On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators

This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail, and illustrate its effectiveness by several examples.Comment: 17 pages, 2 tables and 2 figure

Long-term, treatment-free survival in select patients with distant metastatic papillary thyroid cancer

Well-differentiated thyroid carcinoma (WDTC) generally has a favorable prognosis. However, patients with distant metastatic disease experience progression of disease with a higher mortality. A subset of patients not previously described may challenge the conventional dogma regarding the progressive nature of all metastatic WDTC. Through analysis of our database, we identified patients with distant metastatic WDTC and persistent, minimally progressive disease. In all patients, persistent metastatic disease was confirmed via tissue biopsy, abnormal PET scan, and/or biochemical elevations in thyroglobulin or antibody levels. Progression of disease was monitored clinically and with repeat imaging. We describe five patients with WDTC and pulmonary metastases, aged 8–43 years at diagnosis. All patients underwent initial surgery and radioactive iodine (RAI) ablation, with some receiving multiple treatments. Persistent pulmonary metastatic disease was confirmed over decades (mean 22 years, range 8–42 years) with minimal progression despite no further treatment beyond thyroid hormone suppression. Persistent disease was biopsy-proven in all patients at a mean of 9.6 years from last RAI treatment. All patients had elevated thyroglobulin or anti-thyroglobulin antibody levels, while three demonstrated metabolically active disease with positive FDG uptake on PET scan, and one patient with persistent radioactive iodine avid pulmonary metastasis 36 years after her last RAI treatment. This case series demonstrates that some patients with distant metastases, even if metabolically active and radioactive iodine resistant, remain stable for decades without further treatment. Clinical awareness of such patients and continual reassessment of disease risk following initial therapy are crucial as aggressive treatment may not be necessary

Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case

We consider a possibly degenerate porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analytical properties of the solution

Miniature exoplanet radial velocity array I: design, commissioning, and early photometric results

The MINiature Exoplanet Radial Velocity Array (MINERVA) is a US-based observational facility dedicated to the discovery and characterization of exoplanets around a nearby sample of bright stars. MINERVA employs a robotic array of four 0.7 m telescopes outfitted for both high-resolution spec- troscopy and photometry, and is designed for completely autonomous operation. The primary science program is a dedicated radial velocity survey and the secondary science objective is to obtain high precision transit light curves. The modular design of the facility and the flexibility of our hardware allows for both science programs to be pursued simultaneously, while the robotic control software provides a robust and efficient means to carry out nightly observations. In this article, we describe the design of MINERVA including major hardware components, software, and science goals. The telescopes and photometry cameras are characterized at our test facility on the Caltech campus in Pasadena, CA, and their on-sky performance is validated. New observations from our test facility demonstrate sub-mmag photometric precision of one of our radial velocity survey targets, and we present new transit observations and fits of WASP-52b—a known hot-Jupiter with an inflated radius and misaligned orbit. The process of relocating the MINERVA hardware to its final destination at the Fred Lawrence Whipple Observatory in southern Arizona has begun, and science operations are expected to commence within 2015

First radial velocity results from the MINiature Exoplanet Radial Velocity Array (MINERVA)

The MINiature Exoplanet Radial Velocity Array (MINERVA) is a dedicated observatory of four 0.7m robotic telescopes fiber-fed to a KiwiSpec spectrograph. The MINERVA mission is to discover super-Earths in the habitable zones of nearby stars. This can be accomplished with MINERVA's unique combination of high precision and high cadence over long time periods. In this work, we detail changes to the MINERVA facility that have occurred since our previous paper. We then describe MINERVA's robotic control software, the process by which we perform 1D spectral extraction, and our forward modeling Doppler pipeline. In the process of improving our forward modeling procedure, we found that our spectrograph's intrinsic instrumental profile is stable for at least nine months. Because of that, we characterized our instrumental profile with a time-independent, cubic spline function based on the profile in the cross dispersion direction, with which we achieved a radial velocity precision similar to using a conventional "sum-of-Gaussians" instrumental profile: 1.8 m s$^{-1}$ over 1.5 months on the RV standard star HD 122064. Therefore, we conclude that the instrumental profile need not be perfectly accurate as long as it is stable. In addition, we observed 51 Peg and our results are consistent with the literature, confirming our spectrograph and Doppler pipeline are producing accurate and precise radial velocities.Comment: 22 pages, 9 figures, submitted to PASP, Peer-Reviewed and Accepte

Reduced Transmissibility of East African Indian Strains of Mycobacterium tuberculosis

BACKGROUND: Mycobacterium tuberculosis (MTB) has been classified into 4 main lineages. Some reports have associated certain lineages with particular clinical phenotypes, but there is still insufficient information regarding the clinical and epidemiologic implications of MTB lineage variation. METHODS: Using large sequence polymorphisms we classified MTB isolates from a population-based study in Montreal, Canada into the 4 major lineages, and identified the associated clinical and epidemiologic features. In addition, IS6110-RFLP and spoligotyping were used as indicators of recent TB transmission. The study population was divided into a derivation cohort, diagnosed between 2001 and 2007, and a separate validation cohort, diagnosed between 1996 and 2000. RESULTS: In the derivation cohort, when compared to the other MTB lineages, the East African-Indian (EAI) lineage was associated with lower rates of TB transmission, as measured by: positive TST among close contacts of pulmonary TB cases (adjusted odds ratio 0.6: [95% confidence interval 0.4-0.9]), and clustered TB cases (0.3: [<0.001-0.6]). Severe forms of TB were also less likely among the EAI group (0.4: [<0.001-0.8]). There were no significant differences when comparing patients with the other MTB lineages. In the validation cohort, the EAI lineage was associated with lower rates of positive TST among contacts (0.5: [0.3-0.9]) and a trend towards less clustered TB cases (0.5: [0.1-1.8]) when compared to the other lineages. Disease severity among the different groups was not significantly different in the validation cohort. CONCLUSIONS: We conclude that in Montreal, EAI strains were associated with reduced transmission compared to other MTB lineages

Sensitization in transplantation: Assessment of risk (STAR) 2019 Working Group Meeting Report.

The purpose of the STAR 2019 Working Group was to build on findings from the initial STAR report to further clarify the expectations, limitations, perceptions, and utility of alloimmune assays that are currently in use or in development for risk assessment in the setting of organ transplantation. The goal was to determine the precision and clinical feasibility/utility of such assays in evaluating both memory and primary alloimmune risks. The process included a critical review of biologically driven, state-of-the-art, clinical diagnostics literature by experts in the field and an open public forum in a face-to-face meeting to promote broader engagement of the American Society of Transplantation and American Society of Histocompatibility and Immunogenetics membership. This report summarizes the literature review and the workshop discussions. Specifically, it highlights (1) available assays to evaluate the attributes of HLA antibodies and their utility both as clinical diagnostics and as research tools to evaluate the effector mechanisms driving rejection; (2) potential assays to assess the presence of alloimmune T and B cell memory; and (3) progress in the development of HLA molecular mismatch computational scores as a potential prognostic biomarker for primary alloimmunity and its application in research trial design