Discrete-time staged progression epidemic models

In the Staged Progression (SP) epidemic models, infected individuals are classified into a suitable number of states. The goal of these models is to describe as closely as possible the effect of differences in infectiousness exhibited by individuals going through the different stages. The main objective of this work is to study, from the methodological point of view, the behavior of solutions of the discrete time SP models without reinfection and with a general incidence function. Besides calculating $\mathcal{R}_{0}$, we find bounds for the epidemic final size, characterize the asymptotic behavior of the infected classes, give results about the final monotonicity of the infected classes, and obtain results regarding the initial dynamics of the prevalence of the disease. Moreover, we incorporate into the model the probability distribution of the number of contacts in order to make the model amenable to study its effect in the dynamics of the disease

Discrete epidemic models with two time scales

The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could represent movements between spatial locations, changes of individual activities or behaviours, or others. To include a sufficiently general disease model, we first build up from first principles a discrete-time Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS) model and characterize the eradication or endemicity of the disease with the help of its basic reproduction number R0. Then, we propose a general full model that includes sequentially the two processes at different time scales, and proceed to its analysis through a reduced model. The basic reproduction number R0 of the reduced system gives a good approximation of the R0 of the full model since it serves at analyzing its asymptotic behaviour. As an illustration of the proposed general framework, it is shown that there exist conditions under which a locally endemic disease, considering isolated patches in a metapopulation, can be eradicated globally by establishing the appropriate movements between patches

Approximate reduction of nonlinear discrete models with two time scales

The aim of this work is to present a general class of nonlinear discrete time models with two time scales whose dynamics is susceptible of being approached by means of a reduced system. The reduction process is included in the so-called approximate aggregation of variables methods which consist of describing the dynamics of a complex system involving many coupled variables through the dynamics of a reduced system formulated in terms of a few global variables. For the time unit of the discrete system we use that of the slow dynamics and assume that fast dynamics acts a large number of times during it. After introducing a general two-time scales nonlinear discrete model we present its reduced accompanying model and the relationships between them. The main result proves that certain asymptotic behaviours, hyperbolic asymptotically stable (A.S.) periodic solutions, to the aggregated system entail that to the original system

Creating collaborative groups in a MOOC: a homogeneous engagement grouping approach

Producción CientíficaCollaborative learning can improve the pedagogical effectiveness of MOOCs. Group formation, an essential step in the design of collaborative learning activities, can be challenging in MOOCs given the scale and the wide variety in such contexts. We discuss the need for considering the behaviours of the students in the course to form groups in MOOC contexts, and propose a grouping approach that employs homogeneity in terms of students’ engagement in the course. Two grouping strategies with different degrees of homogeneity are derived from this approach, and their impact to form successful groups is examined in a real MOOC context. The grouping criteria were established using student activity logs (e.g. page-views). The role of the timing of grouping was also examined by carrying out the intervention once in the first and once in the second half of the course. The results indicate that in both interventions, the groups formed with a greater degree of homogeneity had higher rates of task-completion and peer interactions, Additionally, students from these groups reported higher levels of satisfaction with their group experiences. On the other hand, a consistent improvement of all indicators was observed in the second intervention, since student engagement becomes more stable later in the course.Agencia Estatal de Investigación Española - Fondo Europeo de Desarrollo Regional (grants TIN2017-85179-C3-2-R / TIN2014-53199-C3-2-RJunta de Castilla y León - Fondo Europeo de Desarrollo Regional (grant VA257P18)Comisión Europea (grant 588438-EPP-1-2017-1-EL-EPPKA2-KA

Cuaderno de prácticas virtual de Fitopatología Molecular de Plantas

Memoria ID12-0167. Ayudas de la Universidad de Salamanca para la innovación docente, curso 2012-2013

Nitric oxide overproduction by cue1 mutants differs on developmental stages and growth conditions

The cue1 nitric oxide (NO) overproducer mutants are impaired in a plastid phosphoenolpyruvate/phosphate translocator, mainly expressed in Arabidopsis thaliana roots. cue1 mutants present an increased content of arginine, a precursor of NO in oxidative synthesis processes. However, the pathways of plant NO biosynthesis and signaling have not yet been fully characterized, and the role of CUE1 in these processes is not clear. Here, in an attempt to advance our knowledge regarding NO homeostasis, we performed a deep characterization of the NO production of four different cue1 alleles (cue1-1, cue1-5, cue1-6 and nox1) during seed germination, primary root elongation, and salt stress resistance. Furthermore, we analyzed the production of NO in different carbon sources to improve our understanding of the interplay between carbon metabolism and NO homeostasis. After in vivo NO imaging and spectrofluorometric quantification of the endogenous NO levels of cue1 mutants, we demonstrate that CUE1 does not directly contribute to the rapid NO synthesis during seed imbibition. Although cue1 mutants do not overproduce NO during germination and early plant development, they are able to accumulate NO after the seedling is completely established. Thus, CUE1 regulates NO homeostasis during post-germinative growth to modulate root development in response to carbon metabolism, as different sugars modify root elongation and meristem organization in cue1 mutants. Therefore, cue1 mutants are a useful tool to study the physiological effects of NO in post-germinative growth

