Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries

We extend the definition of generalized parity $P$, charge-conjugation $C$ and time-reversal $T$ operators to nondiagonalizable pseudo-Hermitian Hamiltonians, and we use these generalized operators to describe the full set of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold classification. In particular we show that $TP$ and $CTP$ are the generators of the antiunitary symmetries; moreover, a necessary and sufficient condition is provided for a pseudo-Hermitian Hamiltonian $H$ to admit a $P$-reflecting symmetry which generates the $P$-pseudounitary and the $P$-pseudoantiunitary symmetries. Finally, a physical example is considered and some hints on the $P$-unitary evolution of a physical system are also given.Comment: 20 page

Bitangential interpolation in generalized Schur classes

Bitangential interpolation problems in the class of matrix valued functions in the generalized Schur class are considered in both the open unit disc and the open right half plane, including problems in which the solutions is not assumed to be holomorphic at the interpolation points. Linear fractional representations of the set of solutions to these problems are presented for invertible and singular Hermitian Pick matrices. These representations make use of a description of the ranges of linear fractional transformations with suitably chosen domains that was developed in a previous paper.Comment: Second version, corrected typos, changed subsection 5.6, 47 page

Scattering theory for Klein-Gordon equations with non-positive energy

We study the scattering theory for charged Klein-Gordon equations: \{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x, D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)= f_{1}, {array}. where: \epsilon^{2}(x, D_{x})= \sum_{1\leq j, k\leq n}(\p_{x_{j}} \i b_{j}(x))A^{jk}(x)(\p_{x_{k}} \i b_{k}(x))+ m^{2}(x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential $v(x)$ and magnetic potential $\vec{b}(x)$. The flow of the Klein-Gordon equation preserves the energy: h[f, f]:= \int_{\rr^{n}}\bar{f}_{1}(x) f_{1}(x)+ \bar{f}_{0}(x)\epsilon^{2}(x, D_{x})f_{0}(x) - \bar{f}_{0}(x) v^{2}(x) f_{0}(x) \d x. We consider the situation when the energy is not positive. In this case the flow cannot be written as a unitary group on a Hilbert space, and the Klein-Gordon equation may have complex eigenfrequencies. Using the theory of definitizable operators on Krein spaces and time-dependent methods, we prove the existence and completeness of wave operators, both in the short- and long-range cases. The range of the wave operators are characterized in terms of the spectral theory of the generator, as in the usual Hilbert space case

Robustness of circadian clocks to daylight fluctuations: hints from the picoeucaryote Ostreococcus tauri

The development of systemic approaches in biology has put emphasis on identifying genetic modules whose behavior can be modeled accurately so as to gain insight into their structure and function. However most gene circuits in a cell are under control of external signals and thus quantitative agreement between experimental data and a mathematical model is difficult. Circadian biology has been one notable exception: quantitative models of the internal clock that orchestrates biological processes over the 24-hour diurnal cycle have been constructed for a few organisms, from cyanobacteria to plants and mammals. In most cases, a complex architecture with interlocked feedback loops has been evidenced. Here we present first modeling results for the circadian clock of the green unicellular alga Ostreococcus tauri. Two plant-like clock genes have been shown to play a central role in Ostreococcus clock. We find that their expression time profiles can be accurately reproduced by a minimal model of a two-gene transcriptional feedback loop. Remarkably, best adjustment of data recorded under light/dark alternation is obtained when assuming that the oscillator is not coupled to the diurnal cycle. This suggests that coupling to light is confined to specific time intervals and has no dynamical effect when the oscillator is entrained by the diurnal cycle. This intringuing property may reflect a strategy to minimize the impact of fluctuations in daylight intensity on the core circadian oscillator, a type of perturbation that has been rarely considered when assessing the robustness of circadian clocks

