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arXiv 2019年

作者： Zammit-Mangion, Andrew Ng, Tin Lok James Vu, Quan Filippone, Maurizio School of Math. and Applied Stat. University of Wollongong Australia Department of Data Science EURECOM France

Nonstationary, anisotropic spatial processes are often used when modelling, analysing and predicting complex environmental phenomena. One such class of processes considers a stationary, isotropic process on a warped spatial domain. The warping function is generally difficult to fit and not constrained to be bijective, often resulting in ‘space-folding.’ Here, we propose modelling a bijective warping function through a composition of multiple elemental bijective functions in a deep-learning framework. We consider two cases;first, when these functions are known up to some weights that need to be estimated, and, second, when the weights in each layer are random. Inspired by recent methodological and technological advances in deep learning and deep Gaussian processes, we employ approximate Bayesian methods to make inference with these models using graphical processing units. Through simulation studies in one and two dimensions we show that the deep compositional spatial models are quick to fit, and are able to provide better predictions and uncertainty quantification than other deep stochastic models of similar complexity. We also show their remarkable capacity to model highly nonstationary, anisotropic spatial data using radiances from the MODIS instrument aboard the Aqua satellite. Copyright © 2019, The Authors. All rights reserved.

关键词： Stochastic systems

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The master stability function for synchronization in simplicial complexes

arXiv

引用

arXiv 2020年

作者： Gambuzza, L.V. Di Patti, F. Gallo, L. Lepri, S. Romance, M. Criado, R. Frasca, Mattia Latora, V. Boccaletti, S. Department of Electrical Electronics and Computer Science Engineering University of Catania Catania95125 Italy CNR-Institute of Complex Systems Via Madonna del Piano Sesto Fiorentino Florence50019 Italy Department of Physics and Astronomy University of Catania Catania95125 Italy Department of Applied Math. and Data Complex Networks and Cybersecurity Research Institute University Rey Juan Carlos C/Tulipn s/n Mstoles Madrid28933 Spain Department of Physics and Astronomy University of Catania INFN Catania95125 Italy School of Mathematical Sciences Queen Mary University of London LondonE1 4NS United Kingdom The Alan Turing Institute The British Library LondonNW1 2DB United Kingdom Unmanned Systems Research Institute Northwestern Polytechnical University Xi'an710072 China Moscow Institute of Physics and Technology Dolgoprudny Moscow Region141701 Russia

All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as networks of coupled dynamical systems, where the graph links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework that allows to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We consider the most general ensemble of identical dynamical systems, organized on the nodes of a simplicial complex, and interacting through synchronization-non-invasive coupling function. The simplicial complex can be of any dimension, meaning that it can account, at the same time, for pairwise interactions, three-body interactions and so on. In such a broad context, we show that complete synchronization, a circumstance where all the dynamical units arrange their evolution in unison, exists as an invariant solution, and we give the necessary condition for it to be observed as a stable state in terms of a Master Stability Function. This generalizes the existing results valid for pairwise interactions (i.e. graphs) to the case of complex systems with the most general possible architecture. Moreover, we show how the approach can be simplified for specific, yet frequently occurring, instances, and we verify all our theoretical predictions in synthetic and real-world systems. Given the completely general character of the method proposed, our results contribute to the theory of dynamical systems with many-body interactions and can find applications in an extremely wide range of practical cases. Copyright © 2020, The Auth

关键词： Dynamical systems

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