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

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

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

Could Spain be less different? Exploring the effects of macroprudential policy on the house price cycle

Haciendo uso de un modelo basado en agentes del mercado inmobiliario español, exploramos los principales factores responsables de la mayor amplitud de los ciclos del precio de la vivienda en España —en comparación con la mayoría de los otros países europeos—, así como el potencial alcance de la política macroprudencial para reducir esta amplitud. En primer lugar, aprovechamos la disponibilidad de una calibración previa del modelo para el Reino Unido, país caracterizado por una menor amplitud del ciclo del precio de la vivienda, para mostrar el prominente papel desempeñado por las distribuciones de varias métricas de riesgo hipotecario: las ratios préstamo-valor, préstamo-ingresos y servicio de la deuda-ingresos. En segundo lugar, utilizamos el modelo para calibrar tanto un límite rígido de la ratio préstamo-valor como un límite suave de la ratio préstamo-ingresos con el objetivo de suavizar el ciclo del precio de la vivienda español de manera que su amplitud se iguale a la del equivalente británico. Finalmente, caracterizamos los efectos de estas políticas a lo largo de las diferentes fases del ciclo, encontrando que ambos instrumentos reducen el crecimiento del crédito y del precio durante la fase expansiva, mientras que hacen disminuir su declive durante la fase contractiva. Además, ambos instrumentos desencadenan un cambio en la composición de la actividad crediticia: en los dos casos se produce un aumento del crédito a inversores en vivienda de alquiler, pero mientras que el límite préstamo-valor conduce a una reducción del crédito a compradores de primera vivienda, con el límite préstamo-ingresos disminuye el crédito tanto a compradores de primera vivienda como a propietarios en busca de una nueva vivienda principal.Employing an agent-based model of the Spanish housing market, this paper explores the main drivers behind the large amplitude of the Spanish house price cycle —as compared to most other European countries—, as well as the scope for macroprudential policy to reduce this amplitude. First, we exploit the availability of a previous calibration to the UK, which has a less pronounced house price cycle, to show the prominent role played by the distributions of various mortgage risk metrics: loan-to-value, loan-to-income and debt-service-to-income ratios. Second, we use the model to calibrate both a hard loan-to-value limit and a soft loan-to-income limit to smooth the Spanish house price cycle and match the amplitude of the UK equivalent. Finally, we characterise the effects of these calibrated policies over the different phases of the cycle, finding that both instruments reduce credit and price growth during the expansionary phase and also reduce their decline during the contractionary phase. Moreover, both instruments lead to a compositional shift in lending: the loan-to-value policy from first-time buyers to buy-to-let investors and the loan-to-income policy from both first-time buyers and home movers to buy-to-let investors

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

Uncertainty, non-linear contagion and the credit quality channel: an application to the Spanish interbank market

Utilizando datos granulares de la Central de Información de Riesgos del Banco de España, estudiamos uno de los canales de contagio a través de los cuales se pueden transmitir las tensiones en los mercados financieros —el canal de la calidad crediticia—, enfocándonos en el mercado interbancario español. Proponemos un mecanismo de contagio no lineal, que depende de la estructura del balance bancario (específicamente, de la ratio de apalancamiento). Adicionalmente, modelizamos explícitamente la incertidumbre que rodea los análisis de los prestamistas acerca de la probabilidad de incumplimiento de sus prestatarios, incorporando así la ausencia de información completa en los mercados y las expectativas heterogéneas de los agentes en su evaluación de resultados futuros. Realizamos múltiples simulaciones que reflejan una amplia gama de posibles grados de tensión del sistema bancario y buscamos desentrañar los efectos de estos dos componentes clave del modelo al comparar nuestros resultados con los que se obtendrían empleando un modelo lineal y determinista. De esta forma, encontramos que, bajo el supuesto de no linealidad, las pérdidas son sustancialmente mayores para amplios grados intermedios de tensión del sistema, mientras que sus efectos se vuelven insignificantes para grados de tensión tanto muy bajos como muy altos. Asimismo, encontramos que incorporar los efectos de la incertidumbre genera un impacto menor relativo al supuesto de no linealidad, pero aun así relevante y más marcado en torno a los grados de tensión en los que diferentes partes del sistema se vuelven inestables. Curiosamente, las pérdidas pueden verse amplificadas o mitigadas con respecto al caso determinista, dependiendo del grado específico de tensión considerado. Finalmente, la interacción entre ambos componentes del modelo —contagio no lineal e incertidumbre— modifica el área para la que la incertidumbre tiene un impacto relevante.Using granular data from the Spanish Central Credit Register, we study the contagion of financial distress via the credit quality channel in the Spanish interbank market. We propose a non-linear contagion mechanism dependent on banks’ balance-sheet structure (specifically, their leverage ratios). Moreover, we explicitly model uncertainty in lenders’ assessments of the probability of default of their borrowers, thus incorporating agents’ lack of complete information and heterogeneous expectations in their assessment of future outcomes. We perform multiple simulations across a wide range of possible levels of stress in the system, and we focus on disentangling the effects of these two key model components by comparing the results of our model with those of a linear and deterministic counterpart. We find that non-linear contagion leads to substantially larger losses than its linear counterpart for a wide range of intermediate levels of stress in the system, while its effects become negligible for very low and very high stress levels. Regarding uncertainty, we find that its effects, while smaller than those of non-linear contagion, are nonetheless relevant and most important around levels of stress at which different parts of the system become unstable. Interestingly, losses can be amplified or mitigated with respect to the deterministic case depending on the specific level of stress considered. Finally, the interaction between these two model components - non-linear contagion and uncertainty - alters the area where uncertainty matters

