Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

The connection between the method of comparison equations (generalized WKB method) and the Ermakov-Pinney equation is established. A perturbative scheme of solution of the generalized Ermakov-Pinney equation is developed and is applied to the construction of perturbative series for second-order differential equations with and without turning points.Comment: The collective of the authors is enlarged and the calculations in Sec. 3 are correcte

Ideal Stars and General Relativity

We study a system of differential equations that governs the distribution of matter in the theory of General Relativity. The new element in this paper is the use of a dynamical action principle that includes all the degrees of freedom, matter as well as metric. The matter lagrangian defines a relativistic version of non-viscous, isentropic hydrodynamics. The matter fields are a scalar density and a velocity potential; the conventional, four-vector velocity field is replaced by the gradient of the potential and its scale is fixed by one of the eulerian equations of motion, an innovation that significantly affects the imposition of boundary conditions. If the density is integrable at infinity, then the metric approaches the Schwarzschild metric at large distances. There are stars without boundary and with finite total mass; the metric shows rapid variation in the neighbourhood of the Schwarzschild radius and there is a very small core where a singularity indicates that the gas laws break down. For stars with boundary there emerges a new, critical relation between the radius and the gravitational mass, a consequence of the stronger boundary conditions. Tentative applications are suggested, to certain Red Giants, and to neutron stars, but the investigation reported here was limited to polytropic equations of state. Comparison with the results of Oppenheimer and Volkoff on neutron cores shows a close agreement of numerical results. However, in the model the boundary of the star is fixed uniquely by the required matching of the interior metric to the external Schwarzschild metric, which is not the case in the traditional approach.Comment: 26 pages, 7 figure

Label-free detection of human prostate-specific antigen (hPSA) using film bulk acoustic resonators (FBARs)

Label-free detection of cancer biomarkers using low cost biosensors has promising applications in clinical diagnostics. In this work, ZnO-based thin film bulk acoustic wave resonators (FBARs) with resonant frequency of ∼1.5 GHz and mass sensitivity of 0.015 mg/m2 (1.5 ng/cm2) have been fabricated for their deployment as biosensors. Mouse monoclonal antibody, anti-human prostate-specific antigen (Anti-hPSA) has been used to bind human prostate-specific antigen (hPSA), a model cancer used in this study. Ellipsometry was used to characterize and optimise the antibody adsorption and antigen binding on gold surface. It was found that the best amount of antibody at the gold surface for effective antigen binding is around 1 mg/m2, above or below which resulted in the reduced antigen binding due to either the limited binding sites (below 1 mg/m2) or increased steric effect (above 1 mg/m2). The FBAR data were in good agreement with the data obtained from ellipsometry. Antigen binding experiments using FBAR sensors demonstrated that FBARs have the capability to precisely detect antigen binding, thereby making FBARs an attractive low cost alternative to existing cancer diagnostic sensors.This work was supported by the Engineering and Physical Sciences Research Council [grants EP/F062966/1, EP/F063865/1 and EP/F06294X/1], the Royal Society [grant RG120061] and the National Natural Science Foundation of China (NSFC) [grant 61150110485].This is the accepted manuscript version. The final published version of the article is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0925400513011052

Explainable neural networks for trait-based multispecies distribution modelling—A case study with butterflies and moths

Species response traits mediate environmental effects on species distribution. Traits are used in joint and multispecies distribution models (JSDMs and MSDMs) to enable community-wide shared parameters that characterise niche filtering along environmental gradients. Multispecies machine learning SDMs, however, do not use traits as their inclusion requires an additional taxonomic dimension that is incompatible with their usual tabular inputs. This has confined trait mediation in SDMs to hierarchical Bayesian models. Here we provide a novel artificial neural network (ANN) architecture that solves this dimensionality problem. Our ANN includes species traits (via a time distributed layer) and is therefore able to identify not only species-specific responses to the environment, but also shared responses across the community that are mediated by species traits. Model performance evaluated at the species level not only quantifies the reliability of species predictions, but also their departure from an average response dictated by traits only. We apply our model to two unique long-term spatio-temporal of butterfly and moth datasets collected across the United Kingdom between 1990 and 2019. In addition to species traits, predictors include numerous metrics derived from weather, land-cover and topology data. For butterflies and moths we show convincing model performance for classifying species occupancy. We use SHAP (Shapley Additive exPlanations) to explain the ANN and show how trait-mediated and species-specific responses can be approximated, hence yielding ecological insights on the key drivers of species distribution. We highlight a range of drivers of change that determine occupancy, including wind, temperature as well as habitat type. We demonstrate that a trait-based approach can be encoded as an ANN by using a time distributed layer. This brings ANNs unmatched predictive capabilities to the field of MSDMs, at the same time of lifting their reputed drawback of poor explainability

