Algebraic structure for the crossing of balanced and stair nested designs

Stair nesting allows us to work with fewer observations than the most usual form of nesting, the balanced nesting. In the case of stair nesting the amount of information for the different factors is more evenly distributed. This new design leads to greater economy, because we can work with fewer observations. In this work we present the algebraic structure of the cross of balanced nested and stair nested designs, using binary operations on commutative Jordan algebras. This new cross requires fewer observations than the usual cross balanced nested designs and it is easy to carry out inference.

Assessment of the ensembles regional climate models in the representation of precipitation variability and extremes over Portugal

A new data set of daily gridded observations of precipitation, computed from over 400 stations in Portugal, is used to assess the performance of 12 regional climate models at 25 km resolution, from the ENSEMBLES set, all forced by ERA-40 boundary conditions, for the 1961-2000 period. Standard point error statistics, calculated from grid point and basin aggregated data, and precipitation related climate indices are used to analyze the performance of the different models in representing the main spatial and temporal features of the regional climate, and its extreme events. As a whole, the ENSEMBLES models are found to achieve a good representation of those features, with good spatial correlations with observations. There is a small but relevant negative bias in precipitation, especially in the driest months, leading to systematic errors in related climate indices. The underprediction of precipitation occurs in most percentiles, although this deficiency is partially corrected at the basin level. Interestingly, some of the conclusions concerning the performance of the models are different of what has been found for the contiguous territory of Spain; in particular, ENSEMBLES models appear too dry over Portugal and too wet over Spain. Finally, models behave quite differently in the simulation of some important aspects of local climate, from the mean climatology to high precipitation regimes in localized mountain ranges and in the subsequent drier regions.

Crossing balanced and stair nested desings

Balanced nesting is the most usual form of nesting and originates, when used singly or with crossing of such sub-models, orthogonal models. In balanced nesting we are forced to divide repeatedly the plots and we have few degrees of freedom for the first levels. If we apply stair nesting we will have plots all of the same size rendering the designs easier to apply. The stair nested designs are a valid alternative for the balanced nested designs because we can work with fewer observations, the amount of information for the different factors is more evenly distributed and we obtain good results. The inference for models with balanced nesting is already well studied. For models with stair nesting it is easy to carry out inference because it is very similar to that for balanced nesting. Furthermore stair nested designs being unbalanced have an orthogonal structure. Other alternative to the balanced nesting is the staggered nesting that is the most popular unbalanced nested design which also has the advantage of requiring fewer observations. However staggered nested designs are not orthogonal, unlike the stair nested designs. In this work we start with the algebraic structure of the balanced, the stair and the staggered nested designs and we finish with the structure of the cross between balanced and stair nested designs.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

Cobs and stair nesting – segregation and crossing

Stair nesting leads to very light models since the number of their treatments is additive on the numbers of observations in which only the level of one factor various. These groups of observations will be the steps of the design. In stair nested designs we work with fewer observations when compared with balanced nested designs and the amount of information for the different factors is more evenly distributed. We now integrate these models into a special class of models with orthogonal block structure for which there are interesting properties.

Integrated didactics: an example of a curriculum model enhancing knowledge crossing

In this paper, we introduce an innovative course in the Portuguese Context, the Master's Course in “Integrated Didactics in Mother Tongue, Maths, Natural and Social Sciences”, taking place at the Lisbon School of Education and discussing in particular the results of the evaluation made by the students who attended the Curricular Unit - Integrated Didactics (CU-ID). This course was designed for in-service teachers of the first six years of schooling and intends to improve connections between different curriculum areas. In this paper, we start to present a few general ideas about curriculum development; to discuss the concept of integration; to present the principles and objectives of the course created as well as its structure; to describe the methodology used in the evaluation process of the above mentioned CU-ID. The results allow us to state that the students recognized, as positive features of the CU-ID, the presence in all sessions of two teachers simultaneously from different scientific areas, as well as invitations issued to specialists on the subject of integration and to other teachers that already promote forms of integration in schools. As negative features, students noted a lack of integrated purpose, applying simultaneously the four scientific areas of the course, and also indicated the need to be familiar with more models of integrated education. Consequently, the suggestions for improvement derived from these negative features. The students also considered that their evaluation process was correct, due to the fact that it was focused on the design of an integrated project for one of the school years already mentioned.

Angular distributions in t(t)over-barH(H -> b(b)over-bar) reconstructed events at the LHC

The associated production of a Higgs boson and a top-quark pair, t (t) over barH, in proton-proton collisions is addressed in this paper for a center of mass energy of 13 TeV at the LHC. Dileptonic final states of t (t) over barH events with two oppositely charged leptons and four jets from the decays t -> bW(+) -> bl(+)v(l), (t) over bar -> (b) over barW(-) -> (b) over barl(-)(v) over bar (l) and h -> b (b) over bar are used. Signal events, generated with MadGraph5_aMC@NLO, are fully reconstructed by applying a kinematic fit. New angular distributions of the decay products as well as angular asymmetries are explored in order to improve discrimination of t (t) over barH signal events over the dominant irreducible background contribution, t (t) over barb (b) over bar. Even after the full kinematic fit reconstruction of the events, the proposed angular distributions and asymmetries are still quite different in the t (t) over barH signal and the dominant background (t (t) over barb (b) over bar).