Robust Structured Low-Rank Approximation on the Grassmannian

Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to matrices with linear structures which appear in applications such as system identification and data series analysis. At the same time it has been shown how to control the rank of a structured approximation via matrix factorization approaches. The drawbacks of these methods either lie in the lack of robustness against outliers or in their static nature of repeated batch-processing. We present a Robust Structured Low-Rank Approximation method on the Grassmannian that on the one hand allows for fast re-initialization in an online setting due to subspace identification with manifolds, and that is robust against outliers due to a smooth approximation of the $\ell_p$-norm cost function on the other hand. The method is evaluated in online time series forecasting tasks on simulated and real-world data

Principles of Discrete Time Mechanics: I. Particle Systems

We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system functions from classical Lagrangians, Cadzow's variational principle applied to the action sum, Maeda-Noether and Logan invariants of the motion, elliptic and hyperbolic harmonic oscillator behaviour, gauge invariant electrodynamics and charge conservation, and the Grassmannian oscillator. First quantised discrete time mechanics is discussed via the concept of system amplitude, which permits the construction of all quantities of interest such as commutators and scattering amplitudes. We discuss stroboscopic quantum mechanics, or the construction of discrete time quantum theory from continuous time quantum theory and show how this works in detail for the free Newtonian particle. We conclude with an application of the Schwinger action principle to the important case of the quantised discrete time inhomogeneous oscillator.Comment: 35 pages, LateX, To be published in J.Phys.A: Math.Gen. Basic principles stated: applications to field theory in subsequent papers of series contact email address: [email protected]

Stochasticity, decoherence and an arrow of time from the discretization of time?

Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an {\it arrow of time} that follows from the fact that the replacement of the time derivative by the backward difference operator alone can preserve the non-negativity of the phase space density. It is seen that, even for free particles, all the degrees of freedom are {\it correlated} in principle. The forward evolution of functions of phase space variables by a finite number of time steps, in this discrete-time mechanics, depends on the entire continuous-time history in the interval $[0, \infty]$. In this sense, discrete time evolution is {\it nonlocal} in time from a continuous-time point of view. A corresponding quantum mechanical treatment is possible {\it via} the density matrix approach. The interference between non-degenerate quantum mechanical states decays exponentially. This {\it decoherence} is present, in principle, for all systems; however, it is of practical importance only in macroscopic systems, or in processes involving large energy changes.Comment: 10 pages, no figure

A multicentre, randomized, double-blind, controlled trial of nebulized epinephrine in infants with acute bronchiolitis

Background The treatment of infants with bronchiolitis is largely supportive. The role of bronchodilators is controversial. Most studies of the use of bronchodilators have enrolled small numbers of subjects and have examined only short-term outcomes, such as clinical scores. Methods We conducted a randomized, double-blind, controlled trial comparing nebulized single-isomer epinephrine with placebo in 194 infants admitted to four hospitals in Queens-land, Australia, with a clinical diagnosis of bronchiolitis. Three 4-ml doses of 1 percent nebulized epinephrine or three 4-ml doses of normal saline were administered at four-hour intervals after hospital admission. Observations were made at admission and just before, 30 minutes after, and 60 minutes after each dose. The primary outcome measures were the length of the hospital stay and the time until the infant was ready for discharge. The secondary outcome measures were the degree of change in the respiratory rate, the heart rate, and the respiratory-effort score and the time that supplemental oxygen was required. Results There were no significant overall differences between the groups in the length of the hospital stay (P=0.16) or the time until the infant was ready for discharge (P=0.86). Among infants who required supplemental oxygen and intravenous fluids, the time until the infant was ready for discharge was significantly longer in the epinephrine group than in the placebo group (P=0.02). The need for supplemental oxygen at admission had the greatest influence on the score for severity of illness and strongly predicted the length of the hospital stay and the time until the infant was ready for discharge (

Genome-wide characterization of genetic variants and putative regions under selection in meat and egg-type chicken lines

Abstract\ud \ud Background\ud Meat and egg-type chickens have been selected for several generations for different traits. Artificial and natural selection for different phenotypes can change frequency of genetic variants, leaving particular genomic footprints throghtout the genome. Thus, the aims of this study were to sequence 28 chickens from two Brazilian lines (meat and white egg-type) and use this information to characterize genome-wide genetic variations, identify putative regions under selection using Fst method, and find putative pathways under selection.\ud \ud \ud Results\ud A total of 13.93 million SNPs and 1.36 million INDELs were identified, with more variants detected from the broiler (meat-type) line. Although most were located in non-coding regions, we identified 7255 intolerant non-synonymous SNPs, 512 stopgain/loss SNPs, 1381 frameshift and 1094 non-frameshift INDELs that may alter protein functions. Genes harboring intolerant non-synonymous SNPs affected metabolic pathways related mainly to reproduction and endocrine systems in the white-egg layer line, and lipid metabolism and metabolic diseases in the broiler line. Fst analysis in sliding windows, using SNPs and INDELs separately, identified over 300 putative regions of selection overlapping with more than 250 genes. For the first time in chicken, INDEL variants were considered for selection signature analysis, showing high level of correlation in results between SNP and INDEL data. The putative regions of selection signatures revealed interesting candidate genes and pathways related to important phenotypic traits in chicken, such as lipid metabolism, growth, reproduction, and cardiac development.\ud \ud \ud Conclusions\ud In this study, Fst method was applied to identify high confidence putative regions under selection, providing novel insights into selection footprints that can help elucidate the functional mechanisms underlying different phenotypic traits relevant to meat and egg-type chicken lines. In addition, we generated a large catalog of line-specific and common genetic variants from a Brazilian broiler and a white egg layer line that can be used for genomic studies involving association analysis with phenotypes of economic interest to the poultry industry.CB received a fellowship from the program Science Without Borders - National Council for Scientific and Technological Development (CNPq, grant 370620/2013–5). GCMM and TFG received fellowships from São Paulo Research Foundation (FAPESP, grants 14/21380–9 and 15/00616–7). LLC is recipient of productivity fellowship from CNPq. This project was funded by São Paulo Research Foundation (FAPESP) - thematic project (2014/08704–0)