Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

In vivo biochemical 7.0 Tesla magnetic resonance: preliminary results of dGEMRIC, zonal T2, and T2* mapping of articular cartilage

INTRODUCTION: Ultra-high-field whole-body systems (7.0 T) have a high potential for future human in vivo magnetic resonance imaging (MRI). In musculoskeletal MRI, biochemical imaging of articular cartilage may benefit, in particular. Delayed gadolinium-enhanced MRI of cartilage (dGEMRIC) and T2 mapping have shown potential at 3.0 T. Although dGEMRIC, allows the determination of the glycosaminoglycan content of articular cartilage, T2 mapping is a promising tool for the evaluation of water and collagen content. In addition, the evaluation of zonal variation, based on tissue anisotropy, provides an indicator of the nature of cartilage ie, hyaline or hyaline-like articular cartilage.Thus, the aim of our study was to show the feasibility of in vivo dGEMRIC, and T2 and T2* relaxation measurements, at 7.0 T MRI; and to evaluate the potential of T2 and T2* measurements in an initial patient study after matrix-associated autologous chondrocyte transplantation (MACT) in the knee. MATERIALS AND METHODS: MRI was performed on a whole-body 7.0 T MR scanner using a dedicated circular polarization knee coil. The protocol consisted of an inversion recovery sequence for dGEMRIC, a multiecho spin-echo sequence for standard T2 mapping, a gradient-echo sequence for T2* mapping and a morphologic PD SPACE sequence. Twelve healthy volunteers (mean age, 26.7 +/- 3.4 years) and 4 patients (mean age, 38.0 +/- 14.0 years) were enrolled 29.5 +/- 15.1 months after MACT. For dGEMRIC, 5 healthy volunteers (mean age, 32.4 +/- 11.2 years) were included. T1 maps were calculated using a nonlinear, 2-parameter, least squares fit analysis. Using a region-of-interest analysis, mean cartilage relaxation rate was determined as T1 (0) for precontrast measurements and T1 (Gd) for postcontrast gadopentate dimeglumine [Gd-DTPA(2-)] measurements. T2 and T2* maps were obtained using a pixelwise, monoexponential, non-negative least squares fit analysis; region-of-interest analysis was carried out for deep and superficial cartilage aspects. Statistical evaluation was performed by analyses of variance. RESULTS: Mean T1 (dGEMRIC) values for healthy volunteers showed slightly different results for femoral [T1 (0): 1259 +/- 277 ms; T1 (Gd): 683 +/- 141 ms] compared with tibial cartilage [T1 (0): 1093 +/- 281 ms; T1 (Gd): 769 +/- 150 ms]. Global mean T2 relaxation for healthy volunteers showed comparable results for femoral (T2: 56.3 +/- 15.2 ms; T2*: 19.7 +/- 6.4 ms) and patellar (T2: 54.6 +/- 13.0 ms; T2*: 19.6 +/- 5.2 ms) cartilage, but lower values for tibial cartilage (T2: 43.6 +/- 8.5 ms; T2*: 16.6 +/- 5.6 ms). All healthy cartilage sites showed a significant increase from deep to superficial cartilage (P < 0.001). Within healthy cartilage sites in MACT patients, adequate values could be found for T2 (56.6 +/- 13.2 ms) and T2* (18.6 +/- 5.3 ms), which also showed a significant stratification. Within cartilage repair tissue, global mean values showed no difference, with 55.9 +/- 4.9 ms for T2 and 16.2 +/- 6.3 ms for T2*. However, zonal assessment showed only a slight and not significant increase from deep to superficial cartilage (T2: P = 0.174; T2*: P = 0.150). CONCLUSION: In vivo T1 dGEMRIC assessment in healthy cartilage, and T2 and T2* mapping in healthy and reparative articular cartilage, seems to be possible at 7.0 T MRI. For T2 and T2*, zonal variation of articular cartilage could also be evaluated at 7.0 T. This zonal assessment of deep and superficial cartilage aspects shows promising results for the differentiation of healthy and affected articular cartilage. In future studies, optimized protocol selection, and sophisticated coil technology, together with increased signal at ultra-high-field MRI, may lead to advanced biochemical cartilage imaging.