Heterogeneous effects and spillovers of macroprudential policy in an agent-based model of the UK housing market

Desarrollamos un modelo basado en agentes para estudiar el impacto de experimentos de política macroprudencial sobre los principales indicadores del mercado inmobiliario del Reino Unido. La naturaleza heterogénea de este modelo nos permite evaluar el efecto de tales experimentos sobre los mercados de compra, alquiler y crédito hipotecario no solo de forma agregada, sino también a nivel de hogares individuales y subsegmentos tales como los compradores de primera vivienda, los propietarios, los inversores en vivienda para alquilar y los inquilinos. Este enfoque puede así ofrecer una visión general de los efectos desagregados de las políticas de estabilidad financiera. El modelo está calibrado con una amplia selección de fuentes de microdatos: incluye datos tanto de un destacado portal inmobiliario del Reino Unido como de regulación préstamo a préstamo. Mediante una serie de ejercicios de estática comparativa, investigamos el impacto de: i) un límite rígido de la ratio préstamo-valor, y ii) un límite suave de la ratio préstamo-ingresos, permitiendo que una determinada fracción de las nuevas hipotecas supere esta restricción. En primer lugar, encontramos que estos experimentos tienden a mitigar el ciclo de precios del mercado inmobiliario, lo que reduce la disponibilidad de crédito y, por tanto, el apalancamiento. En segundo lugar, un experimento que tenga por objetivo una particular medida del riesgo puede afectar también a otras métricas de riesgo; se hace así necesaria una cuidadosa calibración de la política para lograr una determinada reducción del riesgo. Por último, experimentos enfocados al mercado de compraventa de vivienda principal pueden tener efectos colaterales sobre el sector del alquiler, como resultado de un cambio composicional en la propiedad inmobiliaria desde ocupantes propietarios hacia inversores en vivienda para alquilar que afecta tanto a la oferta como a la demanda de viviendas en alquiler.We develop an agent-based model of the UK housing market to study the impact of macroprudential policy experiments on key housing market indicators. The heterogeneous nature of this model enables us to assess the effects of such experiments on the housing, rental and mortgage markets not only in the aggregate, but also at the level of individual households and sub-segments, such as first-time buyers, homeowners, buy-to-let investors, and renters. This approach can therefore offer a broad picture of the disaggregated effects of financial stability policies. The model is calibrated using a large selection of micro-data, including data from a leading UK real estate online search engine as well as loan-level regulatory data. With a series of comparative statics exercises, we investigate the impact of: i) a hard loan-to-value limit, and ii) a soft loan-to-income limit, allowing for a limited share of unconstrained new mortgages. We find that, first, these experiments tend to mitigate the house price cycle by reducing credit availability and therefore leverage. Second, an experiment targeting a specific risk measure may also affect other risk metrics, thus necessitating a careful calibration of the policy to achieve a given reduction in risk. Third, experiments targeting the owner-occupier housing market can spill over to the rental sector, as a compositional shift in home ownership from owner-occupiers to buy-to-let investors affects both the supply of and demand for rental properties

