Trotter-Kato product formulae in Dixmier ideal

It is shown that for a certain class of the Kato functions the Trotter-Kato product formulae converge in Dixmier ideal C 1,$\infty$ in topology, which is defined by the $\times$ 1,$\infty$-norm. Moreover, the rate of convergence in this topology inherits the error-bound estimate for the corresponding operator-norm convergence. 1 since [24], [14]. Note that a subtle point of this program is the question about the rate of convergence in the corresponding topology. Since the limit of the Trotter-Kato product formula is a strongly continuous semigroup, for the von Neumann-Schatten ideals this topology is the trace-norm $\times$ 1 on the trace-class ideal C 1 (H). In this case the limit is a Gibbs semigroup [25]. For self-adjoint Gibbs semigroups the rate of convergence was estimated for the first time in [7] and [9]. The authors considered the case of the Gibbs-Schr{\"o}dinger semigroups. They scrutinised in these papers a dependence of the rate of convergence for the (exponential) Trotter formula on the smoothness of the potential in the Schr{\"o}dinger generator. The first abstract result in this direction was due to [19]. In this paper a general scheme of lifting the operator-norm rate convergence for the Trotter-Kato product formulae was proposed and advocated for estimation the rate of the trace-nor

Widespread dynamic and pleiotropic expression of the melanocortin-1-receptor (MC1R) system is conserved across chick, mouse and human embryonic development

Background MC1R, a G‐protein coupled receptor with high affinity for alpha‐melanocyte stimulating hormone (αMSH), modulates pigment production in melanocytes from many species and is associated with human melanoma risk. MC1R mutations affecting human skin and hair color also have pleiotropic effects on the immune response and analgesia. Variants affecting human pigmentation in utero alter the congenital phenotype of both oculocutaneous albinism and congenital melanocytic naevi, and have a possible effect on birthweight. Methods and Results By in situ hybridization, RT‐PCR and immunohistochemistry, we show that MC1R is widely expressed during human, chick and mouse embryonic and fetal stages in many somatic tissues, particularly in the musculoskeletal and nervous systems, and conserved across evolution in these three amniotes. Its dynamic pattern differs from that of TUBB3, a gene overlapping the same locus in humans and encoding class III β‐tubulin. The αMSH peptide and the transcript for its precursor, pro‐opiomelanocortin (POMC), are similarly present in numerous extra‐cutaneous tissues. MC1R genotyping of variants p.(V60M) and p.(R151C) was undertaken for 867 healthy children from the Avon Longitudinal Study of Parent and Children (ALSPAC) cohort, and birthweight modeled using multiple logistic regression analysis. A significant positive association initially found between R151C and birth weight, independent of known birth weight modifiers, was not reproduced when combined with data from an independent genome‐wide association study of 6,459 additional members of the same cohort. Conclusions These data clearly show a new and hitherto unsuspected role for MC1R in noncutaneous solid tissues before birth

Longitudinal stroke recovery associated with dysregulation of complement system - A proteomics pathway analysis

Currently the longitudinal proteomic profile of post-ischemic stroke recovery is relativelyunknown with few well-accepted biomarkers or understanding of the biological systemsthat underpin recovery. We aimed to characterize plasma derived biological pathwaysassociated with recovery during the first year post event using a discovery proteomicsworkflow coupled with a topological pathway systems biology approach. Blood samples(n = 180, ethylenediaminetetraacetic acid plasma) were collected from a subgroup of60 first episode stroke survivors from the Australian START study at 3 timepoints: 3–7days (T1), 3-months (T2) and 12-months (T3) post-stroke. Samples were analyzed byliquid chromatography mass spectrometry using label-free quantification (data availableat ProteomeXchange with identifier PXD015006). Differential expression analysis revealedthat 29 proteins between T1 and T2, and 33 proteins between T1 and T3 weresignificantly different, with 18 proteins commonly differentially expressed across thetwo time periods. Pathway analysis was conducted using Gene Graph EnrichmentAnalysis on both the Kyoto Encyclopedia of Genes and Genomes and Reactomedatabases. Pathway analysis revealed that the significantly differentiated proteinsbetween T1 and T2 were consistently found to belong to the complement pathway.Further correlational analyses utilized to examine the changes in regulatory effects ofproteins over time identified significant inhibitory regulation of clusterin on complementcomponent 9. Longitudinal post-stroke blood proteomics profiles suggest that thealternative pathway of complement activation remains in a state of higher activation from3-7 days to 3 months post-stroke, while simultaneously being regulated by clusterin andvitronectin. These findings also suggest that post-stroke induced sterile inflammation andimmunosuppression could inhibit recovery within the 3-month window post-stroke

