Use of Equivalent Hermitian Hamiltonian for PTPT-Symmetric Sinusoidal Optical Lattices

We show how the band structure and beam dynamics of non-Hermitian $PT$-symmetric sinusoidal optical lattices can be approached from the point of view of the equivalent Hermitian problem, obtained by an analytic continuation in the transverse spatial variable $x$. In this latter problem the eigenvalue equation reduces to the Mathieu equation, whose eigenfunctions and properties have been well studied. That being the case, the beam propagation, which parallels the time-development of the wave-function in quantum mechanics, can be calculated using the equivalent of the method of stationary states. We also discuss a model potential that interpolates between a sinusoidal and periodic square well potential, showing that some of the striking properties of the sinusoidal potential, in particular birefringence, become much less prominent as one goes away from the sinusoidal case.Comment: 11 pages, 8 figure

Invisibility in PT-symmetric complex crystals

Bragg scattering in sinusoidal PT-symmetric complex crystals of finite thickness is theoretically investigated by the derivation of exact analytical expressions for reflection and transmission coefficients in terms of modified Bessel functions of first kind. The analytical results indicate that unidirectional invisibility, recently predicted for such crystals by coupled-mode theory [Z. Lin et al., Phys. Rev. Lett. 106, 213901 (2011)], breaks down for crystals containing a large number of unit cells. In particular, for a given modulation depth in a shallow sinusoidal potential, three regimes are encountered as the crystal thickness is increased. At short lengths the crystal is reflectionless and invisible when probed from one side (unidirectional invisibility), whereas at intermediate lengths the crystal remains reflectionless but not invisible; for longer crystals both unidirectional reflectionless and invisibility properties are broken.Comment: 18 page

Secondary infertility caused by the retention of fetal bones after an abortion: a case report

<p>Abstract</p> <p>Introduction</p> <p>Unwanted contraception through prolonged retention of fetal bone is a rare cause of secondary infertility. It is usually associated with a history of abortion, either spontaneous or induced.</p> <p>Case presentation</p> <p>We describe a case of intrauterine retention of fetal bone diagnosed 8 years after the termination of a pregnancy. The patient had no complaints of pain, irregular vaginal bleeding or discharge. A hysteroscopy was performed and irregular structures were removed. These fragments were fetal bones, which probably functioned as an intrauterine contraceptive device. After removal of the fetal bone fragments the patient conceived spontaneously within 6 months.</p> <p>Conclusion</p> <p>This case report stresses the importance of taking a thorough history and evaluation of the endometrium by transvaginal ultrasound or hysteroscopy in women with secondary infertility.</p

Spawning rings of exceptional points out of Dirac cones

The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure--two conical bands touching at a single point--has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformations of the Dirac cone often reveal intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point, also known as the parity-time symmetry breaking point, where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency, unidirectional transmission or reflection, and lasers with reversed pump dependence or single-mode operation. These two fields of research are in fact connected: here we discover the ability of a Dirac cone to evolve into a ring of exceptional points, which we call an "exceptional ring." We experimentally demonstrate this concept in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity-time symmetric systems. Our results indicate that the radiation that exists in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain

Evidence for Altered Basal Ganglia-Brainstem Connections in Cervical Dystonia

Background: There has been increasing interest in the interaction of the basal ganglia with the cerebellum and the brainstem in motor control and movement disorders. In addition, it has been suggested that these subcortical connections with the basal ganglia may help to coordinate a network of regions involved in mediating posture and stabilization. While studies in animal models support a role for this circuitry in the pathophysiology of the movement disorder dystonia, thus far, there is only indirect evidence for this in humans with dystonia. Methodology/Principal Findings: In the current study we investigated probabilistic diffusion tractography in DYT1-negative patients with cervical dystonia and matched healthy control subjects, with the goal of showing that patients exhibit altered microstructure in the connectivity between the pallidum and brainstem. The brainstem regions investigated included nuclei that are known to exhibit strong connections with the cerebellum. We observed large clusters of tractography differences in patients relative to healthy controls, between the pallidum and the brainstem. Tractography was decreased in the left hemisphere and increased in the right hemisphere in patients, suggesting a potential basis for the left/right white matter asymmetry we previously observed in focal dystonia patients. Conclusions/Significance: These findings support the hypothesis that connections between the basal ganglia and brainstem play a role in the pathophysiology of dystonia

