Hierarchically nested networks optimize the analysis of audiovisual speech

In conversational settings, seeing the speaker’s face elicits internal predictions about the upcoming acoustic utterance. Understanding how the listener’s cortical dynamics tune to the temporal statistics of audiovisual (AV) speech is thus essential. Using magnetoencephalography, we explored how large-scale frequency-specific dynamics of human brain activity adapt to AV speech delays. First, we show that the amplitude of phase-locked responses parametrically decreases with natural AV speech synchrony, a pattern that is consistent with predictive coding. Second, we show that the temporal statistics of AV speech affect large-scale oscillatory networks at multiple spatial and temporal resolutions. We demonstrate a spatial nestedness of oscillatory networks during the processing of AV speech: these oscillatory hierarchies are such that high-frequency activity (beta, gamma) is contingent on the phase response of low-frequency (delta, theta) networks. Our findings suggest that the endogenous temporal multiplexing of speech processing confers adaptability within the temporal regimes that are essential for speech comprehension

Synchronization in Complex Networks Under Uncertainty

La sincronització en xarxes és la música dels sistemes complexes. Els ritmes col·lectius que emergeixen de molts oscil·ladors acoblats expliquen el batec constant del cor, els patrons recurrents d'activitat neuronal i la sincronia descentralitzada a les xarxes elèctriques. Els models matemàtics són sòlids i han avançat significativament, especialment en el problema del camp mitjà, on tots els oscil·ladors estan connectats mútuament. Tanmateix, les xarxes reals tenen interaccions complexes que dificulten el tractament analític. Falta un marc general i les soluciones existents en caixes negres numèriques i espectrals dificulten la interpretació. A més, la informació obtinguda en mesures empíriques sol ser incompleta. Motivats per aquestes limitacions, en aquesta tesi proposem un estudi teòric dels oscil·ladors acoblats en xarxes sota incertesa. Apliquem propagació d'errors per predir com una estructura complexa amplifica el soroll des dels pesos microscòpics fins al punt crític de sincronització, estudiem l'efecte d'equilibrar les interaccions de parelles i d'ordre superior en l'optimització de la sincronia i derivem esquemes d'ajust de pesos per mapejar el comportament de sincronització en xarxes diferents. A més, un desplegament geomètric rigorós de l'estat sincronitzat ens permet abordar escenaris descentralitzats i descobrir regles locals òptimes que indueixen transicions globals abruptes. Finalment, suggerim dreceres espectrals per predir punts crítics amb àlgebra lineal i representacions aproximades de xarxa. En general, proporcionem eines analítiques per tractar les xarxes d'oscil·ladors en condicions sorolloses i demostrem que darrere els supòsits predominants d'informació completa s'amaguen explicacions mecanicistes clares. Troballes rellevants inclouen xarxes particulars que maximitzen el ventall de comportaments i el desplegament exitós del binomi estructura-dinàmica des d'una perspectiva local. Aquesta tesi avança la recerca d'una teoria general de la sincronització en xarxes a partir de principis mecanicistes i geomètrics, una peça clau que manca en l'anàlisi, disseny i control de xarxes neuronals biològiques i artificials i sistemes d'enginyeria complexos.La sincronización en redes es la música de los sistemas complejos. Los ritmos colectivos que emergen de muchos osciladores acoplados explican el latido constante del corazón, los patrones recurrentes de actividad neuronal y la sincronía descentralizada de las redes eléctricas. Los modelos matemáticos son sólidos y han avanzado significativamente, especialmente en el problema del campo medio, donde todos los osciladores están conectados entre sí. Sin embargo, las redes reales tienen interacciones complejas que dificultan el tratamiento analítico. Falta un marco general y las soluciones en cajas negras numéricas y espectrales dificultan la interpretación. Además, las mediciones empíricas suelen ser incompletas. Motivados por estas limitaciones, en esta tesis proponemos un estudio teórico de osciladores acoplados en redes bajo incertidumbre. Aplicamos propagación de errores para predecir cómo una estructura compleja amplifica el ruido desde las conexiones microscópicas hasta puntos críticos macroscópicos, estudiamos el efecto de equilibrar interacciones por pares y de orden superior en la optimización de la sincronía y derivamos esquemas de ajuste de pesos para mapear el comportamiento en estructuras distintas. Una expansión geométrica del estado sincronizado nos permite abordar escenarios descentralizados y descubrir reglas locales que inducen transiciones abruptas globales. Por último, sugerimos atajos espectrales para predecir puntos críticos usando álgebra lineal y representaciones aproximadas de red. En general, proporcionamos herramientas analíticas para manejar redes de osciladores en condiciones ruidosas y demostramos que detrás de las suposiciones predominantes de información completa se ocultaban claras explicaciones mecanicistas. Hallazgos relevantes incluyen redes particulares que maximizan el rango de comportamientos y la explicación del binomio estructura-dinámica desde una perspectiva local. Esta tesis avanza en la búsqueda de una teoría general de sincronización en redes desde principios mecánicos y geométricos, una pieza clave que falta en el análisis, diseño y control de redes neuronales biológicas y artificiales y sistemas de ingeniería complejos.Synchronization in networks is the music of complex systems. Collective rhythms emerging from many interacting oscillators appear across all scales of nature, from the steady heartbeat and the recurrent patterns in neuronal activity to the decentralized synchrony in power-grids. The mathematics behind these processes are solid and have significantly advanced lately, especially in the mean-field problem, where oscillators are all mutually connected. However, real networks have complex interactions that difficult the analytical treatment. A general framework is missing and most existing results rely on numerical and spectral black-boxes that hinder interpretation. Also, the information obtained from measurements is usually incomplete. Motivated by these limitations, in this thesis we propose a theoretical study of network-coupled oscillators under uncertainty. We apply error propagation to predict how a complex structure amplifies noise from the link weights to the synchronization onset, study the effect of balancing pair-wise and higher-order interactions in synchrony optimization, and derive weight-tuning schemes to map the synchronization behavior of different structures. Also, we develop a rigorous geometric unfolding of the synchronized state to tackle decentralized scenarios and to discover optimal local rules that induce global abrupt transitions. Last, we suggest spectral shortcuts to predict critical points using linear algebra and network representations with limited information. Overall, we provide analytical tools to deal with oscillator networks under noisy conditions and prove that mechanistic explanations were hidden behind the prevalent assumptions of complete information. Relevant finding include particular networks that maximize the range of behaviors and the successful unfolding of the structure-dynamics interplay from a local perspective. This thesis advances the quest of a general theory of network synchronization built from mechanistic and geometric principles, a key missing piece in the analysis, design and control of biological and artificial neural networks and complex engineering systems

