de Branges-Rovnyak spaces: basics and theory

For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension space ${\mathcal D(S)}$ consisting of pairs of analytic functions on the unit disk ${\mathbb D}$. This survey describes three equivalent formulations (the original geometric de Branges-Rovnyak definition, the Toeplitz operator characterization, and the characterization as a reproducing kernel Hilbert space) of the de Branges-Rovnyak space ${\mathcal H}(S)$, as well as its role as the underlying Hilbert space for the modeling of completely non-isometric Hilbert-space contraction operators. Also examined is the extension of these ideas to handle the modeling of the more general class of completely nonunitary contraction operators, where the more general two-component de Branges-Rovnyak model space ${\mathcal D}(S)$ and associated overlapping spaces play key roles. Connections with other function theory problems and applications are also discussed. More recent applications to a variety of subsequent applications are given in a companion survey article

The Brightness of Colour

Background: The perception of brightness depends on spatial context: the same stimulus can appear light or dark depending on what surrounds it. A less well-known but equally important contextual phenomenon is that the colour of a stimulus can also alter its brightness. Specifically, stimuli that are more saturated (i.e. purer in colour) appear brighter than stimuli that are less saturated at the same luminance. Similarly, stimuli that are red or blue appear brighter than equiluminant yellow and green stimuli. This non-linear relationship between stimulus intensity and brightness, called the Helmholtz-Kohlrausch (HK) effect, was first described in the nineteenth century but has never been explained. Here, we take advantage of the relative simplicity of this 'illusion' to explain it and contextual effects more generally, by using a simple Bayesian ideal observer model of the human visual ecology. We also use fMRI brain scans to identify the neural correlates of brightness without changing the spatial context of the stimulus, which has complicated the interpretation of related fMRI studies.Results: Rather than modelling human vision directly, we use a Bayesian ideal observer to model human visual ecology. We show that the HK effect is a result of encoding the non-linear statistical relationship between retinal images and natural scenes that would have been experienced by the human visual system in the past. We further show that the complexity of this relationship is due to the response functions of the cone photoreceptors, which themselves are thought to represent an efficient solution to encoding the statistics of images. Finally, we show that the locus of the response to the relationship between images and scenes lies in the primary visual cortex (V1), if not earlier in the visual system, since the brightness of colours (as opposed to their luminance) accords with activity in V1 as measured with fMRI.Conclusions: The data suggest that perceptions of brightness represent a robust visual response to the likely sources of stimuli, as determined, in this instance, by the known statistical relationship between scenes and their retinal responses. While the responses of the early visual system (receptors in this case) may represent specifically the statistics of images, post receptor responses are more likely represent the statistical relationship between images and scenes. A corollary of this suggestion is that the visual cortex is adapted to relate the retinal image to behaviour given the statistics of its past interactions with the sources of retinal images: the visual cortex is adapted to the signals it receives from the eyes, and not directly to the world beyond

Real-Time Contrast Enhancement to Improve Speech Recognition

An algorithm that operates in real-time to enhance the salient features of speech is described and its efficacy is evaluated. The Contrast Enhancement (CE) algorithm implements dynamic compressive gain and lateral inhibitory sidebands across channels in a modified winner-take-all circuit, which together produce a form of suppression that sharpens the dynamic spectrum. Normal-hearing listeners identified spectrally smeared consonants (VCVs) and vowels (hVds) in quiet and in noise. Consonant and vowel identification, especially in noise, were improved by the processing. The amount of improvement did not depend on the degree of spectral smearing or talker characteristics. For consonants, when results were analyzed according to phonetic feature, the most consistent improvement was for place of articulation. This is encouraging for hearing aid applications because confusions between consonants differing in place are a persistent problem for listeners with sensorineural hearing loss

Impact of monopolar radiofrequency energy on subchondral bone viability

The purpose of this study was to analyze the impact of monopolar radiofrequency energy treatment on subchondral bone viability. The femoral grooves of six chinchilla bastard rabbits were exposed bilaterally to monopolar radiofrequency energy for 2, 4 and 8 s, creating a total of 36 defects. An intravital fluorescence bone-labeling technique characterized the process of subchondral bone mineralization within the 3 months following exposure to radiofrequency energy and was analyzed by widefield epifluorescence optical sectioning microscopy using an ApoTome. After 2 s of radiofrequency energy exposure, regular fluorescence staining of the subchondral bone was evident in all samples when compared to untreated areas. The depth of osteonecrosis after 4 and 8 s of radiofrequency energy treatment averaged 126 and 942 µm at 22 days (P < .05; P < .01). The 4 s treatment group showed no osteonecrosis after 44 days whereas the depth of osteonecrosis extended from 519 µm at 44 days (P < .01), to 281 µm at 66 days (P < .01) and to 133 µm at 88 days (P < .05) after 8 s of radiofrequency energy application. Though radiofrequency energy may induce transient osteonecrosis in the superficial zone of the subchondral bone, the results of this study suggest that post-arthroscopic osteonecrosis appears to be of only modest risk given the current clinical application in humans

Search for supersymmetric particles in scenarios with a gravitino LSP and stau NLSP

