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The onset and progression of a neurological disease can often be explained in terms of brain-network alteration. They can be formalized as the action of an operator representing the disease, the so-called /C-operator, acting on the network. The healing process can thus be seen as the inverse of the disease mechanism. However, perfect healing is often impossible to achieve. Here, we formalize the ideal healing in terms of perturbative variation of the possible partial healing. The modeling and analytical strategy is based on techniques from theoretical physics, with the language of matrix operators. In addition, using the language of category theory, we also formalize the progressive abstraction from the reality of diseased patients to the definition of a disease and the comparison between different diseases as a natural transformation between colimits. This theoretical presentation can provide a new, interdisciplinary perspective on neurological investigation and possibly foster new theoretical-experimental developments. [ABSTRACT FROM AUTHOR]

Understanding error properties is an essential part in numerical weather prediction. Predictable relationship between errors of different regions due to some underlying systematic or random process can give rise to correlated errors. Estimation of error correlation is crucial for improvement of forecasts. However, the size of the corresponding correlation matrix is larger than what is possible to represent on geographical maps in order to diagnose its full spatial variation. Here, we propose a complex network‐based approach to analyse forecast error correlations that enables us to estimate the spatially varying component of the error. A quantitative study of the spatio‐temporal coherent structures of medium‐range forecast errors of different climate variables using network measures can reveal common sources of errors. Such information is crucial, especially in cases such as the outgoing long‐wave radiation, in which errors are correlated across very long distances, indicating an underlying climate mechanism as the source of the error. We show that the spatial patterns of forecast error co‐variability may not be the same as that of the corresponding climate variable itself, thereby implying that the mechanisms behind the correlated errors may be different from the climate processes responsible for the spatio‐temporal interactions of the climate variable. Our results highlight the importance of diagnosing the full spatial variation of error correlations to understand the origin and propagation of forecast errors, and demonstrate complex networks to be a promising diagnostic tool in this regard. [ABSTRACT FROM AUTHOR]

A deeper understanding of the intricate relationship between the two components of the Asian summer monsoon (ASM)—the Indian summer monsoon (ISM) and the East Asian summer monsoon (EASM)—is crucial to improve the subseasonal forecasting of extreme precipitation events. Using an innovative complex network‐based approach, we identify two dominant synchronization pathways between ISM and EASM—a southern mode between the Arabian Sea and southeastern China occurring in June, and a northern mode between the core ISM zone and northern China which peaks in July—and their associated large‐scale atmospheric circulation patterns. Furthermore, we discover that certain phases of the Madden–Julian oscillation and the lower frequency mode of the boreal summer intraseasonal oscillation (BSISO) seem to favour the overall synchronization of extreme rainfall events between ISM and EASM while the higher‐frequency mode of the BSISO is likely to support the shifting between the modes of ISM–EASM connection. [ABSTRACT FROM AUTHOR]

The urban acoustic environment (AE) provides comprehensive acoustic information related to the diverse systems of urban areas, such as traffic, the built environment, or biodiversity. The decreasing cost of acoustic sensors and rapid growth of storage space and computational power have fostered the collection of large amounts of acoustical data to be processed. However, despite the extensive information that is recorded by modern acoustic sensors, few approaches are established to capture the rich complex dynamics embedded in the time-frequency domain of the urban AE. Quantitative methods need to account for this complexity, while effectively reducing the high dimensionality of acoustic features within the data. Therefore, we introduce complex networks as a tool for analyzing the complex structure of large-scale urban AE data. We present a framework to construct networks based on frequency correlation matrices (FCMs). FCMs have shown to be a promising tool to depict environment specific interrelationships between consecutive power spectra. Accordingly, we show the capabilities of complex networks for the quantification of these interrelationships and thus, to characterize different urban AEs. We demonstrate the scope of the proposed method, using one of the world's most extensive longitudinal audio datasets, considering 3-min audio recordings (n = 319,385 ≙ 665 days) from 23 sites. We construct networks from hour-of-day specific audio recordings for each site. We show that the average shortest path length (ASPL) as an indicator for dominance of sound sources in the urban AE exhibits spatial- and temporal-specific patterns between the sites, which allows us to identify four to seven clusters of distinct urban AEs. To validate our findings, we use the land use mix around each site as a proxy for the AE and compare those between and within the clusters. The identified clusters show high intra- and low inter-cluster correlations of ASPL diel cycles as well as strong intra-similarities in land use mix. Our results indicate that complex networks are a promising approach to analyze large-scale audio data, expanding our understanding of the time-frequency domain of the urban AE. • The introduction of complex networks for the analysis of the acoustic environment. • The application to a dataset of approx. One million minutes of audio recordings. • Average shortest path length as indicator for the acoustic dominance. • Complex networks capture temporal characteristics of the acoustic environment. • Complex networks capture spatial features of the acoustic environment. [ABSTRACT FROM AUTHOR]