T2 mapping in the knee after microfracture at 3.0 T: correlation of global T2 values and clinical outcome - preliminary results

OBJECTIVE: The aim of our study was to correlate global T2 values of microfracture repair tissue (RT) with clinical outcome in the knee joint. METHODS: We assessed 24 patients treated with microfracture in the knee joint. Magnetic resonance (MR) examinations were performed on a 3T MR unit, T2 relaxation times were obtained with a multi-echo spin-echo technique. T2 maps were obtained using a pixel wise, mono-exponential non-negative least squares fit analysis. Slices covering the cartilage RT were selected and region of interest analysis was done. An individual T2 index was calculated with global mean T2 of the RT and global mean T2 of normal, hyaline cartilage. The Lysholm score and the International Knee Documentation Committee (IKDC) knee evaluation forms were used for the assessment of clinical outcome. Bivariate correlation analysis and a paired, two tailed t test were used for statistics. RESULTS: Global T2 values of the RT [mean 49.8ms, standards deviation (SD) 7.5] differed significantly (P<0.001) from global T2 values of normal, hyaline cartilage (mean 58.5ms, SD 7.0). The T2 index ranged from 61.3 to 101.5. We found the T2 index to correlate with outcome of the Lysholm score (r(s)=0.641, P<0.001) and the IKDC subjective knee evaluation form (r(s)=0.549, P=0.005), whereas there was no correlation with the IKDC knee form (r(s)=-0.284, P=0.179). CONCLUSION: These findings indicate that T2 mapping is sensitive to assess RT function and provides additional information to morphologic MRI in the monitoring of microfracture.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

Risks of non-accidental mortality by baseline CD4+ T-cell strata in hepatitis-C-positive and -negative individuals initiating highly active antiretroviral therapy

BACKGROUND: Patients coinfected with hepatitis C virus (HCV) and HIV experience higher mortality rates than patients infected with HIV alone. We designed a study to determine whether risks for later mortality are similar for HCV-positive and HCV-negative individuals when subjects are stratified on the basis of baseline CD4+ T-cell counts. METHODS: Antiretroviral-naive individuals, who initiated highly active antiretroviral therapy (HAART) between 1996 and 2002 were included in the study. HCV-positive and HCV-negative individuals were stratified separately by baseline CD4+ T-cell counts of 50 cell/microl increments. Cox-proportional hazards regression was used to model the effect of these strata with other variables on survival. RESULTS: CD4+ T-cell strata below 200 cells/microl, but not above, imparted an increased relative hazard (RH) of mortality for both HCV-positive and HCV-negative individuals. Among HCV-positive individuals, after adjustment for baseline age, HIV RNA levels, history of injection drug use and adherence to therapy, only CD4+ T-cell strata of <50 cells/microl (RH=4.60; 95% confidence interval [CI] 2.72-7.76) and 50-199 cells/microl (RH=2.49; 95% CI 1.63-3.81) were significantly associated with increased mortality when compared with those initiating therapy at cell counts >500 cells/microl. The same baseline CD4+ T-cell strata were found for HCV-negative individuals. CONCLUSION: In a within-groups analysis, the baseline CD4+ T-cell strata that are associated with increased RHs for mortality are the same for HCV-positive and HCV-negative individuals initiating HAART. However, a between-groups analysis reveals a higher absolute mortality risk for HCV-positive individuals.

Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with complex mass and non-Hermitian potential V lie in the disjoint union of two disks, provided that the L1-norm of V is bounded from above by the speed of light times the reduced Planck constant. The result is sharp; moreover, the analogous sharp result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of non-real eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Urine tested positive for ethyl glucuronide and ethyl sulphate after the consumption of "non-alcoholic" beer

In abstinence maintenance programs, for reissuing the driving licence and in workplace monitoring programs abstinence from ethanol and its proof are demanded. Various monitoring programs that mainly use ethyl glucuronide (EtG) as alcohol consumption marker have been established. To abstain from ethanol, but not from the taste of alcoholic beverages, in particular non-alcoholic beer has become more and more popular. In Germany, these "alcohol-free" beverages may still have an ethanol content of up to 0.5vol.% without the duty of declaration. Due to severe negative consequences resulting from positive EtG tests, a drinking experiment with 2.5L of non-alcoholic beer per person was performed to address the question of measurable concentrations of the direct metabolites EtG and EtS (ethyl sulphate) in urine and blood. Both alcohol consumption markers - determined by LC-MS/MS - were found in high concentrations: maximum concentrations in urine found in three volunteers were EtG 0.30-0.87mg/L and EtS 0.04-0.07mg/L, i.e., above the often applied cut-off value for the proof of abstinence of 0.1mg EtG/L. In the urine samples of one further volunteer, EtG and EtS concentrations cumulated over-night and reached up to 14.1mg/L EtG and 16.1mg/L EtS in the next morning's urine. Ethanol concentrations in blood and urine samples were negative (determined by HS-GC-FID and by an ADH-based method).

