Extended GCD and Hermite normal form algorithms via lattice basis reduction

Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers x(1), ..., x(m) for the equation s = gcd (s(1), ..., s(m)) = x(1)s(1) + ... + x(m)s(m), where s1, ... , s(m) are given integers. The method generalises to produce small unimodular transformation matrices for computing the Hermite normal form of an integer matrix.

The impact of functional connectivity changes on support vector machines mapping of fMRI data

Functional magnetic resonance imaging (fMRI) is currently one of the most widely used methods for studying human brain function in vivo. Although many different approaches to fMRI analysis are available, the most widely used methods employ so called ""mass-univariate"" modeling of responses in a voxel-by-voxel fashion to construct activation maps. However, it is well known that many brain processes involve networks of interacting regions and for this reason multivariate analyses might seem to be attractive alternatives to univariate approaches. The current paper focuses on one multivariate application of statistical learning theory: the statistical discrimination maps (SDM) based on support vector machine, and seeks to establish some possible interpretations when the results differ from univariate `approaches. In fact, when there are changes not only on the activation level of two conditions but also on functional connectivity, SDM seems more informative. We addressed this question using both simulations and applications to real data. We have shown that the combined use of univariate approaches and SDM yields significant new insights into brain activations not available using univariate methods alone. In the application to a visual working memory fMRI data, we demonstrated that the interaction among brain regions play a role in SDM`s power to detect discriminative voxels. (C) 2008 Elsevier B.V. All rights reserved.

Virtual Communities of Practice: Design and Development of Support Platforms and Participation Fostering

Mestrado em Engenharia Informática - Área de Especialização em Sistemas Gráficos e Multimédia

Biographical narratives in teaching: a study of rofessors on postgraduate courses

Literature and research have shown that professional development constitutes an essential dimension in constructing both work and professional identity. An important aspect in such development is training. In the field of adult education, different authors (Pratt, 1993; Mezirow, 1985; Schön, 1996; Silva, 2007) emphasize the importance of placing trainees at the center of the learning and cognitive processes and within their corresponding social and historical contexts. Training is supported by a comprehensive adult learning theory. Therefore, the acquired knowledge is not only the result of an external and objective reality but also of a complex construction in which the appropriation of experience plays a relevant role. This paper reveals the findings obtained through biographical narratives in a five-year work program with teachers at different levels (from pre-school to higher education) on postgraduate courses. The core issue is the importance of biographical narratives, as an identification strategy for personal experience, knowledge construction and professional identity. This strategy provided the opportunity for recognition of practical experience, as a provider of learning, as well as his/her own authorship, which are important conditions in the understanding of professional identity.

Una Aproximació a la construcció significativa del coneixement matemàtic a l'ESO

This study displays and analyzes the contents of the Mathematics subject in ESO’s second cycle from a constructivist perspective. This analysis has been carried out by contrasting two groups of participants (control group and experimental group). These groups were formed by a sample of 240 students between the ages of 14 and 16 from four different educational centres of the Osona area. Research – Action methodology has been employed, combining quantitative techniques (statistical study with the SPSS package) with qualitative analysis (transcriptions of interviews and discussion group). This study has been carried out after years of classroom observation, reflection and action. The theoretical framework employed is a cognitive one, based on Ausubel’s Significative Learning Theory. Quantitative analysis shows how the researcher’s design improves, on the one hand, the students’ academic motivation and, on the other hand, their comprehensive memory, enabling them to achieve a more significant learning of the subjects’ contents. Furthermore, our analysis shows that the proposed method is more comprehensive than those employed by teachers collaborating with control groups. The main aim of the qualitative analysis is that of identifying the elements which configure the programme and contribute to an improvement of the aspects mentioned above. The key elements here are: co-operation as the basis of group dynamics; the employment, in some cases, of easily handled materials; the type of interaction between teacher and students, where, through open discussion, students are lead by teaching staff towards the course objectives; induction, that is, deducing formulae by initially using examples which are close to the students’ knowledge and experience or taken from everyday life (what we could call “down-top” mathematics). We should add here that the qualitative analysis does not only corroborate the results obtained by quantitative techniques, but also displays an increase of motivation in teaching staff. Teachers did show a positive attitude and welcomed the use and development of these materials in the next academic year. Finally, we discuss possible directions for further research.

Entrepreneurial Orientation, Intangible Assets and Firm Growth: the impact of ‘Spirit and Material’ on the growth of Chinese private firms

This paper has three contributions. First, it shows how field work within small firms in PR Chinese has provided new evidence which enables us to measure and calibrate Entrepreneurial Orientation (EO), as ‘spirit’, and Intangible Assets (IA), as ‘material’, for use in models of small firm growth. Second, it uses inter-item correlation analysis and both exploratory and confirmatory factor analysis to provide new measures of EO and IA, in index and in vector form, for use in econometric models of firm growth. Third, it estimates two new econometric models of small firm employment growth in PR China, under the null hypothesis of Gibrat’s Law, using our two new index-based and vector-based measures of EO and IA. Estimation is by OLS with adjustment for heteroscedasticity, and for sample selectivity. Broadly, it finds that EO attributes have had little significant impact on small firm growth, and indeed innovativeness and pro-activity paradoxically may even dampen growth. However, IA attributes have had a positive and significant impact on growth, with networking, and technological knowledge being of prime importance, and intellectual property and human capital being of lesser but still significant importance. In the light of these results, Gibrat’s Law is generalized, and Jovanovic’s learning theory is extended, to emphasise the importance of IA to growth. These findings cast new empirical light on the oft-quoted national slogan in PR China of “spirit and material”. So far as small firms are concerned, this paper suggests that their contribution to PR China’s remarkable economic growth is not so much attributable to the ‘spirit’ of enterprise (as suggested by propaganda) as, more prosaically, to the pursuit of the ‘material’.