Wi-Fi Handshake: analysis of password patterns in Wi-Fi networks

This work is supported by the General Directorate of Culture, Education and University Management of Xunta de Galicia (Ref. ED431G/01, ED431D 2017/16), the Galician Network for Colorectal Cancer Research (Ref. ED431D 2017/23), Competitive Reference Groups (Ref. ED431C 2018/49) and the Spanish Ministry of Economy and Competitiveness via funding of the unique installation BIOCAI (UNLC08-1E-002, UNLC13-13-3503) and the European Regional Development Funds (FEDER). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.[Abstract]: This article seeks to provide a snapshot of the security of Wi-Fi access points in the metropolitan area of A Coruña. First, we discuss the options for obtaining a tool that allows the collection and storage of auditable information from Wi-Fi networks, from location to signal strength, security protocol or the list of connected clients. Subsequently, an analysis is carried out aimed at identifying password patterns in Wi-Fi networks with WEP, WPA and WPA2 security protocols. For this purpose, a password recovery tool called Hashcat was used to execute dictionary or brute force attacks, among others, with various word collections. The coverage of the access points in which passwords were decrypted is displayed on a heat map that represents various levels of signal quality depending on the signal strength. From the handshakes obtained, and by means of brute force, we will try to crack as many passwords as possible in order to create a targeted and contextualized dictionary both by geographical location and by the nature of the owner of the access point. Finally, we will propose a contextualized grammar that minimizes the size of the dictionary with respect to the most used ones and unifies the decryption capacity of the combination of all of them.Xunta de Galicia; ED431G/01Xunta de Galicia; ED431D 2017/16Xunta de Galicia; ED431D 2017/23Xunta de Galicia; ED431C 2018/4

The role of noise and initial conditions in the asymptotic solution of a bounded confidence, continuous-opinion model

We study a model for continuous-opinion dynamics under bounded confidence. In particular, we analyze the importance of the initial distribution of opinions in determining the asymptotic configuration. Thus, we sketch the structure of attractors of the dynamical system, by means of the numerical computation of the time evolution of the agents density. We show that, for a given bound of confidence, a consensus can be encouraged or prevented by certain initial conditions. Furthermore, a noisy perturbation is added to the system with the purpose of modeling the free will of the agents. As a consequence, the importance of the initial condition is partially replaced by that of the statistical distribution of the noise. Nevertheless, we still find evidence of the influence of the initial state upon the final configuration for a short range of the bound of confidence parameter