Synchronous occurrences of heavy rainfall events and the study of their relation in time and space are of large socio-economical relevance, for instance for the agricultural and insurance sectors, but also for the general well-being of the population. In this study, the spatial synchronization structure is analyzed as a regional climate network constructed from precipitation event series. The similarity between event series is determined by the number of synchronous occurrences. We propose a novel standardization of this number that results in synchronization scores which are not biased by the number of events in the respective time series. Additionally, we introduce a new version of the network measure directionality that measures the spatial directionality of weighted links by also taking account of the effects of the spatial embedding of the network. This measure provides an estimate of heavy precipitation isochrones by pointing out directions along which rainfall events synchronize. We propose a climatological interpretation of this measure in terms of propagating fronts or event traces and confirm it for Germany by comparing our results to known atmospheric circulation patterns. [ABSTRACT FROM AUTHOR]

The South American Andes are frequently exposed to intense rainfall events with varying moisture sources and precipitation-forming processes. In this study, we assess the spatiotemporal characteristics and geographical origins of rainfall over the South American continent. Using high-spatiotemporal resolution satellite data (TRMM 3B42 V7), we define four different types of rainfall events based on their (1) high magnitude, (2) long temporal extent, (3) large spatial extent, and (4) high magnitude, long temporal and large spatial extent combined. In a first step, we analyze the spatiotemporal characteristics of these events over the entire South American continent and integrate their impact for the main Andean hydrologic catchments. Our results indicate that events of type 1 make the overall highest contributions to total seasonal rainfall (up to $$50\,\%$$ ). However, each consecutive episode of the infrequent events of type 4 still accounts for up to $$20\,\%$$ of total seasonal rainfall in the subtropical Argentinean plains. In a second step, we employ complex network theory to unravel possibly non-linear and long-ranged climatic linkages for these four event types on the high-elevation Altiplano-Puna Plateau as well as in the main river catchments along the foothills of the Andes. Our results suggest that one to two particularly large squall lines per season, originating from northern Brazil, indirectly trigger large, long-lasting thunderstorms on the Altiplano Plateau. In general, we observe that extreme rainfall in the catchments north of approximately $$20^{\circ }$$ S typically originates from the Amazon Basin, while extreme rainfall at the eastern Andean foothills south of $$20^{\circ }$$ S and the Puna Plateau originates from southeastern South America. [ABSTRACT FROM AUTHOR]

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related to the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches. [ABSTRACT FROM AUTHOR]

Abstract: We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potential of these complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime. [Copyright &y& Elsevier]

Abstract In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series. While both nonlinear time series analysis and complex network theory are widely considered to be established fields of complex systems sciences with strong links to nonlinear dynamics and statistical physics, the thorough combination of both approaches has become an active field of nonlinear time series analysis, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of existing approaches of time series networks, covering their methodological foundations, interpretation and practical considerations with an emphasis on recent developments. After a brief outline of the state-of-the-art of nonlinear time series analysis and the theory of complex networks, we focus on three main network approaches, namely, phase space based recurrence networks, visibility graphs and Markov chain based transition networks, all of which have made their way from abstract concepts to widely used methodologies. These three concepts, as well as several variants thereof will be discussed in great detail regarding their specific properties, potentials and limitations. More importantly, we emphasize which fundamental new insights complex network approaches bring into the field of nonlinear time series analysis. In addition, we summarize examples from the wide range of recent applications of these methods, covering rather diverse fields like climatology, fluid dynamics, neurophysiology, engineering and economics, and demonstrating the great potentials of time series networks for tackling real-world contemporary scientific problems. The overall aim of this report is to provide the readers with the knowledge how the complex network approaches can be applied to their own field of real-world time series analysis. [ABSTRACT FROM AUTHOR]

Abstract: We introduce a geometric method for identifying the coupling direction between two dynamical systems based on a bivariate extension of recurrence network analysis. Global characteristics of the resulting inter-system recurrence networks provide a correct discrimination for weakly coupled Rössler oscillators not yet displaying generalised synchronisation. Investigating two real-world palaeoclimate time series representing the variability of the Asian monsoon over the last 10,000 years, we observe indications for a considerable influence of the Indian summer monsoon on climate in Eastern China rather than vice versa. The proposed approach can be directly extended to studying coupled subsystems. [Copyright &y& Elsevier]