Epidemic processes in complex networks Pastor-Satorras, Romualdo; Castellano, Claudio; Van Mieghem, Piet ...
Reviews of modern physics,
08/2015, Letnik:
87, Številka:
3
Journal Article, Publication
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Complex networks arise in a wide range of biological and sociotechnical systems. Epidemic spreading is central to our understanding of dynamical processes in complex networks, and is of interest to ...physicists, mathematicians, epidemiologists, and computer and social scientists. This review presents the main results and paradigmatic models in infectious disease modeling and generalized social contagion processes. In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.
The ability to effectively control brain dynamics holds great promise for the enhancement of cognitive function in humans and the betterment of their quality of life. Yet, successfully controlling ...dynamics in neural systems is challenging, in part due to the immense complexity of the brain and the large set of interactions that can drive any single change. While some understanding has been gained of the control of single neurons, the control of large-scale neural systems-networks of multiply interacting components-remains poorly understood. Efforts to address this gap include the construction of tools for the control of brain networks, mostly adapted from control and dynamical systems theory. Informed by current opportunities for practical intervention, these theoretical contributions provide models that draw from a wide array of mathematical approaches. Recent developments are presented for effective strategies of control in dynamic brain networks, and potential mechanisms are also described that underlie such processes. Efforts are reviewed on the control of general neurophysiological processes with implications for brain development and cognitive function, as well as the control of altered neurophysiological processes in medical contexts such as anesthesia administration, seizure suppression, and deep-brain stimulation for Parkinson’s disease. This Colloquium is concluded with a forward-looking discussion regarding how emerging results from network control, especially approaches that deal with nonlinear dynamics or more realistic trajectories for control transitions, could be used to directly address pressing questions in neuroscience.
The discovery of physical laws consistent with empirical observations is at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differential equations ...depending on parameters; dynamical systems theory provides, through the appropriate normal forms, an “intrinsic” prototypical characterization of the types of dynamical regimes accessible to a given model. Using an implementation of data-informed geometry learning, we directly reconstruct the relevant “normal forms”: a quantitative mapping from empirical observations to prototypical realizations of the underlying dynamics. Interestingly, the state variables and the parameters of these realizations are inferred from the empirical observations; without prior knowledge or understanding, they parametrize the dynamics intrinsically without explicit reference to fundamental physical quantities.
Agency has attracted considerable attention, especially of late. Nevertheless, perceptions of language learners as nonagentive persist. In this article the Douglas Fir Group's call for a ...transdisciplinary perspective is heeded in a Complex Dynamic Systems Theory's (CDST) conceptualization of agency. It is suggested that CDST maintains the structure-agency complementarity while bringing to the fore the relational and emergent nature of agency. Coordination dynamics is identified as a possible mechanism for the phylogenetic and ontogenetic emergence of agency. CDST further characterizes agency as spatially-temporally situated. It can be achieved and changed through iteration and co-adaptation. It is also multidimensional and heterarchical. In this era of posthumanism, an issue that is also taken up is whether it is only humans who have agency. The article then discusses educational practices that could support learner agency. Finally, the article closes with a discussion of agency and ethical action.
Abstract Epilepsy is defined by the abrupt emergence of harmful seizures, but the nature of these regime shifts remains enigmatic. From the perspective of dynamical systems theory, such critical ...transitions occur upon inconspicuous perturbations in highly interconnected systems and can be modeled as mathematical bifurcations between alternative regimes. The predictability of critical transitions represents a major challenge, but the theory predicts the appearance of subtle dynamical signatures on the verge of instability. Whether such dynamical signatures can be measured before impending seizures remains uncertain. Here, we verified that predictions on bifurcations applied to the onset of hippocampal seizures, providing concordant results from in silico modeling, optogenetics experiments in male mice and intracranial EEG recordings in human patients with epilepsy. Leveraging pharmacological control over neural excitability, we showed that the boundary between physiological excitability and seizures can be inferred from dynamical signatures passively recorded or actively probed in hippocampal circuits. Of importance for the design of future neurotechnologies, active probing surpassed passive recording to decode underlying levels of neural excitability, notably when assessed from a network of propagating neural responses. Our findings provide a promising approach for predicting and preventing seizures, based on a sound understanding of their dynamics.
