A return to observability near exceptional points in a schematic PT-symmetric model

Many indefinite-metric (often called pseudo-Hermitian or PT-symmetric) quantum models H prove "physical" (i.e., Hermitian with respect to an innovated, ad hoc scalar product) inside a characteristic domain of parameters D. This means that the energies get complex (= unobservable) beyond the boundary (= Kato's "exceptional points", EPs). In a solvable example we detect an enlargement of D caused by the emergence of a new degree of freedom. We conjecture that such a beneficial mechanism of a return to the real spectrum near EPs may be generic and largely model-independent.Comment: 14 pp., 1 fi

Strengthened PT-symmetry with P ≠\neq P†^\dagger

Two alternative scenarios are shown possible in Quantum Mechanics working with non-Hermitian $PT-$symmetric form of observables. While, usually, people assume that $P$ is a self-adjoint indefinite metric in Hilbert space (and that their $P-$pseudo-Hermitian Hamiltonians $H$ possess the real spectra etc), we propose to relax the constraint $P=P^\dagger$ as redundant. Non-Hermitian triplet of coupled square wells is chosen for illustration purposes. Its solutions are constructed and the observed degeneracy of their spectrum is attributed to the characteristic nontrivial symmetry $S={P}^{-1} {P}^\dagger \neq I$ of the model $H$. Due to the solvability of the model the determination of the domain where the energies remain real is straightforward. A few remarks on the correct (albeit ambiguous) physical interpretation of the model are added.Comment: 10 pp. + 1 figur

Effects of topical clonidine versus brimonidine on choroidal blood flow and intraocular pressure during squatting

PURPOSE. Clonidine and brimonidine, two ␣-2 agonists, have been shown to reduce intraocular pressure (IOP) in patients with glaucoma. Little is known, however, about the exact role of ␣ receptors in the control of ocular blood flow in the posterior pole of the eye. Hence, the study was conducted to investigate the effects of topical clonidine versus topical brimonidine on choroidal blood flow and intraocular pressure during squatting. METHODS. This was a randomized, double-masked, controlled, two-way crossover study. Twelve healthy male nonsmoking volunteers, aged between 19 and 35 years were included in the study. Two drops of clonidine or brimonidine were administered in the subjects' study eyes. Continuous measurement using the compact laser Doppler flowmeter was performed during a 6-minute squatting period, to assess choroidal blood flow regulation during an increase in ocular perfusion pressure. RESULTS. Both substances induced a pronounced but comparable (P ϭ 0.8) decrease in IOP. Squatting increased mean arterial pressure (MAP) and ocular perfusion pressure (P Ͻ 0.01). This increase was comparable between the clonidine and the brimonidine study day (P ϭ 0.88). Squatting induced an increase in choroidal blood flow that was less pronounced than the increase in ocular perfusion pressure. Compared with baseline the ␣-2 agonists decreased choroidal blood flow during squatting (P ϭ 0.0026) to a comparable degree (P ϭ 0.86). Vascular resistance increased at baseline and during squatting after administration of the ␣-2 agonists (P Ͻ 0.01) in both groups to a comparable degree (P ϭ 0.56). CONCLUSIONS. Topical ␣-2 agonists may induce changes in choroidal blood flow, even after a single administration. Long-term studies are needed to study potential effects of brimonidine and clonidine in the clinical setting. (Invest Ophthalmol Vis Sci. 2007;48:4220 -4225

Determination of the domain of the admissible matrix elements in the four-dimensional PT-symmetric anharmonic model

Many manifestly non-Hermitian Hamiltonians (typically, PT-symmetric complex anharmonic oscillators) possess a strictly real, "physical" bound-state spectrum. This means that they are (quasi-)Hermitian with respect to a suitable non-standard metric. The domain D of the existence of this metric is studied here for a nontrivial though still non-numerical four-parametric "benchmark" matrix model.Comment: 18 pages, 2 figure

Collaborative nowcasting of COVID-19 hospitalization incidences in Germany

Real-time surveillance is a crucial element in the response to infectious disease outbreaks. However, the interpretation of incidence data is often hampered by delays occurring at various stages of data gathering and reporting. As a result, recent values are biased downward, which obscures current trends. Statistical nowcasting techniques can be employed to correct these biases, allowing for accurate characterization of recent developments and thus enhancing situational awareness. In this paper, we present a preregistered real-time assessment of eight nowcasting approaches, applied by independent research teams to German 7-day hospitalization incidences during the COVID-19 pandemic. This indicator played an important role in the management of the outbreak in Germany and was linked to levels of non-pharmaceutical interventions via certain thresholds. Due to its definition, in which hospitalization counts are aggregated by the date of case report rather than admission, German hospitalization incidences are particularly affected by delays and can take several weeks or months to fully stabilize. For this study, all methods were applied from 22 November 2021 to 29 April 2022, with probabilistic nowcasts produced each day for the current and 28 preceding days. Nowcasts at the national, state, and age-group levels were collected in the form of quantiles in a public repository and displayed in a dashboard. Moreover, a mean and a median ensemble nowcast were generated. We find that overall, the compared methods were able to remove a large part of the biases introduced by delays. Most participating teams underestimated the importance of very long delays, though, resulting in nowcasts with a slight downward bias. The accompanying prediction intervals were also too narrow for almost all methods. Averaged over all nowcast horizons, the best performance was achieved by a model using case incidences as a covariate and taking into account longer delays than the other approaches. For the most recent days, which are often considered the most relevant in practice, a mean ensemble of the submitted nowcasts performed best. We conclude by providing some lessons learned on the definition of nowcasting targets and practical challenges

