We study the complexities of isometry and isomorphism classes of separable Banach spaces in the Polish spaces of Banach spaces, recently introduced and investigated by the authors in [14]. We obtain sharp results concerning the most classical separable Banach spaces.

We prove that the infinite-dimensional separable Hilbert space is characterized as the unique separable infinite-dimensional Banach space whose isometry class is closed, and also as the unique separable infinite-dimensional Banach space whose isomorphism class is $F_\sigma $. For $p\in \left [1,2\right )\cup \left (2,\infty \right )$, we show that the isometry classes of $L_p[0,1]$ and $\ell _p$ are $G_\delta $-complete sets and $F_{\sigma \delta }$-complete sets, respectively. Then we show that the isometry class of $c_0$ is an $F_{\sigma \delta }$-complete set.

Additionally, we compute the complexities of many other natural classes of separable Banach spaces; for instance, the class of separable $\mathcal {L}_{p,\lambda +}$-spaces, for $p,\lambda \geq 1$, is shown to be a $G_\delta $-set, the class of superreflexive spaces is shown to be an $F_{\sigma \delta }$-set, and the class of spaces with local $\Pi $-basis structure is shown to be a $\boldsymbol {\Sigma }^0_6$-set. The paper is concluded with many open problems and suggestions for a future research.

Sufficient sleep is necessary for optimal health, daytime performance and wellbeing and the amount required is age-dependent and decreases across the lifespan. Sleep duration is usually affected by age and several different cultural, social, psychological, behavioural, pathophysiological and environmental factors. This review considers how much sleep children and adults need, why this is important, what the consequences are of insufficient sleep and how we can improve sleep. A lack of the recommended amount of sleep for a given age group has been shown to be associated with detrimental effects on health including effects on metabolism, endocrine function, immune function and haemostatic pathways. Obesity has increased worldwide in the last few decades and the WHO has now declared it a global epidemic. A lack of sleep is associated with an increased risk of obesity in children and adults, which may lead to future poor health outcomes. Data from studies in both children and adults suggest that the relationship between sleep and obesity may be mediated by several different mechanisms including alterations in appetite and satiety, sleep timing, circadian rhythm and energy balance. Moreover, there is evidence to suggest that improvements in sleep, in both children and adults, can be beneficial for weight management and diet and certain foods might be important to promote sleep. In conclusion this review demonstrates that there is a wide body of evidence to suggest that sleep and obesity are causally related and recommends that further research is required to inform policy, and societal change.

Histories of Third Worldism have received renewed attention from historians in the past decade. Much of the resulting scholarship has focused on the international to the exclusion of the national. This article addresses this relative neglect by focusing on a particular iteration of Third World nation-state-building: co-operative socialism in Forbes Burnham's Guyana. Refuting the argument that co-operative socialism was imitative and implemented for reasons of political expediency only, the article contends that Burnham's doctrine should be regarded as a meaningful attempt at remaking Guyana's society and economy through its core principles of self-sufficiency, self-reliance, and self-discipline. These principles gave rise to a specific conception of citizenship in 1970s Guyana, where the People's National Congress (PNC) sought to link political belonging and participation with a moral ethic premised on the notion of hard work in service of the nation. The article examines how this collectivist understanding of citizenship gave rise to a particular set of struggles at the turn of the 1980s, as the co-operative republic began to collapse. What emerged from these struggles was an alternate but parallel imagining of citizenship espoused by the Working People's Alliance (WPA), which rejected the PNC's vanguardism in favour of empowering the Guyanese people through the creation of non-hierarchical systems of collective authority. The article concludes by arguing that the failure of the WPA's attempt to overthrow the PNC through popular revolt signified the ends of decolonization and Third Worldism in the Caribbean, and the beginnings of new struggles against new forms of coloniality in the guise of the emerging neoliberal and good governance agendas.

Drawing on the integrative model of uncertainty tolerance, we aimed to investigate whether uncertainty relates to adaptive performance, at the within-person level. We argue that daily uncertainty at work will trigger negative affective reactions that, in turn, will minimize adaptive performance. Moreover, we focus on socio-cognitive mindfulness as a cross-level moderator of the indirect relationship of uncertainty on adaptive performance via negative affect. To capture changes in daily life and test our model, we conducted two diary studies across 5-working days: One with a sample of telecommuters (n = 101*5 = 505), and the other with a sample of non-telecommuters (n = 253*5 = 1,265). Study 1 took place between February and March of 2021 (during the mandatory confinement), and Study 2 occurred between April and May 2021 (out of the mandatory confinement). Both studies were conducted in Portugal. The multilevel results showed that at the day-level of analysis, uncertainty decreased adaptive performance through the enhanced negative affect. Moreover, at the person-level of analysis mindfulness moderated (a) the direct relationship of uncertainty to adaptive performance, and (b) the indirect relationship of uncertainty to adaptive performance via negative affect, in such a way that it became weaker when mindfulness was higher (multilevel-mediated moderation effect). This relation was different between Studies 1 and 2; that is, in Study 1, teleworkers who were high on mindfulness engaged in more adaptive performance when negative affect was high. In Study 2, adaptive performance significantly decreased, when negative affect was higher, even though this effect was weaker for mindful of individuals. The findings show that mindfulness helps to fill in the spaces of the affective uncertainty attenuating its detrimental effects.

