Recursive Definitions of Monadic Functions

Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's imperative programming extension, which results in a convenient definition principle for imperative programs, which were previously hard to define. For such monadic functions, the recursion equation can always be derived without preconditions, even if the function is partial. The construction is easy to automate, and convenient induction principles can be derived automatically.Comment: In Proceedings PAR 2010, arXiv:1012.455

Experimental Measurement of the Berry Curvature from Anomalous Transport

Geometrical properties of energy bands underlie fascinating phenomena in a wide-range of systems, including solid-state materials, ultracold gases and photonics. Most famously, local geometrical characteristics like the Berry curvature can be related to global topological invariants such as those classifying quantum Hall states or topological insulators. Regardless of the band topology, however, any non-zero Berry curvature can have important consequences, such as in the semi-classical evolution of a wave packet. Here, we experimentally demonstrate for the first time that wave packet dynamics can be used to directly map out the Berry curvature. To this end, we use optical pulses in two coupled fibre loops to study the discrete time-evolution of a wave packet in a 1D geometrical "charge" pump, where the Berry curvature leads to an anomalous displacement of the wave packet under pumping. This is both the first direct observation of Berry curvature effects in an optical system, and, more generally, the proof-of-principle demonstration that semi-classical dynamics can serve as a high-resolution tool for mapping out geometrical properties

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

Bypass surgery versus stenting for the treatment of multivessel disease in patients with unstable angina compared with stable angina

BACKGROUND: Earlier reports have shown that the outcome of balloon angioplasty or bypass surgery in unstable angina is less favorable than in stable angina. Recent improvements in percutaneous treatment (stent implantation) and bypass surgery (arterial grafts) warrant reevaluation of the relative merits of either technique in treatment of unstable angina. Methods and Results- Seven hundred fifty-five patients with stable angina were randomly assigned to coronary stenting (374) or bypass surgery (381), and 450 patients with unstable angina were randomly assigned to coronary stenting (226) or bypass surgery (224). All patients had multivessel disease considered to be equally treatable by either technique. Freedom from major adverse events, including death, myocardial infarction, and cerebrovascular events, at 1 year was not different in unstable patients (91.2% versus 88.9%) and stable patients (90.4% versus 92.6%) treated, respectively, with coronary stenting or bypass surgery. Freedom from repeat revascularization at 1 year was similar in unstable and stable angina treated with stenting (79.2% versus 78.9%) or bypass surgery (96.3% versus 96%) but was significantly higher in both unstable and stable patients treated with stenting (16.8% versus 16.9%) compared with bypass surgery (3.6% versus 3.5%). Neither the difference in costs between stented or bypassed stable or unstable angina ($2594 versus$3627) nor the cost-effectiveness was significantly different at 1 year. CONCLUSIONS: There was no difference in rates of death, myocardial infarction, and cerebrovascular event at 1 year in patients with unstable angina and multivessel disease treated with either stented angioplasty or bypass surgery compared with patients with stable angina. The rate of repeat revascularization of both unstable and stable angina was significantly higher in patients with stents

A Framework for Verifying Data-Centric Protocols

International audienceData centric languages, such as recursive rule based languages, have been proposed to program distributed applications over networks. They simplify greatly the code, while still admitting efficient distributed execution. We show that they also provide a promising approach to the verification of distributed protocols, thanks to their data centric orientation, which allows us to explicitly handle global structures such as the topology of the network. We consider a framework using an original formalization in the Coq proof assistant of a distributed computation model based on message passing with either synchronous or asynchronous behavior. The declarative rules of the Netlog language for specifying distributed protocols and the virtual machines for evaluating these rules are encoded in Coq as well. We consider as a case study tree protocols, and show how this framework enables us to formally verify them in both the asynchronous and synchronous setting

Parity-time symmetric coupled microresonators with a dispersive gain/loss

The paper reports on the coupling of Parity-Time (PT)-symmetric whispering gallery resonators with realistic material and gain/loss models. Response of the PT system is analyzed for the case of low and high material and gain dispersion, and also for two practical scenarios when the pump frequency is not aligned with the resonant frequency of the desired whispering gallery mode and when there is imbalance in the gain/loss profile. The results show that the presence of dispersion and frequency misalignment causes skewness in frequency bifurcation and significant reduction of the PT breaking point, respectively. Finally, we demonstrate a lasing mode operation which occurs due to an early PT-breaking by increasing loss in a PT system with unbalanced gain and loss

