Coalgebras of topological types

In This work, we focus on developing the basic theory of coalgebras over the category Top (the category of topological spaces with continuous maps). We argue that, besides Set, the category Top is an interesting base category for coalgebras. We study some endofunctors on Top, in particular, Vietoris functor and P-Vietoris Functor (where P is a set of propositional letters) that due to Hofmann et. al. [42] can be considered as the topological versions of the powerset functor and P-Kripke functor, respectively. We define the notion of compact Kripke structures and we prove that Kripke homomorphisms preserve compactness. Our definition of "compact Kripke structure" coincides with the notion of "modally saturated structures" introduced in Fine [27]. We prove that the class of compact Kripke structures has Hennessy-Milner property. As a consequence we show that in this class of Kripke structures, bihavioral equivalence, modal equivalence and Kripke bisimilarity all coincide.Furthermore, we generalize the notion of descriptive structures defined in Venema et. al. [11] by introducing a notion Vietoris models. We identify Vietoris models as coalgebras for the P-Vietoris functor on the category Top. One can see that each compact Kripke model can be modified to a Vietoris model. This yields an adjunction between the category of Vietoris structures (VS) and the category of compact Kripke structurs (CKS). Moreover, we will prove that the category of Vietoris models has a terminal object. We study the concept of a Vietoris bisimulation between Vietoris models, and we will prove that the closure of a Kripke bisimulation between underlying Kripke models of two Vietoris models is a Vietoris bisimulation. In the end, it will be shown that in the class of Vietoris models, Vietoris bisimilarity, bihavioral equivalence, modal equivalence, all coincide

Game-theoretic analysis of supply chain coordination under advertising and price dependent demand

Supply chain members cannot act independently and they need to act as a part of a unified system and coordinated with other members. Therefore, a coordination mechanism may be necessary to motivate members to achieve coordination. In this paper, the coordination problem is studied in a two-level supply chain consisting of a supplier and a retailer where demand is a function of price and advertising expenditures in two scenarios. The first scenario is “No coordination”, and the other scenario is “coordination with Revenue sharing contract”. The models are solved using game theory, Cooperative and Nash equilibrium. Finally, numerical examples are presented indicating that the average expected profit in the second scenario, coordination with revenue sharing, is higher than the first scenario. In addition numerical examples indicate that as price and advertising elasticity to demand increase, profitability of supply chain decreases

Effects of home confinement on mental health and lifestyle behaviours during the COVID-19 outbreak:insights from the ECLB-COVID19 multicentre study

Although recognised as effective measures to curb the spread of the COVID-19 outbreak, social distancing and self-isolation have been suggested to generate a burden throughout the population. To provide scientific data to help identify risk factors for the psychosocial strain during the COVID-19 outbreak, an international cross-disciplinary online survey was circulated in April 2020. This report outlines the mental, emotional and behavioural consequences of COVID-19 home confinement. The ECLB-COVID19 electronic survey was designed by a steering group of multidisciplinary scientists, following a structured review of the literature. The survey was uploaded and shared on the Google online survey platform and was promoted by thirty-five research organizations from Europe, North Africa, Western Asia and the Americas. Questions were presented in a differential format with questions related to responses “before” and “during” the confinement period. 1047 replies (54% women) from Western Asia (36%), North Africa (40%), Europe (21%) and other continents (3%) were analysed. The COVID-19 home confinement evoked a negative effect on mental wellbeing and emotional status (P < 0.001; 0.43 ≤ d ≤ 0.65) with a greater proportion of individuals experiencing psychosocial and emotional disorders (+10% to +16.5%). These psychosocial tolls were associated with unhealthy lifestyle behaviours with a greater proportion of individuals experiencing (i) physical (+15.2%) and social (+71.2%) inactivity, (ii) poor sleep quality (+12.8%), (iii) unhealthy diet behaviours (+10%), and (iv) unemployment (6%). Conversely, participants demonstrated a greater use (+15%) of technology during the confinement period. These findings elucidate the risk of psychosocial strain during the COVID-19 home confinement period and provide a clear remit for the urgent implementation of technology-based intervention to foster an Active and Healthy Confinement Lifestyle AHCL)

