Institute for Cross-Disciplinary Physics and Complex Systems

The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications for catalysis and species competition. Inspired by the temporal inhomogeneities found in human interactions, one can introduce ageing in the agents: the probability to update decreases with the time elapsed since the last change. This modified dynamics induces an approach to consensus via coarsening in complex networks. Additionally, multilayer networks produce profound changes in the dynamics of models. In this work, we investigate how a multilayer structure affects the dynamics of an ageing voter model. The system is studied as a function of the fraction of nodes sharing states across layers (multiplexity parameter q ). We find that the dynamics of the system suffers a notable change at an intermediate value q*. Above it, the voter model always orders to an absorbing configuration. While, below, a fraction of the realizations falls into dynamical traps associated to a spontaneous symmetry breaking in which the majority opinion in the different layers takes opposite signs and that due to the ageing indefinitely delay the arrival at the absorbing state.

This chapter contains sections titled: Brownian Motion Stochastic Processes Stochastic Differential Equations White Noise Stochastic Integrals. Itô and Stratonovich Interpretations The Ornstein–Uhlenbeck Process The Fokker–Planck Equation Further Reading and References Exercises

Novel methods for information processing are highly desired in our information-driven society. Inspired by the brain's ability to process information, the recently introduced paradigm known as 'reservoir computing' shows that complex networks can efficiently perform computation. Here we introduce a novel architecture that reduces the usually required large number of elements to a single nonlinear node with delayed feedback. Through an electronic implementation, we experimentally and numerically demonstrate excellent performance in a speech recognition benchmark. Complementary numerical studies also show excellent performance for a time series prediction benchmark. These results prove that delay-dynamical systems, even in their simplest manifestation, can perform efficient information processing. This finding paves the way to feasible and resource-efficient technological implementations of reservoir computing. The paradigm of reservoir computing shows that, like the human brain, complex networks can perform efficient information processing. Here, a simple delay dynamical system is demonstrated that can efficiently perform computations capable of replacing a complex network in reservoir computing.

Community structure is one of the main structural features of networks, revealing both their internal organization and the similarity of their elementary units. Despite the large variety of methods proposed to detect communities in graphs, there is a big need for multi-purpose techniques, able to handle different types of datasets and the subtleties of community structure. In this paper we present OSLOM (Order Statistics Local Optimization Method), the first method capable to detect clusters in networks accounting for edge directions, edge weights, overlapping communities, hierarchies and community dynamics. It is based on the local optimization of a fitness function expressing the statistical significance of clusters with respect to random fluctuations, which is estimated with tools of Extreme and Order Statistics. OSLOM can be used alone or as a refinement procedure of partitions/covers delivered by other techniques. We have also implemented sequential algorithms combining OSLOM with other fast techniques, so that the community structure of very large networks can be uncovered. Our method has a comparable performance as the best existing algorithms on artificial benchmark graphs. Several applications on real networks are shown as well. OSLOM is implemented in a freely available software (http://www.oslom.org), and we believe it will be a valuable tool in the analysis of networks.

The increasing demands on information processing require novel computational concepts and true parallelism. Nevertheless, hardware realizations of unconventional computing approaches never exceeded a marginal existence. While the application of optics in super-computing receives reawakened interest, new concepts, partly neuro-inspired, are being considered and developed. Here we experimentally demonstrate the potential of a simple photonic architecture to process information at unprecedented data rates, implementing a learning-based approach. A semiconductor laser subject to delayed self-feedback and optical data injection is employed to solve computationally hard tasks. We demonstrate simultaneous spoken digit and speaker recognition and chaotic time-series prediction at data rates beyond 1 Gbyte/s. We identify all digits with very low classification errors and perform chaotic time-series prediction with 10% error. Our approach bridges the areas of photonic information processing, cognitive and information science. Inspired by neural networks, reservoir computing uses nonlinear transient states to perform computations, offering faster parallel information processing. Brunner et al.show a photonic approach to reservoir computing capable of simultaneous spoken digit and speaker recognition at high data rates.

A large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength. In recent years, the study of an increasing number of large-scale networks has highlighted the statistical heterogeneity of their interaction pattern, with degree and weight distributions that vary over many orders of magnitude. These features, along with the large number of elements and links, make the extraction of the truly relevant connections forming the network's backbone a very challenging problem. More specifically, coarse-graining approaches and filtering techniques come into conflict with the multiscale nature of large-scale systems. Here, we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks, preserving the edges that represent statistically significant deviations with respect to a null model for the local assignment of weights to edges. An important aspect of the method is that it does not belittle small-scale interactions and operates at all scales defined by the weight distribution. We apply our method to real-world network instances and compare the obtained results with alternative backbone extraction techniques.

