Introduction. These are notes for my eight lectures given at the C.I.M.E. session on “Vector bundles on curves. New directions” held at Cetraro (Italy) in June 1995. The work presented here was done in collaboration with M.S. Narasimhan and A. Ramanathan and appeared in [KNR]. These notes differ from [KNR] in that we have added three appendices (A)-(C) containing basic definitions and results (...

The possibility of developing accessible optical music recognition presents an amazing array of opportunities to improve the musical education experience. While the topic has been the subject of research for decades, widespread application of this technology has not reached the general consumer. We have developed a sheet music image processing application targeted towards beginner music to prov...

These lecture notes are based on my course from the winter semester 2009/10. I kept the numbering and the contents of the results presented in the lectures (except for some minor corrections). Typically, the proofs and calculations in the notes are a bit shorter than those given in the lecture. Moreover, the drawings and many additional, mostly oral remarks from the lectures are omitted here. O...

The purpose of these notes is to show that the methods introduced by Bauer and Furuta, see [5, 6, 7], in order to refine the Seiberg-Witten invariants of smooth 4-dimensional manifolds can also be used to obtain stable homotopy classes from 2-dimensional manifolds, using the vortex equations on the latter. So far these notes contain barely more than the necessary analytic estimates to prove thi...

Audio feature estimation is potentially improved by including higherlevel models. One such model is the Auditory Short Term Memory (STM) model. A new paradigm of audio feature estimation is obtained by adding the influence of notes in the STM. These notes are identified when the perceptual spectral flux has a peak, and the spectral content that is increased by the new note is added to the STM. ...

Much surviving 16th-century instrumental music consists of arrangements (‘intabulations’) of vocal music, in tablature for solo lute. Intabulating involved deciding what to omit from a score to fit the instrument, and making it fit under the hand. Notes were usually added as embellishments to the original plain score, using idiomatic patterns, typically at cadences, but often filling simple int...

Foreword These are scribed notes from a graduate courses on Computational Complexity offered at the University of California at Berkeley in the Fall of 2002, based on notes scribed by students in Spring 2001 and on additional notes scribed in Fall 2002. I added notes and references in May 2004. The first 15 lectures cover fundamental material. The remaining lectures cover more advanced material...

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In this article we describe several results based on the paper [Hur98] and which we will refer to as Hurwitz’ theorem. There are several related results: the classification of real normed division algebras, the classification of complex composition algebras and the classification of real composition algebras. The classification of real division algebras is an open problem. Our interest is in co...

Raising domestic tax revenues is a priority for most sub-Saharan African countries. But the tax bases in most African countries are undermined by widespread tax avoidance and evasion. A new study from CMI supports the claim that improved knowledge about the tax system makes a difference in people’s willingness to pay tax. The study shows that exposure to Value-AddedTax (VAT) makes people take a...