Supporting Teachers in the Design and Implementation of Group Formation Policies in MOOCs: A Case Study

Producción CientíficaCollaborative learning strategies, which can promote student learning and achievement, have rarely been incorporated into pedagogies of MOOCs. Such strategies, when implemented properly, can boost the quality of MOOC pedagogy. Nonetheless, the use of collaborative groups in MOOCs is scarce due to several yet critical contextual factors (e.g., massiveness, and variable levels of engagement) that hamper the group formation process. Therefore, there is a need for supporting MOOC teachers in the design and implementation of group formation policies when implementing collaborative strategies. This paper presents a study where two instruments were used to explore solutions to this need: a guide to support teachers during the planning of the group formation, and a technological tool to help them implement the collaborative groups designed and to monitor them. According to the results of the study, the design guide made the teachers aware of the contextual factors to consider when forming the collaborative groups, and allowed teachers inform some configuration parameters of the activity (e.g., duration and assessment type) and the group formation (e.g., criteria and parameters needed to build the groups). The technological tool was successfully incorporated into the MOOC platform. Lessons learned from the findings of the study are shared and their potential to inform the design guide is discussed.Ministerio de Economía, Industria y Competitividad (Projects TIN2014-53199- C3-2-R and TIN2017-85179-C3-2-R)Junta de Castilla y León (programa de apoyo a proyectos de investigación - Ref. VA082U16)European Commission (Proyect 588438-EPP-1-2017-1-EL-EPPKA2-KA

Nitric oxide alters the pattern of auxin maxima and PIN-FORMED1 during shoot development

Hormone patterns tailor cell fate decisions during plant organ formation. Among them, auxins and cytokinins are critical phytohormones during early development. Nitric oxide (NO) modulates root architecture by the control of auxin spatial patterns. However, NO involvement during the coordination of shoot organogenesis remains unclear. Here, we explore the effect of NO during shoot development by using a phenotypic, cellular, and genetic analysis in Arabidopsis thaliana and get new insights into the characterization of NO-mediated leaf-related phenotypes. NO homeostasis mutants are impaired in several shoot architectural parameters, including phyllotactic patterns, inflorescence stem elongation, silique production, leaf number, and margin. Auxin distribution is a key feature for tissue differentiation and need to be controlled at different levels (i.e., synthesis, transport, and degradation mechanisms). The phenotypes resulting from the introduction of the cue1 mutation in the axr1 auxin resistant and pin1 backgrounds exacerbate the relationship between NO and auxins. Using the auxin reporter DR5:GUS, we observed an increase in auxin maxima under NO-deficient mutant backgrounds and NO scavenging, pointing to NO-ASSOCIATED 1 (NOA1) as the main player related to NO production in this process. Furthermore, polar auxin transport is mainly regulated by PIN-FORMED 1 (PIN1), which controls the flow along leaf margin and venations. Analysis of PIN1 protein levels shows that NO controls its accumulation during leaf development, impacting the auxin mediated mechanism of leaf building. With these findings, we also provide evidence for the NO opposite effects to determine root and shoot architecture, in terms of PIN1 accumulation under NO overproduction

Reduction of Discrete Dynamical Systems with Applications to Dynamics Population Models

In this work we review the aggregation of variables method for discrete dynamical systems. These methods consist of describing the asymptotic behaviour of a complex system involving many coupled variables through the asymptotic behaviour of a reduced system formulated in terms of a few global variables. We consider population dynamics models including two processes acting at different time scales. Each process has associated a map describing its effect along its specific time unit. The discrete system encompassing both processes is expressed in the slow time scale composing the map associated to the slow one and the k-th iterate of the map associated to the fast one. In the linear case a result is stated showing the relationship between the corresponding asymptotic elements of both systems, initial and reduced. In the nonlinear case, the reduction result establishes the existence, stability and basins of attraction of steady states and periodic solutions of the original system with the help of the same elements of the corresponding reduced system. Several models looking over the main applications of the method to populations dynamics are collected to illustrate the general results