A note on the error analysis of classical Gram-Schmidt

An error analysis result is given for classical Gram--Schmidt factorization of a full rank matrix $A$ into $A=QR$ where $Q$ is left orthogonal (has orthonormal columns) and $R$ is upper triangular. The work presented here shows that the computed $R$ satisfies \normal{R}=\normal{A}+E where $E$ is an appropriately small backward error, but only if the diagonals of $R$ are computed in a manner similar to Cholesky factorization of the normal equations matrix. A similar result is stated in [Giraud at al, Numer. Math. 101(1):87--100,2005]. However, for that result to hold, the diagonals of $R$ must be computed in the manner recommended in this work.Comment: 12 pages This v2. v1 (from 2006) has not the biliographical reference set (at all). This is the only modification between v1 and v2. If you want to quote this paper, please quote the version published in Numerische Mathemati

Constructive updating/downdating of oblique projectors: a generalization of the Gram-Schmidt process

A generalization of the Gram-Schmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting. The proposed techniques are shown to be relevant to the problem of discriminating signals produced by different phenomena when the order of the signal model needs to be adjusted.Comment: As it will appear in Journal of Physics A: Mathematical and Theoretical (2007

Proton-transfer pathways in the mitochondrial S. cerevisiae cytochrome c oxidase

In cytochrome c oxidase (CytcO) reduction of O2 to water is linked to uptake of eight protons from the negative side of the membrane: four are substrate protons used to form water and four are pumped across the membrane. In bacterial oxidases, the substrate protons are taken up through the K and the D proton pathways, while the pumped protons are transferred through the D pathway. On the basis of studies with CytcO isolated from bovine heart mitochondria, it was suggested that in mitochondrial CytcOs the pumped protons are transferred though a third proton pathway, the H pathway, rather than through the D pathway. Here, we studied these reactions in S. cerevisiae CytcO, which serves as a model of the mammalian counterpart. We analyzed the effect of mutations in the D (Asn99Asp and Ile67Asn) and H pathways (Ser382Ala and Ser458Ala) and investigated the kinetics of electron and proton transfer during the reaction of the reduced CytcO with O2. No effects were observed with the H pathway variants while in the D pathway variants the functional effects were similar to those observed with the R. sphaeroides CytcO. The data indicate that the S. cerevisiae CytcO uses the D pathway for proton uptake and presumably also for proton pumping

Generalized Mutual Subspace Based Methods for Image Set Classification

Abstract. The subspace-based methods are effectively applied to classify sets of feature vectors by modeling them as subspaces. It is, however, difficult to appropriately determine the subspace dimensionality in advance for better performance. For alleviating such issue, we present a generalized mutual subspace method by introducing soft weighting across the basis vectors of the subspace. The bases are effectively combined via the soft weights to measure the subspace similarities (angles) without definitely setting the subspace dimensionality. By using the soft weighting, we consequently propose a novel mutual subspace-based method to construct the discriminative space which renders more discriminative subspace similarities. In the experiments on 3D object recognition using image sets, the proposed methods exhibit stably favorable performances compared to the other subspace-based methods.

Better Nonlinear Models from Noisy Data: Attractors with Maximum Likelihood

A new approach to nonlinear modelling is presented which, by incorporating the global behaviour of the model, lifts shortcomings of both least squares and total least squares parameter estimates. Although ubiquitous in practice, a least squares approach is fundamentally flawed in that it assumes independent, normally distributed (IND) forecast errors: nonlinear models will not yield IND errors even if the noise is IND. A new cost function is obtained via the maximum likelihood principle; superior results are illustrated both for small data sets and infinitely long data streams.Comment: RevTex, 11 pages, 4 figure

Antarctic Glacial History Since the Last Glacial Maximum: An Overview of the Record on Land

This overview examines available circum-Antarctic glacial history archives on land, related to developments after the Last Glacial Maximum (LGM). It considers the glacial-stratigraphic and morphologic records and also biostratigraphical information from moss banks, lake sediments and penguin rookeries, with some reference to relevant glacial marine records. It is concluded that Holocene environmental development in Antarctica differed from that in the Northern Hemisphere. The initial deglaciation of the shelf areas surrounding Antarctica took place before 10000 C-14 yrs before present(sp), and was controlled by rising global sea level. This was followed by the deglaciation of some presently ice-free inner shelf and land areas between 10000 and 8000 yr sp. Continued deglaciation occurred gradually between 8000 yr sp and 5000 yr sp. Mid-Holocene glacial readvances are recorded from various sites around Antarctica. There are strong indications of a circum-Antarctic climate warmer than today 4700-2000 yr sp. The best dated records from the Antarctic Peninsula and coastal Victoria Land suggest climatic optimums there from 4000-3000 yr sp and 3600-2600 yr sp, respectively. Thereafter Neoglacial readvances are recorded. Relatively limited glacial expansions in Antarctica during the past few hundred years correlate with the Little Ice Age in the Northern Hemisphere