Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page

Resonances Width in Crossed Electric and Magnetic Fields

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.Comment: 3 figure

Sums of magnetic eigenvalues are maximal on rotationally symmetric domains

The sum of the first n energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area)^3 on the domain. The result holds for both Dirichlet and Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary conditions too. The square similarly maximizes the eigenvalue sum among parallelograms, and the disk maximizes among ellipses. More generally, a domain with rotational symmetry will maximize the magnetic eigenvalue sum among all linear images of that domain. These results are new even for the ground state energy (n=1).Comment: 19 pages, 1 figur

Production of highly-polarized positrons using polarized electrons at MeV energies

The Polarized Electrons for Polarized Positrons experiment at the injector of the Continuous Electron Beam Accelerator Facility has demonstrated for the first time the efficient transfer of polarization from electrons to positrons produced by the polarized bremsstrahlung radiation induced by a polarized electron beam in a high-$Z$ target. Positron polarization up to 82\% have been measured for an initial electron beam momentum of 8.19~MeV/$c$, limited only by the electron beam polarization. This technique extends polarized positron capabilities from GeV to MeV electron beams, and opens access to polarized positron beam physics to a wide community.Comment: 5 pages, 4 figure

Field demonstration of simultaneous wind and temperaturemeasurements from 5to50 km with a Na double-edge magneto-optic filter in a multi-frequency Doppler lidar

We report the first (to our knowledge) field demonstration of simultaneous wind and temperature measurements with a Na double-edge magneto-optic filter implemented in the receiver of a three-frequency Na Doppler lidar. Reliable winds and temperatures were obtained in the altitude range of 10-45 km with 1 km resolution and 60 min integration under the conditions of 0.4 W lidar power and 75 cm telescope aperture. This edge filter with a multi-frequency lidar concept can be applied to other direct-detection Doppler lidars for profiling both wind and temperature simultaneously from the lower to the upper atmosphere

Combining estimates of interest in prognostic modelling studies after multiple imputation: current practice and guidelines

Background: Multiple imputation (MI) provides an effective approach to handle missing covariate data within prognostic modelling studies, as it can properly account for the missing data uncertainty. The multiply imputed datasets are each analysed using standard prognostic modelling techniques to obtain the estimates of interest. The estimates from each imputed dataset are then combined into one overall estimate and variance, incorporating both the within and between imputation variability. Rubin's rules for combining these multiply imputed estimates are based on asymptotic theory. The resulting combined estimates may be more accurate if the posterior distribution of the population parameter of interest is better approximated by the normal distribution. However, the normality assumption may not be appropriate for all the parameters of interest when analysing prognostic modelling studies, such as predicted survival probabilities and model performance measures. Methods: Guidelines for combining the estimates of interest when analysing prognostic modelling studies are provided. A literature review is performed to identify current practice for combining such estimates in prognostic modelling studies. Results: Methods for combining all reported estimates after MI were not well reported in the current literature. Rubin's rules without applying any transformations were the standard approach used, when any method was stated. Conclusion: The proposed simple guidelines for combining estimates after MI may lead to a wider and more appropriate use of MI in future prognostic modelling studies

The melanoma-specific graded prognostic assessment does not adequately discriminate prognosis in a modern population with brain metastases from malignant melanoma

The melanoma-specific graded prognostic assessment (msGPA) assigns patients with brain metastases from malignant melanoma to 1 of 4 prognostic groups. It was largely derived using clinical data from patients treated in the era that preceded the development of newer therapies such as BRAF, MEK and immune checkpoint inhibitors. Therefore, its current relevance to patients diagnosed with brain metastases from malignant melanoma is unclear. This study is an external validation of the msGPA in two temporally distinct British populations.Performance of the msGPA was assessed in Cohort I (1997-2008, n=231) and Cohort II (2008-2013, n=162) using Kaplan-Meier methods and Harrell's c-index of concordance. Cox regression was used to explore additional factors that may have prognostic relevance.The msGPA does not perform well as a prognostic score outside of the derivation cohort, with suboptimal statistical calibration and discrimination, particularly in those patients with an intermediate prognosis. Extra-cerebral metastases, leptomeningeal disease, age and potential use of novel targeted agents after brain metastases are diagnosed, should be incorporated into future prognostic models.An improved prognostic score is required to underpin high-quality randomised controlled trials in an area with a wide disparity in clinical care

