Universality in percolation of arbitrary Uncorrelated Nested Subgraphs

The study of percolation in so-called {\em nested subgraphs} implies a generalization of the concept of percolation since the results are not linked to specific graph process. Here the behavior of such graphs at criticallity is studied for the case where the nesting operation is performed in an uncorrelated way. Specifically, I provide an analyitic derivation for the percolation inequality showing that the cluster size distribution under a generalized process of uncorrelated nesting at criticality follows a power law with universal exponent $\gamma=3/2$. The relevance of the result comes from the wide variety of processes responsible for the emergence of the giant component that fall within the category of nesting operations, whose outcome is a family of nested subgraphs.Comment: 5 pages, no figures. Mistakes found in early manuscript have been remove

On the origin of ambiguity in efficient communication

This article studies the emergence of ambiguity in communication through the concept of logical irreversibility and within the framework of Shannon's information theory. This leads us to a precise and general expression of the intuition behind Zipf's vocabulary balance in terms of a symmetry equation between the complexities of the coding and the decoding processes that imposes an unavoidable amount of logical uncertainty in natural communication. Accordingly, the emergence of irreversible computations is required if the complexities of the coding and the decoding processes are balanced in a symmetric scenario, which means that the emergence of ambiguous codes is a necessary condition for natural communication to succeed.Comment: 28 pages, 2 figure

Exploring the randomness of Directed Acyclic Networks

The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems -such as some food-webs and electronic and neural wiring- can be described in terms of so-called directed acyclic graphs (DAGs). An important ingredient of the analysis of such networks is a proper comparison of their observed architecture against an ensemble of randomized graphs, thereby quantifying the {\em randomness} of the real systems with respect to suitable null models. This approximation is particularly relevant when the finite size and/or large connectivity of real systems make inadequate a comparison with the predictions obtained from the so-called {\em configuration model}. In this paper we analyze four methods of DAG randomization as defined by the desired combination of topological invariants (directed and undirected degree sequence and component distributions) aimed to be preserved. A highly ordered DAG, called \textit{snake}-graph and a Erd\:os-R\'enyi DAG were used to validate the performance of the algorithms. Finally, three real case studies, namely, the \textit{C. elegans} cell lineage network, a PhD student-advisor network and the Milgram's citation network were analyzed using each randomization method. Results show how the interpretation of degree-degree relations in DAGs respect to their randomized ensembles depend on the topological invariants imposed. In general, real DAGs provide disordered values, lower than the expected by chance when the directedness of the links is not preserved in the randomization process. Conversely, if the direction of the links is conserved throughout the randomization process, disorder indicators are close to the obtained from the null-model ensemble, although some deviations are observed.Comment: 13 pages, 5 figures and 5 table

Resilience theory incorporated into urban wastewater systems management. State of the art

This is the final version of the article. Available from Elsevier via the DOI in this record.Government bodies, utilities, practitioners, and researchers have growing interest in the incorporation of resilience into wastewater management. Since resilience is a multidisciplinary term, it is important to review what has been achieved in the wastewater sector, and describe the future research directions for the forthcoming years. This work presents a critical review of studies that deal with resilience in the wastewater treatment sector, with a special focus on understanding how they addressed the key elements for assessing resilience, such as stressors, system properties, metrics and interventions to increase resilience. The results showed that only 17 peer-reviewed papers and 6 relevant reports, a small subset of the work in wastewater research, directly addressed resilience. The lack of consensus in the definition of resilience, and the elements of a resilience assessment, is hindering the implementation of resilience in wastewater management. To date, no framework for resilience assessment is complete, comprehensive or directly applicable to practitioners; current examples are lacking key elements (e.g. a comprehensive study of stressors, properties and metrics, examples of cases study, ability to benchmark interventions or connectivity with broader frameworks). Furthermore, resilience is seen as an additional cost or extra effort, instead of a means to overcome project uncertainty that could unlock new opportunities for investment.The authors thank the consultancy team in Water Research, Strategic Advisory Services Research in Atkins UK, and Corinne Trommsdorff from IWA, for their constructive comments and support. Their contribution is highly appreciated. This work has been supported by the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642904 - TreatRec ITN-EID project, and by the Ministry of Economy and competitiveness for the Ramon and Cajal grant from Lluís Corominas (RYC-2013-14595) and for the REaCH project (CTM2015-66892-R, MINECO/FEDER, EU). LEQUIA and ICRA were recognized as consolidated research groups by the Catalan Government with codes 2014-SGR-1168 and 2014-SGR-291, respectively. The second and fifth authors acknowledge support from the UK Engineering & Physical Sciences Research Council grant EP/K006924/1

