Manuel Leon - Academia.edu (original) (raw)

Papers by Manuel Leon

Let A be an arbitrary d-dimensional expansive matrix and q = jdet(A)j. Sets K b R d such that = 1... more Let A be an arbitrary d-dimensional expansive matrix and q = jdet(A)j. Sets K b R d such that = 1 _ K is an scaling function for Z d and A were characterized in GH]. For each such K, there exist subsets K 1 ; : : : ; K q?1 of b R d such that f l = 1 _ K l : l = 1; : : : ; q ? 1g is an orthonormal basis (ONBs) of wavelets for the MRA associated to (Z d ; A) with scaling function. Such wavelets have been called Minimally Supported Frequency. The description and characterization of the sets K 1 ; : : : ; K q?1 and examples of such collections for several expansive matrices in R 2 are given in Leo99a]. The issue of path connectedness is addressed in ILP98], where it is proved that for many pairs E, F of wavelet sets in R, not necessarily MRA, the corresponding wavelets can be connected by a continuous path in L 2 (R) for which the Fourier transform has support contained in E S F. In Leo00] the problem of path connectedness for arbitrary expansive matrix A and an arbitrary number L of MSF wavelets, not necessarily MRA, is treated. In this paper it is proved that for an arbitrary expansive matrix A and for two arbitrary Minimally Supported Frequency MRAs associated to A there exists an smooth path of Minimally Supported Frequency MRAs associated to A connecting them. The space of Minimally Supported Frequency wavelets associated to an MRA is therefore path connected. Similarly, the set of the associated scaling functions is path connected. The proof is constructive, and examples of elements of such paths for MRAs in dimension d = 2 are shown. 1. Introduction, Background and Definitions Wavelet functions whose Fourier transform is the characteristic function of subsets of b R d are called Minimally Supported Frequency (MSF) wavelets, and the support of their Fourier transform have been called wavelet sets. Their existence and smoothing has been studied in DL98], DLS97] and HWW96] , HWW97] respectively. For a detailed account of contributions in this topic, see BL99]. For an expansive matrix A, the number of wavelets associated to a Multiresolution Analysis

2014 International Symposium on Power Electronics, Electrical Drives, Automation and Motion, 2014

The European Project TECMEHV, started in October 2011 and extended to September 2014, in the fram... more The European Project TECMEHV, started in October 2011 and extended to September 2014, in the frame of the EU Lifelong Learning Programme Leonardo Da Vinci, is aiming to the definition and development of a Competence Framework with Training Modules for online courses dedicated to operators on electric and hybrid vehicles, especially for maintenance and repair operations and technical assistance. The Training Modules are developed addressing operational and technical competences needed to approach maintenance and repair operations on vehicles in the key technical areas of the system architecture and especially in the field where the safety attention is prominent. The Project is coordinated by ASCAMM, with partners ATA, EPFL, NORAUTO, University Duisburg and associated partners CRF and STA.

Comunicar, 2015

Massive is one of the distinctive features of MOOCs which differentiate them from other e-learnin... more Massive is one of the distinctive features of MOOCs which differentiate them from other e-learning experiences. This massiveness entails certain possibilities, but also some challenges that must be taken into consideration when designing and implementing a Massive Open Online Course, in relation to context, work progress, learning activities, assessment, and feedback. This document presents an analysis of the advantages and disadvantages of the massive aspect of MOOCs, and specifically it narrates the experience of creating a MOOC on Web Science, developed at the University of Southampton (United Kingdom) using the new FutureLearn platform, in autumn 2013. In this document, the importance of Web Science as an emerging field is analyzed and its origins explored. The experience gained from the decisions and the work progress developed for the creation and implementation of a specific MOOC is also shared here. The final section of the paper analyses some data from the MOOC in Web Scien...

Wavelet Applications V, 1998

Pyramidal structures are de ned which are locally a combination of low and highpass ltering. The ... more Pyramidal structures are de ned which are locally a combination of low and highpass ltering. The structures are analogous to but di erent from wavelet packet structures. In particular, new frequency decompositions are obtained; and these decompositions can be parametrized to establish a correspondence with a large class of Cantor sets. Further correspondences are then established to relate such frequency decompositions with more general self-similarities. The role of the lters in de ning these pyramidal structures gives rise to signal reconstruction algorithms, and these, in turn, are used in the analysis of speech data.

