Suppressors of selection

Inspired by recent works on evolutionary graph theory, an area of growing interest in mathematical and computational biology, we present the first known examples of undirected structures acting as suppressors of selection for any fitness value $r > 1$. This means that the average fixation probability of an advantageous mutant or invader individual placed at some node is strictly less than that of this individual placed in a well-mixed population. This leads the way to study more robust structures less prone to invasion, contrary to what happens with the amplifiers of selection where the fixation probability is increased on average for advantageous invader individuals. A few families of amplifiers are known, although some effort was required to prove it. Here, we use computer aided techniques to find an exact analytical expression of the fixation probability for some graphs of small order (equal to $6$, $8$ and $10$) proving that selection is effectively reduced for $r > 1$. Some numerical experiments using Monte Carlo methods are also performed for larger graphs.Comment: New title, improved presentation, and further examples. Supporting Information is also include

Laminaciones afables

Unha maneira usual de constru r exemplos de laminaci ons e a partir de acci ons de grupos de Lie sobre espazos m etricos. Entre os exemplos interesantes obtidos desta maneira at opanse as laminaci ons de nidas por mosaicos. O estudo das s uas propiedades resulta relevante en f sica do estado s olido, na teor a de case-cristais

Evaluación de los procesos matemáticos en la resolución de un problema aritmético

Desde que el NCTM (2000) los incorporó en sus Principios y Estándares para la Educación Matemática con el fin de promover una mayor competencia matemática en el alumnado, los estándares de proceso han cobrado un protagonismo cada vez mayor. La adopción de un enfoque competencial que promueva su presencia en educación matemática infantil requiere de indicadores que permitan evaluar y analizar su tratamiento. Se presenta un análisis de la presencia de los estándares de proceso en una práctica docente con niños de 5 años diseñada en torno a un problema aritmético para el que se ha empleado el instrumento de evaluación propuesto por Alsina y Coronata (2014)

A method for validating Rent's rule for technological and biological networks

Rent’s rule is empirical power law introduced in an effort to describe and optimize the wiring complexity of computer logic graphs. It is known that brain and neuronal networks also obey Rent’s rule, which is consistent with the idea that wiring costs play a fundamental role in brain evolution and development. Here we propose a method to validate this power law for a certain range of network partitions. This method is based on the bifurcation phenomenon that appears when the network is subjected to random alterations preserving its degree distribution. It has been tested on a set of VLSI circuits and real networks, including biological and technological ones. We also analyzed the effect of different types of random alterations on the Rentian scaling in order to test the influence of the degree distribution. There are network architectures quite sensitive to these randomization procedures with significant increases in the values of the Rent exponents

Exploring the topological sources of robustness against invasion in biological and technological networks

For a network, the accomplishment of its functions despite perturbations is called robustness. Although this property has been extensively studied, in most cases, the network is modified by removing nodes. In our approach, it is no longer perturbed by site percolation, but evolves after site invasion. The process transforming resident/healthy nodes into invader/mutant/diseased nodes is described by the Moran model. We explore the sources of robustness (or its counterpart, the propensity to spread favourable innovations) of the US high-voltage power grid network, the Internet2 academic network, and the C. elegans connectome. We compare them to three modular and non-modular benchmark networks, and samples of one thousand random networks with the same degree distribution. It is found that, contrary to what happens with networks of small order, fixation probability and robustness are poorly correlated with most of standard statistics, but they depend strongly on the degree distribution. While community detection techniques are able to detect the existence of a central core in Internet2, they are not effective in detecting hierarchical structures whose topological complexity arises from the repetition of a few rules. Box counting dimension and Rent’s rule are applied to show a subtle trade-off between topological and wiring complexityThis work was supported by the Spanish Excellence Grant MTM2013-46337-C2-2-P, Galician Grant GPC2015/006 and the European Regional Development Fund. Third author was also supported by the European Social Fund and Government of Aragón (Grant E15), and University of Zaragoza/CUD Grant UZCUD2015-CIE-05S

Laboratorio de aprendizaje de la medida en la formación de maestros

¿Cómo podemos favorecer una adecuada construcción de los contenidos relacionados con las magnitudes y su medida en educación primaria? una gran mayoría de textos sobre didáctica de la matemática están de acuerdo en describir una serie de “etapas” o “fases” que es necesario superar en el proceso de enseñanza-aprendizaje de las magnitudes y su medida, sugiriendo un tránsito desde las primeras experiencias perceptivas hasta el manejo de los instrumentos de medida y del sistema internacional de unidades. En la propuesta que se relata, el alumnado de tercer curso del grado en maestro o maestra de educación primaria participa en un laboratorio - en el sentido más literal del término - de aprendizaje de la medida, en el que reflexionan sobre dicho proceso diseñando sus propias actividades y estrategias de intervención

Evaluación de los procesos matemáticos en la resolución de un problema aritmético

Since Process Standards were introduced by the NCTM (2000) in the Principles and Standards for School Mathematics to promote greater mathematical competence in students, their relevance has grown. A competency-based approach in Early Childhood Mathematics incorporating the Process Standards requires indicators to assess and analyze their treatment. We analyze the presence of the Process Standards in a teaching activity with 5 years-old children on solving an arithmetic problem. We use the assessment tool proposed by Alsina and Coronata (2014).Desde que el NCTM (2000) los incorporó en sus Principios y Estándares para la Educación Matemática con el fin de promover una mayor competencia matemática en el alumnado, los estándares de proceso han cobrado un protagonismo cada vez mayor. La adopción de un enfoque competencial que promueva su presencia en educación matemática infantil requiere de indicadores que permitan evaluar y analizar su tratamiento. Se presenta un análisis de la presencia de los estándares de proceso en una práctica docente con niños de 5 años diseñada en torno a un problema aritmético para el que se ha empleado el instrumento de evaluación propuesto por Alsina y Coronata (2014)