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Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab ® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l'environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.

In this paper we assess the snow cover and its dynamics for the western river basins of the Indus River system (IRS) and their sub-basins located in Afghanistan, China, India and Pakistan for the period 2001–2012. First, we validate the Moderate Resolution Imaging Spectroradiometer (MODIS) daily snow products from Terra (MOD10A1) and Aqua (MYD10A1) against the Landsat Thematic Mapper/Enhanced Thematic Mapper plus (TM/ETM+) data set, and then improve them for clouds by applying a validated non-spectral cloud removal technique. The improved snow product has been analysed on a seasonal and annual basis against different topographic parameters (aspect, elevation and slope). Our results show a decreasing tendency for the annual average snow cover for the westerlies-influenced basins (upper Indus basin (UIB), Astore, Hunza, Shigar and Shyok) and an increasing tendency for the monsoon-influenced basins (Jhelum, Kabul, Swat and Gilgit). Seasonal average snow cover decreases during winter and autumn, and increases during spring and summer, which is consistent with the observed cooling and warming trends during the respective seasons. Sub-basins at relatively higher latitudes/altitudes show higher variability than basins at lower latitudes/middle altitudes. Northeastern and northwestern aspects feature greater snow cover. The mean end-of-summer regional snow line altitude (SLA) zones range from 3000 to 5000 m a.s.l. for all basins. Our analysis provides an indication of a descending end-of-summer regional SLA zone for most of the studied basins, which is significant for the Shyok and Kabul basins, thus indicating a change in their water resources. Such results are consistent with the observed hydro-climatic data, recently collected local perceptions and glacier mass balances for the investigated period within the UIB. Moreover, our analysis shows a significant correlation between winter season snow cover and the North Atlantic Oscillation (NAO) index of the previous autumn. Similarly, the inter-annual variability of spring season snow cover and spring season precipitation explains well the inter-annual variability of the summer season discharge from most of the basins. These findings indicate some potential for the seasonal stream flow forecast in the region, suggesting snow cover as a possible predictor.

We analyze the publicly released outputs of the simulations performed by climate models (CMs) in preindustrial (PI) and Special Report on Emissions Scenarios A1B (SRESA1B) conditions. In the PI simulations, most CMs feature biases of the order of 1 W m−2 for the net global and the net atmospheric, oceanic, and land energy balances. This does not result from transient effects but depends on the imperfect closure of the energy cycle in the fluid components and on inconsistencies over land. Thus, the planetary emission temperature is underestimated, which may explain the CMs' cold bias. In the PI scenario, CMs agree on the meridional atmospheric enthalpy transport's peak location (around 40°N/S), while discrepancies of ∼20% exist on the intensity. Disagreements on the oceanic transport peaks' location and intensity amount to ∼10° and ∼50%, respectively. In the SRESA1B runs, the atmospheric transport's peak shifts poleward, and its intensity increases up to ∼10% in both hemispheres. In most CMs, the Northern Hemispheric oceanic transport decreases, and the peaks shift equatorward in both hemispheres. The Bjerknes compensation mechanism is active both on climatological and interannual time scales. The total meridional transport peaks around 35° in both hemispheres and scenarios, whereas disagreements on the intensity reach ∼20%. With increased CO2 concentration, the total transport increases up to ∼10%, thus contributing to polar amplification of global warming. Advances are needed for achieving a self‐consistent representation of climate as a nonequilibrium thermodynamical system. This is crucial for improving the CMs' skill in representing past and future climate changes.