The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions

The nonlinear Schroedinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schroedinger equation can be solved analytically in terms of Jacobi elliptic functions and thus provides useful insight into the features of nonlinear stationary states of periodic potentials. Phenomena well-known from classical chaos are found, such as a bifurcation of periodic stationary states and a transition to spatial chaos. The relation of new features of nonlinear Bloch bands, such as looped and period doubled bands, are analyzed in detail. An analytic expression for the critical nonlinearity for the emergence of looped bands is derived. The results for the delta-comb are generalized to a more realistic potential consisting of a periodic sequence of narrow Gaussian peaks and the dynamical stability of periodic solutions in a Gaussian comb is discussed.Comment: Enhanced and revised version, to appear in J. Nonlin. Math. Phy

A comparative study using Thrombin generation and three different INR methods in patients on vitamin K antagonist treatment

Introduction: Vitamin K antagonist (VKA) treatment requires routine monitoring using the international normalized ratio (INR). However, different INR assays may vary in their results. The aim of this study was to assess the agreement of three different INR methods, compared with thrombin generation, in patients on VKA treatment. Methods: Sixty patients attending the Anticoagulation Clinic at Mater Dei Hospital (Msida, Malta) for VKA monitoring between August and September 2015 were enrolled. The INR was tested using a point-of-care (POC) device (CoaguChek XS Plus, Roche Diagnostics) for both capillary and venous blood samples, a photo-optical (Sysmex CS-2100i/CA-1500, Siemens) and a mechanical clot detection system (Thrombolyzer XRC, Behnk Elektronik). All assays used human recombinant thromboplastin as reagent. Thrombin generation was performed using the calibrated automated thrombogram. Results: There was a negative curvilinear correlation between the endogenous thrombin potential and different INR assays (r\ue2\u89\ua4-.75) and a strong positive linear correlation between the CoaguChek XS Plus on capillary samples and the other INR methodologies (r\ue2\u89\ua5.96). Conclusion: All different INR assays showed good correlation with the thrombin generation potential. The POC INR showed one of the highest correlation coefficients with thrombin generation, confirming the POC devices as an accurate, valid alternative to laboratory INR in VKA patients

Do experts see it in slow motion? Altered timing of action simulation uncovers domain-specific perceptual processing in expert athletes

Accurate encoding of the spatio-temporal properties of others' actions is essential for the successful implementation of daily activities and, even more, for successful sportive performance, given its role in movement coordination and action anticipation. Here we investigated whether athletes are provided with special perceptual processing of spatio-temporal properties of familiar sportive actions. Basketball and volleyball players and novices were presented with short video-clips of free basketball throws that were partially occluded ahead of realization and were asked to judge whether a subsequently presented pose was either taken from the same throw depicted in the occluded video (action identification task) or temporally congruent with the expected course of the action during the occlusion period (explicit timing task). Results showed that basketball players outperformed the other groups in detecting action compatibility when the pose depicted earlier or synchronous, but not later phases of the movement as compared to the natural course of the action during occlusion. No difference was obtained for explicit estimations of timing compatibility. This leads us to argue that the timing of simulated actions in the experts might be slower than that of perceived actions ("slow-motion" bias), allowing for more detailed representation of ongoing actions and refined prediction abilities

Combined metabolome and transcriptome profiling provides new insights into diterpene biosynthesis in S. pomifera glandular trichomes

Background: Salvia diterpenes have been found to have health promoting properties. Among them, carnosic acid and carnosol, tanshinones and sclareol are well known for their cardiovascular, antitumor, antiinflammatory and antioxidant activities. However, many of these compounds are not available at a constant supply and developing biotechnological methods for their production could provide a sustainable alternative. The transcriptome of S. pomifera glandular trichomes was analysed aiming to identify genes that could be used in the engineering of synthetic microbial systems. Results: In the present study, a thorough metabolite analysis of S. pomifera leaves led to the isolation and structure elucidation of carnosic acid-family metabolites including one new natural product. These labdane diterpenes seem to be synthesized through miltiradiene and ferruginol. Transcriptomic analysis of the glandular trichomes from the S. pomifera leaves revealed two genes likely involved in miltiradiene synthesis. Their products were identified and the corresponding enzymes were characterized as copalyl diphosphate synthase (SpCDS) and miltiradiene synthase (SpMilS). In addition, several CYP-encoding transcripts were identified providing a valuable resource for the identification of the biosynthetic mechanism responsible for the production of carnosic acid-family metabolites in S. pomifera. Conclusions: Our work has uncovered the key enzymes involved in miltiradiene biosynthesis in S. pomifera leaf glandular trichomes. The transcriptomic dataset obtained provides a valuable tool for the identification of the CYPs involved in the synthesis of carnosic acid-family metabolites.General Secretariat of Research and Technology (GSRT) {[}09-SYN-23-879]; grant SEE-ERA. NET PLUS {[}ERA 64/01]; grant KRIPIS {[}MIS 448840