Prof. Guido Castelnuovo

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Multigraded Castelnuovo-mumford Regularity

We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomology. We establish the key properties of regularity: its connection with the m...

Pointed Castelnuovo Numbers

Abstract. The classical Castelnuovo numbers count linear series of minimal degree and fixed dimension on a general curve, in the case when this number is finite. For pencils, that is, linear series of dimension one, the Castelnuovo numbers specialize to the better known Catalan numbers. Using the Fulton-Pragacz determinantal formula for flag bundles and combinatorial manipulations, we obtain a ...

GUIDO/MIR - an Experimental Musical Information Retrieval System based on GUIDO Music Notation

Musical databases are growing in number, size, and complexity, and they are becoming increasingly relevant for a broad range of academic as well as commercial applications. The features and performance of musical database systems critically depend on two factors: The nature and representation of the information stored in the database, and the search and retrieval mechanisms available to the use...

Massachusetts Institute of Technology Guido

In this lecture we are concerned with models for stationary (in the weak sense) processes. The focus here will be on linear processes. This is clearly restrictive given the stylized facts of financial time series. However linear time series models are often used as building blocks in nonlinear models. Moreover linear models are easier to handle empirically and have certain optimality properties...