Expanding solitons to the Hermitian curvature flow on complex Lie groups

We investigate the algebraic structure of complex Lie groups equipped with left-invariant metrics which are expanding semi-algebraic solitons to the Hermitian curvature flow (HCF). We show that the Lie algebras of such Lie groups decompose in the semidirect product of a reductive Lie subalgebra with their nilradicals. Furthermore, we give a structural result concerning expanding semi-algebraic solitons on complex Lie groups. It turns out that the restriction of the soliton metric to the nilradical is also an expanding algebraic soliton and we explain how to construct expanding solitons on complex Lie groups starting from expanding solitons on their nilradicals.Comment: 14 pages; section 4 extended; last version, to appear in Differential Geometry and its Application

Multivariate Spectral Estimation based on the concept of Optimal Prediction

In this technical note, we deal with a spectrum approximation problem arising in THREE-like multivariate spectral estimation approaches. The solution to the problem minimizes a suitable divergence index with respect to an a priori spectral density. We derive a new divergence family between multivariate spectral densities which takes root in the prediction theory. Under mild assumptions on the a priori spectral density, the approximation problem, based on this new divergence family, admits a family of solutions. Moreover, an upper bound on the complexity degree of these solutions is provided

On the boundary and intersection motives of genus 2 Hilbert-Siegel varieties

We study genus 2 Hilbert-Siegel varieties, i.e. Shimura varieties $S_K$ corresponding to the group \mbox{GSp}_{4,F} over a totally real field $F$, along with the relative Chow motives $^\lambda \mathcal{V}$ of abelian type over $S_K$ obtained from irreducible representations $V_{\lambda}$ of \mbox{GSp}_{4,F}. We analyse the weight filtration on the degeneration of such motives at the boundary of the Baily-Borel compactification and we find a criterion on the highest weight $\lambda$ which characterises the absence of the middle weights 0 and 1 in the corresponding degeneration. Thanks to Wildeshaus' theory, the absence of these weights allows us to construct Hecke-equivariant Chow motives over $\mathbb{Q}$, whose realizations equal interior (or intersection) cohomology of $S_K$ with $V_{\lambda}$-coefficients. We give applications to the construction of motives associated to automorphic representations.Comment: 39 pages; comments very welcome! (v2): some typos fixed, minor changes in the text (v3): other typos fixed, some prerequisites shortened (now 36 pages), minor changes in the text (v4) final version, accepted for publication in Documenta Mathematica (40 pages

Weak hamiltonian Wilson Coefficients from Lattice QCD

In this work we present a calculation of the Wilson Coefficients $C_1$ and $C_2$ of the Effective Weak Hamiltonian to all-orders in $\alpha_s$, using lattice simulations. Given the current availability of lattice spacings we restrict our calculation to unphysically light $W$ bosons around 2 GeV and we study the systematic uncertainties of the two Wilson Coefficients.Comment: 8 pages, Proceedings of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

A new family of high-resolution multivariate spectral estimators

In this paper, we extend the Beta divergence family to multivariate power spectral densities. Similarly to the scalar case, we show that it smoothly connects the multivariate Kullback-Leibler divergence with the multivariate Itakura-Saito distance. We successively study a spectrum approximation problem, based on the Beta divergence family, which is related to a multivariate extension of the THREE spectral estimation technique. It is then possible to characterize a family of solutions to the problem. An upper bound on the complexity of these solutions will also be provided. Simulations suggest that the most suitable solution of this family depends on the specific features required from the estimation problem

Finite groups acting on 3-manifolds and cyclic branched coverings of knots

We are interested in finite groups acting orientation-preservingly on 3-manifolds (arbitrary actions, ie not necessarily free actions). In particular we consider finite groups which contain an involution with nonempty connected fixed point set. This condition is satisfied by the isometry group of any hyperbolic cyclic branched covering of a strongly invertible knot as well as by the isometry group of any hyperbolic 2-fold branched covering of a knot in the 3-sphere. In the paper we give a characterization of nonsolvable groups of this type. Then we consider some possible applications to the study of cyclic branched coverings of knots and of hyperelliptic diffeomorphisms of 3-manifolds. In particular we analyze the basic case of two distinct knots with the same cyclic branched covering.Comment: This is the version published by Geometry & Topology Monographs on 29 April 200

Convergence analysis of a family of robust Kalman filters based on the contraction principle

In this paper we analyze the convergence of a family of robust Kalman filters. For each filter of this family the model uncertainty is tuned according to the so called tolerance parameter. Assuming that the corresponding state-space model is reachable and observable, we show that the corresponding Riccati-like mapping is strictly contractive provided that the tolerance is sufficiently small, accordingly the filter converges