«Où, quand, et comment ?» : Évolution des conduites agressives en football et en hockey sur glace

RésuméCette étude a pour objectif d'observer l'évolution des actes agressifs dans deux sports d'équipes en fonction de facteurs situationnels (périodes de jeu, lieu de la faute, état du score) et du type d'agressions (instrumentales, hostile). 60 matchs professionnels de football et de hockey sur glace ont été filmés puis analysés à l'aide de grilles d'observation différenciant les deux types d'agressions. Les résultats révèlent que dans ces deux sports, les agressions instrumentales sont plus fréquentes dans les zones importantes du terrain (milieu ou défense) ou lorsque le score est serré. En revanche, les agressions hostiles ne varient pas (ou peu) selon ces facteurs. Les résultats sont discutés au regard de la théorie de l'apprentissage social et de l'hypothèse frustration-agression.AbstractThis study aims at examining observed aggression in two team sports as a function of situational triggers (periods, zones of field, games score) and of type of aggression (instrumental, hostile). 60 soccer and ice hockey games were recorded and analyzed using a grid that differentiates the two types of aggression. The results revealed that theses two sports, instrumental aggressions were more frequent in important zones of field (neutral or defensive ones) and in tied score situations. However, no difference was found for hostile aggression according to these factors. The discussion focused on the social learning theory and frustration-aggression hypothesis.

Automatic low baseline stereo in urban areas

In this work we propose a new automatic methodology for computing accurate digital elevation models (DEMs) in urban environments from low baseline stereo pairs that shall be available in the future from a new kind of earth observation satellite. This setting makes both views of the scene similarly, thus avoiding occlusions and illumination changes, which are the main disadvantages of the commonly accepted large-baseline configuration. There still remain two crucial technological challenges: (i) precisely estimating DEMs with strong discontinuities and (ii) providing a statistically proven result, automatically. The first one is solved here by a piecewise affine representation that is well adapted to man-made landscapes, whereas the application of computational Gestalt theory introduces reliability and automation. In fact this theory allows us to reduce the number of parameters to be adjusted, and tocontrol the number of false detections. This leads to the selection of a suitable segmentation into affine regions (whenever possible) by a novel and completely automatic perceptual grouping method. It also allows us to discriminate e.g. vegetation-dominated regions, where such an affine model does not apply anda more classical correlation technique should be preferred. In addition we propose here an extension of the classical ”quantized” Gestalt theory to continuous measurements, thus combining its reliability with the precision of variational robust estimation and fine interpolation methods that are necessary in the low baseline case. Such an extension is very general and will be useful for many other applications as well.

Mapping of Environmental Data Using Kernel-Based Methods

Recently, kernel-based Machine Learning methods have gained great popularity in many data analysis and data mining fields: pattern recognition, biocomputing, speech and vision, engineering, remote sensing etc. The paper describes the use of kernel methods to approach the processing of large datasets from environmental monitoring networks. Several typical problems of the environmental sciences and their solutions provided by kernel-based methods are considered: classification of categorical data (soil type classification), mapping of environmental and pollution continuous information (pollution of soil by radionuclides), mapping with auxiliary information (climatic data from Aral Sea region). The promising developments, such as automatic emergency hot spot detection and monitoring network optimization are discussed as well.

A sharp concentration inequality with applications

We present a new general concentration-of-measure inequality and illustrate its power by applications in random combinatorics. The results find direct applications in some problems of learning theory.

Automatic classification of MR scans in Alzheimer's disease.

To be diagnostically useful, structural MRI must reliably distinguish Alzheimer's disease (AD) from normal aging in individual scans. Recent advances in statistical learning theory have led to the application of support vector machines to MRI for detection of a variety of disease states. The aims of this study were to assess how successfully support vector machines assigned individual diagnoses and to determine whether data-sets combined from multiple scanners and different centres could be used to obtain effective classification of scans. We used linear support vector machines to classify the grey matter segment of T1-weighted MR scans from pathologically proven AD patients and cognitively normal elderly individuals obtained from two centres with different scanning equipment. Because the clinical diagnosis of mild AD is difficult we also tested the ability of support vector machines to differentiate control scans from patients without post-mortem confirmation. Finally we sought to use these methods to differentiate scans between patients suffering from AD from those with frontotemporal lobar degeneration. Up to 96% of pathologically verified AD patients were correctly classified using whole brain images. Data from different centres were successfully combined achieving comparable results from the separate analyses. Importantly, data from one centre could be used to train a support vector machine to accurately differentiate AD and normal ageing scans obtained from another centre with different subjects and different scanner equipment. Patients with mild, clinically probable AD and age/sex matched controls were correctly separated in 89% of cases which is compatible with published diagnosis rates in the best clinical centres. This method correctly assigned 89% of patients with post-mortem confirmed diagnosis of either AD or frontotemporal lobar degeneration to their respective group. Our study leads to three conclusions: Firstly, support vector machines successfully separate patients with AD from healthy aging subjects. Secondly, they perform well in the differential diagnosis of two different forms of dementia. Thirdly, the method is robust and can be generalized across different centres. This suggests an important role for computer based diagnostic image analysis for clinical practice.

