The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

The mass-hierarchy and CP-violation discovery reach of the LBNO long-baseline neutrino experiment

The next generation neutrino observatory proposed by the LBNO collaboration will address fundamental questions in particle and astroparticle physics. The experiment consists of a far detector, in its first stage a 20 kt LAr double phase TPC and a magnetised iron calorimeter, situated at 2300 km from CERN and a near detector based on a highpressure argon gas TPC. The long baseline provides a unique opportunity to study neutrino flavour oscillations over their 1st and 2nd oscillation maxima exploring the L/E behaviour, and distinguishing effects arising from δCP and matter. In this paper we have reevaluated the physics potential of this setup for determining the mass hierarchy (MH) and discovering CP-violation (CPV), using a conventional neutrino beam from the CERN SPS with a power of 750 kW. We use conservative assumptions on the knowledge of oscillation parameter priors and systematic uncertainties. The impact of each systematic error and the precision of oscillation prior is shown. We demonstrate that the first stage of LBNO can determine unambiguously the MH to > 5δ C.L. over the whole phase space. We show that the statistical treatment of the experiment is of very high importance, resulting in the conclusion that LBNO has ~ 100% probability to determine the MH in at most 4-5 years of running. Since the knowledge of MH is indispensable to extract δCP from the data, the first LBNO phase can convincingly give evidence for CPV on the 3δ C.L. using today’s knowledge on oscillation parameters and realistic assumptions on the systematic uncertainties.

The Martian Gas-Analytic Package for the Landing Platform Experiments of the ExoMars 2018

The paper describes the architecture of the Martian Gas Analytic Package, which is proposed for the Russian ExoMars Lander 2018.

Analytic validation of a gas chromatography-mass spectrometry method for quantification of six amino acids in canine serum samples.

OBJECTIVE To analytically validate a gas concentration of chromatography-mass spectrometry (GC-MS) method for measurement of 6 amino acids in canine serum samples and to assess the stability of each amino acid after sample storage. SAMPLES Surplus serum from 80 canine samples submitted to the Gastrointestinal Laboratory at Texas A&M University and serum samples from 12 healthy dogs. PROCEDURES GC-MS was validated to determine precision, reproducibility, limit of detection, and percentage recovery of known added concentrations of 6 amino acids in surplus serum samples. Amino acid concentrations in serum samples from healthy dogs were measured before (baseline) and after storage in various conditions. RESULTS Intra- and interassay coefficients of variation (10 replicates involving 12 pooled serum samples) were 13.4% and 16.6% for glycine, 9.3% and 12.4% for glutamic acid, 5.1% and 6.3% for methionine, 14.0% and 15.1% for tryptophan, 6.2% and 11.0% for tyrosine, and 7.4% and 12.4% for lysine, respectively. Observed-to-expected concentration ratios in dilutional parallelism tests (6 replicates involving 6 pooled serum samples) were 79.5% to 111.5% for glycine, 80.9% to 123.0% for glutamic acid, 77.8% to 111.0% for methionine, 85.2% to 98.0% for tryptophan, 79.4% to 115.0% for tyrosine, and 79.4% to 110.0% for lysine. No amino acid concentration changed significantly from baseline after serum sample storage at -80°C for ≤ 7 days. CONCLUSIONS AND CLINICAL RELEVANCE GC-MS measurement of concentration of 6 amino acids in canine serum samples yielded precise, accurate, and reproducible results. Sample storage at -80°C for 1 week had no effect on GC-MS results.

Vitamin D Deficiency and Depressive Symptomatology in Psychiatric Patients Hospitalized with a Current Depressive Episode: A Factor Analytic Study.

BACKGROUND Low vitamin D levels have been associated with depressive symptoms in population-based studies and non-clinical samples as well as with clinical depression. This study aimed to examine the association of vitamin D levels with the severity and dimensions of depressive symptoms in hospitalized patients with a current episode of depression taking into account confounding variables. METHODS We investigated 380 patients (mean age 47 ± 12 years, 70% women) who were consecutively hospitalized with a main diagnosis of an ICD-10 depressive episode. All patients self-rated depressive symptom severity with the Hospital Anxiety and Depression Scale (HADS-D), the Beck Depression Inventory-II (BDI-II), and the Brief Symptom Inventory. A principal component analysis was performed with all 34 items of these questionnaires and serum levels of 25-hydroxyvitamin D3 (25-OH D) were measured. RESULTS Vitamin D deficiency (< 50 nmol/l), insufficiency (50-75 nmol/l), and sufficiency (> 75 nmol/l) were present in 55.5%, 31.8% and 12.6%, respectively, of patients. Patients with vitamin D deficiency scored higher on the HADS-D scale and on an anhedonia symptom factor than those with insufficient (p-values ≤ 0.023) or sufficient (p-values ≤ 0.008) vitamin D. Vitamin D deficient patients also scored higher on the BDI-II scale than those with sufficient vitamin D (p = 0.007); BDI-II cognitive/affective symptoms, but not somatic/affective symptoms, were higher in patients with vitamin D deficiency (p = 0.005) and insufficiency (p = 0.041) relative to those with sufficient vitamin D. Effect sizes suggested clinically relevant findings. CONCLUSIONS Low vitamin D levels are frequent in hospitalized patients with a current episode of depression. Especially 25-OH D levels < 50 nmol/l were associated with cognitive/affective depressive symptoms, and anhedonia symptoms in particular.