On Comon's and Strassen's conjectures

Comon's conjecture on the equality of the rank and the symmetric rank of a symmetric tensor, and Strassen's conjecture on the additivity of the rank of tensors are two of the most challenging and guiding problems in the area of tensor decomposition. We survey the main known results on these conjectures, and, under suitable bounds on the rank, we prove them, building on classical techniques used in the case of symmetric tensors, for mixed tensors. Finally, we improve the bound for Comon's conjecture given by flattenings by producing new equations for secant varieties of Veronese and Segre varieties.Comment: 12 page

Tangential weak defectiveness and generic identifiability

We investigate the uniqueness of decomposition of general tensors $T\in {\mathbb C}^{n_1+1}\otimes\cdots\otimes{\mathbb C}^{n_r+1}$ as a sum of tensors of rank $1$. This is done extending the theory developed in a previous paper by the second author to the framework of non twd varieties. In this way we are able to prove the non generic identifiability of infinitely many partially symmetric tensors

Waring identifiability for powers of forms via degenerations

We discuss an approach to the secant non-defectivity of the varieties parametrizing $k$-th powers of forms of degree $d$. It employs a Terracini type argument along with certain degeneration arguments, some of which are based on toric geometry. This implies a result on the identifiability of the Waring decompositions of general forms of degree kd as a sum of $k$-th powers of degree $d$ forms, for which an upper bound on the Waring rank was proposed by Fr\"oberg, Ottaviani and Shapiro.Comment: 26 pages, 2 figures. Fixed a typo in the statement of Theorem 1.2 and Corollary 5.

Forecasting the effects of the Andaman Islands - Sumatra megathrust earthquakes (Dec. 2004 and Mar. 2005) on volcanoes in the surrounding area

The Andaman Islands - Sumatra earthquake (Mw = 9.3, Dec. 2004) and the subsequent Sumatra earthquake (Mw = 8.7, Mar. 2005) represent one of most energetic sequence of earthquakes ever recorded. Since both events occurred in a strongly active volcanic region, their exceptionally strong stress perturbation gives the opportunity to understand the eff ects of stress perturbations on volcanic systems. Here, we set the rules for a forward test of the causal relationship between stress perturbation and subsequent volcanic eruptions, by means of the comparison of the spatio-temporal distribution of the eruptions which follow the earthquakes with the co- and the post-seismic stress field due to the earthquakes. In practice, we forecast that the volcanic activity of the next 30 years will be significantly promoted by the stress perturbation; thus, we define the rules for an objective test of such an hypothesis. Given the extremely high values of stress perturbation due to this sequence of earthquakes, the results of our test will definitively provide a reliable evaluation of the possible statistical impact of earthquake-eruption interaction on long-term volcanic hazard assessments

Complete Singular Collineations and Quadrics

We construct wonderful compactifications of the spaces of linear maps and symmetric linear maps of a given rank as blowups of secant varieties of Segre and Veronese varieties. Furthermore, we investigate their birational geometry and their relations with some spaces of degree two stable maps

Volcanic deformation and flank instability due to magmatic sources and frictional rheology: the case of Mount Etna

The overall picture of Mount Etna deformation emerging since a couple of decades of geodetic surveys shows effects of magma accumulation, characterized by inflation/deflation cycle, accompanied by a sliding instability of the southeast flank, whose manifestation is an increase in the horizontal deformation away from the volcano summit. This is a very interesting case to test whether advanced models, taking into account topography, internal structure and frictional rheology, may contribute to a better understanding of the complex interplay among mechanical response, magmatic activity and gravitational load occurring in a volcanic system. Using finite element numerical models we make predictions of surface displacements associated with a simple expansion source and with a dike like vertical discontinuity. A new methodology is developed to initalize the lithostatic stress field according to the material and geometrical complexities of the models considered. Our results show that, while an amplification of the horizontal displacement can be easily obtained up to a maximum distance of 10 km from the source, we have not been able to find any onfiguration to extend further this signal. For the case of Mount Etna this suggests that the large horizontal displacements observed in the east flank along the coast cannot be directly related to magma accumulation below the volcano's summit

Paul Ricoeur: la constitución narrativa de la identidad personal

Paul Ricoeur (1913) se ha convertido en uno de los pensadores más influyentes del panorama filosófico actual. Su filosofía pretende caracterizar, en los limites de lo posible, las estructuras fundamentales del sujeto de la acción. El actuar humano representa así un eje fundamental de su pensamiento. Es justamente en su último libro, Soi-méme comme un autre (1990), que su filosofía de la acción toma forma e ilumina retrospectivamente el conjunto de sus escritos. El libro busca explorar la variedad de niveles del actuar humano según tres dimensiones básicas: lingüística, narrativa y ética. A través de la constitución narrativa de la identidad personal, Ricoeur intenta mostrar que no existe una ruptura radical entre descripción y prescripción, entre hecho y valor, oponiéndose en ese sentido a la tradición de pensamiento nacida de Hume. La identidad narrativa constituye así un elemento esencial para la elaboración de una antropología filosófica que permita pensar lacapacidad ética y política del hombre. Ricoeur entiende que, sin tal antropología, la filosofía política está condenada a ser puramente procedimental

3D Finite Element Modeling of the 2009 L'Aquila Earthquake Deformation Field

The L'Aquila earthquake (Mw 6.3) occurred on April 6th at 01:32 UTC in the Central Appennines at a depth of about 9 km and was felt all over Central Italy. The main shock was preceded by a long seismic sequence started several months before and was followed by thousands of aftershocks, some of them with Mw>4. We built up a high resolution three-dimensional model, incorporating surface topography, which was discretized using 20-nodes brick elements. The element horizontal size is biased from 500 m to 2 km using the paving meshing algorithm in combination with an appropriate adaptive sizing function. A realistic rheology was introduced from a vp/vpvs travel time tomographic model. We computed the co-seismic deformation induced by the earthquake by means of a recently developed finite elements simulation tool, FEMSA (Finite Element Modeling for Seismic Applications). We used different seismic source models obtained from fault inversion of GPS measurements, joint inversion of strong motion and GPS data and from inversion of DInSAR displacements. The synthetic deformation patterns were compared with the experimental results in order to evaluate which source model better reconciles the data and quantify the trade off introduced by 1D simulations