Statistical physics of network structure and information dynamics

In the last two decades, network science has proven to be an invaluable tool for the analysis of empirical systems across a wide spectrum of disciplines, with applications to data structures admitting a representation in terms of complex networks. On the one hand, especially in the last decade, an increasing number of applications based on geometric deep learning have been developed to exploit, at the same time, the rich information content of a complex network and the learning power of deep architectures, highlighting the potential of techniques at the edge between applied math and computer science. On the other hand, studies at the edge of network science and quantum physics are gaining increasing attention, e.g., because of the potential applications to quantum networks for communications, such as the quantum Internet. In this work, we briefly review a novel framework grounded on statistical physics and techniques inspired by quantum statistical mechanics which have been successfully used for the analysis of a variety of complex systems. The advantage of this framework is that it allows one to define a set of information-theoretic tools which find widely used counterparts in machine learning and quantum information science, while providing a grounded physical interpretation in terms of a statistical field theory of information dynamics. We discuss the most salient theoretical features of this framework and selected applications to protein-protein interaction networks, neuronal systems, social and transportation networks, as well as potential novel applications for quantum network science and machine learning.

An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps

The Lyapunov exponent is primarily used to quantify the chaos of a dynamical system. However, it is difficult to compute the Lyapunov exponent of dynamical systems from a time series. The entropic chaos degree is a criterion for quantifying chaos in dynamical systems through information dynamics, which is directly computable for any time series. However, it requires higher values than the Lyapunov exponent for any chaotic map. Therefore, the improved entropic chaos degree for a one-dimensional chaotic map under typical chaotic conditions was introduced to reduce the difference between the Lyapunov exponent and the entropic chaos degree. Moreover, the improved entropic chaos degree was extended for a multidimensional chaotic map. Recently, the author has shown that the extended entropic chaos degree takes the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. However, the author has assumed a value of infinity for some numbers, especially the number of mapping points. Nevertheless, in actual numerical computations, these numbers are treated as finite. This study proposes an improved calculation formula of the extended entropic chaos degree to obtain appropriate numerical computation results for two-dimensional chaotic maps.

Information dynamics in a model with Hilbert space fragmentation

The fully frustrated ladder – a quasi-1D geometrically frustrated spin one half Heisenberg model – is non-integrable with local conserved quantities on rungs of the ladder, inducing the local fragmentation of the Hilbert space into sectors composed of singlets and triplets on rungs. We explore the far-from-equilibrium dynamics of this model through the entanglement entropy and out-of-time-ordered correlators (OTOC). The post-quench dynamics of the entanglement entropy is highly anomalous as it shows clear non-damped revivals that emerge from short connected chunks of triplets. We find that the maximum value of the entropy follows from a picture where coherences between different fragments co-exist with perfect thermalization within each fragment. This means that the eigenstate thermalization hypothesis holds within all sufficiently large Hilbert space fragments. The OTOC shows short distance oscillations arising from short coupled fragments, which become decoherent at longer distances, and a sub-ballistic spreading and long distance exponential decay stemming from an emergent length scale tied to fragmentation.

Emergency of Tsallis statistics in fractal networks

Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy collisions, or from the number of contacts one person has, on average, to the flux of vehicles in the streets of urban centres, all these complex, non-linear problems are better understood under the light of the scale-free network’s properties. A few mechanisms have been found to explain the emergence of scale invariance in complex networks, and here we discuss a mechanism based on the way information is locally spread among agents in a scale-free network. We show that the correct description of the information dynamics is given in terms of the q-exponential function, with the power-law behaviour arising in the asymptotic limit. This result shows that the best statistical approach to the information dynamics is given by Tsallis Statistics. We discuss the main properties of the information spreading process in the network and analyse the role and behaviour of some of the parameters as the number of agents increases. The different mechanisms for optimization of the information spread are discussed.

Information dynamics in neuronal networks of macaque cerebral cortex reflect cognitive state and behavior

The brain is often described as “processing” information: somehow, the decentralized interactions of billions of neurons collectively are somehow able to give rise to “emergent” behaviors, such as perception, cognition, and action. In neuroscience and cognitive science, however, “information processing” is often vaguely defined, making an exact model connecting neurodynamics, information processing, and behavior difficult to pin down. While considerable previous work has examined the structure of information dynamics in cultures or models, it remains uncertain what insights information dynamics can provide about cognition and behavior in order to interact with the environment. In this paper, we use information theory and the theory of information dynamics as a formal framework to explore information processing in multi area neuronal networks recorded from three macaques engaged in sensory-motor transformations: perceiving a visual cue, preparation of a grasping movement, and movement execution. We found that different states and grasp conditions are associated with significant re-configurations of the effective network structure and the overall information flowing through the system. Crucially, differences between cognitive and behavioral states and conditions were related to changes to higher-order, synergistic information dynamics not localizable to a single pair of source/target neurons. Our results suggest that the combined application of information-theoretic analysis of dynamics and network science inference to networks of neurons is a powerful tool to probe the neuronal basis of cognition and behavior.

Misinformation can prevent the suppression of epidemics

The effectiveness of non-pharmaceutical interventions, such as mask-wearing and social distancing, as control measures for pandemic disease relies upon a conscientious and well-informed public who are aware of and prepared to follow advice. Unfortunately, public health messages can be undermined by competing misinformation and conspiracy theories, spread virally through communities that are already distrustful of expert opinion. In this article, we propose and analyse a simple model of the interaction between disease spread and (mis-)information dynamics in a heterogeneous population composed of both trusting individuals who seek quality information and will take precautionary measures, and distrusting individuals who are susceptible to misinformation. We show that, as the density of the distrusting population increases, the model passes through a phase transition to a state in which major outbreaks cannot be suppressed. Our work highlights the urgent need for effective measures to combat the spread of misinformation.