Sciatic nerve movement in the deep gluteal space during hip rotations maneuvers

We hypothesize that the sciatic nerve in the subgluteal space has a specific behavior during internal and external coxofemoral rotation and during isometric contraction of the internal and external rotator muscles of the hip. In 58 healthy volunteers, sciatic nerve behavior was studied by ultrasound during passive internal and external hip rotation movements and during isometric contraction of internal and external rotators. Using MATLAB software, changes in nerve curvature at the beginning and end of each exercise were evaluated for longitudinal catches and axial movement for transverse catches. In the long axis, it was observed that during the passive internal rotation and during the isometric contraction of external rotators, the shape of the curve increased significantly while during the passive external rotation and the isometric contraction of the internal rotators the curvature flattened out. During passive movements in internal rotation, on the short axis, the nerve tended to move laterally and forward, while during external rotation the tendency of the nerve was to move toward a medial and backward position. During the isometric exercises, this displacement was less in the passive movements. Passive movements of hip rotation and isometric contraction of the muscles affect the sciatic nerve in the subgluteal space. Retrotrochanteric pain may be related to both the shear effect of the subgluteus muscles and the endoneural and mechanosensitive aggression to which the sciatic nerve is subjected

Comparing the hierarchy of keywords in on-line news portals

The tagging of on-line content with informative keywords is a widespread phenomenon from scientific article repositories through blogs to on-line news portals. In most of the cases, the tags on a given item are free words chosen by the authors independently. Therefore, relations among keywords in a collection of news items is unknown. However, in most cases the topics and concepts described by these keywords are forming a latent hierarchy, with the more general topics and categories at the top, and more specialised ones at the bottom. Here we apply a recent, cooccurrence-based tag hierarchy extraction method to sets of keywords obtained from four different on-line news portals. The resulting hierarchies show substantial differences not just in the topics rendered as important (being at the top of the hierarchy) or of less interest (categorised low in the hierarchy), but also in the underlying network structure. This reveals discrepancies between the plausible keyword association frameworks in the studied news portals

Dynamics on expanding spaces: modeling the emergence of novelties

Novelties are part of our daily lives. We constantly adopt new technologies, conceive new ideas, meet new people, experiment with new situations. Occasionally, we as individuals, in a complicated cognitive and sometimes fortuitous process, come up with something that is not only new to us, but to our entire society so that what is a personal novelty can turn into an innovation at a global level. Innovations occur throughout social, biological and technological systems and, though we perceive them as a very natural ingredient of our human experience, little is known about the processes determining their emergence. Still the statistical occurrence of innovations shows striking regularities that represent a starting point to get a deeper insight in the whole phenomenology. This paper represents a small step in that direction, focusing on reviewing the scientific attempts to effectively model the emergence of the new and its regularities, with an emphasis on more recent contributions: from the plain Simon's model tracing back to the 1950s, to the newest model of Polya's urn with triggering of one novelty by another. What seems to be key in the successful modelling schemes proposed so far is the idea of looking at evolution as a path in a complex space, physical, conceptual, biological, technological, whose structure and topology get continuously reshaped and expanded by the occurrence of the new. Mathematically it is very interesting to look at the consequences of the interplay between the "actual" and the "possible" and this is the aim of this short review.Comment: 25 pages, 10 figure

Diversity, competition, extinction: the ecophysics of language change

As early indicated by Charles Darwin, languages behave and change very much like living species. They display high diversity, differentiate in space and time, emerge and disappear. A large body of literature has explored the role of information exchanges and communicative constraints in groups of agents under selective scenarios. These models have been very helpful in providing a rationale on how complex forms of communication emerge under evolutionary pressures. However, other patterns of large-scale organization can be described using mathematical methods ignoring communicative traits. These approaches consider shorter time scales and have been developed by exploiting both theoretical ecology and statistical physics methods. The models are reviewed here and include extinction, invasion, origination, spatial organization, coexistence and diversity as key concepts and are very simple in their defining rules. Such simplicity is used in order to catch the most fundamental laws of organization and those universal ingredients responsible for qualitative traits. The similarities between observed and predicted patterns indicate that an ecological theory of language is emerging, supporting (on a quantitative basis) its ecological nature, although key differences are also present. Here we critically review some recent advances lying and outline their implications and limitations as well as open problems for future research.Comment: 17 Pages. A review on current models from statistical Physics and Theoretical Ecology applied to study language dynamic