Drawing on early work on ethical leadership, we argue that when leaders engage in leader moral hypocrisy (i.e., ethical promotion without ethical demonstration), followers can experience psychological reactance—a negative response to a perceived restriction of freedom—which can have negative downstream consequences. In a survey of employee–manager dyads (study 1), we demonstrate that leader moral hypocrisy is positively associated with follower psychological reactance, which increases follower deviance. In two subsequent laboratory experiments, we find similar patterns of results (study 2) and explore potential alternative mechanisms (study 3). We demonstrate in a final experiment with working adults that the relationship between leader moral hypocrisy and psychological reactance is partly explained by increased perceptions of a leader’s use of power (study 4). We discuss the implications of our findings and advocate for further understanding of the risks associated with psychological reactance in response to leaders and other workplace situations.

This article examines the relationship between legislative civility and legislative productivity in US state legislatures. The research employs data from the National Survey of State Legislative Lobbyists and from the State Policy Innovation and Diffusion (SPID) database. The former dataset is used to generate an overall civility index for each state as developed by Kettler et al. The SPID database allows one to measure the legislative productivity of a state legislature. Employing these data, negative binomial and Poisson regression models reveal that state legislatures rated as more civil by their own lobbyists produced significantly more pieces of noteworthy legislation than those legislative bodies rated as less civil. These results suggest that the quality of internal legislative dynamics matters for legislative productivity.

Evidence suggests that differences in meal timing between weekends and weekdays can disrupt the body’s circadian rhythm, leading to a higher BMI. We aimed to investigate the associations between mealtime variation from weekdays to weekends (eating midpoint jetlag), dietary intake and anthropometric parameters, based on individuals’ chronotype. The study utilised data from National Health and Nutrition Examination Survey 2017–2018. Food consumption was estimated by weighted average of participants’ food intake on weekdays and weekends. Eating midpoint jetlag, defined as the difference between the midpoint of the first and last mealtimes on weekends and weekdays, was calculated. Chronotype was assessed by participants’ mid-sleep time on weekends, adjusted for sleep debt. Linear regression analysis was conducted to investigate the associations between variables. The sample was categorised into chronotype tertiles. Among individuals in the third chronotype tertile, there was a positive association between eating midpoint jetlag and BMI (β = 1·2; 95 % CI (1·13, 1·27)). Individuals in the first tertile showed a positive association between eating midpoint jetlag and energy (β = 96·9; 95 % CI (92·9, 101·7)), carbohydrate (β = 11·96; 95 % CI (11·2, 12·6)), fat (β = 3·69; 95 % CI (3·4, 3·8)), cholesterol (β = 32·75; 95 % CI (30·9, 34·6)) and sugar (β = 8·84; 95 % CI (8·3, 9·3)) intake on weekends. Among individuals with an evening tendency, delaying meals on weekends appears to be linked to a higher BMI. Conversely, among individuals with a morning tendency, eating meals later on weekends is associated with higher energetic intake on weekends.

This study aimed to identify the longitudinal association between seaweed and type 2 diabetes mellitus (T2DM) in the Korean population. Data from 148 404 Korean adults aged 40 years and older without a history of T2DM, cardiovascular disease or cancer at baseline were obtained from the Korean Genome and Epidemiology Study data. The participants’ seaweed intake was obtained using a validated semi-quantitative food frequency questionnaire, and the diagnosis of T2DM was surveyed through a self-reported questionnaire during follow-up. The hazard ratio (HR) and 95 % confidence interval (CI) for T2DM were calculated using the Cox proportional hazard regression, and the dose–response relationship was analysed using a restricted cubic spline regression. Participants had a mean follow-up period of 5 years. Participants with the highest seaweed intake had a 7 % lower risk of T2DM compared with the group with the lowest intake (95 % CI (0·87, 0·99)). Interestingly, this association was stronger in those with normal weight (HR: 0·88, 95 % CI (0·81, 0·95)), while no association was observed in participants with obesity. Spline regression revealed an inverse linear relationship between seaweed intake and T2DM risk in participants with normal weight, showing a trend where increased seaweed intake is related to lower instances of T2DM (Pfor nonlinearity = 0·48). Seaweed intake is inversely associated with the onset of T2DM in Korean adults with normal weight.

