Polynomial Time corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length

We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential equations with polynomial right-hand side. This result gives a purely continuous (time and space) elegant and simple characterization of $\operatorname{PTIME}$. This is the first time such classes are characterized using only ordinary differential equations. Our characterization extends to functions computable in polynomial time over the reals in the sense of computable analysis. This extends to deterministic complexity classes above polynomial time. This may provide a new perspective on classical complexity, by giving a way to define complexity classes, like $\operatorname{PTIME}$, in a very simple way, without any reference to a notion of (discrete) machine. This may also provide ways to state classical questions about computational complexity via ordinary differential equations, i.e.~by using the framework of analysis

Microbiology education: The case of the SARS-CoV-2 and COVID-19 pandemic in didactic transposition

The school constitutes a privileged setting for learning international scientific knowledge and local socio-economic and political context knowledge. Selecting content to be learned in school is a permanent tension matter of great social and political relevance. The didactic transposition looks at how and when scientific contents ("International scientific knowledge") are selected to be taught in school ("Knowledge to be taught") in the External Didactic Transposition (EDT) process and how this knowledge is taught and learned at school ("Learned knowledge") in the Internal Didactic Transposition (IDT). In the EDT process, policymakers select the knowledge to be taught in schools from international scientific knowledge, creating national school programmes that also serve as textbook guidelines to be used as pedagogical resources in the classroom. These decisions are subject to the influences of several sectors of society, such as politicians, agencies, educators and other stakeholders, and so they take a long time to be established. This work shows how critical social issues such as the SARS-CoV-2 and Covid-19 pandemic could disturb the usual process of didactic transposition. Indeed, usually, there is a considerable period between the emergence of a scientific concept and its appearance in the national curriculum called Didactic Transposition Delay (DTD). Therefore, it was expected that the SARS-CoV-2 and Covid-19 pandemic topics would be added, in the future, to the national curricula and textbooks of most countries. However, being a matter of great social interest, the SARS-CoV-2 and Covid-19 pandemic topic, which emerged in late 2019 and had a massive social impact on the whole planet in 2020, started almost immediately to be a matter of classroom discussions between teachers and students ("learned knowledge"), much time before textbooks were available to support the teaching and learning process and national programmes would be published even much later. Therefore, in this process, there was a shortcut where the SARS-CoV-2 and Covid-19 pandemic topic ("International scientific knowledge") surpassed the curriculum step ("Knowledge to be taught") to be taught in school ("Learned knowledge") at once.This research had partial financial support from Portuguese national funds through the FCT (Foundation for Science and Technology) within the framework of the CIEC project UIDB/00317/2020 and CEB project UIDB/04469/2020. It also had the partial support of the European Union's Horizon 2020 research and innovation programme under grant agreement nº 871129 - IS_MIRRI21 Projectinfo:eu-repo/semantics/publishedVersio

Computing the exact number of periodic orbits for planar flows

In this paper, we consider the problem of determining the \emph{exact} number of periodic orbits for polynomial planar flows. This problem is a variant of Hilbert's 16th problem. Using a natural definition of computability, we show that the problem is noncomputable on the one hand and, on the other hand, computable uniformly on the set of all structurally stable systems defined on the unit disk. We also prove that there is a family of polynomial planar systems which does not have a computable sharp upper bound on the number of its periodic orbits

The "Planning Health in School” programme (PHS-pro) to improve healthy eating and physical activity: design, methodology, and process evaluation

Few interventions have successfully promoted healthy eating and active living among children with effective changes in anthropometric health outcomes. Well-designed interventions involving multiple strategies to convert the knowledge already available into action are needed for preventing childhood obesity. In this study, an educational programme called “Planning Health in School” (PHS-pro) was designed, implemented and evaluated to contribute to the prevention of obesity in childhood. The PHS-pro aimed at improving the eating behaviours and lifestyles of Portuguese grade-6 children towards healthier nutritional status. This paper describes and evaluates the PHS-pro concerning: (i) the research design within the theoretical framework grounded on “The Transtheoretical Model” and the stages of change; (ii) the educational components and the application of the participatory methodology to engage children to meet their needs, as active participants in their change process; and (iii) the process evaluation of the intervention. The implementation of the PHS-pro took into account the views and inputs of the participants for evaluating the educational components that should be considered in the designing of interventions aiming to be effective strategies. From the health promotion perspective, this study is important because it examines new approaches and pathways to effectively prevent overweight and obesity in children.Foundation for Science and Technology (FCT), grant numbers SFRH/BD/79512/2011 and Research Centre on Child Studies (R&D Unit 317 of FCT; projects UIDB/00317/2020 and UIDP/00317/2020)

Sleep quality in adolescents: What´s discriminates good from poor sleepers?

The present research had a support of Erasmus Mundus 15.Background: The study focused on discriminating adolescents with good versus poor sleep quality. Method: The sample consisted of 272 adolescents and a transversal design was used. The instruments assessed socio-demographic data, psychological morbidity, sleep quality, family sleep behavior, excessive daytime sleepiness, sleep habits and social skills. Results: The results revealed that age, caffeine intake, psychological morbidity, excessive daytime sleepiness, and family sleep behavior were variables that discriminated good from poorer sleepers in terms of adolescents’ sleep quality. Conclusions: The results emphasize the role of family on sleep quality and the need to include family members in intervention programs. Programs should be sensitive to adolescents’ age and gender.Erasmus Mundus 15