53 research outputs found

    Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching

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    © 2020, The Author(s). Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units, i.e., three- and four-way interactions in addition to pairwise interactions, and their role in shaping collective behavior. Here we show that higher-order interactions between coupled phase oscillators, encoded microscopically in a simplicial complex, give rise to added nonlinearity in the macroscopic system dynamics that induces abrupt synchronization transitions via hysteresis and bistability of synchronized and incoherent states. Moreover, these higher-order interactions can stabilize strongly synchronized states even when the pairwise coupling is repulsive. These findings reveal a self-organized phenomenon that may be responsible for the rapid switching to synchronization in many biological and other systems that exhibit synchronization without the need of particular correlation mechanisms between the oscillators and the topological structure

    An Initial Framework Assessing the Safety of Complex Systems

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    Trabajo presentado en la Conference on Complex Systems, celebrada online del 7 al 11 de diciembre de 2020.Atmospheric blocking events, that is large-scale nearly stationary atmospheric pressure patterns, are often associated with extreme weather in the mid-latitudes, such as heat waves and cold spells which have significant consequences on ecosystems, human health and economy. The high impact of blocking events has motivated numerous studies. However, there is not yet a comprehensive theory explaining their onset, maintenance and decay and their numerical prediction remains a challenge. In recent years, a number of studies have successfully employed complex network descriptions of fluid transport to characterize dynamical patterns in geophysical flows. The aim of the current work is to investigate the potential of so called Lagrangian flow networks for the detection and perhaps forecasting of atmospheric blocking events. The network is constructed by associating nodes to regions of the atmosphere and establishing links based on the flux of material between these nodes during a given time interval. One can then use effective tools and metrics developed in the context of graph theory to explore the atmospheric flow properties. In particular, Ser-Giacomi et al. [1] showed how optimal paths in a Lagrangian flow network highlight distinctive circulation patterns associated with atmospheric blocking events. We extend these results by studying the behavior of selected network measures (such as degree, entropy and harmonic closeness centrality)at the onset of and during blocking situations, demonstrating their ability to trace the spatio-temporal characteristics of these events.This research was conducted as part of the CAFE (Climate Advanced Forecasting of sub-seasonal Extremes) Innovative Training Network which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 813844

    Synchronization in Complex Networks Under Uncertainty

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    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

    MediaSync: Handbook on Multimedia Synchronization

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    This book provides an approachable overview of the most recent advances in the fascinating field of media synchronization (mediasync), gathering contributions from the most representative and influential experts. Understanding the challenges of this field in the current multi-sensory, multi-device, and multi-protocol world is not an easy task. The book revisits the foundations of mediasync, including theoretical frameworks and models, highlights ongoing research efforts, like hybrid broadband broadcast (HBB) delivery and users' perception modeling (i.e., Quality of Experience or QoE), and paves the way for the future (e.g., towards the deployment of multi-sensory and ultra-realistic experiences). Although many advances around mediasync have been devised and deployed, this area of research is getting renewed attention to overcome remaining challenges in the next-generation (heterogeneous and ubiquitous) media ecosystem. Given the significant advances in this research area, its current relevance and the multiple disciplines it involves, the availability of a reference book on mediasync becomes necessary. This book fills the gap in this context. In particular, it addresses key aspects and reviews the most relevant contributions within the mediasync research space, from different perspectives. Mediasync: Handbook on Multimedia Synchronization is the perfect companion for scholars and practitioners that want to acquire strong knowledge about this research area, and also approach the challenges behind ensuring the best mediated experiences, by providing the adequate synchronization between the media elements that constitute these experiences