Ultrafilters play a significant role in model theory to characterize logics having various compactness and interpolation properties. They also provide a general method to construct extensions of first-order logic having these properties. A main result of this paper is that every class $\Omega $ of uniform ultrafilters generates a $\Delta $-closed logic ${\mathcal {L}}_\Omega $. ${\mathcal {L}}_\Omega $ is $\omega $-relatively compact iff some $D\in \Omega $ fails to be $\omega _1$-complete iff ${\mathcal {L}}_\Omega $ does not contain the quantifier “there are uncountably many.” If $\Omega $ is a set, or if it contains a countably incomplete ultrafilter, then ${\mathcal {L}}_\Omega $ is not generated by Mostowski cardinality quantifiers. Assuming $\neg 0^\sharp $ or $\neg L^{\mu }$, if $D\in \Omega $ is a uniform ultrafilter over a regular cardinal $\nu $, then every family $\Psi $ of formulas in ${\mathcal {L}}_\Omega $ with $|\Phi |\leq \nu $ satisfies the compactness theorem. In particular, if $\Omega $ is a proper class of uniform ultrafilters over regular cardinals, ${\mathcal {L}}_\Omega $ is compact.

The asymptotic mean value Laplacian—AMV Laplacian—extends the Laplace operator from $\mathbb {R}^n$ to metric measure spaces through limits of averaging integrals. The AMV Laplacian is however not a symmetric operator in general. Therefore, we consider a symmetric version of the AMV Laplacian, and focus lies on when the symmetric and non-symmetric AMV Laplacians coincide. Besides Riemannian and 3D contact sub-Riemannian manifolds, we show that they are identical on a large class of metric measure spaces, including locally Ahlfors regular spaces with suitably vanishing distortion. In addition, we study the context of weighted domains of $\mathbb {R}^n$—where the two operators typically differ—and provide explicit formulae for these operators, including points where the weight vanishes.

Undernutrition is a major public health problem in developing countries. Around 40·2 % of children are stunted in Pakistan. This longitudinal study aimed to assess the effectiveness of locally produced ready-to-use supplementary foods in the prevention of stunting by detecting change in of children in intervention v. control arm against the 2006 WHO growth reference. A community-based non-randomised cluster-controlled trial was conducted from January 2018 to December 2020 in the district of Kurram, Khyber Pakhtunkhwa, Pakistan. A total of 80 clusters (each cluster comprising ≈ 250–300 households) were defined in the catchment population of twelve health facilities. Children aged 6–18 months were recruited n 1680. The intervention included a daily ration of 50 g – locally produced ready-to-use-supplementary food (Wawa-Mum). The main outcome of this study was a change in length for age z-score (LAZ) v. WHO growth standards. Comparison between the interventions was by t test and ANOVA. Cox proportional hazard models were used to assess the association between stunting occurrence and the utilisation of locally produced supplement. Out of the total 1680, fifty-one out of the total 1680, 51·1 out of the total 1680 and 51·1 % (n 859) were male. Mean age 13·9 months (sd + 859) were male. Mean age 13·9 months (sd + –4·4). At baseline, 36·9 % (n 618) were stunted. In the intervention group, mean LAZ score significantly increased from −1·13(2·2 sd) at baseline to −0·93(1·8 sd) at 6-month follow-up (P value 0·01) compared with the control group. The incidence rate of stunting in the intervention arm was 1·3 v. 3·4 per person year in the control arm. The control group had a significantly increased likelihood of stunting (Hazard Ratio (HR) 1·7, 95 % CI 1·46, 2·05, P value < 0·001) v. the intervention group. Locally produced ready-to-use supplementary food is an effective intervention for reducing stunting in children below 2 years of age. This can be provided as part of a malnutrition prevention package to overcome the alarming rates of stunting in Pakistan.

In Latin America, Colombia stands out for its more significant and persistent rural–urban educational performance gaps. This paper studies the evolution of this under-performance of Colombian rural areas by conducting a long-term descriptive analysis of a new dataset. The results suggest that the role of the national government is a source of these educational inequalities because rural education was introduced late and deficiently. That is, the national government delayed the provision of education to rural areas. Moreover, even when implemented, these rural educational initiatives proved deficient due to their lack of funds, lower quality, curricula detached from the rural context and a design that amplified regional disparities, thus producing and maintaining significant and persistent rural–urban gaps in education.