Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization

Correlations in weighted networks

We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of structural constraints. We also introduce an algorithm for generating maximally random weighted networks with arbitrary P(k,s) to be used as null models. The application of our measures to real networks reveals the importance of weights in a correct understanding and modeling of these heterogeneous systems

Relationship between medio-lateral oscillation of the foot, during statics and previous ankle sprains

This study tries to determine how is stability in the medio-lateral direction of the center of force of the ankle joint axis, during quiet standing and barefoot, before the production of ankle sprains. This result is going to compare with feet that haven´t ankle sprains to establish a connection of similarity or diference between two situations.This study tries to determine how is stability in the medio-lateral direction of the center of force of the ankle joint axis, during quiet standing and barefoot, before the production of ankle sprains. This result is going to compare with feet that haven´t ankle sprains to establish a connection of similarity or diference between two situations

Generalized percolation in random directed networks

We develop a general theory for percolation in directed random networks with arbitrary two-point correlations and bidirectional edgesthat is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions

Navigable maps of structural brain networks across species

Connectomes are spatially embedded networks whose architecture has been shaped by physical constraints and communication needs throughout evolution. Using a decentralized navigation protocol, we investigate the relationship between the structure of the connec- tomes of different species and their spatial layout. As a navigation strategy, we use greedy routing where nearest neighbors, in terms of geometric distance, are visited. We measure the fraction of successful greedy paths and their length as compared to shortest paths in the topology of connectomes. In Euclidean space, we find a striking difference between the nav- igability properties of mammalian and non-mammalian species, which implies the inability of Euclidean distances to fully explain the structural organization of their connectomes. In con- trast, we find that hyperbolic space, the effective geometry of complex networks, provides almost perfectly navigable maps of connectomes for all species, meaning that hyperbolic distances are exceptionally congruent with the structure of connectomes. Hyperbolic maps therefore offer a quantitative meaningful representation of connectomes that suggests a new cartography of the brain based on the combination of its connectivity with its effective geometry rather than on its anatomy only. Hyperbolic maps also provide a universal frame- work to study decentralized communication processes in connectomes of different species and at different scales on an equal footing

Presente y futuro de los medios de pago en el comercio físico español

El presente Trabajo Final de Grado (TFG) es una investigación de mercados sobre la evolución del sector de los medios de pago en el comercio físico español. El objetivo principal es obtener información útil y objetiva de modo que pueda ser utilizada por la empresa Paypal España, para reducir el riesgo de sus decisiones estratégicas orientadas a la expansión del negocio a través de soluciones de pago innovadoras para el comercio físico. Para logarlo, primero, se ha analizado información ya publicada sobre datos más específicos del sector y del mercado lo que ha permitido establecer los objetivos y, posteriormente, concretar las hipótesis de trabajo a validar al término de la investigación. A continuación, se ejecutado una fase exploratoria a fin de reunir información y contrastar opiniones acerca de los comportamientos, motivaciones y actitudes de los compradores. A partir de la información obtenida, una posterior fase concluyente apoyada en el análisis estadístico es la que ha permitido cubrir los objetivos establecidos, es decir, elaborar los diferentes perfiles de compradores según el uso de los medios de pago, cuantificar los comportamientos y preferencias, así como evaluar los atributos y otras variables externas al comprador más significativas a la hora de decidir entre los diferentes medios de pago. Finalmente, como conclusiones más relevantes cabe confirmar la hegemonía del efectivo como el medio más usado, lo que lleva a pensar en su durabilidad a largo plazo. No obstante, los altos índices de uso de las tarjetas y la cada vez mayor predisposición ante los nuevos medios electrónicos ponen en jaque esta posición dominante del efectivo y dan paso nuevos grandes competidores como el contactless y los pagos por móvil; los cuales, definitivamente, han llegado para quedarse.This Final Degree Work is a market research on the evolution of the physical payment sector in Spanish trade. The main objective is to obtain useful and objective information that can be used by the directors of the company Paypal Spain to reduce the risk of its strategic decisions oriented to the expansion of the business through innovative payment solutions for physical commerce. To achieve this, first, information already published on more specific data from the sector and the market has been analysed, which has made it possible to establish the objectives and, subsequently, to specify the working hypotheses to be validated at the end of the investigation. An exploratory phase was then executed to gather information and contrast opinions about behaviours, motivations and attitudes of buyers. Based on the information obtained, a subsequent conclusive phase supported by statistical analysis has enabled meet the stated objectives, that is, to develop different profiles of buyers according to their use of the payment systems, to quantify the behaviours and preferences, as well as evaluating the most significant attributes and other external variables to the buyer when deciding between different payment systems. Finally, the most relevant conclusions can confirm the hegemony effective as the most widely used system, leading to think about their long-term durability. However, high rates of card usage and the increasing disposition to new electronic payment systems put in check this dominant position of cash and give way new major competitors such as contactless and mobile payments which definitely, they are here to stay.El present Treball Final de Grau (TFG) és una investigació de mercats sobre l'evolució del sector dels mitjans de pagament en el comerç físic espanyol. L'objectiu principal és obtenir informació útil i objectiva de manera que pugui ser utilitzada per l'empresa Paypal Espanya, per reduir el risc de les seves decisions estratègiques orientades a l'expansió del negoci a través de solucions de pagament innovadores per al comerç físic. Per assolir-ho, primer, s'ha analitzat la informació ja publicada sobre el sector; cosa que ha permès establir els objectius i, posteriorment, concretar les hipòtesis de treball a validar. A continuació, s'ha executat una fase exploratòria per tal de reunir informació i contrastar opinions sobre els comportaments, motivacions i actituds dels compradors. Una anàlisi estadística ha permès cobrir els objectius establerts, és a dir, elaborar els diferents perfils de compradors segons l'ús dels mitjans de pagament, quantificar els comportaments i preferències, així com avaluar els atributs i altres variables externes més significatives a l'hora de decidir entre els diferents mitjans de pagament. Finalment, com a conclusions més rellevants cal confirmar, l'efectiu com el mitjà més usat, el que porta a pensar en la seva durabilitat a llarg termini. No obstant això, els alts índexs d'ús de les targetes i la cada vegada major predisposició davant els nous mitjans electrònics posen en perill aquesta posició dominant de l'efectiu i donen pas nous grans competidors com el contactless i els pagaments per mòbil; els quals, definitivament, han arribat per quedar-se

