Study of perturbed periodic systems of differential equations - The Stroboscopic method

Stroboscopic method for solving perturbed periodic systems of differential equation

Quantum Computing and Hidden Variables I: Mapping Unitary to Stochastic Matrices

This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a stochastic matrix that maps the initial probability distribution to the final one in some fixed basis. We list seven axioms that we might want such a theory to satisfy, and then investigate which of the axioms can be satisfied simultaneously. Toward this end, we construct a new hidden-variable theory that is both robust to small perturbations and indifferent to the identity operation, by exploiting an unexpected connection between unitary matrices and network flows. We also analyze previous hidden-variable theories of Dieks and Schrodinger in terms of our axioms. In a companion paper, we will show that actually sampling the history of a hidden variable under reasonable axioms is at least as hard as solving the Graph Isomorphism problem; and indeed is probably intractable even for quantum computers.Comment: 19 pages, 1 figure. Together with a companion paper to appear, subsumes the earlier paper "Quantum Computing and Dynamical Quantum Models" (quant-ph/0205059

Fasting plasma glucose and risk factor assessment: Comparing sensitivity and specificity in identifying gestational diabetes in urban black African women

Background. Identifying women with gestational diabetes mellitus (GDM) allows interventions to improve perinatal outcomes. A fasting plasma glucose (FPG) level ≥5.1 mmol/L is 100% specific for a diagnosis of GDM. The International Association of Diabetes and Pregnancy Study Groups acknowledges that FPG <4.5 mmol/L is associated with a low probability of GDM.Objectives. The validity of selective screening based on the presence of risk factors was compared with the universal application of FPG ≥4.5 mmol/L to identify women with GDM. FPG ≥4.5 mmol/L or the presence of one or more risk factors was assumed to indicate an intermediate to high risk of GDM and therefore the need for an oral glucose tolerance test (OGTT).Methods. Consecutive black South African (SA) women were recruited to a 2-hour 75 g OGTT at 24 - 28 weeks’ gestation in an urban community health clinic. Of 969 women recruited, 666 underwent an OGTT, and of these 589 were eligible for analysis. The glucose oxidase laboratory method was used to measure plasma glucose concentrations. The World Health Organization GDM diagnostic criteria were applied. All participants underwent a risk factor assessment. The χ2 test was used to determine associations between risk factors and a positive diagnosis of GDM. The sensitivity and specificity of a positive diagnosis of GDM were calculated for FPG ≥4.5 mmol/L, FPG ≥5.1 mmol/L, and the presence of one or more risk factors.Results. The prevalence of overt diabetes mellitus and GDM was 0.5% and 7.0%, respectively. Risk factor-based selective screening indicated that 204/589 (34.6%) of participants needed an OGTT, but 18/41 (43.9%) of positive GDM diagnoses were missed. Universal screening using the FPG threshold of ≥4.5 mmol/L indicated that 152/589 (25.8%) of participants needed an OGTT, and 1/41 (2.4%) of positive diagnoses were missed. An FPG of ≥5.1 mmol/L identified 36/41 (87.8%) of GDM-positive participants. The sensitivity and specificity of the presence of one or more risk factors were 56% and 67%, respectively. The sensitivity and specificity of FPG ≥4.5 mmol/L were 98% and 80%, respectively.Conclusions. Universal screening using FPG ≥4.5 mmol/L had greater sensitivity and specificity in identifying GDM-affected women and required fewer women to undergo a resource-intensive diagnostic OGTT than risk factor-based selective screening. A universal screening strategy using FPG ≥4.5 mmol/L may be more efficient and cost-effective than risk factor-based selective screening for GDM in black SA women.