Journal of Personality and Social Psychology, 1973

Integration theory was applied to moral judgments of groups. Subjects judged badness of groups of... more Integration theory was applied to moral judgments of groups. Subjects judged badness of groups of criminals, each of whom was guilty of one offense. The data supported the averaging hypothesis of information integration, with much greater weighting of the more serious offenses. A subgroup of subjects carried this tendency to an extreme, basing their judgment on the most serious offense and ignoring the lesser offenses in the group. Functional measurement procedure was used to scale the offenses. Results were comparable to the Coombs-Thurstone paired-comparison scales of the same stimuli, though some nonlinearity appeared at the extremes, possibly a result of bias in the pairedcomparison choice data. Advantages of functional scales for group processes are discussed.

Journal of Experimental Child Psychology, 1982

Abstract The study examined children's use of multiplying and proportionality rules in judgme... more Abstract The study examined children's use of multiplying and proportionality rules in judgments of area. In two experiments children judged the area of rectangles. Seven-year-olds used linear extent as an index of area. Eight- and nine-year-olds replaced the extent rule with the height × width rule. In a third experiment 8-through 11-year-olds were presented with a rectangle and a horizontal line representing the width of a second rectangle. Children were asked to indicate the height that would make the second rectangle equal in area to the first. The correct response was proportional to the product of the ratio of the widths of the two rectangles and the height of the first rectangle. Graphical and statistical analyses indicated that children applied the ratio rule to these judgments. The implications for Piaget's theory of cognitive development were discussed.

Child Development, 1984

... These rules are assumed to represent a two-step pro-cess of information integration (see Ande... more ... These rules are assumed to represent a two-step pro-cess of information integration (see Anderson, 1980, 1981). ... Requests for reprints should be sent to Manuel Leon, 1717 Klamath River Drive, Rancho Cordova, California 95670. [Child Development, 1984, 55, 2106-2113. ? ...

Annali di Matematica Pura ed Applicata, 1986

In this paper we develop a theory of prolongations of G-structures on a differentiable manifold M... more In this paper we develop a theory of prolongations of G-structures on a differentiable manifold M to appropiate G-structures on the bundle ff J3l of linear frames over M. Thus, the different definitions of lifts of tensor fields and connections on M to ff M become clear and motivated. O.-Introduction and notations. Let M be an n-dimensionM differentiable manifold, TM its tangent bundle and ~M its frame bundle. Let G1 (n) denote the linear general group. The theory of lifts to TM of geometric objects, as tensor fields, connections, etc., has been extensively studied for many years, but it was after 3'[orimoto's papers on prolongations oi G-structures on M, G c G1 (n), to appropriate G-structures on TM, @c G1 (2n), that the different definitions involved there, as well as many results of that theory, became clear and motivated ([8], [9]). Recently, K. P. ~oK ([6], [7]) has initiated a similar theory of lifts to the frame bundle 5M of geometric objects on M; in [1, 2], wo have extended and completed 5Iok's theory, both studies, Mok's and ours, being done in such a way that their results can be closely compared to those in the theory of lifts to TM. At this poimt, it wus natural to ~sk if it would be possible to develop a theory of prolongations of G-structures oa M to G-structures on 5M, with Gc G1 (n~-n2), that theory being similar to ~orimoto's. In the present paper, such a theory of prolongations is constructed, and we show, by studying the prolongations of some classicM G-structures on M, how the different definitions of lifts given in [1, 2] and [6, 7] fit nicely in this general ~ramework. Also, we briefly describe some simple examples which illustrate how this theory may serve as starting point to go further in the study of the differential geometry of ~M for a manifold M with some extra structure. In the following, R ~ will demote the n-dimensionM Euclidean space, gl (n) the Lie ulgebra of G1 (n), and (a~) the matrix whose (i, j)-entry is a~. For a manifold M, (*) Entrat~ in Redazione il 28 ottobre 1982; versione rivedut~ il 3 aprile 1984.

