The noisy voter model on complex networks

We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for uncorrelated networks, allowing to deal with the network structure as parametric heterogeneity. As an illustration, we study the noisy voter model, a modification of the original voter model including random changes of state. The proposed method is able to unfold the dependence of the model not only on the mean degree (the mean-field prediction) but also on more complex averages over the degree distribution. In particular, we find that the degree heterogeneity ---variance of the underlying degree distribution--- has a strong influence on the location of the critical point of a noise-induced, finite-size transition occurring in the model, on the local ordering of the system, and on the functional form of its temporal correlations. Finally, we show how this latter point opens the possibility of inferring the degree heterogeneity of the underlying network by observing only the aggregate behavior of the system as a whole, an issue of interest for systems where only macroscopic, population level variables can be measured.Comment: 28 pages, 9 figure

Coupled dynamics of node and link states in complex networks: A model for language competition

Inspired by language competition processes, we present a model of coupled evolution of node and link states. In particular, we focus on the interplay between the use of a language and the preference or attitude of the speakers towards it, which we model, respectively, as a property of the interactions between speakers (a link state) and as a property of the speakers themselves (a node state). Furthermore, we restrict our attention to the case of two socially equivalent languages and to socially inspired network topologies based on a mechanism of triadic closure. As opposed to most of the previous literature, where language extinction is an inevitable outcome of the dynamics, we find a broad range of possible asymptotic configurations, which we classify as: frozen extinction states, frozen coexistence states, and dynamically trapped coexistence states. Moreover, metastable coexistence states with very long survival times and displaying a non-trivial dynamics are found to be abundant. Interestingly, a system size scaling analysis shows, on the one hand, that the probability of language extinction vanishes exponentially for increasing system sizes and, on the other hand, that the time scale of survival of the non-trivial dynamical metastable states increases linearly with the size of the system. Thus, non-trivial dynamical coexistence is the only possible outcome for large enough systems. Finally, we show how this coexistence is characterized by one of the languages becoming clearly predominant while the other one becomes increasingly confined to "ghetto-like" structures: small groups of bilingual speakers arranged in triangles, with a strong preference for the minority language, and using it for their intra-group interactions while they switch to the predominant language for communications with the rest of the population.Comment: 21 pages, 15 figure

Markets, herding and response to external information

We focus on the influence of external sources of information upon financial markets. In particular, we develop a stochastic agent-based market model characterized by a certain herding behavior as well as allowing traders to be influenced by an external dynamic signal of information. This signal can be interpreted as a time-varying advertising, public perception or rumor, in favor or against one of two possible trading behaviors, thus breaking the symmetry of the system and acting as a continuously varying exogenous shock. As an illustration, we use a well-known German Indicator of Economic Sentiment as information input and compare our results with Germany's leading stock market index, the DAX, in order to calibrate some of the model parameters. We study the conditions for the ensemble of agents to more accurately follow the information input signal. The response of the system to the external information is maximal for an intermediate range of values of a market parameter, suggesting the existence of three different market regimes: amplification, precise assimilation and undervaluation of incoming information.Comment: 30 pages, 8 figures. Thoroughly revised and updated version of arXiv:1302.647

Resistance to learning and the evolution of cooperation

In many evolutionary algorithms, crossover is the main operator used in generating new individuals from old ones. However, the usual mechanism for generating offsprings in spatially structured evolutionary games has to date been clonation. Here we study the effect of incorporating crossover on these models. Our framework is the spatial Continuous Prisoner's Dilemma. For this evolutionary game, it has been reported that occasional errors (mutations) in the clonal process can explain the emergence of cooperation from a non-cooperative initial state. First, we show that this only occurs for particular regimes of low costs of cooperation. Then, we display how crossover gets greater the range of scenarios where cooperative mutants can invade selfish populations. In a social context, where crossover involves a general rule of gradual learning, our results show that the less that is learnt in a single step, the larger the degree of global cooperation finally attained. In general, the effect of step-by-step learning can be more efficient for the evolution of cooperation than a full blast one

