The influence of early literacy competences on later mathematical attainment: Evidence from TIMSS & PIRLS 2011

Children’s competence levels in numeracy and literacy before or at school onset are good predictors of their attainment over the school years. Nevertheless, there are large differences in the level of numeracy and literacy knowledge among children at school entry. This initial knowledge gap has long-lasting negative consequences for the poor performers. Here we used international secondary data from the PIRLS&TIMSS 2011 as well as TIMSS 2011, including background data collected with the Learning to Read Survey, to identify early literacy practices that predict later mathematical attainment. Previous studies conducted using the same dataset have reported that early numeracy and literacy abilities before school onset (as reported by parents) are associated with students’ later mathematical and reading attainment, respectively. Nevertheless recent theoretical frameworks of early mathematical development include certain literacy skills as an independent predictors of mathematical performance. Using ordinary least square regression models we found that early numeracy competences consistently predicted later mathematical attainment while the effects of early literacy competences were variable and not always significant for the individual countries. Results also showed a stronger influence of early reading abilities than of early writing abilities on later mathematical attainment. The identified effects were independent of children’s gender, home resources for learning, parents’ highest education and occupation level, student years of pre-school attendance and early numeracy abilities. This report complements and extents previous body of research by determining the relative impact that early literacy skills have on later mathematical attainment across EU countries. Findings highlight the importance of including numeracy and literacy practices in the preprimary curriculum as well as the challenges of implementing ECEC curricula on the basis of identified best practices from international research

A robust optimization hybrid algorithm for solving the direct kinematics of the general Gough-Stewart platform

El problema de cinemática directa para los robots paralelos se puede enunciar como sigue: dado un conjunto de valores de las variables articulares, se deben encontrar los valores correspondientes en las variables cartesianas, es decir, la posición y orientación del órgano terminal. En muchas ocasiones, el problema de cinemática directa requiere la resolución de un sistema de ecuaciones no-lineales. Los métodos más eficientes para resolver problemas de este tipo suponen convexidad de una función de costo cuyo mínimo es la solución del sistema. La capacidad de tales métodos de optimización para encontrar una solución adecuada depende fuertemente del punto inicial. Un problema bien conocido es la selección de tal punto inicial, el cual requiere información a priori sobre una vecindad convexa donde se encuentra la solución. Este artículo propone un método eficiente para seleccionar y generar el punto inicial basado en aprendizaje probabilístico. El método evita eficientemente los mínimos locales, sin necesidad de intervención humana o información a priori, lo cual lo hace más robusto si se compara con el método Dogleg u otro método de minimización local basado en gradiente. Con el propósito de mostrar el desempeño del método híbrido, se presentan experimentos y su discusión correspondiente. La propuesta se puede extender a otras estructuras con cadenas cinemáticas cerradas, o a la solución en general de sistemas de ecuaciones no-lineales, y por supuesto, para problemas de optimización no-lineales.The direct kinematics problem for parallel robots can be stated as follows: given values of the joint variables, the corresponding Cartesian variable values, the pose of the end-effector, must be found. Most of the times the direct kinematics problem involves the solution of a system of non-linear equations. The most efficient methods to solve such kind of equations assume convexity in a cost function which minimum is the solution of the non-linear system. In consequence, the capacity of such methods depends on the knowledge about an starting point which neighboring region is convex, hence the method can find the global minimum. This article propose a method based on probabilistic learning about an adequate starting point for the Dogleg method which assumes local convexity of the function. The proposed method efficiently avoids the local minima, without need of human intervention or apriori knowledge, thus it shows a more robust performance than the simple Dogleg method or other gradient based methods. To demonstrate the performance of the proposed hybrid method, numerical experiments and the respective discussion are presented. The proposal can be extended to other structures of closed-kinematics chains, to the general solution of systems of non-linear equations, and to the minimization of non-linear functions.Peer Reviewe

An integer representation for periodic tilings of the plane by regular polygons

We describe a representation for periodic tilings of the plane by regular polygons. Our approach is to represent explicitly a small subset of seed vertices from which we systematically generate all elements of the tiling by translations. We represent a tiling concretely by a (2+n)×4 integer matrix containing lattice coordinates for two translation vectors and n seed vertices. We discuss several properties of this representation and describe how to exploit the representation elegantly and efficiently for reconstruction, rendering, and automatic crystallographic classification by symmetry detection

Optimizing omnidirectional reflection by multilayer mirrors

Periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. Quarter-wave stacks at normal incidence are commonplace in the design of such omnidirectional reflectors. We discuss alternative design criteria to optimize these systems.Comment: 9 pages, 6 figures. To be published in J. Opt. A: Pure and Applied Optic

Graph states in phase space

The phase space for a system of $n$ qubits is a discrete grid of $2^{n} \times 2^{n}$ points, whose axes are labeled in terms of the elements of the finite field \Gal{2^n} to endow it with proper geometrical properties. We analyze the representation of graph states in that phase space, showing that these states can be identified with a class of non-singular curves. We provide an algebraic representation of the most relevant quantum operations acting on these states and discuss the advantages of this approach.Comment: 14 pages. 2 figures. Published in Journal of Physics

Entanglement measure for general pure multipartite quantum states

We propose an explicit formula for an entanglement measure of pure multipartite quantum states, then study a general pure tripartite state in detail, and at end we give some simple but illustrative examples on four-qubits and m-qubits states.Comment: 5 page

Effective Hamiltonians in quantum optics: a systematic approach

We discuss a general and systematic method for obtaining effective Hamiltonians that describe different nonlinear optical processes. The method exploits the existence of a nonlinear deformation of the usual su(2) algebra that arises as the dynamical symmetry of the original model. When some physical parameter, dictated by the process under consideration, becomes small, we immediately get a diagonal effective Hamiltonian that correctly represents the dynamics for arbitrary states and long times. We extend the technique to su(3) and su(N), finding the corresponding effective Hamiltonians when some resonance conditions are fulfilled.Comment: 13 Pages, no figures, submitted for publicatio