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

Evidence for the η_b(1S) Meson in Radiative Υ(2S) Decay

We have performed a search for the η_b(1S) meson in the radiative decay of the Υ(2S) resonance using a sample of 91.6 × 10^6 Υ(2S) events recorded with the BABAR detector at the PEP-II B factory at the SLAC National Accelerator Laboratory. We observe a peak in the photon energy spectrum at E_γ = 609.3^(+4.6)_(-4.5)(stat)±1.9(syst) MeV, corresponding to an η_b(1S) mass of 9394.2^(+4.8)_(-4.9)(stat) ± 2.0(syst) MeV/c^2. The branching fraction for the decay Υ(2S) → γη_b(1S) is determined to be [3.9 ± 1.1(stat)^(+1.1)_(-0.9)(syst)] × 10^(-4). We find the ratio of branching fractions B[Υ(2S) → γη_b(1S)]/B[Υ(3S) → γη_b(1S)]= 0.82 ± 0.24(stat)^(+0.20)_(-0.19)(syst)

A versatile all-optical parity-time signal processing device using a Bragg grating induced using positive and negative Kerr-nonlinearity

The properties of gratings with Kerr nonlinearity and PT symmetry are investigated in this paper. The impact of the gain and loss saturation on the response of the grating is analysed for different input intensities and gain/loss parameters. Potential applications of these gratings as switches, logic gates and amplifiers are also shown

Informal Caregiving in Amyotrophic Lateral Sclerosis (ALS): A High Caregiver Burden and Drastic Consequences on Caregivers’ Lives

Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease that causes progressive autonomy loss and need for care. This does not only affect patients themselves, but also the patients’ informal caregivers (CGs) in their health, personal and professional lives. The big efforts of this multi-center study were not only to evaluate the caregivers’ burden and to identify its predictors, but it also should provide a specific understanding of the needs of ALS patients’ CGs and fill the gap of knowledge on their personal and work lives. Using standardized questionnaires, primary data from patients and their main informal CGs (n = 249) were collected. Patients’ functional status and disease severity were evaluated using the Barthel Index, the revised Amyotrophic Lateral Sclerosis Functional Rating Scale (ALSFRS-R) and the King’s Stages for ALS. The caregivers’ burden was recorded by the Zarit Burden Interview (ZBI). Comorbid anxiety and depression of caregivers were assessed by the Hospital Anxiety and Depression Scale. Additionally, the EuroQol Five Dimension Five Level Scale evaluated their health-related quality of life. The caregivers’ burden was high (mean ZBI = 26/88, 0 = no burden, ≥24 = highly burdened) and correlated with patients’ functional status (rp = −0.555, p < 0.001, n = 242). It was influenced by the CGs’ own mental health issues due to caregiving (+11.36, 95% CI [6.84; 15.87], p < 0.001), patients’ wheelchair dependency (+9.30, 95% CI [5.94; 12.66], p < 0.001) and was interrelated with the CGs’ depression (rp = 0.627, p < 0.001, n = 234), anxiety (rp = 0.550, p < 0.001, n = 234), and poorer physical condition (rp = −0.362, p < 0.001, n = 237). Moreover, female CGs showed symptoms of anxiety more often, which also correlated with the patients’ impairment in daily routine (rs = −0.280, p < 0.001, n = 169). As increasing disease severity, along with decreasing autonomy, was the main predictor of caregiver burden and showed to create relevant (negative) implications on CGs’ lives, patient care and supportive therapies should address this issue. Moreover, in order to preserve the mental and physical health of the CGs, new concepts of care have to focus on both, on not only patients but also their CGs and gender-associated specific issues. As caregiving in ALS also significantly influences the socioeconomic status by restrictions in CGs’ work lives and income, and the main reported needs being lack of psychological support and a high bureaucracy, the situation of CGs needs more attention. Apart from their own multi-disciplinary medical and psychological care, more support in care and patient management issues is required