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

Window functions and sigmoidal behaviour of memristive systems

Summary: A common approach to model memristive systems is to include empirical window functions to describe edge effects and nonlinearities in the change of the memristance. We demonstrate that under quite general conditions, each window function can be associated with a sigmoidal curve relating the normalised time-dependent memristance to the time integral of the input. Conversely, this explicit relation allows us to derive window functions suitable for the mesoscopic modelling of memristive systems from a variety of well-known sigmoidals. Such sigmoidal curves are defined in terms of measured variables and can thus be extracted from input and output signals of a device and then transformed to its corresponding window. We also introduce a new generalised window function that allows the flexible modelling of asymmetric edge effects in a simple manner

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

Flow-Based Network Analysis of the Caenorhabditis elegans Connectome

We exploit flow propagation on the directed neuronal network of the nematode C. elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system. A systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions of the multi-resolution flow structure. Such ablations are linked to functionally relevant neurons, and suggest potential candidates for further in vivo investigation. In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify flow profiles for the neurons in the connectome, without pre-imposing a priori categories. The four flow roles identified are linked to signal propagation motivated by biological input-response scenarios

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

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

El concepto de software libre

El software libre es cada vez más habitual en casi cualquier entorno informático. Sin embargo, es también un gran desconocido. En este artículo se exponen las condiciones que tiene que cumplir un programa para ser considerado como software libre, compiladas en varias definiciones. A partir de ellas se repasa brevemente su historia y se exploran algunas de sus características y consecuencias. También se comentan algunos aspectos relacionados con las licencias de software libre que son tan fundamentales para su existencia.El programari lliure és cada vegada més habitual en qualsevol entorn informàtic. Tanmateix, és també un gran desconegut. En aquest article s'exposen les condicions que ha de complir un programa per a ser considerat com a programari lliure, compilades en diverses definicions. A partir d'elles es repassa breument la seva història i s'exploren algunes de les seves característiques i conseqüències. També es comenten alguns aspectes relacionats amb les llicències de programari lliure que són tan bàsiques per a la seva existència.Free, open source software is increasingly more usual in almost any computing environment. However, it is also a great unknown: not many people knows what it truly is. This paper presents the conditions that some piece of software has to comply with to be considered as free or open source software, which are compiled in several definitions. Starting from them, its history is briefly exposed, and some of its characteristics and consequences are explored. In addition, some aspects related to free software licensing are commented, since they are so fundamental for its very existence