Relevance of In-vitro Tests of Adhesive and Composite Dental Materials. A Review in 3 Parts. Part 2: Non-standardized tests of composite materials

Summary The first part of this review examined ISO approval requirements and in vitro testing. In the second part, non-standardized test methods for composite materials are presented and discussed. Physical tests are primarily described. Analyses of surface gloss and alterations, as well as aging simulations of dental materials are presented. Again, the importance of laboratory tests in determining clinical outcomes is evaluated. Differences in the measurement protocols of the various testing institutes and how these differences can in?uence the results are also discussed. Because there is no standardization of test protocols, the values determined by different institutes cannot be directly compared. However, the ranking of the tested materials should be the same if a valid protocol is applied by different institutes. The modulus of elasticity, the expansion after water sorption, and the polishability of the material are all clinically relevant, whereas factors measured by other test protocols may have no clinical correlation. The handling properties of the materials are highly dependent on operators' preferences. Therefore, no standard values can be given.

Quantitative PCR to diagnose Pneumocystis pneumonia in immunocompromised non-HIV patients

The utility of quantitative Pneumocystis jirovecii PCR in clinical routine for diagnosing Pneumocystis pneumonia (PCP) in immunocompromised non-HIV patients is unknown. We analysed bronchoalveolar lavage fluid with real-time quantitative P. jirovecii PCR in 71 cases with definitive PCP defined by positive immunofluorescence (IF) tests and in 171 randomly selected patients with acute lung disease. In those patients, possible PCP cases were identified by using a novel standardised PCP probability algorithm and chart review. PCR performance was compared with IF testing, clinical judgment and the PCP probability algorithm. Quantitative P. jirovecii PCR values >1,450 pathogens·mL(-1) had a positive predictive value of 98.0% (95% CI 89.6-100.0%) for diagnosing definitive PCP. PCR values of between 1 and 1,450 pathogens·mL(-1) were associated with both colonisation and infection; thus, a cut-off between the two conditions could not be identified and diagnosis of PCP in this setting relied on IF and clinical assessment. Clinical PCP could be ruled out in 99.3% of 153 patients with negative PCR results. Quantitative PCR is useful for diagnosing PCP and is complementary to IF. PCR values of >1,450 pathogens·mL(-1) allow reliable diagnosis, whereas negative PCR results virtually exclude PCP. Intermediate values require additional clinical assessment and IF testing. On the basis of our data and for economic and logistical limitations, we propose a clinical algorithm in which IF remains the preferred first test in most cases, followed by PCR in those patients with a negative IF and strong clinical suspicion for PCP.

Cupiennin 1a exhibits a remarkably broad, non-stereospecific cytolytic activity on bacteria, protozoan parasites, insects, and human cancer cells

Cupiennin 1a, a cytolytic peptide isolated from the venom of the spider Cupiennius salei, exhibits broad membranolytic activity towards bacteria, trypanosomes, and plasmodia, as well as human blood and cancer cells. In analysing the cytolytic activity of synthesised all-d- and all-l-cupiennin 1a towards pro- and eukaryotic cells, a stereospecific mode of membrane destruction could be excluded. The importance of negatively charged sialic acids on the outer leaflet of erythrocytes for the binding and haemolytic activity of l-cupiennin 1a was demonstrated. Reducing the overall negative charges of erythrocytes by partially removing their sialic acids or by protecting them with tri- or pentalysine results in reduced haemolytic activity of the peptide.