Simplifying functional network representation and interpretation through causality clustering

Functional networks, i.e. networks representing the interactions between the elements of a complex system and reconstructed from the observed elements’ dynamics, are becoming a fundamental tool to unravel the structures created by the movement of information in systems like the human brain. They also present drawbacks, one of the most important being the inherent difficulty in representing and interpreting the resulting structures for large number of nodes and links. I here propose a causality clustering approach, based on grouping nodes into clusters according to their similarity in the overall information dynamics, the latter one being measured by a causality metric. The whole system can then arbitrarily be simplified, with nodes being grouped in e.g. sources, brokers and sinks of information. The advantages and limitations of the proposed approach are discussed using a set of synthetic and real-world data sets, the latter ones representing two neuroscience and technological problems.

Developmental differences in perceptual anticipation underlie different sensitivities to coarticulatory dynamics

Anticipatory coarticulation is an indispensable feature of speech dynamics contributing to spoken language fluency. Research has shown that children speak with greater degrees of vowel anticipatory coarticulation than adults – that is, greater vocalic influence on previous segments. The present study examined how developmental differences in anticipatory coarticulation transfer to the perceptual domain. Using a gating paradigm, we tested 29 seven-year-olds and 93 German adult listeners with sequences produced by child and adult speakers, hence corresponding to low versus high vocalic anticipatory coarticulation degrees. First, children predicted vowel targets less successfully than adults. Second, greater perceptual accuracy was found for low compared to highly coarticulated speech. We propose that variations in coarticulation degrees reflect perceptually important differences in information dynamics and that listeners are more sensitive to fast changes in information than to a large amount of vocalic information spread across long segmental spans.

Topology-informed information dynamics modeling in cyber–physical–social system networks

Cyber–physical–social systems (CPSS) are physical devices that are embedded in human society and possess highly integrated functionalities of sensing, computing, communication, and control. CPSS rely on their intense collaboration and information sharing through networks to be functioning. In this paper, topology-informed network information dynamics models are proposed to characterize the evolution of information processing capabilities of CPSS nodes in networks. The models are based on a mesoscale probabilistic graph model, where the sensing and computing capabilities of the nodes are captured as the probabilities of correct predictions. A topology-informed vector autoregression model and a latent variable vector autoregression model are proposed to model the correlations between prediction capabilities of nodes as linear functional relationships. A hybrid Gaussian process regression model is also developed to capture both the nonlinear spatial and temporal correlations between nodes. The new information dynamics models are demonstrated and tested with a simulator of CPSS networks. The results show that the topological information of networks can improve the efficiency in constructing the time series models. The network topology also has influences on the prediction capabilities of CPSS.

Dinámicas de información en profesionales de enfermería desde el análisis de redes sociales

Introducción: El conocimiento es una herramienta necesaria para la investigación científica y el progreso de cualquier disciplina. Pero el conocimiento científico y las dinámicas de información no sólo están sostenidas por los individuos, sino que son producidas y mantenidas por grupos de personas que trabajan en un mismo entorno donde los vínculos y las relaciones pueden influir en el proceso. Objetivo: Analizar las redes sociales de utilización de fuentes de información, de ayuda/consejo para la transferencia de conocimiento y los lugares donde los profesionales de enfermería comparten información.Método: Análisis de Redes Sociales a través de un cuestionario validado. Se reclutaron profesionales de 6 unidades hospitalarias.Resultados: Participaron 77 profesionales con una edad media de 42,9 (DE:11,48). Los compañeros son la fuente de información más utilizada (76 elecciones) frente a las bases de datos y artículos científicos que son la menos seleccionada (63 elecciones). Las redes homófilas horizontales (profesionales con estatus/intereses similares) son las más frecuentes para obtener información sobre resultados de investigación (74 elecciones). La unidad asistencial es el entorno más señalado para compartir información (50 elecciones).Conclusiones: Los profesionales consideran el conocimiento de sus compañeros como la principal fuente para obtener información sobre resultados de investigación. Unidades con determinado grado de especialización utilizan guías de práctica clínica y protocolos como fuente principal de información. Los profesionales de enfermería utilizan redes homófilas-horizontales para obtener información. El entorno laboral en sus diferentes ámbitos (unidad, office, reuniones) es el más utilizado para compartir información sobre resultados de investigación. Introduction: Knowledge is a necessary tool for scientific research and progress in any discipline. But scientific knowledge and information dynamics are not only sustained by individuals but are produced and maintained by groups of people working in the same environment where links and relationships can influence the process. Aim: To analyze the social networks of information source utilization, help/advice for knowledge transfer and the places where nursing professionals share information.Method: Analysis of social networks through a validated questionnaire. Professionals from 6 hospital units were recruited.Results: 77 professionals participated with a mean age of 42.9 (SD:11.48). Peers were the most frequently used source of information (76 choices) compared to databases and scientific articles, which were the least selected (63 choices). Horizontal homophilous networks (professionals with similar status/interests) are the most frequent for obtaining information on research results (74 choices). The care unit is the most pointed environment for sharing information (50 choices).Conclusions: Professionals consider the knowledge of their peers as the main source for obtaining information on research results. Units with a certain degree of specialization use clinical practice guidelines and protocols as the main source of information. Nursing professionals use homophilic-horizontal networks to obtain information. The work environment in its different settings (unit, office, meetings) is the most used for sharing information on research results.