Aumentar competencias y motivación mediante la participación en competiciones matemáticas

Cabe prestar atención a la desmotivación que los alumnos manifiestan ante el aprendizaje de las Matemáticas por razones como la desconexión manifiesta entre lo que aprenden y el entorno real (Fernández y Pérez, 2011), la dificultad al realizar los distintos problemas surgidos, la falta de metodologías de trabajo donde se intensifique el trabajo en equipo y cooperativo (Hidalgo et al, 2004). Así como la heterogeneidad mostrada en el alumnado actual siendo muchos los niveles presentes en un aula. Las competiciones matemáticas, como Olimpiadas o Pruebas Cangur, y, sobre todo, las sesiones de preparación a éstas, aúnan muchas de las características que adolecen en las actividades de enseñanza-aprendizaje presentadas en el aula de Matemáticas

Using network-flow techniques to solve an optimization problem from surface-physics

The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination of the ground state of this model leads to a combinatorial problem, which is reduced to an uncapacitated, convex minimum-circulation problem. We will show that the successive shortest path algorithm solves the problem in polynomial time.Comment: 8 Pages LaTeX, using Elsevier preprint style (macros included

Switchable Genetic Oscillator Operating in Quasi-Stable Mode

Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behavior in transient and stochastic environments such as the cell. We show here that even repressilators possess quasi-stable, travelling-wave periodic solutions that are reachable, long-lived and robust to parameter changes. These solutions underlie the sustained oscillations observed in even rings in the stochastic regime, even if these circuits are expected to behave as switches. The existence of such solutions can also be exploited for control purposes: operation of the system around the quasi-stable orbit allows us to turn on and off the oscillations reliably and on demand. We illustrate these ideas with a simple protocol based on optical interference that can induce oscillations robustly both in the stochastic and deterministic regimes.Comment: 24 pages, 5 main figure

Lower Critical Dimension of Ising Spin Glasses

Exact ground states of two-dimensional Ising spin glasses with Gaussian and bimodal (+- J) distributions of the disorder are calculated using a ``matching'' algorithm, which allows large system sizes of up to N=480^2 spins to be investigated. We study domain walls induced by two rather different types of boundary-condition changes, and, in each case, analyze the system-size dependence of an appropriately defined ``defect energy'', which we denote by DE. For Gaussian disorder, we find a power-law behavior DE ~ L^\theta, with \theta=-0.266(2) and \theta=-0.282(2) for the two types of boundary condition changes. These results are in reasonable agreement with each other, allowing for small systematic effects. They also agree well with earlier work on smaller sizes. The negative value indicates that two dimensions is below the lower critical dimension d_c. For the +-J model, we obtain a different result, namely the domain-wall energy saturates at a nonzero value for L\to \infty, so \theta = 0, indicating that the lower critical dimension for the +-J model exactly d_c=2.Comment: 4 pages, 4 figures, 1 table, revte

Form Factor of Eucalyptus Saligna Species in a Commercial Forest Plantation

The present investigation proposes to determine the form factor of the species Eucalyptus saligna in a commercial forest plantation of the Tambillo bajo sector, of the Colta canton, Chimborazo province. For this purpose, 100 individual specimens with straight shafts and without bifurcations were taken as a sample, and each individual’s commercial and total height, diameter at breast height, and diameters along the stem were measured, to determine the real volume of the wood using the Smalian and Newton formulas, the graphical method, and with a form factor of 0.70. Based on the measured data, a comparative analysis of the calculation of real volume by the method used was performed; the results obtained showed significant differences between calculation methods. In addition, five potential volume equations that presented the highest adjusted coefficient of determination and the lowest mean square error were selected. To verify the commercial volume calculated with the estimated form factors against the volume equations, the commercial volume was recalculated based on the form factors and equations found. The calculation of the commercial volume by the Smalian formula is taken as the exact value, and the other methods are taken as approximated values. Keywords: dasometry, form factor, forest plantation, volumen equations, commercial volume. Resumen La presente investigación propone: determinar el factor de forma de la especie Eucalyptus saligna en una plantación forestal comercial; para lo cual se toma como muestra 100 individuos con fustes rectos y sin bifurcaciones, a cada individuo se midió la altura comercial y total, diámetro a la altura del pecho y diámetros a lo largo del fuste, para determinar el volumen real de madera utilizando la fórmula de Smalian, Newton, método gráfico y con un factor de forma de 0,70. En base a los datos medidos, se realiza un análisis comparativo del cálculo de volumen real por método empleado, los resultados obtenidos mostraron diferencias significativas entre métodos de cálculo empleados. Además, se seleccionó 5 ecuaciones de volumen potenciales los cuales presentaron mayor coeficiente de determinación ajustado y menor error cuadrático medio. Para la verificación del volumen comercial calculado con los factores de forma estimados frente a las ecuaciones de volumen se vuelve a calcular el volumen comercial a partir de los factores de forma y ecuaciones encontrados, se toma como valor exacto el cálculo de volumen comercial por la fórmula de Smalian y como valor de aproximación los demás métodos. Palabras clave: dasometría, ecuaciones de volumen, factor de forma, plantación forestal, volumen comercial