Intramammary infections with the contagious Staphylococcus aureus genotype B in Swiss dairy cows are associated with low prevalence of coagulase-negative staphylococci and Streptococcus spp

The association between the contagious Staphylococcus aureus genotype B (GTB) and the presence of coagulase-negative staphylococci (CNS) and Streptococcus spp. (non-agalactiae streptococci), was investigated, and the identification of problem herds without genotyping was evaluated. Milk samples from 10 herds with Staph. aureus GTB herd problems (PH cases) were compared with samples from 19 herds with at least one Staph. aureus isolate of non-B genotype (CH cases). All samples were bacteriologically analysed and Staph. aureus genotyping carried out using a ribosomal spacer-PCR. Cow and quarter prevalences of Staph. aureus, CNS and Streptococcus spp. differed significantly between PH and CH groups. PH cases were highly associated with decreased cow prevalences of CNS and Streptococcus spp. These altered prevalences also contributed significantly to the identification of problem herds without resorting to genotyping. Common herd-level risk factors did not explain the difference between the prevalences in PH and CH cases.

Impedance-pH reflux patterns can differentiate non-erosive reflux disease from functional heartburn patients

Symptom association is important to distinguish non-erosive reflux disease [NERD; abnormal oesophageal acid exposure time (AET) and/or positive symptom association] from functional heartburn (FH; normal AET and negative symptom association). Asymptomatic patients during reflux monitoring are challenging as symptom association cannot be assessed.

Liver breath tests non-invasively predict higher stages of non-alcoholic steatohepatitis

Effectively assessing subtle hepatic metabolic functions by novel non-invasive tests might be of clinical utility in scoring NAFLD (non-alcoholic fatty liver disease) and in identifying altered metabolic pathways. The present study was conducted on 39 (20 lean and 19 obese) hypertransaminasemic patients with histologically proven NAFLD {ranging from simple steatosis to severe steatohepatitis [NASH (non-alcoholic steatohepatitis)] and fibrosis} and 28 (20 lean and eight overweight) healthy controls, who underwent stable isotope breath testing ([(13)C]methacetin and [(13)C]ketoisocaproate) for microsomal and mitochondrial liver function in relation to histology, serum hyaluronate, as a marker of liver fibrosis, and body size. Compared with healthy subjects and patients with simple steatosis, NASH patients had enhanced methacetin demethylation (P=0.001), but decreased (P=0.001) and delayed (P=0.006) ketoisocaproate decarboxylation, which was inversely related (P=0.001) to the degree of histological fibrosis (r=-0.701), serum hyaluronate (r=-0.644) and body size (r=-0.485). Ketoisocaproate decarboxylation was impaired further in obese patients with NASH, but not in patients with simple steatosis and in overweight controls. NASH and insulin resistance were independently associated with an abnormal ketoisocaproate breath test (P=0.001). The cut-off value of 9.6% cumulative expired (13)CO(2) for ketoisocaproate at 60 min was associated with the highest prediction (positive predictive value, 0.90; negative predictive value, 0.73) for NASH, yielding an overall sensitivity of 68% and specificity of 94%. In conclusion, both microsomal and mitochondrial functions are disturbed in NASH. Therefore stable isotope breath tests may usefully contribute to a better and non-invasive characterization of patients with NAFLD.

Epidermal growth factor receptor inhibitors plus chemotherapy in non-small-cell lung cancer: biologic rationale for combination strategies

Chemotherapy continues to play an essential role in the treatment of most stages of non-small-cell lung cancer (NSCLC). In fact, within the past 5 years, this role has greatly expanded into adjuvant therapy for early-stage resected disease. Likewise, agents targeting the epidermal growth factor receptor (EGFR), particularly the tyrosine kinase inhibitors gefitinib and erlotinib, have proven to be clinically active in patients with advanced-stage NSCLC. Because of these findings, it is logical to expect that combinations of these 2 classes of antineoplastic agents would prove more efficacious than either one alone. Yet 4 large randomized phase III trials of chemotherapy with or without an EGFR tyrosine kinase inhibitor in unselected patients with advanced-stage NSCLC, altogether totaling > 4000 patients, did not demonstrate improvement in clinical outcomes with the combination. Whether these negative results will be reproduced in ongoing combination studies of chemotherapy plus monoclonal antibodies directed against EGFR remain to be determined. Herein, we review recent preclinical and clinical data addressing this topic and explore the biologic rationale for developing new combination strategies based on patient selection by molecular and clinical factors, or by pharmacodynamic parameters.