Solidly Mounted Resonators with Carbon Nanotube Electrodes for Biosensing Applications

The work reported here shows a direct experimental comparison of the sensitivities of AlN solidly mounted resonators (SMR)-based biosensors fabricated with standard metal electrodes and with carbon nanotube electrodes. SMRs resonating at frequencies around 1.75 GHz have been fabricated, some devices using a thin film of multi-wall carbon nanotubes (CNTs) as the top electrode material and some identical devices using a chromium/gold electrode. Protein solutions with different concentrations were loaded on the top of the resonators and their responses to mass-load from physically adsorbed coatings were investigated. Results show that resonators using CNTs as the top electrode material exhibited higher frequency change for a given load due to the higher active surface area of a thin film of interconnecting CNTs compared to that of a metal thin film electrode and hence exhibited greater mass loading sensitivity. It is therefore concluded that the use of CNT electrodes on resonators for their use as gravimetric biosensors is viable and worthwhile

AlN-based BAW resonators with CNT electrodes for gravimetric biosensing

Solidly mounted resonators (SMRs) with a top carbon nanotubes (CNTs) surface coating that doubles as an electrode and as a sensing layer have been fabricated. The influence of the CNTs on the frequency response of the resonators was studied by direct comparison to identical devices with a top metallic electrode. It was found that the CNTs introduced significantly less mass load on the resonators and these devices exhibited a greater quality factor, Q (>2000, compared to ∼1000 for devices with metal electrodes), which increases the gravimetric sensitivity of the devices by allowing the tracking of smaller frequency shifts. Protein solutions with different concentrations were loaded on the top of the resonators and their responses to mass-load from physically adsorbed coatings were investigated. Results show that resonators using CNTs as the top electrode exhibited a higher frequency change for a given load (∼0.25 MHz cm2 ng−1) compared to that of a metal thin film electrode (∼0.14 MHz cm2 ng−1), due to the lower mass of the CNT electrodes and their higher active surface area compared to that of a thin film metal electrode. It is therefore concluded that the use of CNT electrodes on resonators for their use as gravimetric biosensors is a significant improvement over metallic electrodes that are normally employed

Algebraic approach in the study of time-dependent nonlinear integrable systems: Case of the singular oscillator

The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability of this system is established by evaluating the exact invariant closely related to the Lewis and Riesenfeld invariant for the time-dependent harmonic oscillator. We study extensively the special and interesting case of a kicked quadratic potential from which we derive a new integrable, nonlinear, area preserving, two-dimensional map which may, for instance, be used in numerical algorithms that integrate the Calogero-Sutherland-Moser Hamiltonian. The dynamics, both classical and quantal, is studied via the time-evolution operator which we evaluate using a recent method of integrating the quantum Liouville-Bloch equations \cite{rau}. The results show the exact one-to-one correspondence between the classical and the quantal dynamics. Our analysis also sheds light on the connection between properties of the SU(1,1) algebra and that of simple dynamical systems.Comment: 17 pages, 4 figures, Accepted in PR

The reliability and validity of three non-radiological measures of thoracic kyphosis and their relations to the standing radiological Cobb angle