The Intraocular Cytokine Profile and Therapeutic Response in Persistent Neovascular Age-Related Macular Degeneration

Citation: Rezar-Dreindl S, Sacu S, Eibenberger K, et al. The intraocular cytokine profile and therapeutic response in persistent neovascular agerelated macular degeneration. Invest Ophthalmol Vis Sci. 2016;57:4144-4150. DOI:10.1167/iovs.16-19772 PURPOSE. To investigate the course of inflammatory and angiogenic cytokines in the aqueous humor of patients with persistent/recurrent neovascular age-related macular degeneration (nAMD) under ranibizumab monotherapy (IVM) or ranibizumab plus dexamethasone combination treatment. METHODS. In this 12-month prospective study, 40 eyes with nAMD were treated with either IVM or combined treatment with ranibizumab plus intravitreal dexamethasone implant (IVC). Patients in the IVM group were treated following an ''as needed'' treatment regimen; patients in the IVC group received ranibizumab and a dexamethasone implant at baseline and were retreated with ranibizumab. At baseline and at each time of retreatment aqueous humor samples were taken. RESULTS. Before treatment, levels of macrophage chemoattractant protein (MCP)-1, monokine induced by c interferon (MIG), and lipocalin-2/ neutrophil gelatinase-associated lipocalin (NGAL) were elevated in nAMD patients compared to healthy controls (P ¼ 0.024; P ¼ 0.04; P ¼ 0.01). In contrast, tumor necrosis factor a, IL-12p70, and secreted protein acidic and rich in cysteine (SPARC) concentrations were lower (P ¼ 0.001; P ¼ 0.008; P ¼ 0.03), while vascular endothelial growth factor (VEGF) was not altered (45 6 6/51 6 12 pg/mL nAMD/ control group; P ¼ 0.6). During IVC, levels of VEGF, MIG, platelet-derived growth factor (PDGF)-AA, and transforming growth factor b1 (P ¼ 0.005; P ¼ 0.011; P ¼ 0.008; P ¼ 0.013) were reduced. Ranibizumab monotherapy did not influence the course of any inflammatory/ angiogenic cytokine. Interleukin 6 and PDGF-AA levels correlated with central retinal thickness changes (P ¼ 0.007; P ¼ 0.022). Over the 12-month period visual function was maintained with no significant differences during or between both treatment groups. CONCLUSIONS. Inflammatory proteins are involved in the pathogenesis of chronic macular edema due to AMD and are associated with disease activity. During combined treatment, levels of inflammatory and angiogenic cytokines decreased over a 12-month period with no superiority in functional outcome

Positioning Performance Evaluation of a Dual Frequency Multi-GNSS Smartphone

Published in “Proceedings of the 16th International Conference on Location Based Services (LBS 2021)”, edited by Anahid Basiri, Georg Gartner and Haosheng Huang, LBS 2021, 24-25 November 2021, Glasgow, UK/online.Smartphones with dual-frequency multi-constellation GNSS (Global Navigation Satellite Systems) receivers are now available on the market. This study examines their usage in simple surveying tasks, such as data acquisition for GIS, e.g. for a tree cadastre, lantern cadastre, traffic signs, etc., as well as line documentation, such as for underground power lines. For the experiments, the Pixel 5 from the manufacturer Google LLC is chosen. Code and phase observations are recorded in different scenarios. Evaluation in post-processing based on these observations in Single Positioning (SPP) and Precise Positioning (PPP) mode are carried out. In the analyses, the main focus is led on the achievable positioning accuracies and resulting deviations from reference points serving as ground truth. Apart from these parameters, other criteria, such as the measurement effort and costs, quality, accuracy and repeatability of the measurements are investigated. The results of the experiments indicate that the Pixel 5, although it enables the recording of satellite data on two frequency bands, can only be used to a limited extent in practical surveying tasks because it does not meet the accuracy requirements on the centimeter level. The main reason for this is the quite low quality of the observations. With long observation times, however, results with a positioning accuracy of less than half a meter are achievable with the smartphone. Thus, the Pixel 5 is capable to achieve the requirements in terms of positioning accuracy and reliability for applications such as data acquisition for Geographic Information Systems (GIS) and especially in Location-based Services (LBS).42622