    Network Formation and Dynamics under Economic Constraints

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    Networks describe a broad range of systems across a wide variety of topics from social and economic interactions over technical infrastructures such as power grids and the internet to biological contexts such as food webs or neural networks. A number of large scale failures and events in these interconnected systems in recent years has shown that understanding the behavior of individual units of these networks is not necessarily sufficient to handle the increasing complexity of these systems. Many theoretical models have been studied to understand the fundamental mechanisms underlying the formation and function of networked systems and a general framework was developed to describe and understand networked systems. However, most of these models ignore a constraint that affects almost all realistic systems: limited resources. In this thesis I study the effects of economic constraints, such as a limited budget or cost minimization, both on the control of network formation and dynamics as well as on network formation itself. I introduce and analyze a new coupling scheme for coupled dynamical systems, showing that synchronization of chaotic units can be enhanced by restricting the interactions based on the states of the individual units, thus saving interactions costs. This new interaction scheme guarantees synchronizability of arbitrary networks of coupled chaotic oscillators, independent of the network topology even with strongly limited interactions. I then propose a new order parameter to measure the degree of phase coherence of networks of coupled phase oscillators. This new order parameter accurately describes the phase coherence in all stages of incoherent movement, partial and full phase locking up to full synchrony. Importantly, I analytically relate this order parameter directly to the stability of the phase locked state. In the second part, I consider the formation of networks under economic constraints from two different points of view. First I study the effects of explicitly limited resources on the control of random percolation, showing that optimal control can have undesired side effects. Specifically, maximal delay of percolation with a limited budget results in a discontinuous percolation transition, making the transition itself uncontrollable in the sense that a single link can have a macroscopic effect on the connectivity. Finally, I propose a model where network formation is driven by cost minimization of the individual nodes in the network. Based on a simple economically motivated supply problem, the resulting network structure is given as the solution of a large number of individual but interaction optimization problem. I show that these network states directly correspond to the final states of a local percolation algorithm and analyze the effects of local optimization on the network formation process. Overall, I reveal mechanisms and phenomena introduced by these economic constraints that are typically not considered in the standard models, showing that economic constraints can strongly alter the formation and function of networked systems. Thereby, I extend the theoretical understanding that we have of networked systems to economic considerations. I hope that this thesis enables better prediction and control networked systems in realistic settings

    Modeling phase synchronization of interacting neuronal populations:from phase reductions to collective behavior of oscillatory neural networks

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    Synchronous, coherent interaction is key for the functioning of our brain. The coordinated interplay between neurons and neural circuits allows to perceive, process and transmit information in the brain. As such, synchronization phenomena occur across all scales. The coordination of oscillatory activity between cortical regions is hypothesized to underlie the concept of phase synchronization. Accordingly, phase models have found their way into neuroscience. The concepts of neural synchrony and oscillations are introduced in Chapter 1 and linked to phase synchronization phenomena in oscillatory neural networks. Chapter 2 provides the necessary mathematical theory upon which a sound phase description builds. I outline phase reduction techniques to distill the phase dynamics from complex oscillatory networks. In Chapter 3 I apply them to networks of weakly coupled Brusselators and of Wilson-Cowan neural masses. Numerical and analytical approaches are compared against each other and their sensitivity to parameter regions and nonlinear coupling schemes is analysed. In Chapters 4 and 5 I investigate synchronization phenomena of complex phase oscillator networks. First, I study the effects of network-network interactions on the macroscopic dynamics when coupling two symmetric populations of phase oscillators. This setup is compared against a single network of oscillators whose frequencies are distributed according to a symmetric bimodal Lorentzian. Subsequently, I extend the applicability of the Ott-Antonsen ansatz to parameterdependent oscillatory systems. This allows for capturing the collective dynamics of coupled oscillators when additional parameters influence the individual dynamics. Chapter 6 draws the line to experimental data. The phase time series of resting state MEG data display large-scale brain activity at the edge of criticality. After reducing neurophysiological phase models from the underlying dynamics of Wilson-Cowan and Freeman neural masses, they are analyzed with respect to two complementary notions of critical dynamics. A general discussion and an outlook of future work are provided in the final Chapter 7

    Minimal Diagnosis and Diagnosability of Discrete-Event Systems Modeled by Automata