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

IntroductionThe disruption of minimal Self is believed to be a core element of Schizophrenia and intimately connected to a disruption of bodily self, which in turn leads to impairments in intersubjectivity dimension. Motor abnormalities have been associated to Schizophrenia since the early conceptualization of the disorder, as well as inefficient body-related multisensory integration processes are considered nowadays a plausible origin of disembodied Self. In particular, there is evidence for significant abnormalities in Peripersonal Space (PPS) extension in Schizophrenia patients. PPS is the plastic sector of space immediately surrounding our body, whose coherent representation is based on efficient body-related multisensory integration processes. With a specific experimental task based on multisensory integration processing, we estimated PPS size and PPS boundary’s demarcation in 27 Schizophrenia patients, confirming a narrower PPS size and weaker bodily boundary in patients, thus paving the way for a deeper investigation of the mechanisms underlying the disruption of bodily self (Ferroni et al., Schziophr.Bull.2022, 5 1085-1093). We suggest that disembodiment might be responsible for the loss of the immediate linkage between Self and others (“intercorporeality”), so linking the disruption of the corporeal dimension to specific anomalies of intersubjectivity in Schizophrenia patients. Since language is one of the most important instrument through which intersubjectivity unfolds, it is intriguing to hypothesize a connection between language and multi-sensory processing.ObjectivesTherefore, the present study was aimed at investigating possible correlations between patients’ motor impairments in multi-sensory integration processes and their alterations in language and communicative interactions.MethodsTwenty-five outpatients were recruited in an experimental task investigating PPS extension; they were administered the Scale for the Assessment of Thought, Language and Communication (TLC) and the Clinical Language Disorder Rating Scale (CLANG).ResultsOur data showed significant correlations between TLC and CLANG total scores and PPS size, with narrower PPS size for more severe formal thought disorders and higher language and communication impairments.ConclusionsOur preliminary results seem to confirm the presence of a link between language impairment and multi-sensory processing, suggesting that bodily and linguistic disorganization may have a common origin which has yet to be explored in depth. Future research is needed to identify linguistic and motor endophenotypic patterns, potentially intertwined with each other, capable of early predicting Schizophrenia development and thus usable as early diagnostic tools.Disclosure of InterestNone Declared

Using a recent theoretical approach, we study how global warming impacts the thermodynamics of the climate system by performing experiments with a simplified yet Earth-like climate model. The intensity of the Lorenz energy cycle, the Carnot efficiency, the material entropy production, and the degree of irreversibility of the system change monotonically with the CO2 concentration. Moreover, these quantities feature an approximately linear behaviour with respect to the logarithm of the CO2 concentration in a relatively wide range. These generalized sensitivities suggest that the climate becomes less efficient, more irreversible, and features higher entropy production as it becomes warmer, with changes in the latent heat fluxes playing a predominant role. These results may be of help for explaining recent findings obtained with state of the art climate models regarding how increases in CO2 concentration impact the vertical stratification of the tropical and extratropical atmosphere and the position of the storm tracks.

IntroductionIn schizophrenia, there is evidence for anomalies in the extension and plasticity of the peripersonal space (PPS), the portion of space surrounding our body, plastically shaped through motor experiences. An impaired multisensory integration at the PPS level would underpin the disembodiment, a core feature of the disorder linked to subjective perturbations of the sense of self (“Self-disorders”) and of the intersubjective dimension (“schizophrenic autism”).ObjectivesThe present study was aimed at: 1) exploring possible associations between PPS data, psychopathological dimensions, and subjective experiences in schizophrenia; 2) identifying a specific PPS profile in patients with early-onset schizophrenia.MethodsA motor training with a tool was used to assess the PPS size and boundaries demarcation in twenty-seven schizophrenia outpatients. Moreover, they underwent a thorough psychopathological evaluation with the Positive And Negative Syndrome Scale (PANSS), the Examination of Anomalous Self Experience scale (EASE) and the Autism Rating Scale (ARS). Subsequently, the sample was divided into early (EOS) and adult-onset (AOS) subgroups, that were compared with respect to their PPS and psychopathological profiles.ResultsPPS features (size and boundaries demarcation) were associated with PANSS negative score, subjective experiences of existential reorientation (EASE Domain 5 scores) and traits of schizophrenic autism (ARS scores; Fig. 1). PPS parameters (Fig. 2) and ARS scores, but not PANSS and EASE differentiated between early and adult-onset subgroups.Image:Image 2:ConclusionsOur results suggest a link between PPS patterns, negative symptoms, and disturbances of the subjective experience, particularly in the intersubjective domain, in schizophrenia. Moreover, they candidate specific PPS profiles and schizophrenic autism traits as EOS markers.Disclosure of InterestNone Declared

This paper discusses the relative performance of several climate models in providing reliable forcing for hydrological modeling in six representative catchments in the Mediterranean region. We consider 14 Regional Climate Models (RCMs), from the EU-FP6 ENSEMBLES project, run for the A1B emission scenario on a common 0.22° (about 24 km) rotated grid over Europe and the Mediterranean region. In the validation period (1951 to 2010) we consider daily precipitation and surface temperatures from the observed data fields (E-OBS) data set, available from the ENSEMBLES project and the data providers in the ECA&D project. Our primary objective is to rank the 14 RCMs for each catchment and select the four best-performing ones to use as common forcing for hydrological models in the six Mediterranean basins considered in the EU-FP7 CLIMB project. Using a common suite of four RCMs for all studied catchments reduces the (epistemic) uncertainty when evaluating trends and climate change impacts in the 21st century. We present and discuss the validation setting, as well as the obtained results and, in some detail, the difficulties we experienced when processing the data. In doing so we also provide useful information and advice for researchers not directly involved in climate modeling, but interested in the use of climate model outputs for hydrological modeling and, more generally, climate change impact studies in the Mediterranean region.