Individual-based models of collective dynamics in socio-economic systems

The main purpose of this thesis is to contribute to the understanding of how complex collective behaviors emerge in social and economic systems. To this end, we use a combination of mathematical analysis and computational simulations along the lines of the agent- or individual-based modeling paradigm. In particular, we focus on three main topics: opinion dynamics, herding behavior in financial markets, and language competition. Opinion dynamics models focus on the processes of opinion formation within a society consisting of an ensemble of interacting individuals with diverse opinions. One of the main problems addressed by these models is whether these processes of opinion formation will eventually lead to the emergence of a consensus within the society or to the fragmentation of its constituent individuals into different opinion groups. We are interested here in situations where the particular issue under consideration allows for opinions to vary continuously, and thus opinions are modeled as real variables. In particular, we focus on a model consisting of two mechanisms or rules for the evolution of the agents' opinions: a mechanism of social influence, by which two interacting agents reach a compromise at the midpoint opinion, and a mechanism of homophily, by which two agents do only interact if their opinion difference is less than a given threshold value. In this context, we study the influence of the initial distribution of opinions in the asymptotic solution of the model. Financial time series are characterized by a number of stylized facts or non-Gaussian statistical regularities found across a wide range of markets, assets and time periods, such as volatility clustering or fat-tailed distributions of returns. A growing number of contributions based on heterogeneous interacting agents have interpreted these stylized facts as the macroscopic outcome of the diversity among the economic actors, and the interplay and connections between them. In particular, we focus here on a stochastic model of information transmission in financial markets based on a competition between pairwise copying interactions between market agents (herding behavior) and random changes of state (idiosyncratic behavior). On the one hand, we develop a generalization of this herding model accounting for the arrival of information from external sources, and study the influence of this incoming information on the market. On the other hand, we study a network-embedded version of the herding model and focus on the influence of the underlying topology of interactions on the asymptotic behavior of the system. Language competition models address the dynamics of language use in multilingual social systems due to social interactions. The main goal of these models is to distinguish between the interaction mechanisms that lead to the coexistence of different languages and those leading to the extinction of all but one of them. While traditionally conceptualized as a property of the speaker, it has been recently proposed that the use of a language can be more clearly described as a feature of the relationship between two speakers ---a link state--- than as an attribute of the speakers themselves ---a node state---. Inspired by this link-state perspective, we first develop a coevolving model that couples a majority rule dynamics of link states with the evolution of the network topology due to random rewiring of links in a local minority. Finally, we develop a model where the coupled dynamics of language use, as a property of the links between speakers, and language preference, as a property of the speakers themselves, are considered in a fixed network topology.El propósito principal de esta tesis es el de contribuir a la comprensión del modo en el que comportamientos colectivos complejos emergen en sistemas sociales y económicos. En particular, nos centramos en tres temas principales: dinámica de opiniones, comportamiento gregario en mercados financieros y competición lingüística. Los modelos de dinámica de opiniones se centran en los procesos de formación de opiniones en el seno de una sociedad compuesta por un conjunto de individuos en interacción y con opiniones diversas. Uno de los principales problemas abordados por estos modelos es el de determinar si estos procesos de formación de opiniones llevan a la emergencia de un consenso en la sociedad, o si llevan a la segregación de los individuos en diferentes grupos. Nos interesamos aquí por situaciones en las que el asunto que se discute permite la existencia de un contínuo de opiniones y por tanto las opiniones pueden ser modeladas como variables reales. En particular, nos centramos en un modelo consistente en dos mecanismos para la evolución de las opiniones: un mecanismo de influencia social, por el cual dos agentes interaccionantes llegan a un compromiso en el punto medio entre sus opiniones, y un mecanismo de homofilia, por el cual dos agentes interaccionan únicamente si la diferencia entre sus opiniones es inferior a un cierto umbral. En este contexto, estudiamos la influencia de la distribución inicial de opiniones. Las series temporales financieras están caracterizadas por una serie de hechos estilizados o regularidades estadísticas no gaussianas observadas en un amplio rango de mercados, activos y períodos temporales, como el agrupamiento de la volatilidad o las distribuciones de retornos con colas pesadas. Un número creciente de contribuciones basadas en agentes heterogéneos en interacción han venido a ofrecer una interpretación de estos hechos estilizados como el resultado emergente de la diversidad entre actores económicos y de las interacciones y conexiones entre ellos. En particular, nos centramos aquí en un modelo estocástico de transmisión de información en mercados financieros basado en una competición entre interacciones de copia a pares entre agentes de mercado (comportamiento gregario) y cambios de estado aleatorios (comportamiento idiosincrático). Por un lado, desarrollamos una generalización de este modelo de comportamiento gregario para tener en cuenta la llegada de información desde fuentes externas y estudiamos la influencia de esta información entrante en el mercado. Por otro lado, estudiamos una versión en red del modelo de comportamiento gregario y nos centramos en la influencia de la topología subyacente en el comportamiento asintótico del sistema. Los modelos de competición lingüística abordan la dinámica del uso de lenguas en sistemas sociales multilingües debida a interacciones sociales. El principal objetivo de estos modelos es el de diferenciar entre aquellos mecanismos de interacción que llevan a la coexistencia de diferentes lenguas y aquellos que llevan a la extinción de todas menos una. Aunque tradicionalmente se ha conceptualizado como una propiedad del hablante, recientemente se ha propuesto que el uso de una lengua puede ser más claramente descrito como una propiedad de la relación entre dos hablantes ---un estado del enlace--- que como una propiedad de los hablantes ---un estado del nodo---. Inspirados por esta perspectiva, desarrollamos primero un modelo de coevolución que acopla una dinámica de estados en los enlaces basada en una regla de mayoría con la evolución de la topología de la red debida al re-enlace aleatorio de enlaces en una minoría local. Finalmente, desarrollamos un modelo en el que las dinámicas acopladas de uso de la lengua, como propiedad de los enlaces entre hablantes, y preferencia lingüística, como propiedad de los hablantes mismos, son consideradas en una topología de red fija