Implicit QR for Companion-like Pencils

A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zerofinding problems . The modified QZ algorithm computes the generalized eigenvalues of certain NxN rank structured matrix pencils using O(N^2) ops and O(N) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method

A contour integral approach to the computation of invariant pairs

We study some aspects of the invariant pair problem for matrix polynomials, as introduced by Betcke and Kressner [3] and by Beyn and Thümmler [6]. Invariant pairs extend the notion of eigenvalue–eigenvector pairs, providing a counterpart of invariant subspaces for the nonlinear case. We compute formulations for the condition numbers and the backward error for invariant pairs and solvents. We then adapt the Sakurai–Sugiura moment method [1] to the computation of invariant pairs, including some classes of problems that have multiple eigenvalues. Numerical refinement via a variant of Newton's method is also studied. Furthermore, we investigate the relation between the matrix solvent problem and the triangularization of matrix polynomials

Isotope partitioning between cow milk and farm water: A tool for verification of milk provenance

Rationale: The oxygen and hydrogen isotope compositions of the water component of the milk from nine Italian dairy farms were studied together with the farm water for one year. The aim was to verify the importance of farm water and seasonal temperature variation on milk isotope values and propose mathematical relations as new tools to identify the milk origin. Methods: Milk was centrifuged to separate the solids and then distilled under vacuum to separate water. δ(18O/16O) and δ(2H/1H) analyses of the water molecules were carried out using a water equilibrator online with a mass spectrometer. For oxygen and hydrogen isotope determination, water was equilibrated with pure CO2 for 7.5 h and with pure H2 for 5 h, respectively. The isotope ratio value is indicated with δ (expressed on the VSMOW/SLAP scale) as defined by IUPAC. Results: The average annual isotope value of milk at the different cattle sheds is mostly related to the farm water suggesting that the drinking water is the most important factor influencing the isotopic values of the milk water. The milk/water fractionation factor correlates with the milking time and, thus, the seasonal temperature is best described by a 4th order polynomial regression line. A two-level check model was used to verify the milking provenance. Conclusions: This study shows that it is essential to analyze both milk and farm water to indicate provenance. A two-step verification tool, based on the difference between the measured and calculated δ(18O/16O)M values, and the difference between the calculated and estimated milk-water fractionation factors, allowed the source determination of milk. Both conditions must be met if the milk is considered to be from the Parmigiano-Reggiano production region. Although this approach was developed for this region, it can easily be tested and adapted to other dairy production areas

Scalar resonances in a unitary π−π\pi-\pi SS-wave model for D+→π+π−π+D^+ \to \pi^+ \pi^- \pi^+

We propose a model for $D^+ \to \pi^+ \pi^- \pi^+$ decays following experimental results which indicate that the two-pion interaction in the $S$-wave is dominated by the scalar resonances $f_0(600)/\sigma$ and $f_0(980)$. The weak decay amplitude for $D^+\to R \pi^+$, where $R$ is a resonance that subsequently decays into $\pi^+\pi^-$, is constructed in a factorization approach. In the $S$-wave, we implement the strong decay $R\to \pi^-\pi^+$ by means of a scalar form factor. This provides a unitary description of the pion-pion interaction in the entire kinematically allowed mass range $m_{\pi\pi}^2$ from threshold to about 3 GeV$^2$. In order to reproduce the experimental Dalitz plot for \Dppp, we include contributions beyond the $S$-wave. For the $P$-wave, dominated by the $\rho(770)^0$, we use a Breit-Wigner description. Higher waves are accounted for by using the usual isobar prescription for the $f_2(1270)$ and $\rho(1450)^0$. The major achievement is a good reproduction of the experimental $m_{\pi\pi}^2$ distribution, and of the partial as well as the total \Dppp branching ratios. Our values are generally smaller than the experimental ones. We discuss this shortcoming and, as a byproduct, we predict a value for the poorly known $D\to \sigma$ transition form factor at $q^2=m_\pi^2$.Comment: 23 pages, 2 figures. Two new equations. The value for the strength of the contribution of the scalar form factor now agrees with other results in the literature. Main results unchanged. Version to appear in Phys. Rev.

D^+ \to K^- \p^+ \p^+ : the low-energy sector

An effective $SU(3)\times SU(3)$ chiral lagrangian, which includes scalar resonances, is used to describe the process D^+ \rar K^- \p^+ \p^+ at low-energies. Our main result is a set of five $S$-wave amplitudes, suited to be used in analyses of production data.Comment: Talk given at SCADRON 70 - Workshop on Scalar Mesons and Related Topics - Lisbon - February 200

A Very Low Resource Language Speech Corpus for Computational Language Documentation Experiments

Most speech and language technologies are trained with massive amounts of speech and text information. However, most of the world languages do not have such resources or stable orthography. Systems constructed under these almost zero resource conditions are not only promising for speech technology but also for computational language documentation. The goal of computational language documentation is to help field linguists to (semi-)automatically analyze and annotate audio recordings of endangered and unwritten languages. Example tasks are automatic phoneme discovery or lexicon discovery from the speech signal. This paper presents a speech corpus collected during a realistic language documentation process. It is made up of 5k speech utterances in Mboshi (Bantu C25) aligned to French text translations. Speech transcriptions are also made available: they correspond to a non-standard graphemic form close to the language phonology. We present how the data was collected, cleaned and processed and we illustrate its use through a zero-resource task: spoken term discovery. The dataset is made available to the community for reproducible computational language documentation experiments and their evaluation.Comment: accepted to LREC 201

Implicit QR with compression

AbstractIn this paper, we elaborate on the implicit shifted QR eigenvalue algorithm given in [D.A. Bini, P. Boito, Y. Eidelman, L. Gemignani, I. Gohberg, A fast implicit QR eigenvalue algorithm for companion matrices, Linear Algebra Appl. 432 (2010), 2006–2031]. The algorithm is substantially simplified and speeded up while preserving its numerical robustness. This allows us to obtain a potentially important advance towards a proof of its backward stability together with both cost reductions and implementative benefits