UnlabelledHyperkyphosis is implicated in a mounting list of negative outcomes, including higher mortality. Hyperkyphosis research is hindered due to difficulties inherent in its measurement. By showing that three clinical measures of kyphosis are suitable for use in large scale, longitudinal, hyperkyphosis studies, we will facilitate much needed research in this field.IntroductionThe objective of this study is to describe the reliability of three non-radiological kyphosis measures (Debrunner kyphosis angle, flexicurve kyphosis index, and flexicurve kyphosis angle) and their validity compared to the Cobb angle and to approximate a Cobb angle from non-radiological kyphosis measures.MethodsWe analyzed data from 113 participants aged ≥ 60 years with kyphosis angle ≥ 40°. Cobb angle was measured on a standing lateral thoracolumbar radiograph using bounds at T4 and T12. Non-radiological measures of kyphosis were made three times by a single rater and a 4th time by a blinded second rater.ResultsIntra- and inter-rater reliabilities for non-radiological assessments were high (intra-class correlations of 0.96 to 0.98) and did not differ from each other. Pearson correlations, estimating validity, ranged from 0.62 to 0.69 and did not differ. The Debrunner angle was close to the Cobb angle, with scaling factor of 1.067 and an offset of 5°. The Flexicurve kyphosis angle had to be scaled by 1.53 to obtain the equivalent Cobb angle. The scaling factor for the Flexicurve kyphosis index to Cobb angle was 315, with an offset of 5°. Compared to the measured Cobb angle, Cobb angles predicted using the non-radiological measures had similar magnitude errors (standard deviations of the differences ranging between 10.24 and 11.26).ConclusionsEach non-radiological measurement had similar reliability and validity. Low cost, ease of use, and robustness to variations in spine contour argue for the Flexicurve in longitudinal kyphosis assessments. The approximate conversion factors provided will permit translation of non-radiological measures to Cobb angles

High Viral Diversity and Mixed Infections in Cerebral Spinal Fluid From Cases of Varicella Zoster Virus Encephalitis.

Background Varicella zoster virus (VZV) may cause encephalitis, both with and without rash. Here we investigate whether viruses recovered from the central nervous system (CNS; encephalitis or meningitis) differ genetically from those recovered from non-CNS samples. Methods Enrichment-based deep sequencing of 45 VZV genomes from cerebral spinal fluid (CSF), plasma, bronchoalveolar lavage (BAL), and vesicles was carried out with samples collected from 34 patients with and without VZV infection of the CNS. Results Viral sequences from multiple sites in the same patient were identical at the consensus level. Virus from vesicle fluid and CSF in cases of meningitis showed low-level diversity. By contrast, plasma, BAL, and encephalitis had higher numbers of variant alleles. Two CSF-encephalitis samples had high genetic diversity, with variant frequency patterns typical of mixed infections with different clades. Conclusions Low viral genetic diversity in vesicle fluid is compatible with previous observations that VZV skin lesions arise from single or low numbers of virions. A similar result was observed in VZV from cases of VZV meningitis, a generally self-limiting infection. CSF from cases of encephalitis had higher diversity with evidence for mixed clade infections in 2 cases. We hypothesize that reactivation from multiple neurons may contribute to the pathogenesis of VZV encephalitis

Early Observations And Analysis Of The Type Ia SN 2014J In M82

We present optical and near infrared (NIR) observations of the nearby Type Ia SN 2014J. Seventeen optical and 23 NIR spectra were obtained from 10 days before (-10d) to 10 days after (+10d) the time of maximum B-band brightness. The relative strengths of absorption features and their patterns of development can be compared at one day intervals throughout most of this period. Carbon is not detected in the optical spectra, but we identify C I lambda 1.0693 in the NIR spectra. Mg II lines with high oscillator strengths have higher initial velocities than other Mg II lines. We show that the velocity differences can be explained by differences in optical depths due to oscillator strengths. The spectra of SN 2014J show that it is a normal SN Ia, but many parameters are near the boundaries between normal and high-velocity subclasses. The velocities for OI, Mg II, Si II, S Ca a, and Fell suggest that SN 2014J has a layered structure with little or no mixing. That result is consistent with the delayed detonation explosion models. We also report photometric observations, obtained from -10d to +29d, in the UBVRIJH and K-s bands. The template fitting package SNooPy is used to interpret the light curves and to derive photometric parameters. Using R-v = 1.46, which is consistent with previous studies, SNooPy finds that A(v) = 1.80 for E(B - V)(host) = 1.23 +/- 0.06 mag. The maximum B-band brightness of -19.19 +/- 0.10 mag was reached on February 1.74 UT +/- 0.13 days and the supernova has a decline parameter, Delta m(15), of 1.12 +/- 0.02 mag.Department of Space, Government of IndiaHungarian OTKA NN-107637NSF AST-1109801, AST-1151462, AST-1211196NSF Astronomy and Astrophysics Postdoctoral Fellowship AST-1302771NASA through a grant from the Space Telescope Science Institute GO-12540NASA NAS5-26555Swedish Research CouncilSwedish National Space BoardDanish Agency for Science and Technology and Innovation realized through a Sapere Aude Level 2 grantAstronom