Laplacian Dynamics and Multiscale Modular Structure in Networks

Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The time-scale of the process acts as an intrinsic parameter that uncovers community structures at different resolutions. The stability extends and unifies standard notions for community detection: modularity and spectral partitioning can be seen as limiting cases of our dynamic measure. Similarly, recently proposed multi-resolution methods correspond to linearisations of the stability at short times. The connection between community detection and Laplacian dynamics enables us to establish dynamically motivated stability measures linked to distinct null models. We apply our method to find multi-scale partitions for different networks and show that the stability can be computed efficiently for large networks with extended versions of current algorithms.Comment: New discussions on the selection of the most significant scales and the generalisation of stability to directed network

Community detection and role identification in directed networks: understanding the Twitter network of the care.data debate

With the rise of social media as an important channel for the debate and discussion of public affairs, online social networks such as Twitter have become important platforms for public information and engagement by policy makers. To communicate effectively through Twitter, policy makers need to understand how influence and interest propagate within its network of users. In this chapter we use graph-theoretic methods to analyse the Twitter debate surrounding NHS Englands controversial care.data scheme. Directionality is a crucial feature of the Twitter social graph - information flows from the followed to the followers - but is often ignored in social network analyses; our methods are based on the behaviour of dynamic processes on the network and can be applied naturally to directed networks. We uncover robust communities of users and show that these communities reflect how information flows through the Twitter network. We are also able to classify users by their differing roles in directing the flow of information through the network. Our methods and results will be useful to policy makers who would like to use Twitter effectively as a communication medium

Protein multi-scale organization through graph partitioning and robustness analysis: Application to the myosin-myosin light chain interaction

Despite the recognized importance of the multi-scale spatio-temporal organization of proteins, most computational tools can only access a limited spectrum of time and spatial scales, thereby ignoring the effects on protein behavior of the intricate coupling between the different scales. Starting from a physico-chemical atomistic network of interactions that encodes the structure of the protein, we introduce a methodology based on multi-scale graph partitioning that can uncover partitions and levels of organization of proteins that span the whole range of scales, revealing biological features occurring at different levels of organization and tracking their effect across scales. Additionally, we introduce a measure of robustness to quantify the relevance of the partitions through the generation of biochemically-motivated surrogate random graph models. We apply the method to four distinct conformations of myosin tail interacting protein, a protein from the molecular motor of the malaria parasite, and study properties that have been experimentally addressed such as the closing mechanism, the presence of conserved clusters, and the identification through computational mutational analysis of key residues for binding.Comment: 13 pages, 7 Postscript figure

Relative, local and global dimension in complex networks

Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogeneities, or to intrinsically discrete systems such as networks. To take into account locality, finiteness and discreteness, dynamical processes can be used to probe the space geometry and define its dimension. Here we show that each point in space can be assigned a relative dimension with respect to the source of a diffusive process, a concept that provides a scale-dependent definition for local and global dimension also applicable to networks. To showcase its application to physical systems, we demonstrate that the local dimension of structural protein graphs correlates with structural flexibility, and the relative dimension with respect to the active site uncovers regions involved in allosteric communication. In simple models of epidemics on networks, the relative dimension is predictive of the spreading capability of nodes, and identifies scales at which the graph structure is predictive of infectivity. We further apply our dimension measures to neuronal networks, economic trade, social networks, ocean flows, and to the comparison of random graphs

Distributional extensions of Carollia castanea and Micronycteris minuta from Guatemala, Central America

Field expeditions in 2011 that inventoried the terrestrial vertebrate fauna of two wildlife protected areas in the tropical Caribbean of Guatemala have produced the first confirmed records of two bats for the country: the white-bellied big-eared bat, Micronycteris (Schizonycteris) minuta (Gervais 1856) and the Chesnut short-tailed bat Carollia castanea H. Allen, 1890, both of neotropical distribution and with their current northern limit at Lancetilla, Honduras. The record of M. minuta at Sierra de Caral, Guatemala extends the range of this species 137 km to the west, and the record of C. castanea at Cerro San Gil extends its range 147 km to the west

Using network-flow techniques to solve an optimization problem from surface-physics

The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination of the ground state of this model leads to a combinatorial problem, which is reduced to an uncapacitated, convex minimum-circulation problem. We will show that the successive shortest path algorithm solves the problem in polynomial time.Comment: 8 Pages LaTeX, using Elsevier preprint style (macros included

Evaluation of an entraining droplet activation parameterization using in situ cloud data

This study investigates the ability of a droplet activation parameterization (which considers the effects of entrainment and mixing) to reproduce observed cloud droplet number concentration (CDNC) in ambient clouds. Predictions of the parameterization are compared against cloud averages of CDNC from ambient cumulus and stratocumulus clouds sampled during CRYSTAL‐FACE (Key West, Florida, July 2002) and CSTRIPE (Monterey, California, July 2003), respectively. The entrainment parameters required by the parameterization are derived from the observed liquid water content profiles. For the cumulus clouds considered in the study, CDNC is overpredicted by 45% with the adiabatic parameterization. When entrainment is accounted for, the predicted CDNC agrees within 3.5%. Cloud‐averaged CDNC for stratocumulus clouds is well captured when entrainment is not considered. In all cases considered, the entraining parameterization compared favorably against a statistical correlation developed from observations to treat entrainment effects on droplet number. These results suggest that including entrainment effects in the calculation of CDNC, as presented here, could address important overprediction biases associated with using adiabatic CDNC to represent cloud‐scale average values

Forage Quality and the Environment

The influence of environmental factors on forage quality of temperate and tropical grasses has been reviewed by several authors, who summarized how light, temperature, drought and soil nutrients influence chemical composition, and digestibility of forages grown in contrasting areas of the world. The effects of season of the year on forage growth, grazing behavior and animal performance have also been the subject of numerous papers and reviews. However, there are few recent reviews that summarize how changes in climatic and edaphic factors influence forage quality of legumes with variable levels of condensed tannins (CT), which are important secondary compounds in some temperate and tropical legume species adapted to acid infertile soils. In this paper we summarize properties of CT and their positive and negative effects on forage quality of legumes. We also review published work on the effect of temperature, drought, CO2 concentration, season of the year and soil fertility on the accumulation of CT in temperate and tropical legumes. Results from experiments under controlled conditions indicate that high temperature alone can significantly increase the accumulation of CT in some temperate legume species (i.e. Lotus pedunculatus) but not in others (i.e. L. corniculatus). However, the effect of low or high temperature on accumulation of CT is considerably greater when accompanied with other environmental factors such as drought, high CO2 concentration and soil nutrient deficiencies. Soil nutrient deficiencies can have a major effect on elevation of CT concentration and overall feed value of temperate and tropical legumes, but only when deficiencies are such that they affect plant growth. Soil fertility and climatic conditions affect not only the concentration of CT but also their monomer composition and MW (molecular weight), as was observed in a tropical legume species well adapted to acid infertile soils. The nutritional significance of these findings are not all that well understood, but it would seem that CT in forage legumes are not a uniform chemical entity given that they can change with edaphic and climatic factors. Finally we suggest that there is a need to investigate alternatives to enhance the feed value of legumes with tannins adapted to acid soils through selection of genotypes with less CT and /or through manipulation of environmental factors such as soil fertility. For this we need to better understand how edaphic and climatic factors affect not only accumulation of CT but also their chemical structure and biological activity and relate these changes to forage intake, digestibility, N utilization, and, ultimately, to performance of ruminant animals