Oceans have become substantially noisier since the Industrial Revolution. Shipping, resource exploration, and infrastructure development have increased the anthrophony (sounds generated by human activities), whereas the biophony (sounds of biological origin) has been reduced by hunting, fishing, and habitat degradation. Climate change is affecting geophony (abiotic, natural sounds). Existing evidence shows that anthrophony affects marine animals at multiple levels, including their behavior, physiology, and, in extreme cases, survival. This should prompt management actions to deploy existing solutions to reduce noise levels in the ocean, thereby allowing marine animals to reestablish their use of ocean sound as a central ecological trait in a healthy ocean.

Many information processing challenges are difficult to solve with traditional Turing or von Neumann approaches. Implementing unconventional computational methods is therefore essential and optics provides promising opportunities. Here we experimentally demonstrate optical information processing using a nonlinear optoelectronic oscillator subject to delayed feedback. We implement a neuro-inspired concept, called Reservoir Computing, proven to possess universal computational capabilities. We particularly exploit the transient response of a complex dynamical system to an input data stream. We employ spoken digit recognition and time series prediction tasks as benchmarks, achieving competitive processing figures of merit.

The subtropical ocean gyres are recognized as great marine accummulation zones of floating plastic debris; however, the possibility of plastic accumulation at polar latitudes has been overlooked because of the lack of nearby pollution sources. In the present study, the Arctic Ocean was extensively sampled for floating plastic debris from the Tara Oceans circumpolar expedition. Although plastic debris was scarce or absent in most of the Arctic waters, it reached high concentrations (hundreds of thousands of pieces per square kilometer) in the northernmost and easternmost areas of the Greenland and Barents seas. The fragmentation and typology of the plastic suggested an abundant presence of aged debris that originated from distant sources. This hypothesis was corroborated by the relatively high ratios of marine surface plastic to local pollution sources. Surface circulation models and field data showed that the poleward branch of the Thermohaline Circulation transfers floating debris from the North Atlantic to the Greenland and Barents seas, which would be a dead end for this plastic conveyor belt. Given the limited surface transport of the plastic that accumulated here and the mechanisms acting for the downward transport, the seafloor beneath this Arctic sector is hypothesized as an important sink of plastic debris.

Complex phenomena in photonics, in particular, dynamical properties of semiconductor lasers due to delayed coupling, are reviewed. Although considered a nuisance for a long time, these phenomena now open interesting perspectives. Semiconductor laser systems represent excellent test beds for the study of nonlinear delay-coupled systems, which are of fundamental relevance in various areas. At the same time delay-coupled lasers provide opportunities for photonic applications. In this review an introduction into the properties of single and two delay-coupled lasers is followed by an extension to network motifs and small networks. A particular emphasis is put on emerging complex behavior, deterministic chaos, synchronization phenomena, and application of these properties that range from encrypted communication and fast random bit sequence generators to bioinspired information processing.

Abstract We review a novel paradigm that has emerged in analogue neuromorphic optical computing. The goal is to implement a reservoir computer in optics, where information is encoded in the intensity and phase of the optical field. Reservoir computing is a bio‐inspired approach especially suited for processing time‐dependent information. The reservoir’s complex and high‐dimensional transient response to the input signal is capable of universal computation. The reservoir does not need to be trained, which makes it very well suited for optics. As such, much of the promise of photonic reservoirs lies in their minimal hardware requirements, a tremendous advantage over other hardware‐intensive neural network models. We review the two main approaches to optical reservoir computing: networks implemented with multiple discrete optical nodes and the continuous system of a single nonlinear device coupled to delayed feedback.

After the emergence of the H1N1 influenza in 2009, some countries responded with travel-related controls during the early stage of the outbreak in an attempt to contain or slow down its international spread. These controls along with self-imposed travel limitations contributed to a decline of about 40% in international air traffic to/from Mexico following the international alert. However, no containment was achieved by such restrictions and the virus was able to reach pandemic proportions in a short time. When gauging the value and efficacy of mobility and travel restrictions it is crucial to rely on epidemic models that integrate the wide range of features characterizing human mobility and the many options available to public health organizations for responding to a pandemic. Here we present a comprehensive computational and theoretical study of the role of travel restrictions in halting and delaying pandemics by using a model that explicitly integrates air travel and short-range mobility data with high-resolution demographic data across the world and that is validated by the accumulation of data from the 2009 H1N1 pandemic. We explore alternative scenarios for the 2009 H1N1 pandemic by assessing the potential impact of mobility restrictions that vary with respect to their magnitude and their position in the pandemic timeline. We provide a quantitative discussion of the delay obtained by different mobility restrictions and the likelihood of containing outbreaks of infectious diseases at their source, confirming the limited value and feasibility of international travel restrictions. These results are rationalized in the theoretical framework characterizing the invasion dynamics of the epidemics at the metapopulation level.