Network-based scoring system for genome-scale metabolic reconstructions

Background: Network reconstructions at the cell level are a major development in Systems Biology. However, we are far from fully exploiting its potentialities. Often, the incremental complexity of the pursued systems overrides experimental capabilities, or increasingly sophisticated protocols are underutilized to merely refine confidence levels of already established interactions. For metabolic networks, the currently employed confidence scoring system rates reactions discretely according to nested categories of experimental evidence or model-based likelihood. Results: Here, we propose a complementary network-based scoring system that exploits the statistical regularities of a metabolic network as a bipartite graph. As an illustration, we apply it to the metabolism of Escherichia coli. The model is adjusted to the observations to derive connection probabilities between individual metabolite-reaction pairs and, after validation, to assess the reliability of each reaction in probabilistic terms. This network-based scoring system uncovers very specific reactions that could be functionally or evolutionary important, identifies prominent experimental targets, and enables further confirmation of modeling results. Conclusions: We foresee a wide range of potential applications at different sub-cellular or supra-cellular levels of biological interactions given the natural bipartivity of many biological networks

The interconnected wealth of nations: Shock propagation on global trade-investment multiplex networks

The increasing integration of world economies, which organize in complex multilayer networks of interactions, is one of the critical factors for the global propagation of economic crises. We adopt the network science approach to quantify shock propagation on the global trade-investment multiplex network. To this aim, we propose a model that couples a spreading dynamics, describing how economic distress propagates between connected countries, with an internal contagion mechanism, describing the spreading of such economic distress within a given country. At the local level, we find that the interplay between trade and financial interactions influences the vulnerabilities of countries to shocks. At the large scale, we find a simple linear relation between the relative magnitude of a shock in a country and its global impact on the whole economic system, albeit the strength of internal contagion is country-dependent and the inter-country propagation dynamics is non-linear. Interestingly, this systemic impact can be associated to intra-layer and inter-layer scale factors that we name network multipliers, that are independent of the magnitude of the initial shock. Our model sets-up a quantitative framework to stress-test the robustness of individual countries and of the world economy

Regulation of burstiness by network-driven activation

We prove that complex networks of interactions have the capacity to regulate and buffer unpredictable fluctuations in production events. We show that non-bursty network-driven activation dynamics can effectively regulate the level of burstiness in the production of nodes, which can be enhanced or reduced. Burstiness can be induced even when the endogenous inter-event time distribution of nodes' production is non-bursty. We find that hubs tend to be less susceptible to the networked regulatory effects than low degree nodes. Our results have important implications for the analysis and engineering of bursty activity in a range of systems, from communication networks to transcription and translation of genes into proteins in cells

Multiscale unfolding of real networks by geometric renormalization

Symmetries in physical theories denote invariance under some transformation, such as self-similarity under a change of scale. The renormalization group provides a powerful framework to study these symmetries, leading to a better understanding of the universal properties of phase transitions. However, the small-world property of complex networks complicates application of the renormalization group by introducing correlations between coexisting scales. Here, we provide a framework for the investigation of complex networks at different resolutions. The approach is based on geometric representations, which have been shown to sustain network navigability and to reveal the mechanisms that govern network structure and evolution. We define a geometric renormalization group for networks by embedding them into an underlying hidden metric space. We find that real scale-free networks show geometric scaling under this renormalization group transformation. We unfold the networks in a self-similar multilayer shell that distinguishes the coexisting scales and their interactions. This in turn offers a basis for exploring critical phenomena and universality in complex networks. It also affords us immediate practical applications, including high-fidelity smaller-scale replicas of large networks and a multiscale navigation protocol in hyperbolic space, which betters those on single layers