User-friendly tail bounds for sums of random matrices

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.Comment: Current paper is the version of record. The material on Freedman's inequality has been moved to a separate note; other martingale bounds are described in Caltech ACM Report 2011-0

Patents and Industrialisation. An Historical Overview of the British Case, 1624-1907

A Report to the Strategic Advisory Board on Intellectual Property Policy (SABIP), U

Effects of two contrasting canopy manipulations on growth and water use of London plane (Platanus x acerifolia) trees

Aims: Two contrasting canopy manipulations were compared to unpruned controls on London plane trees, to determine the effects on canopy regrowth, soil and leaf water relations. Methods: ‘Canopy reduction’, was achieved by removing the outer 30 % length of all major branches and ‘canopy thinning’, by removing 30 % of lateral branches arising from major branches. Results: Total canopy leaf areas recovered within two and three years of pruning for the canopy-thinned and reduced trees respectively. Canopy reduction increased mean leaf size, nitrogen concentration, canopy leaf area density and conserved soil moisture for up to 3 years, whereas canopy thinning had no effects. Another experiment compared more severe canopy reduction to unpruned trees. This produced a similar growth response to the previous experiment, but soil moisture was conserved nearer to the trunk. Analysis of 13C and 18O signals along with leaf water relations and soil moisture data suggested that lower boundary layer conductance within the canopy-reduced trees restricted tree water use, whereas for the canopy-thinned trees the opposite occurred. Conclusions: Only canopy reduction conserved soil moisture and this was due to a combination of reduced total canopy leaf area and structural changes in canopy architecture

Drosophila Genome-Wide RNAi Screen Identifies Multiple Regulators of HIF–Dependent Transcription in Hypoxia

Hypoxia-inducible factors (HIFs) are a family of evolutionary conserved alpha-beta heterodimeric transcription factors that induce a wide range of genes in response to low oxygen tension. Molecular mechanisms that mediate oxygen-dependent HIF regulation operate at the level of the alpha subunit, controlling protein stability, subcellular localization, and transcriptional coactivator recruitment. We have conducted an unbiased genome-wide RNA interference (RNAi) screen in Drosophila cells aimed to the identification of genes required for HIF activity. After 3 rounds of selection, 30 genes emerged as critical HIF regulators in hypoxia, most of which had not been previously associated with HIF biology. The list of genes includes components of chromatin remodeling complexes, transcription elongation factors, and translational regulators. One remarkable hit was the argonaute 1 (ago1) gene, a central element of the microRNA (miRNA) translational silencing machinery. Further studies confirmed the physiological role of the miRNA machinery in HIF–dependent transcription. This study reveals the occurrence of novel mechanisms of HIF regulation, which might contribute to developing novel strategies for therapeutic intervention of HIF–related pathologies, including heart attack, cancer, and stroke

The Apache Point Observatory Galactic Evolution Experiment (APOGEE)

The Apache Point Observatory Galactic Evolution Experiment (APOGEE), one of the programs in the Sloan Digital Sky Survey III (SDSS-III), has now completed its systematic, homogeneous spectroscopic survey sampling all major populations of the Milky Way. After a three-year observing campaign on the Sloan 2.5 m Telescope, APOGEE has collected a half million high-resolution (R ~ 22,500), high signal-to-noise ratio (>100), infrared (1.51–1.70 μm) spectra for 146,000 stars, with time series information via repeat visits to most of these stars. This paper describes the motivations for the survey and its overall design—hardware, field placement, target selection, operations—and gives an overview of these aspects as well as the data reduction, analysis, and products. An index is also given to the complement of technical papers that describe various critical survey components in detail. Finally, we discuss the achieved survey performance and illustrate the variety of potential uses of the data products by way of a number of science demonstrations, which span from time series analysis of stellar spectral variations and radial velocity variations from stellar companions, to spatial maps of kinematics, metallicity, and abundance patterns across the Galaxy and as a function of age, to new views of the interstellar medium, the chemistry of star clusters, and the discovery of rare stellar species. As part of SDSS-III Data Release 12 and later releases, all of the APOGEE data products are publicly available