Research priorities for European paediatric emergency medicine

Objective Research in European Paediatric Emergency Medicine (REPEM) network is a collaborative group of 69 paediatric emergency medicine (PEM) physicians from 20 countries in Europe, initiated in 2006. To further improve paediatric emergency care in Europe, the aim of this study was to define research priorities for PEM in Europe to guide the development of future research projects. Design and Setting We carried out an online survey in a modified three-stage Delphi study. Eligible participants were members of the REPEM network. In stage 1, the REPEM steering committee prepared a list of research topics. In stage 2, REPEM members rated on a 6-point scale research topics and they could add research topics and comment on the list for further refinement. Stage 3 included further prioritisation using the Hanlon Process of Prioritisation (HPP) to give more emphasis to the feasibility of a research topic. Results Based on 52 respondents (response rates per stage varying from 41% to 57%), we identified the conditions 'fever', 'sepsis' and 'respiratory infections', and the processes/interventions 'biomarkers', 'risk stratification' and 'practice variation' as common themes of research interest. The HPP identified highest priority for 4 of the 5 highest prioritised items by the Delphi process, incorporating prevalence and severity of each condition and feasibility of undertaking such research. Conclusions While the high diversity in emergency department (ED) populations, cultures, healthcare systems and healthcare delivery in European PEM prompts to focus on practice variation of ED conditions, our defined research priority list will help guide further collaborative research efforts within the REPEM network to improve PEM care in Europe.publishersversionPeer reviewe

<em>TESS</em> Cycle 2 observations of roAp stars with 2-min cadence data

\ua9 The Author(s) 2023.We present the results of a systematic search of the Transiting Exoplanet Survey Satellite (TESS) 2-min cadence data for new rapidly oscillating Ap (roAp) stars observed during the Cycle 2 phase of its mission. We find seven new roAp stars previously unreported as such and present the analysis of a further 25 roAp stars that are already known. Three of the new stars show multiperiodic pulsations, while all new members are rotationally variable stars, leading to almost 70 per cent (22) of the roAp stars presented being α2 CVn-type variable stars. We show that targeted observations of known chemically peculiar stars are likely to overlook many new roAp stars, and demonstrate that multiepoch observations are necessary to see pulsational behaviour changes. We find a lack of roAp stars close to the blue edge of the theoretical roAp instability strip, and reaffirm that mode instability is observed more frequently with precise, space-based observations. In addition to the Cycle 2 observations, we analyse TESS data for all-known roAp stars. This amounts to 18 further roAp stars observed by TESS. Finally, we list six known roAp stars that TESS is yet to observe. We deduce that the incidence of roAp stars amongst the Ap star population is just 5.5 per cent, raising fundamental questions about the conditions required to excite pulsations in Ap stars. This work, coupled with our previous work on roAp stars in Cycle 1 observations, presents the most comprehensive, homogeneous study of the roAp stars in the TESS nominal mission, with a collection of 112 confirmed roAp stars in total

Laser-induced modification of the patellar ligament tissue: comparative study of structural and optical changes

The effects of non-ablative infrared (IR) laser treatment of collagenous tissue have been commonly interpreted in terms of collagen denaturation spread over the laser-heated tissue area. In this work, the existing model is refined to account for the recently reported laser-treated tissue heterogeneity and complex collagen degradation pattern using comprehensive optical imaging and calorimetry toolkits. Patella ligament (PL) provided a simple model of type I collagen tissue containing its full structural content from triple-helix molecules to gross architecture. PL ex vivo was subjected to IR laser treatments (laser spot, 1.6 mm) of equal dose, where the tissue temperature reached the collagen denaturation temperature of 60 ± 2°C at the laser spot epicenterin the first regime, and was limited to 67 ± 2°C in the second regime. The collagen network was analyzed versus distance from the epicenter. Experimental characterization of the collagenous tissue at all structural levels included cross-polarization optical coherence tomography, nonlinear optical microscopy, light microscopy/histology, and differential scanning calorimetry. Regressive rearrangement of the PL collagen network was found to spread well outside the laser spot epicenter (>2 mm) and was accompanied by multilevel hierarchical reorganization of collagen. Four zones of distinct optical and morphological properties were identified, all elliptical in shape, and elongated in the direction perpendicular to the PL long axis. Although the collagen transformation into a random-coil molecular structure was occasionally observed, it was mechanical integrity of the supramolecular structures that was primarily compromised. We found that the structural rearrangement of the collagen network related primarily to the heat-induced thermo-mechanical effects rather than molecular unfolding. The current body of evidence supports the notion that the supramolecular collagen structure suffered degradation of various degrees, which gave rise to the observed zonal character of the laser-treated lesion