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

Macroscopic insights from mechanistic ecological network models in a data void

Complexity science has come into the limelight in recent years as the scientific community begins to grapple with higher-order natural phenomena that cannot be fully explained via the behaviour of components at lower levels of organization. Network modeling and analysis, being a powerful tool that can capture the interconnections that embody complex behaviour, has therefore been at the forefront of complexity science. In ecology, the network paradigm is relatively young and there remain limitations in many ecological network studies, such as modeling only one type of species interaction at a time, lack of realistic network structure, or non-inclusion of community dynamics and environmental stochasticity. I introduce bioenergetic network models that bring together for the first time many of the fundamental structures and mechanisms of species interactions present in real ecological communities. I then use these models to address some outstanding questions that are relevant to understanding ecological networks at the systems level rather than at the level of subsets of interactions. Firstly, I find that realistic red-shifted environmental noise, and synchrony of species responses to noise, are associated with increased variability in ecosystem properties, with implications for predictive ecological modeling which usually assumes white noise. Next, I look at simultaneous species extinction and invasion, finding that as their individual impacts increase, their combined impact becomes decreasingly additive. In addition, the greater the impact of extinction or invasion, the lesser their reversibility via reintroduction or eradication of the species in question. For modifications of pairwise species interactions by third-party species, a phenomenon that has so far been studied one interaction at a time, I find that the many interaction modifications that occur concurrently in a community can collectively have systematic effects on total biomass and species evenness. Finally, examining a higher level of organization in the form of compartmentalized networks, I find that the relationship between intercompartment connectivity and the impacts of species decline depends considerably on network topology and whether the consumer-resource functional response is prey- or ratio-dependent. Overall, the results vary considerably across model communities with different parameterizations, underscoring the contingency and context dependence of nature that scientists and policy makers alike should no longer ignore. This work hopes to contribute to a growing multidisciplinary understanding, appreciation and management of complex systems that is fundamentally transforming the modern world and giving us insights on how to live more harmoniously within our environment

Macroscopic insights from mechanistic ecological network models in a data void

Complexity science has come into the limelight in recent years as the scientific community begins to grapple with higher-order natural phenomena that cannot be fully explained via the behaviour of components at lower levels of organization. Network modeling and analysis, being a powerful tool that can capture the interconnections that embody complex behaviour, has therefore been at the forefront of complexity science. In ecology, the network paradigm is relatively young and there remain limitations in many ecological network studies, such as modeling only one type of species interaction at a time, lack of realistic network structure, or non-inclusion of community dynamics and environmental stochasticity. I introduce bioenergetic network models that bring together for the first time many of the fundamental structures and mechanisms of species interactions present in real ecological communities. I then use these models to address some outstanding questions that are relevant to understanding ecological networks at the systems level rather than at the level of subsets of interactions. Firstly, I find that realistic red-shifted environmental noise, and synchrony of species responses to noise, are associated with increased variability in ecosystem properties, with implications for predictive ecological modeling which usually assumes white noise. Next, I look at simultaneous species extinction and invasion, finding that as their individual impacts increase, their combined impact becomes decreasingly additive. In addition, the greater the impact of extinction or invasion, the lesser their reversibility via reintroduction or eradication of the species in question. For modifications of pairwise species interactions by third-party species, a phenomenon that has so far been studied one interaction at a time, I find that the many interaction modifications that occur concurrently in a community can collectively have systematic effects on total biomass and species evenness. Finally, examining a higher level of organization in the form of compartmentalized networks, I find that the relationship between intercompartment connectivity and the impacts of species decline depends considerably on network topology and whether the consumer-resource functional response is prey- or ratio-dependent. Overall, the results vary considerably across model communities with different parameterizations, underscoring the contingency and context dependence of nature that scientists and policy makers alike should no longer ignore. This work hopes to contribute to a growing multidisciplinary understanding, appreciation and management of complex systems that is fundamentally transforming the modern world and giving us insights on how to live more harmoniously within our environment

Structure-oriented prediction in complex networks

Complex systems are extremely hard to predict due to its highly nonlinear interactions and rich emergent properties. Thanks to the rapid development of network science, our understanding of the structure of real complex systems and the dynamics on them has been remarkably deepened, which meanwhile largely stimulates the growth of effective prediction approaches on these systems. In this article, we aim to review different network-related prediction problems, summarize and classify relevant prediction methods, analyze their advantages and disadvantages, and point out the forefront as well as critical challenges of the field