Clean thermal decomposition of tertiary-alkyl metal thiolates to metal sulfides: Environmentally-benign, non-polar inks for solution-processed chalcopyrite solar cells

We report the preparation of Cu2S, In2S3, CuInS2 and Cu(In,Ga)S2 semiconducting films via the spin coating and annealing of soluble tertiary-alkyl thiolate complexes. The thiolate compounds are readily prepared via the reaction of metal bases and tertiary-alkyl thiols. The thiolate complexes are soluble in common organic solvents and can be solution processed by spin coating to yield thin films. Upon thermal annealing in the range of 200-400 ??C, the tertiary-alkyl thiolates decompose cleanly to yield volatile dialkyl sulfides and metal sulfide films which are free of organic residue. Analysis of the reaction byproducts strongly suggests that the decomposition proceeds via an SN1 mechanism. The composition of the films can be controlled by adjusting the amount of each metal thiolate used in the precursor solution yielding bandgaps in the range of 1.2 to 3.3 eV. The films form functioning p-n junctions when deposited in contact with CdS films prepared by the same method. Functioning solar cells are observed when such p-n junctions are prepared on transparent conducting substrates and finished by depositing electrodes with appropriate work functions. This method enables the fabrication of metal chalcogenide films on a large scale via a simple and chemically clear process.ope

Modern tests of Lorentz invariance

Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.Comment: Modified and expanded discussions of various points. Numerous references added. Version matches that accepted by Living Reviews in Relativit

An AP Endonuclease 1–DNA Polymerase β Complex: Theoretical Prediction of Interacting Surfaces

Abasic (AP) sites in DNA arise through both endogenous and exogenous mechanisms. Since AP sites can prevent replication and transcription, the cell contains systems for their identification and repair. AP endonuclease (APEX1) cleaves the phosphodiester backbone 5′ to the AP site. The cleavage, a key step in the base excision repair pathway, is followed by nucleotide insertion and removal of the downstream deoxyribose moiety, performed most often by DNA polymerase beta (pol-β). While yeast two-hybrid studies and electrophoretic mobility shift assays provide evidence for interaction of APEX1 and pol-β, the specifics remain obscure. We describe a theoretical study designed to predict detailed interacting surfaces between APEX1 and pol-β based on published co-crystal structures of each enzyme bound to DNA. Several potentially interacting complexes were identified by sliding the protein molecules along DNA: two with pol-β located downstream of APEX1 (3′ to the damaged site) and three with pol-β located upstream of APEX1 (5′ to the damaged site). Molecular dynamics (MD) simulations, ensuring geometrical complementarity of interfaces, enabled us to predict interacting residues and calculate binding energies, which in two cases were sufficient (∼−10.0 kcal/mol) to form a stable complex and in one case a weakly interacting complex. Analysis of interface behavior during MD simulation and visual inspection of interfaces allowed us to conclude that complexes with pol-β at the 3′-side of APEX1 are those most likely to occur in vivo. Additional multiple sequence analyses of APEX1 and pol-β in related organisms identified a set of correlated mutations of specific residues at the predicted interfaces. Based on these results, we propose that pol-β in the open or closed conformation interacts and makes a stable interface with APEX1 bound to a cleaved abasic site on the 3′ side. The method described here can be used for analysis in any DNA-metabolizing pathway where weak interactions are the principal mode of cross-talk among participants and co-crystal structures of the individual components are available

