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

CPT-symmetric discrete square well

A new version of an elementary PT-symmetric square well quantum model is proposed in which a certain Hermiticity-violating end-point interaction leaves the spectrum real in a large domain of couplings $\lambda\in (-1,1)$. Within this interval we employ the usual coupling-independent operator P of parity and construct, in a systematic Runge-Kutta discrete approximation, a coupling-dependent operator of charge C which enables us to classify our P-asymmetric model as CPT-symmetric or, equivalently, hiddenly Hermitian alias cryptohermitian.Comment: 12 pp., presented to conference PHHQP IX (http://www.math.zju.edu.cn/wjd/

Simulating magnetized neutron stars with discontinuous Galerkin methods

Discontinuous Galerkin methods are popular because they can achieve high order where the solution is smooth, because they can capture shocks while needing only nearest-neighbor communication, and because they are relatively easy to formulate on complex meshes. We perform a detailed comparison of various limiting strategies presented in the literature applied to the equations of general relativistic magnetohydrodynamics. We compare the standard minmod/$\Lambda\Pi^N$ limiter, the hierarchical limiter of Krivodonova, the simple WENO limiter, the HWENO limiter, and a discontinuous Galerkin-finite-difference hybrid method. The ultimate goal is to understand what limiting strategies are able to robustly simulate magnetized TOV stars without any fine-tuning of parameters. Among the limiters explored here, the only limiting strategy we can endorse is a discontinuous Galerkin-finite-difference hybrid method

Prognostic value of physicians' assessment of compliance regarding all-cause mortality in patients with type 2 diabetes: primary care follow-up study

BACKGROUND: Whether the primary care physician's assessment of patient compliance is a valuable prognostic marker to identify patients who are at increased risk of death, or merely reflects measurement of various treatment parameters such as HbA(1C )or other laboratory markers is unclear. The objective of this prospective cohort study was to investigate the prognostic value of the physicians' assessment of patient compliance and other factors with respect to all-cause mortality during a one year follow-up period. METHODS: A prospective cohort study was conducted among 1014 patients with type 2 diabetes aged 40 and over (mean age 69 years, SD 10.4, 45% male) who were under medical treatment in 11 participating practices of family physicians and internists working in primary care in a defined region in South Germany between April and June 2000. Baseline data were gathered from patients and physicians by standardized questionnaire. The physician's assessment of patient compliance was assessed by means of a 4-point Likert scale (very good, rather good, rather bad, very bad). In addition, we carried out a survey among physicians by means of a questionnaire to find out which aspects for the assessment of patient compliance were of importance to make this assessment. Active follow-up of patients was conducted after one year to determine mortality. RESULTS: During the one year follow-up 48 (4.7%) of the 1014 patients died. Among other factors such as patient type (patients presenting at office, nursing home or visited patients), gender, age and a history of macrovascular disease, the physician's assessment of patient compliance was an important predictor of all-cause mortality. Patients whose compliance was assessed by the physician as "very bad" (6%) were significantly more likely to die during follow-up (OR = 2.67, 95% CI 1.02–6.97) after multivariable adjustment compared to patients whose compliance was assessed as "rather good" (45%) or "very good" (18%). The HbA(1C)-value and the cholesterol level at baseline showed no statistically significant association with all-cause mortality. According to our survey for most of the physicians self-acceptance of disease, treatment adherence, patient's interest in physician's explanations, attendance at appointments, a good self-management, and a good physician-patient relationship were key elements in the assessment of patient compliance. CONCLUSION: The primary care physician's assessment of patient compliance is a valuable prognostic marker for mortality among patients with type 2 diabetes. Identification of patients in need of improved compliance may help to target preventive measures

Low Q^2 Jet Production at HERA and Virtual Photon Structure

The transition between photoproduction and deep-inelastic scattering is investigated in jet production at the HERA ep collider, using data collected by the H1 experiment. Measurements of the differential inclusive jet cross-sections dsigep/dEt* and dsigmep/deta*, where Et* and eta* are the transverse energy and the pseudorapidity of the jets in the virtual photon-proton centre of mass frame, are presented for 0 < Q2 < 49 GeV2 and 0.3 < y < 0.6. The interpretation of the results in terms of the structure of the virtual photon is discussed. The data are best described by QCD calculations which include a partonic structure of the virtual photon that evolves with Q2.Comment: 20 pages, 5 Figure