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    In the last several decades, the model-based diagnosis of discrete-event systems (DESs) has increasingly become an active research topic in both control engineering and artificial intelligence. However, in contrast with the widely applied minimal diagnosis of static systems, in most approaches to the diagnosis of DESs, all possible candidate diagnoses are computed, including nonminimal candidates, which may cause intractable complexity when the number of nonminimal diagnoses is very large. According to the principle of parsimony and the principle of joint-probability distribution, generally, the minimal diagnosis of DESs is preferable to a nonminimal diagnosis. To generate more likely diagnoses, the notion of the minimal diagnosis of DESs is presented, which is supported by a minimal diagnoser for the generation of minimal diagnoses. Moreover, to either strongly or weakly decide whether a minimal set of faulty events has definitely occurred or not, two notions of minimal diagnosability are proposed. Necessary and sufficient conditions for determining the minimal diagnosability of DESs are proven. The relationships between the two types of minimal diagnosability and the classical diagnosability are analysed in depth

    Investigation of the impact of fibre impairments and SOA-based devices on 2D-WH/TS OCDMA codes

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    In seeking efficient last-mile solutions for high-capacity, optical code division multiple access (OCDMA) emerges as a promising alternative high-speed optical network that can securely support a multitude of simultaneous users without requiring extensive equipment. This multiplexing technique has recently been the subject of comprehensive research, highlighting its potential for facilitating high-bandwidth multi-access networking. When contrasted with techniques such as wavelength division multiplexing (WDM) and optical time division multiplexing (OTDM), OCDMA offers a more effective and equitable split of available fibre bandwidth among the users. This thesis presents my research focused on the incoherent OCDMA under the influence of optical fibre impairments that uses picosecond multiwavelength pulses to form two-dimensional wavelength hopping time-spreading (2D-WH/TS) incoherent OCDMA codes. In particular, self-phase modulation, temperature induced fibre dispersion, chromatic dispersion, as well as the impact of semiconductor optical amplifier SOA devices deployment on 2D-WH/TS OCDMA code integrity were investigated. These aspects were investigated using a 17-km long bidirectional fibre link between Strathclyde and Glasgow University. In particular, I investigated the impact of temporal skewing among OCDMA code carriers and the importance of selecting small range of wavelengths as code carriers where wide range manifest high dependency on wavelength. This wavelength dependency is exploited furthermore to measure the induced temperature dispersion coefficient accurately and economically. I have conducted experiments to characterise the impact of SOA-device on 2D OCDMA code carries which is evaluated under different bias conditions. This evaluation addressed the potential challenges and ramifications of the gain recovery time of SOA and its wavelength dependency with respect to gain ratio and self-phase modulation (SPM). The OCDMA code was built using multiplexers and delay lines to create a 2D OCDMA code to allow studying the impact of deploying a SOA under different conditions on each wavelength. The concept described above is then extended to the investigation of the SOA’s impact on a 2D-WH/TS OCDMA prime code under high bias current/gain conditions. The overall performance of two different 2D-WH/TS OCDMA systems deploying the SOA was also calculated. I have also investigated the possibility of manipulating chirp in 2D-WH/TS incoherent OCDMA to counteract the self-phase modulation-induced red shift by using single mode fibre and lithium crystals. I have investigated the performance of the picosecond code based optical signal when subjected to temperature variations similar to that experience by most buried fibre systems. I have proposed and demonstrated a novel technique, which I examined analytically and experimentally, that utilises a SOA at the transmitter to create a new code with a new wavelength hopping and spreading time sequences to achieve a unique physical improved secure incoherent OCDMA communication method. A novel fully automated tuneable compensation testbed is also proposed of an autonomous dispersion management in a WH/TS incoherent OCDMA system. The system proposed manipulates the chirp of OCDMA code carriers to limit chromatic dispersion detrimental effect on transmission systems.In seeking efficient last-mile solutions for high-capacity, optical code division multiple access (OCDMA) emerges as a promising alternative high-speed optical network that can securely support a multitude