The climate is a forced, dissipative, nonlinear, complex, and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time ...as well as space, and it is subject to various external forcings, natural as well as anthropogenic. This review covers the observational evidence on climate phenomena and the governing equations of planetary-scale flow and presents the key concept of a hierarchy of models for use in the climate sciences. Recent advances in the application of dynamical systems theory, on the one hand, and nonequilibrium statistical physics, on the other hand, are brought together for the first time and shown to complement each other in helping understand and predict the system's behavior. These complementary points of view permit a self-consistent handling of subgrid-scale phenomena as stochastic processes, as well as a unified handling of natural climate variability and forced climate change, along with a treatment of the crucial issues of climate sensitivity, response, and predictability.
Within education, the importance of creativity is recognized as an essential 21st-century skill. Based on this premise, the first aim of this article is to provide a theoretical integration through ...the development of a framework based on the principles of complex dynamic systems theory, which describes and explains children's creativity. This model is used to explain differing views on the role of education in developing children's creativity. Our second aim is empirical integration. On the basis of a three-dimensional taxonomy, we performed a systematic review of the recent literature (2006-2017, 184 studies) on primary school students 'creativity. Our results show that creativity is most often measured as a static, aggregated construct. In line with our theoretical model, we suggest ways that future research can elaborate on the moment-to-moment interactions that form the basis of long-term creative development, as well as on the mechanisms that connect different levels of creativity.
The classical, disembodied approach to music cognition conceptualizes action and perception as separate, peripheral processes. In contrast, embodied accounts of music cognition emphasize the central ...role of the close coupling of action and perception. It is a commonly established fact that perception spurs action tendencies. We present a theoretical framework that captures the ways in which the human motor system and its actions can reciprocally influence the perception of music. The cornerstone of this framework is the common coding theory, postulating a representational overlap in the brain between the planning, the execution, and the perception of movement. The integration of action and perception in so-called internal models is explained as a result of associative learning processes. Characteristic of internal models is that they allow intended or perceived sensory states to be transferred into corresponding motor commands (inverse modeling), and vice versa, to predict the sensory outcomes of planned actions (forward modeling). Embodied accounts typically refer to inverse modeling to explain action effects on music perception (Leman, 2007). We extend this account by pinpointing forward modeling as an alternative mechanism by which action can modulate perception. We provide an extensive overview of recent empirical evidence in support of this idea. Additionally, we demonstrate that motor dysfunctions can cause perceptual disabilities, supporting the main idea of the paper that the human motor system plays a functional role in auditory perception. The finding that music perception is shaped by the human motor system and its actions suggests that the musical mind is highly embodied. However, we advocate for a more radical approach to embodied (music) cognition in the sense that it needs to be considered as a dynamical process, in which aspects of action, perception, introspection, and social interaction are of crucial importance.
The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to a series of computational techniques for numerical solutions. Although numerous latest advances are ...accomplished in developing neural operators, a kind of neural-network-based PDE solver, these solvers become less accurate and explainable while learning long-term behaviors of non-linear PDE families. In this paper, we propose the Koopman neural operator (KNO), a new neural operator, to overcome these challenges. With the same objective of learning an infinite-dimensional mapping between Banach spaces that serves as the solution operator of the target PDE family, our approach differs from existing models by formulating a non-linear dynamic system of equation solution. By approximating the Koopman operator, an infinite-dimensional operator governing all possible observations of the dynamic system, to act on the flow mapping of the dynamic system, we can equivalently learn the solution of a non-linear PDE family by solving simple linear prediction problems. We validate the KNO in mesh-independent, long-term, and zero-shot predictions on five representative PDEs (e.g., the Navier-Stokes equation and the Rayleigh-Bénard convection) and three real dynamic systems (e.g., global water vapor patterns and western boundary currents). In these experiments, the KNO exhibits notable advantages compared with previous state-of-the-art models, suggesting the potential of the KNO in supporting diverse science and engineering applications (e.g., PDE solving, turbulence modeling, and precipitation forecasting).
•We propose a new neural operator model for partial differential equation (PDE) solving and realize an effective linear prediction of non-linear dynamics via Koopman operator.•Our approach achieves robust and accurate modeling of the long-term non-linear dynamics of PDE families or real systems.•Our model may serve as a basic unit for constructing new frameworks of PDE solving and dynamic system modeling.
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