Fragmentation transition in a coevolving network with link-state dynamics

We study a network model that couples the dynamics of link states with the evolution of the network topology. The state of each link, either A or B, is updated according to the majority rule or zero-temperature Glauber dynamics, in which links adopt the state of the majority of their neighboring links in the network. Additionally, a link that is in a local minority is rewired to a randomly chosen node. While large systems evolving under the majority rule alone always fall into disordered topological traps composed by frustrated links, any amount of rewiring is able to drive the network to complete order, by relinking frustrated links and so releasing the system from traps. However, depending on the relative rate of the majority rule and the rewiring processes, the system evolves towards different ordered absorbing configurations: either a one-component network with all links in the same state or a network fragmented in two components with opposite states. For low rewiring rates and finite size networks there is a domain of bistability between fragmented and non-fragmented final states. Finite size scaling indicates that fragmentation is the only possible scenario for large systems and any nonzero rate of rewiring.Comment: 10 pages, 13 figure

Binary and Multivariate Stochastic Models of Consensus Formation

A current paradigm in computer simulation studies of social sciences problems by physicists is the emergence of consensus. The question is to establish when the dynamics of a set of interacting agents that can choose among several options (political vote, opinion, cultural features, etc.) leads to a consensus in one of these options, or when a state with several coexisting social options prevail. We consider here stochastic dynamic models naturally studied by computer simulations. We will first review some basic results for the voter model. This is a binary option stochastic model, and probably the simplest model of collective behavior. Next we consider a model proposed by Axelrod for the dissemination of culture. This model can be considered as a multivariable elaboration of the voter model dynamics.Comment: (16 pages, 8 figures; for simililar work visit http://www.imedea.uib.es/physdept

Recent Advances in Homogeneous Metal-Catalyzed Aerobic C–H Oxidation of Benzylic Compounds

Csp(3)-H oxidation of benzylic methylene compounds is an established strategy for the synthesis of aromatic ketones, esters, and amides. The need for more sustainable oxidizers has encouraged researchers to explore the use of molecular oxygen. In particular, homogeneous metal-catalyzed aerobic oxidation of benzylic methylenes has attracted much attention. This account summarizes the development of this oxidative strategy in the last two decades, examining key factors such as reaction yields, substrate: catalyst ratio, substrate scope, selectivity over other oxidation byproducts, and reaction conditions including solvents and temperature. Finally, several mechanistic proposals to explain the observed results will be discussed.(IT-774-13 (Basque Government) and CTQ2017-86630-P (Spanish Ministry of Economy and Competitiveness) projects

History and memory in digital culture. Methodological innovations and networks of stories [Editorial]

El dossier al que pertenece esta editorial se enmarca en el proyecto de investigación HISMEDI, Historia y Memoria Histórica on line. Retos y oportunidades para el conocimiento del pasado en Internet con referencia HAR-2015-63582-P (MINECO/FEDER

Egitura-zehaztapenerako ariketa ebatziak

104 p.Egitura-determinazioan jarduten duten ikasleen zein profesionalen trebakuntzan laguntzea da ariketa ebatziz osoturiko liburu honen helburu nagusia. Azken finean, lehen ariketa errazetatik hasita azken adibide konplexuenera, ikaslea gidatzea da liburu honen zeregina. UV-Vis, IR, MS, eta NMR espektro sinpleak lantzen dira lehenik, ondoren gaur egungo esperimentu aurreratuagoetara helduz, seinale/banda/tontorren esanahaia eta beren ondorioa igarri nahi den konposatu ezezagunaren egituran adibide praktikoen bitartez azaltzen direlarik. Halaber, eskuratutako informazioa nola bildu, ustezko egitura kimikoa (ezaugarri estereokimikoak ere barne) proposatzeko eta esleipenerako irispideak ematen dira