion equation. The validity of the reduction can be established with considerably less information than one might expect: it suffices to know just two characteristic timescales within the dynamics of a single pair of reacting particles. We develop methods to identify these timescales, and apply them to deterministic and random network structures. We focus in particular on how the ordering time is affected by degree correlations, since such effects are hard to access by existing theoretical approaches.Comment: 37 pages, 10 figures. Revised version with additional discussion and simulation results to appear in J Phys

DAWN: a resource for yielding insights into the diversity among wheat genomes

Background: Democratising the growing body of whole genome sequencing data available for Triticum aestivum (bread wheat) has been impeded by the lack of a genome reference and the large computational requirements for analysing these data sets. Results: DAWN (Diversity Among Wheat geNomes) integrates data from the T. aestivum Chinese Spring (CS) IWGSC RefSeq v1.0 genome with public WGS and exome data from 17 and 62 accessions respectively, enabling researchers and breeders alike to investigate genotypic differences between wheat accessions at the level of whole chromosomes down to individual genes. Conclusions: Using DAWN we show that it is possible to visualise small and large chromosomal deletions, identify haplotypes at a glance and spot the consequences of selective breeding. DAWN allows us to detect the break points of alien introgression segments brought into an accession when transferring desired genes. Furthermore, we can find possible explanations for reduced recombination in parts of a chromosome, we can predict regions with linkage drag, and also look at diversity in centromeric regions.Nathan S. Watson-Haigh, Radosław Suchecki, Elena Kalashyan, Melissa Garcia and Ute Bauman

Application of next-generation sequencing technology to study genetic diversity and identify unique SNP markers in bread wheat from Kazakhstan

BACKGROUND: New SNP marker platforms offer the opportunity to investigate the relationships between wheat cultivars from different regions and assess the mechanism and processes that have led to adaptation to particular production environments. Wheat breeding has a long history in Kazakhstan and the aim of this study was to explore the relationship between key varieties from Kazakhstan and germplasm from breeding programs for other regions. RESULTS: The study revealed 5,898 polymorphic markers amongst ten cultivars, of which 2,730 were mapped in the consensus genetic map. Mapped SNP markers were distributed almost equally across the A and B genomes, with between 279 and 484 markers assigned to each chromosome. Marker coverage was approximately 10-fold lower in the D genome. There were 863 SNP markers identified as unique to specific cultivars, and clusters of these markers (regions containing more than three closely mapped unique SNPs) showed specific patterns on the consensus genetic map for each cultivar. Significant intra-varietal genetic polymorphism was identified in three cultivars (Tzelinnaya 3C, Kazakhstanskaya rannespelaya and Kazakhstanskaya 15). Phylogenetic analysis based on inter-varietal polymorphism showed that the very old cultivar Erythrospermum 841 was the most genetically distinct from the other nine cultivars from Kazakhstan, falling in a clade together with the American cultivar Sonora and genotypes from Central and South Asia. The modern cultivar Kazakhstanskaya 19 also fell into a separate clade, together with the American cultivar Thatcher. The remaining eight cultivars shared a single sub-clade but were categorised into four clusters. CONCLUSION: The accumulated data for SNP marker polymorphisms amongst bread wheat genotypes from Kazakhstan may be used for studying genetic diversity in bread wheat, with potential application for marker-assisted selection and the preparation of a set of genotype-specific markers.Yuri Shavrukov, Radoslaw Suchecki, Serik Eliby, Aigul Abugalieva, Serik Kenebayev and Peter Langridg