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

We consider one-dimensional Schroedinger-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 in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

Regulation of Axonal HCN1 Trafficking in Perforant Path Involves Expression of Specific TRIP8b Isoforms

The functions of HCN channels in neurons depend critically on their subcellular localization, requiring fine-tuned machinery that regulates subcellular channel trafficking. Here we provide evidence that regulatory mechanisms governing axonal HCN channel trafficking involve association of the channels with specific isoforms of the auxiliary subunit TRIP8b. In the medial perforant path, which normally contains HCN1 channels in axon terminals in immature but not in adult rodents, we found axonal HCN1 significantly increased in adult mice lacking TRIP8b (TRIP8b−/−). Interestingly, adult mice harboring a mutation that results in expression of only the two most abundant TRIP8b isoforms (TRIP8b[1b/2]−/−) exhibited an HCN1 expression pattern similar to wildtype mice, suggesting that presence of one or both of these isoforms (TRIP8b(1a), TRIP8b(1a-4)) prevents HCN1 from being transported to medial perforant path axons in adult mice. Concordantly, expression analyses demonstrated a strong increase of expression of both TRIP8b isoforms in rat entorhinal cortex with age. However, when overexpressed in cultured entorhinal neurons of rats, TRIP8b(1a), but not TRIP8b(1a-4), altered substantially the subcellular distribution of HCN1 by promoting somatodendritic and reducing axonal expression of the channels. Taken together, we conclude that TRIP8b isoforms are important regulators of HCN1 trafficking in entorhinal neurons and that the alternatively-spliced isoform TRIP8b(1a) could be responsible for the age-dependent redistribution of HCN channels out of perforant path axon terminals

PT-Symmetric Dimer in a Generalized Model of Coupled Nonlinear Oscillators

Abstract In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrödinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one of each oscillator. Finally, the considerations are extended to the original oscillator model, where periodic orbits and their stability are obtained. When the solutions are found to be unstable their dynamics is monitored by means of direct numerical simulations

Improved adherence with once-daily versus twice-daily dosing of mometasone furoate administered via a dry powder inhaler: a randomized open-label study

Background Poor adherence with prescribed asthma medication is a major barrier to positive treatment outcomes. This study was designed to determine the effect of a once-daily administration of mometasone furoate administered via a dry powder inhaler (MF-DPI) on treatment adherence compared with a twice-daily administration. Methods This was a 12-week open-label study designed to mimic an actual clinical setting in patients ≥12 years old with mild-to-moderate persistent asthma. Patients were randomized to receive MF-DPI 400 μg once-daily in the evening or MF-DPI 200 μg twice-daily. Adherence was assessed primarily using the number of actual administered doses reported from the device counter divided by the number of scheduled doses. Self-reports were also used to determine adherence. Health-related quality of life, healthcare resource utilization, and days missed from work or school were also reported. Results 1233 patients were randomized. The mean adherence rates, as measured by the automatic dose counter, were significantly better (P < 0.001) with MF-DPI 400 μg once-daily in the evening (93.3%) than with MF-DPI 200 μg twice-daily (89.5%). Mean adherence rates based on self-reports were also significantly better (P < 0.001) with MF-DPI 400 μg QD PM (97.2%) than with MF-DPI 200 μg twice-daily (95.3%). Adherence rates were lower in adolescents (12-17 years old). Health-related quality of life improved by 20% in patients using MF-DPI once-daily in the evening and by 14% in patients using MF-DPI twice-daily. Very few (<8%) patients missed work/school. Conclusion Mean adherence rates were greater with a once-daily dosing regimen of MF-DPI than with a twice-daily dosing regimen. This trial was completed prior to the ISMJE requirements for trial registration

Role of the Endogenous Antioxidant System in the Protection of Schistosoma mansoni Primary Sporocysts against Exogenous Oxidative Stress

