Los ejemplos y contraejemplos como herramientas para facilitar el proceso de generalización conceptual

La generalización es una de las operaciones conceptuales que más se utiliza en la matemática. En el trabajo se presenta una organización del conocimiento escolar de siete de las veintitrés generalizaciones del concepto de derivada puntual de una función f, que no exceden la extensión del concepto de función real de una variable real; tomando como criterio de generalización el debilitamiento sucesivo de las exigencias sobre la existencia del límite de la función Fc(h)=[f(c+h)-f(c)]/h, h≠0, cuando h tiende a cero, o de las características topológicas de c con respecto al dominio de f. En el trabajo se hace, además, un análisis de la utilidad de la construcción de ejemplos y contraejemplos para facilitar la realización de los procesos de generalización; y se presenta un conjunto de tareas que también facilitan y dan orden a estos procesos

Reconstruction of noisy signals by minimization of non-convex functionals

Non-convex functionals have shown sharper results in signal reconstruction as compared to convex ones, although the existence of a minimum has not been established in general. This paper addresses the study of a general class of either convex or non-convex functionals for denoising signals which combines two general terms for fitting and smoothing purposes, respectively. The first one measures how close a signal is to the original noisy signal. The second term aims at removing noise while preserving some expected characteristics in the true signal such as edges and fine details. A theoretical proof of the existence of a minimum for functionals of this class is presented. The main merit of this result is to show the existence of minimizer for a large family of non-convex functionals.The rst author gratefully acknowledges many helpful discussion with Professor H. Frid from IMPA. Also thanks the Promeps Project that support this work. The second author is grateful to the Spanish Ministry of Economy and Competitiveness for the grant TIN2013-46522-P, and to the Generalitat Valenciana for the grant PROMETEOII/2014/062

Caracterizaciones del concepto de métrica

En este trabajo se propone un conjunto de tareas didácticas, que, a juicio de los autores, son necesarias para que los estudiantes participen en el aprendizaje del concepto de caracterización conceptual y se construyen, a modo de ejemplo de aplicación de tales tareas, catorce caracterizaciones del concepto de métrica

Prediction of time series using wavelet Gaussian process for wireless sensor networks

Articulo de investigacion idizado en JCR con factor de impacto 2.2The detection and transmission of a physical variable over time, by a node of a sensor network to its sink node, represents a significant communication overload and consequently one of the main energy consumption processes. In this article we present an algorithm for the prediction of time series, with which it is expected to reduce the energy consumption of a sensor network, by reducing the number of transmissions when reporting to the sink node only when the prediction of the sensed value differs in certain magnitude, to the actual sensed value. For this end, the proposed algorithm combines a wavelet multiresolution transform with robust prediction using Gaussian process. The data is processed in wavelet domain, taking advantage of the transform ability to capture geometric information and decomposition in more simple signals or subbands. Subsequently, the decomposed signal is approximated by Gaussian process one for each subband of the wavelet, in this manner the Gaussian process is given to learn a much simple signal. Once the process is trained, it is ready to make predictions. We compare our method with pure Gaussian process prediction showing that the proposed method reduces the prediction error and is improves large horizons predictions, thus reducing the energy consumption of the sensor network

Surface Reconstruction from Noisy Point Clouds

We show that a simple modification of the power crust algorithm for surface reconstruction produces correct outputs in presence of noise. This is proved using a fairly realistic noise model. Our theoretical results are related to the problem of computing a stable subset of the medial axis. We demostrate the effectiveness of our algorithm with a number of experimental results

Gait recognition from corrupted silhouettes: a robust statistical approach

This paper introduces a method based on robust statistics to build reliable gait signatures from averaging silhouette descriptions, mainly when gait sequences are affected by severe and persistent defects. The term robust refers to the ability of reducing the impact of silhouette defects (outliers) on the average gait pattern, while taking advantage of clean silhouette regions. An extensive experimental framework was defined based on injecting three types of realistic defects (salt and pepper noise, static occlusion, and dynamic occlusion) to clean gait sequences, both separately in an easy setting and jointly in a hard setting. The robust approach was compared against two other operation modes: (1) simple mean (weak baseline) and (2) defect exclusion (strong benchmark). Three gait representation methods based on silhouette averaging were used: Gait Energy Image (GEI), Gradient Histogram Energy Image (GHEI), and the joint use of GEI and HOG descriptors. Quality of gait signatures was assessed by their discriminant power in a large number of gait recognition tasks. Nonparametric statistical tests were applied on recognition results, searching for significant differences between operation modes.This work has been supported by the grants P1-1B2012-22 and PREDOC/2012/05 from Universitat Jaume I, PROMETEOII/2014/062 from Generalitat Valenciana, and TIN2013-46522-P from Spanish Ministry of Economy and Competitiveness

Compress sensing algorithm for estimation of signals in sensor networks

ARTICULO DE INVESTIGACION IDEXADO EN JCR CON FACTOR DE IMPACTO 2.4In this research, we present a data recovery scheme for wireless sensor networks. In some sensor networks, each node must be able to recover the complete information of the network, which leads to the problem of the high cost of energy in communication and storage of information. We proposed a modified gossip algorithm for acquire distributed measurements and communicate the information across all nodes of the network using compressive sampling and Gossip algorithms to compact the data to be stored and transmitted through a network. The experimental results on synthetic data show that the proposed method reconstruct better the signal and in less iterations than with a similar method using a thresholding algorithm

Reconstruction of PET Images Using Cross-Entropy and Field of Experts

The reconstruction of positron emission tomography data is a difficult task, particularly at low count rates because Poisson noise has a significant influence on the statistical uncertainty of positron emission tomography (PET) measurements. Prior information is frequently used to improve image quality. In this paper, we propose the use of a field of experts to model a priori structure and capture anatomical spatial dependencies of the PET images to address the problems of noise and low count data, which make the reconstruction of the image difficult. We reconstruct PET images by using a modified MXE algorithm, which minimizes a objective function with the cross-entropy as a fidelity term, while the field of expert model is incorporated as a regularizing term. Comparisons with the expectation maximization algorithm and a iterative method with a prior penalizing relative differences showed that the proposed method can lead to accurate estimation of the image, especially with acquisitions at low count rate

GRAFICANDO FUNCIONES VECTORIALES USANDO MATHEMATICA

A medida que avanza la tecnología deberíamos dejar atrás lápiz, papel, pizarrón y gis y hacer uso de nuevas herramientas para enseñar a nuestros futuros profesionistas. Ayudar al estudiante, con el fin de facilitar el aprendizaje, a visualizar y resolver problemas empleando la tecnología que tenemos a nuestro alcance facilitara y acelerara el proceso de aprendizaje del alumno. En este caso, el software Mathematica fue utilizado con exito para graficar funciones vectoriales que representen a la velocidad y la aceleración de una partícula en dos dimensiones