602 research outputs found
On complex and real identifiability of tensors
We report about the state of the art on complex and real generic
identifiability of tensors, we describe some of our recent results obtained in
[6] and we present perspectives on the subject.Comment: To appear on Rivista di Matematica dell'Universit\`a di Parma, Volume
8, Number 2, 2017, pages 367-37
Higher secants of spinor varieties
Let be the even pure spinors variety of a complex vector space of
even dimension endowed with a non degenerate quadratic form and let
be the -secant variety of . We decribe a probabilistic
algorithm which computes the complex dimension of . Then, by
using an inductive argument, we get our main result: has the
expected dimension except when . Also we provide theoretical
arguments which prove that has a defective 3-secant variety and has
defective 3-secant and 4-secant varieties.Comment: 23 page
On the identifiability of ternary forms
We describe a new method to determine the minimality and identifiability of a
Waring decomposition of a specific form (symmetric tensor) in three
variables. Our method, which is based on the Hilbert function of , can
distinguish between forms in the span of the Veronese image of , which in
general contains both identifiable and not identifiable points, depending on
the choice of coefficients in the decomposition. This makes our method
applicable for all values of the length of the decomposition, from up
to the generic rank, a range which was not achievable before. Though the method
in principle can handle all cases of specific ternary forms, we introduce and
describe it in details for forms of degree
Econometric analyses with backdated data: unified Germany and the euro area
In this paper we compare alternative approaches for the construction of time series of macroeconomic variables for Unified Germany prior to 1991, and then use them for the construction of corresponding time series for the euro area. The resulting series for Germany and the euro area are compared with existing ones on the basis of both descriptive statistics and results of econometric analyses conducted with the alternative time series. We find that more sophisticated time series methods for backdating can yield sizeable gains. JEL Classification: C32, C43, C82Backdating, euro area, factor model, Unified Germany
Identifiability for a class of symmetric tensors
We use methods of algebraic geometry to find new, effective methods for
detecting the identifiability of symmetric tensors. In particular, for ternary
symmetric tensors T of degree 7, we use the analysis of the Hilbert function of
a finite projective set, and the Cayley-Bacharach property, to prove that, when
the Kruskal's rank of a decomposition of T are maximal (a condition which holds
outside a Zariski closed set of measure 0), then the tensor T is identifiable,
i.e. the decomposition is unique, even if the rank lies beyond the range of
application of both the Kruskal's and the reshaped Kruskal's criteria
Estimating and forecasting the euro area monthly national accounts from a dynamic factor model
We estimate and forecast growth in euro area monthly GDP and its components from a dynamic factor model due to Doz et al. (2005), which handles unbalanced data sets in an efficient way. We extend the model to integrate interpolation and forecasting together with cross-equation accounting identities. A pseudo real-time forecasting exercise indicates that the model outperforms various benchmarks, such as quarterly time series models and bridge equations in forecasting growth in quarterly GDP and its components. JEL Classification: E37, C53Dynamic Factor Models, Interpolation, nowcasting
Waring decompositions and identifiability via Bertini and Macaulay2 software
Starting from our previous papers [AGMO] and [ABC], we prove the existence of
a non-empty Euclidean open subset whose elements are polynomial vectors with 4
components, in 3 variables, degrees, respectively, 2,3,3,3 and rank 6, which
are not identifiable over but are identifiable over . This result has been obtained via computer-aided procedures suitably adapted
to investigate the number of Waring decompositions for general polynomial
vectors over the fields of complex and real numbers. Furthermore, by means of
the Hessian criterion ([COV]), we prove identifiability over for
polynomial vectors in many cases of sub-generic rank.Comment: 15 page
Logarithmic Bundles Of Hypersurface Arrangements In P^n
Let D = {D_{1},...,D_{l}} be an arrangement of smooth hypersurfaces with
normal crossings on the complex projective space P^n and let
\Omega^{1}_{P^n}(log D) be the logarithmic bundle attached to it. Following
[1], we show that \Omega^{1}_{P^n}(log D) admits a resolution of lenght 1 which
explicitly depends on the degrees and on the equations of D_{1},...,D_{l}. Then
we prove a Torelli type theorem when all the D_{i}'s have the same degree d and
l >= {{n+d} \choose {d}}+3: indeed, we recover the components of D as unstable
smooth hypersurfaces of \Omega^{1}_{P^n}(log D). Finally we analyze the cases
of one quadric and a pair of quadrics, which yield examples of non-Torelli
arrangements. In particular, through a duality argument, we prove that two
pairs of quadrics have isomorphic logarithmic bundles if and only if they have
the same tangent hyperplanes.Comment: 21 pages, 2 figures, Collectanea Mathematica 201
Diffusion index-based inflation forecasts for the euro area
Diffusion indexes based on dynamic factors have recently been advocated by Stock and Watson (1998), and further used to perform forecasting tests by the same authors on US data. This technique is explored for the euro area using a multi-country data set and a broad array of variables, in order to test the inflation forecasting performance of extracted factors at the aggregate euro area level. First, a description of factors extracted from different data sets is performed using a number of different approaches. Conclusions reached are that nominal phenomena in the original variables might be well captured in-sample using the factor approach. Out-of-sample tests have more ambiguous interpretation, as factors seem to be good leading indicators of inflation, but the comparative advantage of the factors is less clear. Nevertheless, alternative indicators such as unemployment or money growth do not outperform them JEL Classification: C53, E31, E37
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