A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at √ s = 8 TeV with the ATLAS detector

Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb−1 of √ s = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between Emiss T > 150 GeV and Emiss T > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presente

Extracting a stroke phenotype risk factor from Veteran Health Administration clinical reports: an information content analysis

In the United States, 795,000 people suffer strokes each year; 10-15 % of these strokes can be attributed to stenosis caused by plaque in the carotid artery, a major stroke phenotype risk factor. Studies comparing treatments for the management of asymptom

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)

Neuroarchitecture of Aminergic Systems in the Larval Ventral Ganglion of Drosophila melanogaster

Biogenic amines are important signaling molecules in the central nervous system of both vertebrates and invertebrates. In the fruit fly Drosophila melanogaster, biogenic amines take part in the regulation of various vital physiological processes such as feeding, learning/memory, locomotion, sexual behavior, and sleep/arousal. Consequently, several morphological studies have analyzed the distribution of aminergic neurons in the CNS. Previous descriptions, however, did not determine the exact spatial location of aminergic neurite arborizations within the neuropil. The release sites and pre-/postsynaptic compartments of aminergic neurons also remained largely unidentified. We here used gal4-driven marker gene expression and immunocytochemistry to map presumed serotonergic (5-HT), dopaminergic, and tyraminergic/octopaminergic neurons in the thoracic and abdominal neuromeres of the Drosophila larval ventral ganglion relying on Fasciclin2-immunoreactive tracts as three-dimensional landmarks. With tyrosine hydroxylase- (TH) or tyrosine decarboxylase 2 (TDC2)-specific gal4-drivers, we also analyzed the distribution of ectopically expressed neuronal compartment markers in presumptive dopaminergic TH and tyraminergic/octopaminergic TDC2 neurons, respectively. Our results suggest that thoracic and abdominal 5-HT and TH neurons are exclusively interneurons whereas most TDC2 neurons are efferent. 5-HT and TH neurons are ideally positioned to integrate sensory information and to modulate neuronal transmission within the ventral ganglion, while most TDC2 neurons appear to act peripherally. In contrast to 5-HT neurons, TH and TDC2 neurons each comprise morphologically different neuron subsets with separated in- and output compartments in specific neuropil regions. The three-dimensional mapping of aminergic neurons now facilitates the identification of neuronal network contacts and co-localized signaling molecules, as exemplified for DOPA decarboxylase-synthesizing neurons that co-express crustacean cardioactive peptide and myoinhibiting peptides

Measurement of VH, H → b b ¯ production as a function of the vector-boson transverse momentum in 13 TeV pp collisions with the ATLAS detector

Cross-sections of associated production of a Higgs boson decaying into bottom-quark pairs and an electroweak gauge boson, W or Z, decaying into leptons are measured as a function of the gauge boson transverse momentum. The measurements are performed in kinematic fiducial volumes defined in the `simplified template cross-section' framework. The results are obtained using 79.8 fb-1 of proton-proton collisions recorded by the ATLAS detector at the Large Hadron Collider at a centre-of-mass energy of 13 TeV. All measurements are found to be in agreement with the Standard Model predictions, and limits are set on the parameters of an effective Lagrangian sensitive to modifications of the Higgs boson couplings to the electroweak gauge bosons

Measurement of the t¯tZ and t¯tW cross sections in proton-proton collisions at √s=13 TeV with the ATLAS detector

A measurement of the associated production of a top-quark pair (t¯t) with a vector boson (W, Z) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented, using 36.1  fb−1 of integrated luminosity collected by the ATLAS detector at the Large Hadron Collider. Events are selected in channels with two same- or opposite-sign leptons (electrons or muons), three leptons or four leptons, and each channel is further divided into multiple regions to maximize the sensitivity of the measurement. The t¯tZ and t¯tW production cross sections are simultaneously measured using a combined fit to all regions. The best-fit values of the production cross sections are σt¯tZ=0.95±0.08stat±0.10syst pb and σt¯tW=0.87±0.13stat±0.14syst pb in agreement with the Standard Model predictions. The measurement of the t¯tZ cross section is used to set constraints on effective field theory operators which modify the t¯tZ vertex

Performance of missing transverse momentum reconstruction with the ATLAS detector using proton–proton collisions at √s = 13 TeV

The performance of the missing transverse momentum (EmissT) reconstruction with the ATLAS detector is evaluated using data collected in proton–proton collisions at the LHC at a centre-of-mass energy of 13 TeV in 2015. To reconstruct EmissT, fully calibrated electrons, muons, photons, hadronically decaying τ -leptons, and jets reconstructed from calorimeter energy deposits and charged-particle tracks are used. These are combined with the soft hadronic activity measured by reconstructed charged-particle tracks not associated with the hard objects. Possible double counting of contributions from reconstructed charged-particle tracks from the inner detector, energy deposits in the calorimeter, and reconstructed muons from the muon spectrometer is avoided by applying a signal ambiguity resolution procedure which rejects already used signals when combining the various EmissT contributions. The individual terms as well as the overall reconstructed EmissT are evaluated with various performance metrics for scale (linearity), resolution, and sensitivity to the data-taking conditions. The method developed to determine the systematic uncertainties of the EmissT scale and resolution is discussed. Results are shown based on the full 2015 data sample corresponding to an integrated luminosity of 3.2 fb−1

Search for heavy neutral Higgs bosons produced in association with b-quarks and decaying into b-quarks at root s=13 TeV with the ATLAS detector

A search for heavy neutral Higgs bosons produced in association with one or two b -quarks and decaying to b -quark pairs is presented using 27.8  fb − 1 of √ s = 13  TeV proton-proton collision data recorded by the ATLAS detector at the Large Hadron Collider during 2015 and 2016. No evidence of a signal is found. Upper limits on the heavy neutral Higgs boson production cross section times its branching ratio to b ¯ b are set, ranging from 4.0 to 0.6 pb at 95% confidence level over a Higgs boson mass range of 450 to 1400 GeV. Results are interpreted within the two-Higgs-doublet model and the minimal supersymmetric Standard Model