of simultaneous users without requiring extensive equipment. This multiplexing technique has recently been the subject of comprehensive research, highlighting its potential for facilitating high-bandwidth multi-access networking. When contrasted with techniques such as wavelength division multiplexing (WDM) and optical time division multiplexing (OTDM), OCDMA offers a more effective and equitable split of available fibre bandwidth among the users. This thesis presents my research focused on the incoherent OCDMA under the influence of optical fibre impairments that uses picosecond multiwavelength pulses to form two-dimensional wavelength hopping time-spreading (2D-WH/TS) incoherent OCDMA codes. In particular, self-phase modulation, temperature induced fibre dispersion, chromatic dispersion, as well as the impact of semiconductor optical amplifier SOA devices deployment on 2D-WH/TS OCDMA code integrity were investigated. These aspects were investigated using a 17-km long bidirectional fibre link between Strathclyde and Glasgow University. In particular, I investigated the impact of temporal skewing among OCDMA code carriers and the importance of selecting small range of wavelengths as code carriers where wide range manifest high dependency on wavelength. This wavelength dependency is exploited furthermore to measure the induced temperature dispersion coefficient accurately and economically. I have conducted experiments to characterise the impact of SOA-device on 2D OCDMA code carries which is evaluated under different bias conditions. This evaluation addressed the potential challenges and ramifications of the gain recovery time of SOA and its wavelength dependency with respect to gain ratio and self-phase modulation (SPM). The OCDMA code was built using multiplexers and delay lines to create a 2D OCDMA code to allow studying the impact of deploying a SOA under different conditions on each wavelength. The concept described above is then extended to the investigation of the SOA’s impact on a 2D-WH/TS OCDMA prime code under high bias current/gain conditions. The overall performance of two different 2D-WH/TS OCDMA systems deploying the SOA was also calculated. I have also investigated the possibility of manipulating chirp in 2D-WH/TS incoherent OCDMA to counteract the self-phase modulation-induced red shift by using single mode fibre and lithium crystals. I have investigated the performance of the picosecond code based optical signal when subjected to temperature variations similar to that experience by most buried fibre systems. I have proposed and demonstrated a novel technique, which I examined analytically and experimentally, that utilises a SOA at the transmitter to create a new code with a new wavelength hopping and spreading time sequences to achieve a unique physical improved secure incoherent OCDMA communication method. A novel fully automated tuneable compensation testbed is also proposed of an autonomous dispersion management in a WH/TS incoherent OCDMA system. The system proposed manipulates the chirp of OCDMA code carriers to limit chromatic dispersion detrimental effect on transmission systems

    Network Science for IoT

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    The research work presented in this thesis is based on the concept and defintion of network that can spread in several and different real world contexts. Indeed, we can refer to a network in a telecommunications sense considering a collection of transmitters, receivers, and communication channels that send or are used to send information to one another. However, as a matter of fact, in nature there are other several examples of networks: the human brain is one of them. The relationship between the actors in Hollywood can be studied in terms of network as well, a generic social community can be compared to a network, eco-systems are networks of species. The recent Network Science aims at studying all these systems using a set of common mathematical methods. In the following of the thesis, we will focus on some of well known telecommunications networks issues using standard telecommunications procedures to address them, with relevant reference to video flow transmissions and management of electric vehicles networks. At the same time, different models aiming at reach the same goals in contexts that may differ from a telecommunications setup can be used. In more details, we will evaluate queueing systems, jamming problems, groups recognition in networks, and mobile computing using game theoretic approaches. It is worth noting that this aspect can be also seen in a reverse order. Indeed, we will discuss how standard telecommunications analysis can be used to investigate on problems not directly related to a telecommunications background. In particular, one of our future purposes is to investigate on the brain connectivity that is raising significant interest in the recent scientific society
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