Kernel-based Mapping of Meteorological Fields in Complex Orography

Due to the advances in sensor networks and remote sensing technologies, the acquisition and storage rates of meteorological and climatological data increases every day and ask for novel and efficient processing algorithms. A fundamental problem of data analysis and modeling is the spatial prediction of meteorological variables in complex orography, which serves among others to extended climatological analyses, for the assimilation of data into numerical weather prediction models, for preparing inputs to hydrological models and for real time monitoring and short-term forecasting of weather.In this thesis, a new framework for spatial estimation is proposed by taking advantage of a class of algorithms emerging from the statistical learning theory. Nonparametric kernel-based methods for nonlinear data classification, regression and target detection, known as support vector machines (SVM), are adapted for mapping of meteorological variables in complex orography.With the advent of high resolution digital elevation models, the field of spatial prediction met new horizons. In fact, by exploiting image processing tools along with physical heuristics, an incredible number of terrain features which account for the topographic conditions at multiple spatial scales can be extracted. Such features are highly relevant for the mapping of meteorological variables because they control a considerable part of the spatial variability of meteorological fields in the complex Alpine orography. For instance, patterns of orographic rainfall, wind speed and cold air pools are known to be correlated with particular terrain forms, e.g. convex/concave surfaces and upwind sides of mountain slopes.Kernel-based methods are employed to learn the nonlinear statistical dependence which links the multidimensional space of geographical and topographic explanatory variables to the variable of interest, that is the wind speed as measured at the weather stations or the occurrence of orographic rainfall patterns as extracted from sequences of radar images. Compared to low dimensional models integrating only the geographical coordinates, the proposed framework opens a way to regionalize meteorological variables which are multidimensional in nature and rarely show spatial auto-correlation in the original space making the use of classical geostatistics tangled.The challenges which are explored during the thesis are manifolds. First, the complexity of models is optimized to impose appropriate smoothness properties and reduce the impact of noisy measurements. Secondly, a multiple kernel extension of SVM is considered to select the multiscale features which explain most of the spatial variability of wind speed. Then, SVM target detection methods are implemented to describe the orographic conditions which cause persistent and stationary rainfall patterns. Finally, the optimal splitting of the data is studied to estimate realistic performances and confidence intervals characterizing the uncertainty of predictions.The resulting maps of average wind speeds find applications within renewable resources assessment and opens a route to decrease the temporal scale of analysis to meet hydrological requirements. Furthermore, the maps depicting the susceptibility to orographic rainfall enhancement can be used to improve current radar-based quantitative precipitation estimation and forecasting systems and to generate stochastic ensembles of precipitation fields conditioned upon the orography.

Les cançons a l'educació infantil. Com i per què s'utilitzen? Anàlisi d’un cas

Les cançons a l’Educació Infantil. Com i per què s’utilitzen? constitueix el títol del tema estudiat en aquest treball d’investigació qualitativa basada en la teoria constructivista de l’aprenentatge. Amb aquest procés de recerca hem volgut conèixer quina importància tenen les cançons en l’àmbit escolar, com cal treballar-les a l’aula i per a què es poden utilitzar. A partir d’aquesta informació extreta de la fonamentació teòrica hem realitzat l’aplicació pràctica basada en l’observació directa del treball de les cançons a l’aula de P5 de l’Escola Peranton de Granollers, centre que basa la seva metodologia en un Projecte Musical. Per últim, hem comparat, analitzat i extret conclusions entre el tractament de les cançons que defensen els teòrics i la realitat observada en el centre.

Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.

El Aprendizaje dialógico y sus contribuciones a la teoría de la educación

This article highlights the contributions of the dialogic learning approach to educational theory, with the aim of providing some orientations in order to promote egalitarian and scientific educational practice. The seven principles of dialogic learning are discussed, along with other reproductionist theories and practices from the educational field, demonstrating how the former both surpass the latter. The article also reflects open dialogue with the critical theories of education which the dialogic learning theory is based on. These basic theories are, on the one hand, by authors who are distant in time but very close in their educational approach, such as Ferrer i Guàrdia, Vygotsky, or Paulo Freire, and, on the other hand, by other contemporary authors in critical pedagogy. Each of the seven principles presented are provided along with a critical examination of a specific educational practice. The consequences of the implementation of dialogic learning are underlined here through an analysis of innovative and critical educational projects which are academically successful