Invariants of solvable rigid Lie algebras up to dimension 8

The invariants of all complex solvable rigid Lie algebras up to dimension eight are computed. Moreover we show, for rank one solvable algebras, some criteria to deduce to non-existence of non-trivial invariants or the existence of fundamental sets of invariants formed by rational functions of the Casimir invariants of the associated nilradical.Comment: 16 pages, 7 table

Rabbit and Human Non-Keratinising Stratified Squamous Oesophageal Epithelium Displays Similar Microridge Structure by Scanning Electron Microscopy

Since the oesophageal epithelium of common laboratory animals, rats and mice, is keratinized it is unsuitable for comparison with typical non-keratinized stratified squamous human epithelium. It is thus important to find a suitable animal model for the study of human oesophageal tissue changes. This study investigated the microridge structure of immature and adult rabbit specimens, and adult human biopsies by scanning electron microscopy and morphometry. The investigation revealed a similarity between typical squamous human and adult rabbit oesophageal mucosal epithelium. While human epithelium specimens subdivided into two other groups (non-typical squamous and non-squamous); all typical squamous human biopsies were from patients who had normal endoscopy reports and no reflux symptoms. The surface cells of typical squamous human epithelium displayed complex microridge patterns (64% of cell surface) but patterns in non-typical squamous specimens were more variable (38%) (P \u3c 0.001) and cell boundaries less obvious. Rabbit squames displayed clear microridge patterns with an elevation in the percentage of cell surface covered by microridges, with increasing age, from immature to adult specimens (P \u3c 0.001). There was no statistically significant differences between adult rabbit, and \u27typical squamous\u27 human biopsies (range 51-65%), results which suggest potential use of a rabbit model to study changes in human oesophageal tissue

Entanglement in a quantum annealing processor

Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have built a series of scalable QA processors consisting of networks of manufactured interacting spins (qubits). Here, we use qubit tunneling spectroscopy to measure the energy eigenspectrum of two- and eight-qubit systems within one such processor, demonstrating quantum coherence in these systems. We present experimental evidence that, during a critical portion of QA, the qubits become entangled and that entanglement persists even as these systems reach equilibrium with a thermal environment. Our results provide an encouraging sign that QA is a viable technology for large-scale quantum computing.Comment: 13 pages, 8 figures, contact corresponding author for Supplementary Informatio

Extensive dissolution of live pteropods in the Southern Ocean

The carbonate chemistry of the surface ocean is rapidly changing with ocean acidification, a result of human activities. In the upper layers of the Southern Ocean, aragonite—a metastable form of calcium carbonate with rapid dissolution kinetics—may become undersaturated by 2050 (ref. 2). Aragonite undersaturation is likely to affect aragonite-shelled organisms, which can dominate surface water communities in polar regions. Here we present analyses of specimens of the pteropod Limacina helicina antarctica that were extracted live from the Southern Ocean early in 2008. We sampled from the top 200m of the water column, where aragonite saturation levels were around 1, as upwelled deep water is mixed with surface water containing anthropogenic CO2. Comparing the shell structure with samples from aragonite-supersaturated regions elsewhere under a scanning electron microscope, we found severe levels of shell dissolution in the undersaturated region alone. According to laboratory incubations of intact samples with a range of aragonite saturation levels, eight days of incubation in aragonite saturation levels of 0.94– 1.12 produces equivalent levels of dissolution. As deep-water upwelling and CO2 absorption by surface waters is likely to increase as a result of human activities2,4, we conclude that upper ocean regions where aragonite-shelled organisms are affected by dissolution are likely to expand

PKS2250-41: a case study for triggering

We present the results of a multiwavelength study of the z = 0.31 radio source PKS2250-41. Integral field unit and long-slit spectroscopy obtained using VIMOS and FORS1 on the VLT, and archival HST optical imaging observations are used to study the morphology, kinematics and ionisation state of the extended emission line region (EELR) surrounding this source, and also a companion galaxy at a similar redshift. Near-infrared imaging observations obtained using the NTT are used to analyse the underlying galaxy morphologies. The EELR displays a complex variety of different gas kinematics and ionization states, consistent with a mixture of radio source shocks and AGN photoionization. The radio galaxy is likely to lie within a group environment, and is plausibly undergoing interactions with one or more other objects. The disk-like galaxy to the northeast of the radio source lies at a similar redshift to the radio galaxy itself, and has its major axis position angle aligned with the filamentary continuum and line emission extending outwards from the radio galaxy. This filamentary structure is most plausibly interpreted as a tidal structure associated with an interaction involving the radio source host galaxy and the aligned companion galaxy to the north-east; this encounter may have potentially triggered the current epoch of radio source activity. Overall, PKS2250-41 displays some of the best evidence that radio source activity can be triggered in this manner. [abridged]Comment: 16 pages, 13 figures (some colour). Accepted for publication in MNRAS. Abstract abridge