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LECTURE NOTES ON CHERNSIMONS (SUPER)GRAVITIES
, 2008
"... This is intended to be a broad introduction to ChernSimons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant system –with a fiber bundle formulation – in more than three dimensions, which could provide a firm ground for constructing a quantum t ..."
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This is intended to be a broad introduction to ChernSimons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant system –with a fiber bundle formulation – in more than three dimensions, which could provide a firm ground for constructing a quantum theory of the gravitational field. The starting point is a gravitational action which generalizes the Einstein theory for dimensions D> 4 –Lovelock gravity. It is then shown that in odd dimensions there is a particular choice of the arbitrary parameters of the action that makes the theory gauge invariant under the (anti)de Sitter or the Poincaré groups. The resulting lagrangian is a ChernSimons form for a connection of the corresponding gauge groups and the vielbein and the spin connection are parts of this connection field. These theories also admit a natural supersymmetric extension for all odd D where the local supersymmetry algebra closes offshell and without a need for auxiliary fields. No analogous construction is available in even dimensions. A cursory discussion of the unexpected dynamical features of these theories and a number of open problems are also presented. These notes were prepared for the Fifth CBPF Graduate School, held in Rio de Janeiro in July 2004, published in Portuguese [1]. These notes were in turn based on a lecture series presented at the Villa de Leyva
Formant Centralization Ratio: A Proposal for a New Acoustic Measure of Dysarthric Speech
"... Purpose: The vowel space area (VSA) has been used as an acoustic metric of dysarthric speech, but with varying degrees of success. In this study, the authors aimed to test an alternative metric to the VSAthe formant centralization ratio (FCR), which is hypothesized to more effectively differentiate ..."
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Purpose: The vowel space area (VSA) has been used as an acoustic metric of dysarthric speech, but with varying degrees of success. In this study, the authors aimed to test an alternative metric to the VSAthe formant centralization ratio (FCR), which is hypothesized to more effectively differentiate dysarthric from healthy speech and register treatment effects. Method: Speech recordings of 38 individuals with idiopathic Parkinson's disease and dysarthria (19 of whom received 1 month of intensive speech therapy [Lee Silverman Voice Treatment; LSVT LOUD]) and 14 healthy control participants were acoustically analyzed. Vowels were extracted from short phrases. The same vowelformant
Historical Projects in Discrete Mathematics and Computer Science
"... A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itse ..."
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A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itself, with the notion of counting a discrete operation, usually cited as the first mathematical development
Improving The Classroom Environment
 Journal of Engineering Education
, 2000
"... This paper summarizes effective teaching techniques identified during one of the technical sessions of the 1999 Frontiers in Education Conference in San Juan, Puerto Rico. The paper involves the perspectives of twelve experienced college teachers engaged in a roundtable discussion of "Ways to imp ..."
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This paper summarizes effective teaching techniques identified during one of the technical sessions of the 1999 Frontiers in Education Conference in San Juan, Puerto Rico. The paper involves the perspectives of twelve experienced college teachers engaged in a roundtable discussion of "Ways to improve a classroom environment" and "Behaviors to avoid in the classroom." In this paper, those ideas are discussed and then supplemented with general advice and specific suggestions from the experience of the authors. The paper includes a bibliography of related reference material. Advice presented in this paper could benefit any teacher seeking to improve classroom effectiveness.
A New Look At Euclid's Second Proposition
 The Mathematical Intelligencer
, 1993
"... There has been considerable interest during the past 2300 years in comparing different models of geometric computation in terms of their computing power. One of the most well known results is Mohr's proof in 1672 that all constructions that can be executed with straightedge and compass can be carri ..."
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There has been considerable interest during the past 2300 years in comparing different models of geometric computation in terms of their computing power. One of the most well known results is Mohr's proof in 1672 that all constructions that can be executed with straightedge and compass can be carried out with compass alone. The earliest such proof of the equivalence of models of computation is due to Euclid in his second proposition of Book I of the Elements in which he establishes that the collapsing compass is equivalent in power to the modern compass. Therefore in the theory of equivalence of models of computation Euclid's second proposition enjoys a singular place. However, like much of Euclid's work and particularly his constructions involving cases, his second proposition has received a great deal of criticism over the centuries. Here it is argued that it is Euclid's early Greek commentators and more recent expositors and translators that are at fault and that Euclid's original...
An Imaginary Tale: The Story of
, 1999
"... h a cartoon strip in which an imaginary tiger professes to instinctively understand imaginary numbers. If only real humans were so blessed. Each year a new crop of high school students becomes acquainted with the Quadratic Formula and, along with it, negative discriminants. The number i is magically ..."
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h a cartoon strip in which an imaginary tiger professes to instinctively understand imaginary numbers. If only real humans were so blessed. Each year a new crop of high school students becomes acquainted with the Quadratic Formula and, along with it, negative discriminants. The number i is magically invoked to resolve the difficulty. Is it a real number ? The correct answer is Clintonesque: "It depends on how you define `real'." So we compromise: we say that it is an imaginary number, but we make sure that it is on the examthat will make it seem real enough. Happily for most students, imaginary numbers are often no more than a fleeting nuisance. Those who do continue beyond high school algebra pass into an imaginaryfree zone called calculus. Because we are often successful at extending this respite through linear algebra and ordinary differential equations, many mathematics majors never see an imaginary number during their entire college careers. It
Center of Gravity – Still Relevant After All These Years
"... Clausewitz’s concept of center of gravity has generated much discussion in the last twentyfive ..."
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Clausewitz’s concept of center of gravity has generated much discussion in the last twentyfive
Sequences of density ζ(k) − 1
, 2009
"... At a recent postseminar gathering, Herb Wilf casually mentioned to those of ..."
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At a recent postseminar gathering, Herb Wilf casually mentioned to those of