Antioxidants produced by the parasite Schistosoma mansoni are believed to be involved in the maintenance of cellular redox balance, thus contributing to larval survival in their intermediate snail host, Biomphalaria glabrata. Here, we focused on specific antioxidant enzymes, including glutathione-S-transferases 26 and 28 (GST26 and 28), glutathione peroxidase (GPx), peroxiredoxin 1 and 2 (Prx1 and 2) and Cu/Zn superoxide dismutase (SOD), known to be involved in cellular redox reactions, in an attempt to evaluate their endogenous antioxidant function in the early-developing primary sporocyst stage of S. mansoni. Previously we demonstrated a specific and consistent RNA interference (RNAi)-mediated knockdown of GST26 and 28, Prx1 and 2, and GPx transcripts, and an unexpected elevation of SOD transcripts in sporocysts treated with gene-specific double-stranded (ds)RNA. In the present followup study, in vitro transforming sporocysts were exposed to dsRNAs for GST26 and 28, combined Prx1/2, GPx, SOD or green-fluorescent protein (GFP, control) for 7 days in culture, followed by assessment of the effects of specific dsRNA treatments on protein levels using semi-quantitative Western blot analysis (GST26, Prx1/2 only), and larval susceptibility to exogenous oxidative stress in in vitro killing assays. Significant decreases (80% and 50%) in immunoreactive GST26 and Prx1/2, respectively, were observed in sporocysts treated with specific dsRNA, compared to control larvae treated with GFP dsRNA. Sporocysts cultured with dsRNAs for GST26, GST28, Prx1/2 and GPx, but not SOD dsRNA, were significantly increased in their susceptibility to H2O2 oxidative stress (60–80% mortalities at 48 hr) compared to GFP dsRNA controls (∼18% mortality). H2O2-mediated killing was abrogated by bovine catalase, further supporting a protective role for endogenous sporocyst antioxidants. Finally, in vitro killing of S. mansoni sporocysts by hemocytes of susceptible NMRI B. glabrata snails was increased in larvae treated with Prx1/2, GST26 and GST28 dsRNA, compared to those treated with GFP or SOD dsRNAs. Results of these experiments strongly support the hypothesis that endogenous expression and regulation of larval antioxidant enzymes serve a direct role in protection against external oxidative stress, including immune-mediated cytotoxic reactions. Moreover, these findings illustrate the efficacy of a RNAi-type approach in investigating gene function in larval schistosomes

Introduction to the functional RG and applications to gauge theories

These lectures contain an introduction to modern renormalization group (RG) methods as well as functional RG approaches to gauge theories. In the first lecture, the functional renormalization group is introduced with a focus on the flow equation for the effective average action. The second lecture is devoted to a discussion of flow equations and symmetries in general, and flow equations and gauge symmetries in particular. The third lecture deals with the flow equation in the background formalism which is particularly convenient for analytical computations of truncated flows. The fourth lecture concentrates on the transition from microscopic to macroscopic degrees of freedom; even though this is discussed here in the language and the context of QCD, the developed formalism is much more general and will be useful also for other systems.Comment: 60 pages, 14 figures, Lectures held at the 2006 ECT* School "Renormalization Group and Effective Field Theory Approaches to Many-Body Systems", Trento, Ital

Application of fuzzy logic to assess the quality of BPMN models

© Springer International Publishing AG, part of Springer Nature 2018. Modeling is the first stage in a Business Process’s (BP) lifecycle. A high-quality BP model is vital to the successful implementation, execution, and monitoring stages. Different works have evaluated BP models from a quality perspective. These works either used formal verification or a set of quality metrics. This paper adopts quality metric and targets models represented in Business Process Modeling and Notation (BPMN). It proposes an approach based on fuzzy logic along with a tool system developed under eclipse framework. The preliminary experimental evaluation of the proposed system shows encouraging results

Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss

A parity-time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrödinger equations (dimer) is studied. It is shown that the problem can be reduced to a perturbed pendulum-like equation. This is done by finding two constants of motion. Firstly, a generalized problem using Melnikov-type analysis and topological degree arguments is studied for showing the existence of periodic (libration), shift- periodic (rotation), and chaotic solutions. Then these general results are applied to the PT-symmetric dimer. It is interestingly shown that if a sufficient condition is satisfied, then rotation modes, which do not exist in the dimer with constant gain–loss, will persist. An approximate threshold for PT-broken phase corresponding to the disappearance of bounded solutions is also presented. Numerical study is presented accompanying the analytical results

Microbial Functional Capacity Is Preserved Within Engineered Soil Formulations Used In Mine Site Restoration

Mining of mineral resources produces substantial volumes of crushed rock based wastes that are characterised by poor physical structure and hydrology, unstable geochemistry and potentially toxic chemical conditions. Recycling of these substrates is desirable and can be achieved by blending waste with native soil to form a 'novel substrate' which may be used in future landscape restoration. However, these post-mining substrate based 'soils' are likely to contain significant abiotic constraints for both plant and microbial growth. Effective use of these novel substrates for ecosystem restoration will depend on the efficacy of stored topsoil as a potential microbial inoculum as well as the subsequent generation of key microbial soil functions originally apparent in local pristine sites. Here, using both marker gene and shotgun metagenome sequencing, we show that topsoil storage and the blending of soil and waste substrates to form planting substrates gives rise to variable bacterial and archaeal phylogenetic composition but a high degree of metabolic conservation at the community metagenome level. Our data indicates that whilst low phylogenetic conservation is apparent across substrate blends we observe high functional redundancy in relation to key soil microbial pathways, allowing the potential for functional recovery of key belowground pathways under targeted management