A Search for Selectrons and Squarks at HERA

Data from electron-proton collisions at a center-of-mass energy of 300 GeV are used for a search for selectrons and squarks within the framework of the minimal supersymmetric model. The decays of selectrons and squarks into the lightest supersymmetric particle lead to final states with an electron and hadrons accompanied by large missing energy and transverse momentum. No signal is found and new bounds on the existence of these particles are derived. At 95% confidence level the excluded region extends to 65 GeV for selectron and squark masses, and to 40 GeV for the mass of the lightest supersymmetric particle.Comment: 13 pages, latex, 6 Figure

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Paradoxical Evidence Integration in Rapid Decision Processes

Decisions about noisy stimuli require evidence integration over time. Traditionally, evidence integration and decision making are described as a one-stage process: a decision is made when evidence for the presence of a stimulus crosses a threshold. Here, we show that one-stage models cannot explain psychophysical experiments on feature fusion, where two visual stimuli are presented in rapid succession. Paradoxically, the second stimulus biases decisions more strongly than the first one, contrary to predictions of one-stage models and intuition. We present a two-stage model where sensory information is integrated and buffered before it is fed into a drift diffusion process. The model is tested in a series of psychophysical experiments and explains both accuracy and reaction time distributions

Feasibility and outcome of reproducible clinical interpretation of high-dimensional molecular data: a comparison of two molecular tumor boards

BACKGROUND: Structured and harmonized implementation of molecular tumor boards (MTB) for the clinical interpretation of molecular data presents a current challenge for precision oncology. Heterogeneity in the interpretation of molecular data was shown for patients even with a limited number of molecular alterations. Integration of high-dimensional molecular data, including RNA- (RNA-Seq) and whole-exome sequencing (WES), is expected to further complicate clinical application. To analyze challenges for MTB harmonization based on complex molecular datasets, we retrospectively compared clinical interpretation of WES and RNA-Seq data by two independent molecular tumor boards. METHODS: High-dimensional molecular cancer profiling including WES and RNA-Seq was performed for patients with advanced solid tumors, no available standard therapy, ECOG performance status of 0-1, and available fresh-frozen tissue within the DKTK-MASTER Program from 2016 to 2018. Identical molecular profiling data of 40 patients were independently discussed by two molecular tumor boards (MTB) after prior annotation by specialized physicians, following independent, but similar workflows. Identified biomarkers and resulting treatment options were compared between the MTBs and patients were followed up clinically. RESULTS: A median of 309 molecular aberrations from WES and RNA-Seq (n = 38) and 82 molecular aberrations from WES only (n = 3) were considered for clinical interpretation for 40 patients (one patient sequenced twice). A median of 3 and 2 targeted treatment options were identified per patient, respectively. Most treatment options were identified for receptor tyrosine kinase, PARP, and mTOR inhibitors, as well as immunotherapy. The mean overlap coefficient between both MTB was 66%. Highest agreement rates were observed with the interpretation of single nucleotide variants, clinical evidence levels 1 and 2, and monotherapy whereas the interpretation of gene expression changes, preclinical evidence levels 3 and 4, and combination therapy yielded lower agreement rates. Patients receiving treatment following concordant MTB recommendations had significantly longer overall survival than patients receiving treatment following discrepant recommendations or physician's choice. CONCLUSIONS: Reproducible clinical interpretation of high-dimensional molecular data is feasible and agreement rates are encouraging, when compared to previous reports. The interpretation of molecular aberrations beyond single nucleotide variants and preclinically validated biomarkers as well as combination therapies were identified as additional difficulties for ongoing harmonization efforts

Generalized Fano lineshapes reveal exceptional points in photonic molecules

The optical behavior of coupled systems, in which the breaking of parity and time-reversal symmetry occurs, is drawing increasing attention to address the physics of the exceptional point singularity, i.e., when the real and imaginary parts of the normal-mode eigenfrequencies coincide. At this stage, fascinating phenomena are predicted, including electromagnetic-induced transparency and phase transitions. To experimentally observe the exceptional points, the near-field coupling to waveguide proposed so far was proved to work only in peculiar cases. Here, we extend the interference detection scheme, which lies at the heart of the Fano lineshape, by introducing generalized Fano lineshapes as a signature of the exceptional point occurrence in resonant-scattering experiments. We investigate photonic molecules and necklace states in disordered media by means of a near-field hyperspectral mapping. Generalized Fano profiles in material science could extend the characterization of composite nanoresonators, semiconductor nanostructures, and plasmonic and metamaterial devices