No spin-glass transition in the "mobile-bond" model

The recently introduced ``mobile-bond'' model for two-dimensional spin glasses is studied. The model is characterized by an annealing temperature T_q. On the basis of Monte Carlo simulations of small systems it has been claimed that this model exhibits a non-trivial spin-glass transition at finite temperature for small values of T_q. Here the model is studied by means of exact ground-state calculations of large systems up to N=256^2. The scaling of domain-wall energies is investigated as a function of the system size. For small values T_q<0.95 the system behaves like a (gauge-transformed) ferromagnet having a small fraction of frustrated plaquettes. For T_q>=0.95 the system behaves like the standard two-dimensional +-J spin-glass, i.e. it does NOT exhibit a phase transition at T>0.Comment: 4 pages, 5 figures, RevTe

A Fixed-Parameter Algorithm for the Max-Cut Problem on Embedded 1-Planar Graphs

We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut} problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane with at most one crossing per edge. Our algorithm recursively reduces a 1-planar graph to at most $3^k$ planar graphs, using edge removal and node contraction. The \textsc{Max-Cut} problem is then solved on the planar graphs using established polynomial-time algorithms. We show that a maximum cut in the given 1-planar graph can be derived from the solutions for the planar graphs. Our algorithm computes a maximum cut in an embedded 1-planar graph with $n$ nodes and $k$ edge crossings in time $\mathcal{O}(3^k \cdot n^{3/2} \log n)$.Comment: conference version from IWOCA 201

Spontaneous creation of discrete breathers in Josephson arrays

We report on the experimental generation of discrete breather states (intrinsic localized modes) in frustrated Josephson arrays. Our experiments indicate the formation of discrete breathers during the transition from the static to the dynamic (whirling) system state, induced by a uniform external current. Moreover, spatially extended resonant states, driven by a uniform current, are observed to evolve into localized breather states. Experiments were performed on single Josephson plaquettes as well as open-ended Josephson ladders with 10 and 20 cells. We interpret the breather formation as the result of the penetration of vortices into the system.Comment: 5 pages, 5 figure

Low-Temperature Excitations of Dilute Lattice Spin Glasses

A new approach to exploring low-temperature excitations in finite-dimensional lattice spin glasses is proposed. By focusing on bond-diluted lattices just above the percolation threshold, large system sizes $L$ can be obtained which lead to enhanced scaling regimes and more accurate exponents. Furthermore, this method in principle remains practical for any dimension, yielding exponents that so far have been elusive. This approach is demonstrated by determining the stiffness exponent for dimensions $d=3$, $d=6$ (the upper critical dimension), and $d=7$. Key is the application of an exact reduction algorithm, which eliminates a large fraction of spins, so that the reduced lattices never exceed $\sim10^3$ variables for sizes as large as L=30 in $d=3$, L=9 in $d=6$, or L=8 in $d=7$. Finite size scaling analysis gives $y_3=0.24(1)$ for $d=3$, significantly improving on previous work. The results for $d=6$ and $d=7$, $y_6=1.1(1)$ and $y_7=1.24(5)$, are entirely new and are compared with mean-field predictions made for d>=6.Comment: 7 pages, LaTex, 7 ps-figures included, added result for stiffness in d=7, as to appear in Europhysics Letters (see http://www.physics.emory.edu/faculty/boettcher/ for related information

Methodology of Building An Expert System Using Induction Rules with Structured Programming

This article aims to give an idea of how to develop expert systems to help society in all senses. The rules of induction used with MYCIN can help us in medicine, agricultura, and the financial system, implementing an inference engine with different rules so that in case there are no people, the expert system can diagnose in a clear and precise way, based on a knowledge base with some consequents and their corresponding antecedents, these artificial intelligence algorithms used will allow us to determine what type of consequence or conclusion it gives us, of the chaining of several antecedents with structured programming to give us its corresponding answer, then this research is aimed at obtaining an agile methodology for expert systems that will help us in the development and implementation of this type of systems. &nbsp; &nbsp; Keywords: algorithms of artificial intelligence, knowledge base, artificial intelligence, inference machine, production rules, real-time systems, expert system