DECONSTRUCT

"Decomposition of Structured Tensors, Algorithms and Characterization."

Coordinatore	INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE    more  Organization address address: Domaine de Voluceau, Rocquencourt city: LE CHESNAY Cedex postcode: 78153 contact info Titolo: Ms. Nome: Frédérique Cognome: Lavirotte Email: send email Telefono: +33 4 92 38 77 00 Fax: +33 4 92 38 79 55
Nazionalità Coordinatore	France [FR]
Totale costo	157˙945 €
EC contributo	157˙945 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-2009-IEF
Funding Scheme	MC-IEF
Anno di inizio	2010
Periodo (anno-mese-giorno)	2010-11-08   -   2012-11-07

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE  Organization address address: Domaine de Voluceau, Rocquencourt city: LE CHESNAY Cedex postcode: 78153 contact info Titolo: Ms. Nome: Frédérique Cognome: Lavirotte Email: send email Telefono: +33 4 92 38 77 00 Fax: +33 4 92 38 79 55	FR (LE CHESNAY Cedex)	coordinator	157˙945.60

Mappa

 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

 Obiettivo del progetto (Objective)

'Tensors play a wide role in numerous application areas as Signal Processing for Telecommunications, Arithmetic Complexity or Data Analysis. In some applications tensors may be completely symmetric, or symmetric only in some modes, or may not be symmetric. In most of these applications, the decomposition of a tensor into a sum of rank-1 terms is relevant, since tensors of interest have a reduced rank. Most of them are structured i.e. they are either symmetric or enjoy some index-invariance. Lastly, they are often real, which raises open problems concerning the existence and calculation of the decompositions. These issues build the basic bricks of the research program we propose. The classes of tensors described above have a geometric translations in terms of classical algebraic varieties: Segre, Veronese, Segre-Veronese varieties and Grassmannians and their secant varieties. A complete description of equations for those secant varieties and their dimensions is still not known (only dimensions of secant varieties to Veronsean are classified), although they have been studied by algebraic and differential geometers and algebraists for a long period up to now. The aim of this research project is: -to attack both the description of the ideal of those secant varieties and their dimensions, starting from low dimensions and low degrees, -to propose algorithms able to compute the rank of structured tensors. Workshops in Palo Alto (CA-USA, 2008) and in Nice (FR, 2009) showed that Italy and France are among the most active in Europe in the field of tensor decompositions. Both the coordinator of this project and the hosting organization have already obtained results in this field regarding equations and algorithms. Hence this program is crucial for the development of those research areas in the European Community, along with the numerous international collaborations already existing. The impact of this project will be visible in both academic and industrial worlds.'