Stress-Induced Reinstatement of Drug Seeking: 20 Years of Progress

In human addicts, drug relapse and craving are often provoked by stress. Since 1995, this clinical scenario has been studied using a rat model of stress-induced reinstatement of drug seeking. Here, we first discuss the generality of stress-induced reinstatement to different drugs of abuse, different stressors, and different behavioral procedures. We also discuss neuropharmacological mechanisms, and brain areas and circuits controlling stress-induced reinstatement of drug seeking. We conclude by discussing results from translational human laboratory studies and clinical trials that were inspired by results from rat studies on stress-induced reinstatement. Our main conclusions are (1) The phenomenon of stress-induced reinstatement, first shown with an intermittent footshock stressor in rats trained to self-administer heroin, generalizes to other abused drugs, including cocaine, methamphetamine, nicotine, and alcohol, and is also observed in the conditioned place preference model in rats and mice. This phenomenon, however, is stressor specific and not all stressors induce reinstatement of drug seeking. (2) Neuropharmacological studies indicate the involvement of corticotropin-releasing factor (CRF), noradrenaline, dopamine, glutamate, kappa/dynorphin, and several other peptide and neurotransmitter systems in stress-induced reinstatement. Neuropharmacology and circuitry studies indicate the involvement of CRF and noradrenaline transmission in bed nucleus of stria terminalis and central amygdala, and dopamine, CRF, kappa/dynorphin, and glutamate transmission in other components of the mesocorticolimbic dopamine system (ventral tegmental area, medial prefrontal cortex, orbitofrontal cortex, and nucleus accumbens). (3) Translational human laboratory studies and a recent clinical trial study show the efficacy of alpha-2 adrenoceptor agonists in decreasing stress-induced drug craving and stress-induced initial heroin lapse

Did Corporate Governance Compliance Have an Impact on Auditor Selection and Quality? Evidence From FTSE 350

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This paper examines the possible effects of corporate governance (GC) on audit quality (AQ) among the FTSE 350 companies. Using a sample of 180 companies from 2012 to 2017 (i.e., 1080 firm-year observations) a binary logistic model has been employed to investigate the CG-AQ nexus. This analysis was supported by conducting a probit logistic model as a sensitivity analysis. Our findings are associative of a heterogeneous impact of CG on AQ post the implementation of the 2012 CG reforms in the UK. For example, although institutional ownership and management ownership are positively associated with auditor selection and AQ, board independence, non-executive directors and audit committee are not attributed to AQ in the UK. This implies that corporate compliance with good CG practices has a limited impact on the decision to select a Big4 auditor in the UK. Despite the limitations of our study, we hope it can motivate further investigations in this area

Reduced prefrontal gyrification in obsessive–compulsive disorder

Structural magnetic resonance imaging (MRI) studies reveal evidence for brain abnormalities in obsessive–compulsive disorder (OCD), for instance, reduction of gray matter volume in the prefrontal cortex. Disturbances of gyrification in the prefrontal cortex have been described several times in schizophrenia pointing to a neurodevelopmental etiology, while gyrification has not been studied so far in OCD patients. In 26 OCD patients and 38 healthy control subjects MR-imaging was performed. Prefrontal cortical folding (gyrification) was measured bilaterally by an automated version of the automated-gyrification index (A-GI), a ratio reflecting the extent of folding, from the slice containing the inner genu of the corpus callosum up to the frontal pole. Analysis of covariance (ANCOVA, independent factor diagnosis, covariates age, duration of education) demonstrated that compared with control subjects, patients with OCD displayed a significantly reduced A-GI in the left hemisphere (p = 0.021) and a trend for a decreased A-GI in the right hemisphere (p = 0.076). Significant correlations between prefrontal lobe volume and A-GI were only observed in controls, but not in OCD patients. In conclusion, prefrontal hypogyrification in OCD patients may be a structural correlate of the impairment in executive function of this patient group and may point to a neurodevelopmental origin of this disease