Sleptons, neutralinos and charginos were searched for in the context of scenarios where the lightest supersymmetric particle is the gravitino. It was assumed that the stau is the next-to-lightest supersymmetric particle. Data collected with the DELPHI detector at a centre-of-mass energy near 189 GeV were analysed combining the methods developed in previous searches at lower energies. No evidence for the production of these supersymmetric particles was found. Hence, limits were derived at 95% confidence level.Comment: 31 pages, 14 figure

Jet energy measurement with the ATLAS detector in proton-proton collisions at root s=7 TeV

The jet energy scale and its systematic uncertainty are determined for jets measured with the ATLAS detector at the LHC in proton-proton collision data at a centre-of-mass energy of √s = 7TeV corresponding to an integrated luminosity of 38 pb-1. Jets are reconstructed with the anti-kt algorithm with distance parameters R=0. 4 or R=0. 6. Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate jets with transverse momenta pT≥20 GeV and pseudorapidities {pipe}η{pipe}<4. 5. The jet energy systematic uncertainty is estimated using the single isolated hadron response measured in situ and in test-beams, exploiting the transverse momentum balance between central and forward jets in events with dijet topologies and studying systematic variations in Monte Carlo simulations. The jet energy uncertainty is less than 2. 5 % in the central calorimeter region ({pipe}η{pipe}<0. 8) for jets with 60≤pT<800 GeV, and is maximally 14 % for pT<30 GeV in the most forward region 3. 2≤{pipe}η{pipe}<4. 5. The jet energy is validated for jet transverse momenta up to 1 TeV to the level of a few percent using several in situ techniques by comparing a well-known reference such as the recoiling photon pT, the sum of the transverse momenta of tracks associated to the jet, or a system of low-pT jets recoiling against a high-pT jet. More sophisticated jet calibration schemes are presented based on calorimeter cell energy density weighting or hadronic properties of jets, aiming for an improved jet energy resolution and a reduced flavour dependence of the jet response. The systematic uncertainty of the jet energy determined from a combination of in situ techniques is consistent with the one derived from single hadron response measurements over a wide kinematic range. The nominal corrections and uncertainties are derived for isolated jets in an inclusive sample of high-pT jets. Special cases such as event topologies with close-by jets, or selections of samples with an enhanced content of jets originating from light quarks, heavy quarks or gluons are also discussed and the corresponding uncertainties are determined. © 2013 CERN for the benefit of the ATLAS collaboration

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal

Measurement of Trilinear Gauge Couplings in e+e−e^+ e^- Collisions at 161 GeV and 172 GeV

Trilinear gauge boson couplings are measured using data taken by DELPHI at 161~GeV and 172~GeV. Values for $WWV$ couplings ($V=Z, \gamma$) are determined from a study of the reactions \eeWW\ and \eeWev, using differential distributions from the $WW$ final state in which one $W$ decays hadronically and the other leptonically, and total cross-section data from other channels. Limits are also derived on neutral $ZV\gamma$ couplings from an analysis of the reaction \eegi

Search for neutral heavy leptons produced in ZZ decays

Weak isosinglet Neutral Heavy Leptons (νm) have been searched for using data collected by the DELPHI detector corresponding to 3.3 × 106 hadronic Z0 decays at LEP1. Four separate searches have been performed, for short-lived νm production giving monojet or acollinear jet topologies, and for long-lived νm giving detectable secondary vertices or calorimeter clusters. No indication of the existence of these particles has been found, leading to an upper limit for the branching ratio BR(Z0 → νmν̄) of about 1.3 × 10-6 at 95% confidence level for νm masses between 3.5 and 50 GeV/c2. Outside this range the limit weakens rapidly with the νm mass. The results are also interpreted in terms of limits for the single production of excited neutrinos. © Springer-Verlag 1997

Study of B0_s anti-B0_s oscillations and B0_s lifetimes using hadronic decays of B0_s mesons

Oscillations of B0s mesons have been studied in samples selected from about 3.5 million hadronic Z decays detected by DELPHI between 1992 and 1995. One analysis uses events in the exclusive decay channels: B0s -> Ds- pi+ or Ds- a1+ and B0s -> anti-D0 K- pi+ or anti-D0 K- a1+, where the D decays are completely reconstructed. In addition, B0s anti-B0s oscillations have been studied in events with an exclusively reconstructed Ds accompanied in the same hemisphere by a high momentum hadron of opposite charge. Combining the two analyses, a limit on the mass difference between the physical B0s states has been obtained: Delta(m_B0s) > 4.0 ps^{-1} at the 95% C.L. with a sensitivity of Delta(m_B0s) = 3.2 ps^{-1}. Using the latter sample of events, the B0s lifetime has been measured and an upper limit on the decay width difference between the two physical B0s states has been obtained: tau(B0s) = 1.53^{+0.16}_{-0.15}(stat.) +/- {0.07}(syst.) ps \Delta\Gamma(B0s)/\Gamma(B0s) < 0.69 at the 95% C.L. The combination of these results with those obtained using Ds+- lepton-+ sample gives: Delta(m_B0s) > 4.9 ps^{-1} at the 95% C.L. with a sensitivity of Delta(m_B0s) = 8.7 ps^{-1}. tau(B0s) = 1.46 +/- 0.11 ps and \Delta\Gamma(B0s)/\Gamma(B0s) < 0.45 at the 95% C.L.Comment: 42 pages, 13 figure