Group and total dissipativity and stability of multi-equilibria hybrid automata

Complex systems, which consist of different interdependent and interlocking subsystems, typically have multiple equilibrium points associated with different set points of each operation mode. These systems are usually interpreted as switched systems, or in general, as hybrid systems. Surprisingly, the consideration of multiple equilibria is not common in hybrid systems’ literature, being typically focused on the study of stability and dissipativity properties for switched systems whose subsystems share the same equilibrium point. This paper will expand the discussion to the case of having multiple co-existing equilibrium points for hybrid systems modelled as hybrid automata, which are more general than switched systems. A classification of equilibria for hybrid automata is offered, and some stability related properties are shown for them. Moreover, some dissipativity-related properties are studied. The chief idea of our approach is to identify stable and dissipative components as group of discrete locations within the hybrid automaton. Two examples are used to illustrate our conclusions

A novel hybrid automaton framework for multi-phase epidemic modelling

This is an accepted manuscript of an article published by IEEE on behalf of SCS on 05/10/2021 The accepted version of the publication may differ from the final published version.A framework for the multi-phase epidemic modelling of SEIARD (Susceptible-Exposed-symptomatic Infectious-Asymptomatic infectious-Recovered by immunity or by vaccination-Dead due to the disease) subpopulations is produced with switching transmission rate, basic reproduction ratio and vaccination strategy. Thekey novel featureof our modelis that we reproduce the different phasesof theevolutionof the infectious diseasebyusingahybrid automatonwithdifferent discrete locations correspondingtoeachof the phases of the disease. This is a general modelling framework applicable to the spreading of infectious diseases.We showhow the proposed modelworks with the simulationof different scenarios

Detecting shifts in metropolitan structure: a spatial network perspective

© 2022 The Authors. Published by SAGE. This is an open access article available under a Creative Commons licence. The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1177/23998083211065767The spatial distribution of metropolitan areas creates a complex system of competing and cooperating economic units. Understanding the size, scale and functional structure of such systems is an important topic in regional science. This paper uses commuter flow data over a forty year period to analyse the changing structure of the Greater Manchester metropolitan area. We apply a combination of complex network analysis, residual network analysis and spatial network visualisation to detect Greater Manchester’s polycentric structure and identify intra-regional communities. This method is able to identify economic geographies in a highly complex and interdependent commuter network. We comment on the role of administrative boundaries in shaping metropolitan regions and discuss the potential of our work to inform debates on regional governance geographies and local government planning practices

Validation of the Spanish versions of the long (26 items) and short (12 items) forms of the Self-Compassion Scale (SCS)

Background: Self-compassion is a key psychological construct for assessing clinical outcomes in mindfulness-based interventions. the aim of this study was to validate the Spanish versions of the long (26 item) and short (12 item) forms of the Self-Compassion Scale (SCS).Methods: the translated Spanish versions of both subscales were administered to two independent samples: Sample 1 was comprised of university students (n = 268) who were recruited to validate the long form, and Sample 2 was comprised of Aragon Health Service workers (n = 271) who were recruited to validate the short form. in addition to SCS, the Mindful Attention Awareness Scale (MAAS), the State-Trait Anxiety Inventory-Trait (STAI-T), the Beck Depression Inventory (BDI) and the Perceived Stress Questionnaire (PSQ) were administered. Construct validity, internal consistency, test-retest reliability and convergent validity were tested.Results: the Confirmatory Factor Analysis (CFA) of the long and short forms of the SCS confirmed the original six-factor model in both scales, showing goodness of fit. Cronbach's a for the 26 item SCS was 0.87 (95% CI = 0.85-0.90) and ranged between 0.72 and 0.79 for the 6 subscales. Cronbach's a for the 12-item SCS was 0.85 (95% CI = 0.81-0.88) and ranged between 0.71 and 0.77 for the 6 subscales. the long (26-item) form of the SCS showed a test-retest coefficient of 0.92 (95% CI = 0.89-0.94). the Intraclass Correlation (ICC) for the 6 subscales ranged from 0.84 to 0.93. the short (12-item) form of the SCS showed a test-retest coefficient of 0.89 (95% CI: 0.87-0.93). the ICC for the 6 subscales ranged from 0.79 to 0.91. the long and short forms of the SCS exhibited a significant negative correlation with the BDI, the STAI and the PSQ, and a significant positive correlation with the MAAS. the correlation between the total score of the long and short SCS form was r = 0.92.Conclusion: the Spanish versions of the long (26-item) and short (12-item) forms of the SCS are valid and reliable instruments for the evaluation of self-compassion among the general population. These results substantiate the use of this scale in research and clinical practice.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Miguel Servet Hosp, Aragon Inst Hlth Sci I CS, Dept Psychiat, Zaragoza, SpainPrimary Care Prevent & Hlth Promot Res Network Re, Zaragoza, SpainBit&Brain Technol, Zaragoza, Spain12 Octubre Res Inst, Madrid, SpainUniv Zaragoza, Fac Hlth Sci & Sports, Huesca, SpainLozano Blesa Univ, Clin Hosp, Zaragoza, SpainUniversidade Federal de São Paulo UNIFESP, Escola Paulista Med, Dept Prevent Med, Ctr Mindfulness & Hlth Promot, São Paulo, BrazilUniversidade Federal de São Paulo UNIFESP, Escola Paulista Med, Dept Prevent Med, Ctr Mindfulness & Hlth Promot, São Paulo, BrazilWeb of Scienc