Let A be an arbitrary d-dimensional expansive matrix and q = jdet(A)j. Sets K b R d such that = 1... more Let A be an arbitrary d-dimensional expansive matrix and q = jdet(A)j. Sets K b R d such that = 1 _ K is an scaling function for Z d and A were characterized in GH]. For each such K, there exist subsets K 1 ; : : : ; K q?1 of b R d such that f l = 1 _ K l : l = 1; : : : ; q ? 1g is an orthonormal basis (ONBs) of wavelets for the MRA associated to (Z d ; A) with scaling function. Such wavelets have been called Minimally Supported Frequency. The description and characterization of the sets K 1 ; : : : ; K q?1 and examples of such collections for several expansive matrices in R 2 are given in Leo99a]. The issue of path connectedness is addressed in ILP98], where it is proved that for many pairs E, F of wavelet sets in R, not necessarily MRA, the corresponding wavelets can be connected by a continuous path in L 2 (R) for which the Fourier transform has support contained in E S F. In Leo00] the problem of path connectedness for arbitrary expansive matrix A and an arbitrary number L of MSF wavelets, not necessarily MRA, is treated. In this paper it is proved that for an arbitrary expansive matrix A and for two arbitrary Minimally Supported Frequency MRAs associated to A there exists an smooth path of Minimally Supported Frequency MRAs associated to A connecting them. The space of Minimally Supported Frequency wavelets associated to an MRA is therefore path connected. Similarly, the set of the associated scaling functions is path connected. The proof is constructive, and examples of elements of such paths for MRAs in dimension d = 2 are shown. 1. Introduction, Background and Definitions Wavelet functions whose Fourier transform is the characteristic function of subsets of b R d are called Minimally Supported Frequency (MSF) wavelets, and the support of their Fourier transform have been called wavelet sets. Their existence and smoothing has been studied in DL98], DLS97] and HWW96] , HWW97] respectively. For a detailed account of contributions in this topic, see BL99]. For an expansive matrix A, the number of wavelets associated to a Multiresolution Analysis

2014 International Symposium on Power Electronics, Electrical Drives, Automation and Motion, 2014

The European Project TECMEHV, started in October 2011 and extended to September 2014, in the fram... more The European Project TECMEHV, started in October 2011 and extended to September 2014, in the frame of the EU Lifelong Learning Programme Leonardo Da Vinci, is aiming to the definition and development of a Competence Framework with Training Modules for online courses dedicated to operators on electric and hybrid vehicles, especially for maintenance and repair operations and technical assistance. The Training Modules are developed addressing operational and technical competences needed to approach maintenance and repair operations on vehicles in the key technical areas of the system architecture and especially in the field where the safety attention is prominent. The Project is coordinated by ASCAMM, with partners ATA, EPFL, NORAUTO, University Duisburg and associated partners CRF and STA.

Comunicar, 2015

Massive is one of the distinctive features of MOOCs which differentiate them from other e-learnin... more Massive is one of the distinctive features of MOOCs which differentiate them from other e-learning experiences. This massiveness entails certain possibilities, but also some challenges that must be taken into consideration when designing and implementing a Massive Open Online Course, in relation to context, work progress, learning activities, assessment, and feedback. This document presents an analysis of the advantages and disadvantages of the massive aspect of MOOCs, and specifically it narrates the experience of creating a MOOC on Web Science, developed at the University of Southampton (United Kingdom) using the new FutureLearn platform, in autumn 2013. In this document, the importance of Web Science as an emerging field is analyzed and its origins explored. The experience gained from the decisions and the work progress developed for the creation and implementation of a specific MOOC is also shared here. The final section of the paper analyses some data from the MOOC in Web Scien...

Wavelet Applications V, 1998

Pyramidal structures are de ned which are locally a combination of low and highpass ltering. The ... more Pyramidal structures are de ned which are locally a combination of low and highpass ltering. The structures are analogous to but di erent from wavelet packet structures. In particular, new frequency decompositions are obtained; and these decompositions can be parametrized to establish a correspondence with a large class of Cantor sets. Further correspondences are then established to relate such frequency decompositions with more general self-similarities. The role of the lters in de ning these pyramidal structures gives rise to signal reconstruction algorithms, and these, in turn, are used in the analysis of speech data.

