Stochastic blockmodels with growing number of classes

We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least poly-logarithmically in this size. We also establish finite-sample confidence bounds on maximum-likelihood blockmodel parameter estimates from data comprising independent Bernoulli random variates; these results hold uniformly over class assignment. We provide simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stochastic blockmodel with covariates to a network data example comprising a collection of Facebook profiles, resulting in block estimates that reveal residual structure.Comment: 12 pages, 3 figures; revised versio

Bayesian stochastic blockmodeling

This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping generalizations. We focus on nonparametric formulations that allow their inference in a manner that prevents overfitting, and enables model selection. We discuss aspects of the choice of priors, in particular how to avoid underfitting via increased Bayesian hierarchies, and we contrast the task of sampling network partitions from the posterior distribution with finding the single point estimate that maximizes it, while describing efficient algorithms to perform either one. We also show how inferring the SBM can be used to predict missing and spurious links, and shed light on the fundamental limitations of the detectability of modular structures in networks.Comment: 44 pages, 16 figures. Code is freely available as part of graph-tool at https://graph-tool.skewed.de . See also the HOWTO at https://graph-tool.skewed.de/static/doc/demos/inference/inference.htm

Behavioral responses of voles along fences patrolled by natural predators

Fuelling, O., Buehler, E., Airoldi, J.-P., Nentwig, W

Etude par capture et recapture d’une population de campagnols terrestres, Arvicola terrestris scherman shaw (Mammalia, rodentia)

Une population semi-isolée de campagnols terrestres, Arvicola terrestris scherman Schaw, a été étudiée par capture et recapture entre juillet 1975 et mai 1976, sur une parcelle de 700 m2. Une série de 15 piégeages, d’une durée de deux jours et comprenant nor malement 9 contrôles par jour a été effectuée à des intervalles de trois semaines. L’effort de piégeage a varié entre 526 et 950 trappes X heures. Le réseau de pièges est visité très rapidement et permet de capturer en moyenne 80 % (70-95 %) de la population en deux jours. Le nombre moyen de captures et recaptures par individu et par piégeage est de 4,2 (2, 7-6, 5). Les nombres moyens de change ments de trappes (x = 1,7) et de trappes différentes visitées (x = 1,9) qui lui sont fortement liés permettent d’établir les rela tions entre individus et de délimiter leurs domaines vitaux avec suffisamment de précision. Les différentes méthodes d’estimation de populations basées sur une droite de régression ou sur les rapports entre individus marqués et non marqués concordent mal avec l’effectif réel de la population, dont la meilleure approximation est donnée par le calendrier de captures. Celles utilisant les distributions des fré quences de captures coïncident généralement mieux. La densité de population atteint un maximum en novembre et en avril, et un minimum au début mars. La reproduction a cessé à mi-novembre, pour reprendre à mi-mars. Pendant la période de reproduction, l’indice de turnover entre deux piégeages est de 1,38. La survie des cohortes nées entre juillet et novembre est différente suivant les sexes et conduit à une sex ratio en faveur des femelles en hiver. L’émigration a pu être mise en évidence. Les déplace ments individuels dans la population sont les plus nombreux entre juillet et novembre. La plupart des groupes familieux sont stables et la fidélité au domaine vital et entre individus est grande. Les campagnols vivent généralement en couples. En dehors de la pé riode de reproduction, ils forment souvent des groupements plus complexes comprenant un ou plusieurs mâles et plusieurs fe melles.A semi-isolated population of the fossorial form of the water vole, Arvicola terrestris scherman Shaw, was studied by the capture-recapture method, over an area of 700 m2 from July 1975 to May 1976. A series of 15 trapping periods lasting 2 days each and normally made of 9 trap-controls a day ware carried out at intervals of three weeks. The trapping effort varied between 526 and 950 trap-hours. Traps were very quickly occupied and an average of 80 % (70-95 %) of the population caught within 2 days. Individuals were captured and recaptured at the average of 4.2 (2.7-6.5) times per trapping period. The average number of trap changes (x = 1.7) and of different traps occupied (x = 1.9) correlated with the afore mentioned quantity allows to establish the relationships between individuals and set the boundaries of their home ranges with reasonable precision. The methods of population estimation based on a regression line or on the ratio between marked and unmarked individuals, do not agree with the actual population size, whose best approxi mation is given by the calendar of captures. Those using the distri bution of captures frequencies generally coincide better. The population density reached a maximum in November and in April and a minimum at the beginning of March. Breeding ceased at the middle of August and started again at the middle of March. During the breeding period, the turnover index between two trapping periods was 1.38. The survival of cohorts born bet ween July and November was different for both sexes and leading to a sex ratio in favour of females in winter. Emigration was observed and individual movements within the population were most numerous from July to November. Most family groups were stable and there was a great attachment to the home range and between individuals. Water voles live generally in pairs. Outside the breeding period, they often live in more complex groups made of one or more males and several females

Stochastic blockmodels and community structure in networks

Stochastic blockmodels have been proposed as a tool for detecting community structure in networks as well as for generating synthetic networks for use as benchmarks. Most blockmodels, however, ignore variation in vertex degree, making them unsuitable for applications to real-world networks, which typically display broad degree distributions that can significantly distort the results. Here we demonstrate how the generalization of blockmodels to incorporate this missing element leads to an improved objective function for community detection in complex networks. We also propose a heuristic algorithm for community detection using this objective function or its non-degree-corrected counterpart and show that the degree-corrected version dramatically outperforms the uncorrected one in both real-world and synthetic networks.Comment: 11 pages, 3 figure

TTG1 proteins regulate circadian activity as well as epidermal cell fate and pigmentation.

The Arabidopsis genome contains three genes encoding proteins of the TRANSPARENT TESTA GLABRA 1 (TTG1) WD-repeat (WDR) subfamily. TTG1 is a known regulator of epidermal cell differentiation and pigment production, while LIGHT-REGULATED WD1 and LIGHT-REGULATED WD2 are known regulators of the circadian clock. Here, we discovered a new central role for TTG1 WDR proteins as regulators of the circadian system, as evidenced by the lack of detectable circadian rhythms in a triple lwd1 lwd2 ttg1 mutant. This shows that there has been subfunctionalization via protein changes within the angiosperms, with some TTG1 WDR proteins developing a stronger role in circadian clock regulation while losing the protein characteristics essential for pigment production and epidermal cell specification, and others weakening their ability to drive circadian clock regulation. Our work shows that even where proteins are very conserved, small changes can drive big functional differences.CAA acknowledges support from the Cambridge University Botanic Garden Research Fund. TJH was supported by BBSRC UK grant BB/M006212/1 awarded to AARW