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

A new bound of the ℒ2[0, T]-induced norm and applications to model reduction

We present a simple bound on the finite horizon ℒ2/[0, T]-induced norm of a linear time-invariant (LTI), not necessarily stable system which can be efficiently computed by calculating the ℋ∞ norm of a shifted version of the original operator. As an application, we show how to use this bound to perform model reduction of unstable systems over a finite horizon. The technique is illustrated with a non-trivial physical example relevant to the appearance of time-irreversible phenomena in statistical physics

Estimating development effort in free/open source software projects by mining software repositories: A case study of OpenStack

Because of the distributed and collaborative nature of free/open source software (FOSS) projects, the development effort invested in a project is usually unknown, even after the software has been released. However, this information is becoming of major interest, especially-but not only-because of the growth in the number of companies for which FOSS has become relevant for their business strategy. In this paper we present a novel approach to estimate effort by considering data from source code management repositories. We apply our model to the OpenStack project, a FOSS project with more than 1,000 authors, in which several tens of companies cooperate. Based on data from its repositories and together with the input from a survey answered by more than 100 developers, we show that the model offers a simple, but sound way of obtaining software development estimations with bounded margins of error.Gregorio Robles, Carlos Cervig on and Jes us M. Gonz alez-Barahona, project SobreSale (TIN2011-28110). and The work of Daniel Izquierdo has been funded in part by the Torres Quevedo program (PTQ-12-05577

Observation of magnetization reversal in epitaxial Gd0.67Ca0.33MnO3 thin films

High quality epitaxial thin films of Gd0.67Ca0.33MnO3 have been deposited onto (100) SrTiO3 substrates by pulsed-laser deposition. Enhanced properties in comparison with bulk samples were observed. The magnetic transition temperature (Tc) of the as-grown films is much higher than the corresponding bulk values. Most interestingly, magnetization measurements performed under small applied fields, exhibit magnetization reversals below Tc, no matter whether the film is field-cooled (FC) or zero-field-cooled (ZFC). A rapid magnetization reversal occurs at 7 K when field cooled, while as for the ZFC process the magnetization decreases gradually with increasing temperatures, taking negative values above 7 K and changing to positive values again, above 83 K. In higher magnetic fields the magnetization does not change sign. The reversal mechanism is discussed in terms of a negative exchange f-d interaction and magnetic anisotropy, this later enhanced by strain effects induced by the lattice mismatch between the film and the substrate.Comment: 16 pages, 4 figure

Stability of graph communities across time scales

The complexity of biological, social and engineering networks makes it desirable to find natural partitions into communities that can act as simplified descriptions and provide insight into the structure and function of the overall system. Although community detection methods abound, there is a lack of consensus on how to quantify and rank the quality of partitions. We show here that the quality of a partition can be measured in terms of its stability, defined in terms of the clustered autocovariance of a Markov process taking place on the graph. Because the stability has an intrinsic dependence on time scales of the graph, it allows us to compare and rank partitions at each time and also to establish the time spans over which partitions are optimal. Hence the Markov time acts effectively as an intrinsic resolution parameter that establishes a hierarchy of increasingly coarser clusterings. Within our framework we can then provide a unifying view of several standard partitioning measures: modularity and normalized cut size can be interpreted as one-step time measures, whereas Fiedler's spectral clustering emerges at long times. We apply our method to characterize the relevance and persistence of partitions over time for constructive and real networks, including hierarchical graphs and social networks. We also obtain reduced descriptions for atomic level protein structures over different time scales.Comment: submitted; updated bibliography from v

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

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

Learning spatiotemporal signals using a recurrent spiking network that discretizes time

Learning to produce spatiotemporal sequences is a common task that the brain has to solve. The same neural substrate may be used by the brain to produce different sequential behaviours. The way the brain learns and encodes such tasks remains unknown as current computational models do not typically use realistic biologically-plausible learning. Here, we propose a model where a spiking recurrent network of excitatory and inhibitory biophysical neurons drives a read-out layer: the dynamics of the driver recurrent network is trained to encode time which is then mapped through the read-out neurons to encode another dimension, such as space or a phase. Different spatiotemporal patterns can be learned and encoded through the synaptic weights to the read-out neurons that follow common Hebbian learning rules. We demonstrate that the model is able to learn spatiotemporal dynamics on time scales that are behaviourally relevant and we show that the learned sequences are robustly replayed during a regime of spontaneous activity

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

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