Journal of Personality and Social Psychology, 1973

Integration theory was applied to moral judgments of groups. Subjects judged badness of groups of... more Integration theory was applied to moral judgments of groups. Subjects judged badness of groups of criminals, each of whom was guilty of one offense. The data supported the averaging hypothesis of information integration, with much greater weighting of the more serious offenses. A subgroup of subjects carried this tendency to an extreme, basing their judgment on the most serious offense and ignoring the lesser offenses in the group. Functional measurement procedure was used to scale the offenses. Results were comparable to the Coombs-Thurstone paired-comparison scales of the same stimuli, though some nonlinearity appeared at the extremes, possibly a result of bias in the pairedcomparison choice data. Advantages of functional scales for group processes are discussed.

Journal of Experimental Child Psychology, 1982

Abstract The study examined children's use of multiplying and proportionality rules in judgme... more Abstract The study examined children's use of multiplying and proportionality rules in judgments of area. In two experiments children judged the area of rectangles. Seven-year-olds used linear extent as an index of area. Eight- and nine-year-olds replaced the extent rule with the height × width rule. In a third experiment 8-through 11-year-olds were presented with a rectangle and a horizontal line representing the width of a second rectangle. Children were asked to indicate the height that would make the second rectangle equal in area to the first. The correct response was proportional to the product of the ratio of the widths of the two rectangles and the height of the first rectangle. Graphical and statistical analyses indicated that children applied the ratio rule to these judgments. The implications for Piaget's theory of cognitive development were discussed.

Child Development, 1984

... These rules are assumed to represent a two-step pro-cess of information integration (see Ande... more ... These rules are assumed to represent a two-step pro-cess of information integration (see Anderson, 1980, 1981). ... Requests for reprints should be sent to Manuel Leon, 1717 Klamath River Drive, Rancho Cordova, California 95670. [Child Development, 1984, 55, 2106-2113. ? ...

Annali di Matematica Pura ed Applicata, 1986

In this paper we develop a theory of prolongations of G-structures on a differentiable manifold M... more In this paper we develop a theory of prolongations of G-structures on a differentiable manifold M to appropiate G-structures on the bundle ff J3l of linear frames over M. Thus, the different definitions of lifts of tensor fields and connections on M to ff M become clear and motivated. O.-Introduction and notations. Let M be an n-dimensionM differentiable manifold, TM its tangent bundle and ~M its frame bundle. Let G1 (n) denote the linear general group. The theory of lifts to TM of geometric objects, as tensor fields, connections, etc., has been extensively studied for many years, but it was after 3'[orimoto's papers on prolongations oi G-structures on M, G c G1 (n), to appropriate G-structures on TM, @c G1 (2n), that the different definitions involved there, as well as many results of that theory, became clear and motivated ([8], [9]). Recently, K. P. ~oK ([6], [7]) has initiated a similar theory of lifts to the frame bundle 5M of geometric objects on M; in [1, 2], wo have extended and completed 5Iok's theory, both studies, Mok's and ours, being done in such a way that their results can be closely compared to those in the theory of lifts to TM. At this poimt, it wus natural to ~sk if it would be possible to develop a theory of prolongations of G-structures oa M to G-structures on 5M, with Gc G1 (n~-n2), that theory being similar to ~orimoto's. In the present paper, such a theory of prolongations is constructed, and we show, by studying the prolongations of some classicM G-structures on M, how the different definitions of lifts given in [1, 2] and [6, 7] fit nicely in this general ~ramework. Also, we briefly describe some simple examples which illustrate how this theory may serve as starting point to go further in the study of the differential geometry of ~M for a manifold M with some extra structure. In the following, R ~ will demote the n-dimensionM Euclidean space, gl (n) the Lie ulgebra of G1 (n), and (a~) the matrix whose (i, j)-entry is a~. For a manifold M, (*) Entrat~ in Redazione il 28 ottobre 1982; versione rivedut~ il 3 aprile 1984.