Globally altered sleep patterns and physical activity levels by confinement in 5056 individuals:ECLB COVID-19 international online survey

Symptoms of psychological distress and disorder have been widely reported in people under quarantine during the COVID-19 pandemic; in addition to severe disruption of peoples' daily activity and sleep patterns. This study investigates the association between physical-activity levels and sleep patterns in quarantined individuals. An international Google online survey was launched in April 6th, 2020 for 12-weeks. Forty-one research organizations from Europe, North-Africa, Western-Asia, and the Americas promoted the survey through their networks to the general society, which was made available in 14 languages. The survey was presented in a differential format with questions related to responses "before" and "during" the confinement period. Participants responded to the Pittsburgh Sleep Quality Index (PSQI) questionnaire and the short form of the International Physical Activity Questionnaire. 5056 replies (59.4% female), from Europe (46.4%), Western-Asia (25.4%), America (14.8%) and North-Africa (13.3%) were analysed. The COVID-19 home confinement led to impaired sleep quality, as evidenced by the increase in the global PSQI score (4.37 +/- 2.71 before home confinement vs. 5.32 +/- 3.23 during home confinement) (p &lt; 0.001). The frequency of individuals experiencing a good sleep decreased from 61% (n = 3063) before home confinement to 48% (n = 2405) during home confinement with highly active individuals experienced better sleep quality (p &lt; 0.001) in both conditions. Time spent engaged in all physical-activity and the metabolic equivalent of task in each physical-activity category (i.e., vigorous, moderate, walking) decreased significantly during COVID-19 home confinement (p &lt; 0.001). The number of hours of daily-sitting increased by similar to 2 hours/days during home confinement (p &lt; 0.001). COVID-19 home confinement resulted in significantly negative alterations in sleep patterns and physical-activity levels. To maintain health during home confinement, physical-activity promotion and sleep hygiene education and support are strongly warranted.</p

Sleep Quality and Physical Activity as Predictors of Mental Wellbeing Variance in Older Adults during COVID-19 Lockdown:ECLB COVID-19 International Online Survey

Background. The COVID-19 lockdown could engender disruption to lifestyle behaviors, thus impairing mental wellbeing in the general population. This study investigated whether sociodemographic variables, changes in physical activity, and sleep quality from pre- to during lockdown were predictors of change in mental wellbeing in quarantined older adults. Methods. A 12-week international online survey was launched in 14 languages on 6 April 2020. Forty-one research institutions from Europe, Western-Asia, North-Africa, and the Americas, promoted the survey. The survey was presented in a differential format with questions related to responses "pre" and "during" the lockdown period. Participants responded to the Short Warwick-Edinburgh Mental Wellbeing Scale, the Pittsburgh Sleep Quality Index (PSQI) questionnaire, and the short form of the International Physical Activity Questionnaire. Results. Replies from older adults (aged &gt;55 years, n = 517), mainly from Europe (50.1%), Western-Asia (6.8%), America (30%), and North-Africa (9.3%) were analyzed. The COVID-19 lockdown led to significantly decreased mental wellbeing, sleep quality, and total physical activity energy expenditure levels (all p &lt; 0.001). Regression analysis showed that the change in total PSQI score and total physical activity energy expenditure (F-(2,F- 514) = 66.41 p &lt; 0.001) were significant predictors of the decrease in mental wellbeing from pre- to during lockdown (p &lt; 0.001, R-2: 0.20). Conclusion. COVID-19 lockdown deleteriously affected physical activity and sleep patterns. Furthermore, change in the total PSQI score and total physical activity energy expenditure were significant predictors for the decrease in mental wellbeing.</p