IntroductionPatients with schizophrenia present severe communication difficulties in various linguistic areas. In the last two decades research has invested significant effort in trying to better characterize the linguistic profile of patients with schizophrenia, with the purpose to help and guide diagnosis and treatment. Moreover, speech data could be easily gathered through non-invasive techniques and are therefore seen as particularly promising by clinicians. However, surprisingly very little is known about interactional dialogue management, i.e. turn-taking, in these patients. ‘Schizophrenic autism’, the peculiar intersubjective experience also linked to anomalies in the sense of the self (‘Self-disorders’) presented by these patients, could be at the basis of an unusual turn-taking management.ObjectivesThe objective of the present study was to investigate turn-taking patterns of patients with schizophrenia and to explore their possible associations with psychopathological dimensions and subjective experiences.MethodsWe obtained double-channel audio-recordings from interviews with twenty patients with schizophrenia (SCZ) and twenty healthy controls (HC). Participants answered general questions to elicit spontaneous dialogues, to improve the ecological validity of the task. The audio files obtained were then analyzed with Praat, a software widely used in experimental phonetics. We subsequently quantified a set of conversational metrics (participant floor occupation, mutual silence, overlap between speakers, speaking turn and pause duration). Patients also underwent a thorough psychopathological and phenomenological evaluation with the Positive And Negative Syndrome Scale (PANSS), the Examination of Anomalous Self Experience scale (EASE) and the Autism Rating Scale (ARS).ResultsOur results show that the SCZ group displayed a reduced participant floor occupation, an increased mutual silence, and shorter speaking turns as compared to the HC. (Fig. 1, Fig. 2). We found significant associations between conversational features and psychopathology (Fig. 3). Two multivariate linear regressions showed that the participant occupation floor and the average speaking turn duration (dependent variables) were negatively related to the severity of negative symptoms and Self-Disorders. Interestingly, Self-Disorders were the best predictors of conversational engagement.Image:Image 2:Image 3:ConclusionsOur results, although preliminary, suggest the existence of peculiar turn-taking patterns in schizophrenia, linked to negative symptoms and disturbances of the subjective experience, particularly in the Self domain. Our results suggest also how the use of experimental linguistic methodology is applicable to clinical settings and underscores the importance of research projects in this field that are strongly interdisciplinary in both design and conduct.Disclosure of InterestNone Declared

IntroductionLanguage and conversation are deeply interrelated: language is acquired, structured, practiced in social interactions and linguistic resources (specifically syntactic, prosodic and pragmatic aspects) contribute to finely tuning turn-taking. Nevertheless, most studies focused on verbal aspects of speech in schizophrenia, with scant attention to their relation to conversation, where language is experienced at most.ObjectivesThe present study was aimed at investigating a possible association between language impairment and conversational characteristics in a sample of clinically stable patients diagnosed with schizophrenia (N = 35, ages 18-65).MethodsA spontaneous speech sample was recorded. For the assessment of language skills, the Scale for the Assessment of Thought, Language and Communication (TLC) and the Clinical Language Disorder Rating Scale (CLANG) were used, while conversational variables were extracted with an innovative method of semi-automatic analysis. The possible associations were investigated through the Pearson Correlation.ResultsFigure 1 represents graphically the correlational matrix between conversational variables and linguistic scale scores. In the heatmap, blue means negative and red positive correlations, the stronger the colour, the larger the correlation magnitude. Moreover, the significant associations are indicated with stars.ConclusionsThe results suggest that in schizophrenia spectrum disorders the disturbances of language, at a syntactic, prosodic and pragmatic level, have significant impact on communicative interaction.Thus, conversation analysis might be a promising method to quantify objectively communicative impairment with the benefit of representing an ecological assessment, examining the performance of patients in the real situation of language use, which is social interaction.DisclosureNo significant relationships.