Studies of cultural differentiation have shown that social mechanisms that normally lead to cultural convergence—homophily and influence—can also explain how distinct cultural groups can form. However, this emergent cultural diversity has proven to be unstable in the face of cultural drift—small errors or innovations that allow cultures to change from within. The authors develop a model of cultural differentiation that combines the traditional mechanisms of homophily and influence with a third mechanism of network homophily, in which network structure co-evolves with cultural interaction. Results show that in certain regions of the parameter space, these co-evolutionary dynamics can lead to patterns of cultural diversity that are stable in the presence of cultural drift. The authors address the implications of these findings for understanding the stability of cultural diversity in the face of increasing technological trends toward globalization.

Pervasive infrastructures, such as cell phone networks, enable to capture large amounts of human behavioral data but also provide information about the structure of cities and their dynamical properties. In this article, we focus on these last aspects by studying phone data recorded during 55 days in 31 Spanish cities. We first define an urban dilatation index which measures how the average distance between individuals evolves during the day, allowing us to highlight different types of city structure. We then focus on hotspots, the most crowded places in the city. We propose a parameter free method to detect them and to test the robustness of our results. The number of these hotspots scales sublinearly with the population size, a result in agreement with previous theoretical arguments and measures on employment datasets. We study the lifetime of these hotspots and show in particular that the hierarchy of permanent ones, which constitute the 'heart' of the city, is very stable whatever the size of the city. The spatial structure of these hotspots is also of interest and allows us to distinguish different categories of cities, from monocentric and "segregated" where the spatial distribution is very dependent on land use, to polycentric where the spatial mixing between land uses is much more important. These results point towards the possibility of a new, quantitative classification of cities using high resolution spatio-temporal data.

The segmentation clock is an oscillating genetic network thought to govern the rhythmic and sequential subdivision of the elongating body axis of the vertebrate embryo into somites: the precursors of the segmented vertebral column. Understanding how the rhythmic signal arises, how it achieves precision and how it patterns the embryo remain challenging issues. Recent work has provided evidence of how the period of the segmentation clock is regulated and how this affects the anatomy of the embryo. The ongoing development of real-time clock reporters and mathematical models promise novel insight into the dynamic behavior of the clock.

The increasing integration of technology into our lives has created unprecedented volumes of data on society’s everyday behaviour. Such data opens up exciting new opportunities to work towards a quantitative understanding of our complex social systems, within the realms of a new discipline known as Computational Social Science. Against a background of financial crises, riots and international epidemics, the urgent need for a greater comprehension of the complexity of our interconnected global society and an ability to apply such insights in policy decisions is clear. This manifesto outlines the objectives of this new scientific direction, considering the challenges involved in it, and the extensive impact on science, technology and society that the success of this endeavour is likely to bring about.

Photonic neural network implementation has been gaining considerable attention as a potentially disruptive future technology. Demonstrating learning in large-scale neural networks is essential to establish photonic machine learning substrates as viable information processing systems. Realizing photonic neural networks with numerous nonlinear nodes in a fully parallel and efficient learning hardware has been lacking so far. We demonstrate a network of up to 2025 diffractively coupled photonic nodes, forming a large-scale recurrent neural network. Using a digital micro mirror device, we realize reinforcement learning. Our scheme is fully parallel, and the passive weights maximize energy efficiency and bandwidth. The computational output efficiently converges, and we achieve very good performance.

Micro-blogging systems such as Twitter expose digital traces of social discourse with an unprecedented degree of resolution of individual behaviors. They offer an opportunity to investigate how a large-scale social system responds to exogenous or endogenous stimuli, and to disentangle the temporal, spatial and topical aspects of users' activity. Here we focus on spikes of collective attention in Twitter, and specifically on peaks in the popularity of hashtags. Users employ hashtags as a form of social annotation, to define a shared context for a specific event, topic, or meme. We analyze a large-scale record of Twitter activity and find that the evolution of hashtag popularity over time defines discrete classes of hashtags. We link these dynamical classes to the events the hashtags represent and use text mining techniques to provide a semantic characterization of the hashtag classes. Moreover, we track the propagation of hashtags in the Twitter social network and find that epidemic spreading plays a minor role in hashtag popularity, which is mostly driven by exogenous factors.

Multielectrode recordings have revealed zero time lag synchronization among remote cerebral cortical areas. However, the axonal conduction delays among such distant regions can amount to several tens of milliseconds. It is still unclear which mechanism is giving rise to isochronous discharge of widely distributed neurons, despite such latencies. Here, we investigate the synchronization properties of a simple network motif and found that, even in the presence of large axonal conduction delays, distant neuronal populations self-organize into lag-free oscillations. According to our results, cortico-cortical association fibers and certain cortico-thalamo-cortical loops represent ideal circuits to circumvent the phase shifts and time lags associated with conduction delays.

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