PT-symetrically regularized Eckart,Poeschl-Teller and Hulthen potentials

Version 1: The well known Eckart's singular s-wave potential is PT-symmetrically regularized and continued to the whole real line. The new model remains exactly solvable and its bound states remain proportional to Jacobi polynomials. Its real and discrete spectrum exhibits several unusual features. Version 2: Parity times time-reversal symmetry of complex Hamiltonians with real spectra is usually interpreted as a weaker mathematical substitute for Hermiticity. Perhaps an equally important role is played by the related strengthened analyticity assumptions. In a constructive illustration we complexify a few potentials solvable only in s-wave. Then we continue their domain from semi-axis to the whole axis and get the new exactly solvable models. Their energies come out real as expected. The new one-dimensional spectra themselves differ quite significantly from their s-wave predecessors.Comment: Original 10-page letter ``PT-symmetrized exact solution of the singular Eckart oscillator" is extended to a full pape

Using ordinal logistic regression to evaluate the performance of laser-Doppler predictions of burn-healing time

Background Laser-Doppler imaging (LDI) of cutaneous blood flow is beginning to be used by burn surgeons to predict the healing time of burn wounds; predicted healing time is used to determine wound treatment as either dressings or surgery. In this paper, we do a statistical analysis of the performance of the technique. Methods We used data from a study carried out by five burn centers: LDI was done once between days 2 to 5 post burn, and healing was assessed at both 14 days and 21 days post burn. Random-effects ordinal logistic regression and other models such as the continuation ratio model were used to model healing-time as a function of the LDI data, and of demographic and wound history variables. Statistical methods were also used to study the false-color palette, which enables the laser-Doppler imager to be used by clinicians as a decision-support tool. Results Overall performance is that diagnoses are over 90% correct. Related questions addressed were what was the best blood flow summary statistic and whether, given the blood flow measurements, demographic and observational variables had any additional predictive power (age, sex, race, % total body surface area burned (%TBSA), site and cause of burn, day of LDI scan, burn center). It was found that mean laser-Doppler flux over a wound area was the best statistic, and that, given the same mean flux, women recover slightly more slowly than men. Further, the likely degradation in predictive performance on moving to a patient group with larger %TBSA than those in the data sample was studied, and shown to be small. Conclusion Modeling healing time is a complex statistical problem, with random effects due to multiple burn areas per individual, and censoring caused by patients missing hospital visits and undergoing surgery. This analysis applies state-of-the art statistical methods such as the bootstrap and permutation tests to a medical problem of topical interest. New medical findings are that age and %TBSA are not important predictors of healing time when the LDI results are known, whereas gender does influence recovery time, even when blood flow is controlled for. The conclusion regarding the palette is that an optimum three-color palette can be chosen 'automatically', but the optimum choice of a 5-color palette cannot be made solely by optimizing the percentage of correct diagnoses

Mitigation of Moral Hazard and Adverse Selection in Venture Capital Financing: The Influence of the Country’s Institutional Setting

A venture capitalist (VC) needs to trade off benefits and costs when attempting to mitigate agency problems in their investor-investee relationship. We argue that signals of ventures complement the VC’s capacity to screen and conduct a due diligence during the pre-investment phase, but its attractiveness may diminish in institutional settings supporting greater transparency. Similarly, whereas a VC may opt for contractual covenants to curb potential opportunism by ventures in the post-investment phase, this may only be effective in settings supportive of shareholder rights enforcement. Using an international sample of VC contracts, our study finds broad support for these conjectures. It delineates theoretical and practical implications for how investors can best deploy their capital in different institutional settings whilst nurturing their relationships with entrepreneurs