The a-number of hyperelliptic curves

It is known that for a smooth hyperelliptic curve to have a large $a$-number, the genus must be small relative to the characteristic of the field, $p>0$, over which the curve is defined. It was proven by Elkin that for a genus $g$ hyperelliptic curve $C$ to have $a_C=g-1$, the genus is bounded by $g<\frac{3p}{2}$. In this paper, we show that this bound can be lowered to $g <p$. The method of proof is to force the Cartier-Manin matrix to have rank one and examine what restrictions that places on the affine equation defining the hyperelliptic curve. We then use this bound to summarize what is known about the existence of such curves when $p=3,5$ and $7$.Comment: 7 pages. v2: revised and improved the proof of the main theorem based on suggestions from the referee. To appear in the proceedings volume of Women in Numbers Europe-

Next-generation sequencing of prostate cancer: genomic and pathway alterations, potential actionability patterns, and relative rate of use of clinical-grade testing.

Despite being one of the most common cancers, treatment options for prostate cancer are limited. Novel approaches for advanced disease are needed. We evaluated the relative rate of use of clinical-grade next generation sequencing (NGS) in prostate cancer, as well as genomic alterations identified and their potential actionability. Of 4864 patients from multiple institutions for whom NGS was ordered by physicians, only 67 (1.4%) had prostate cancer, representing 1/10 the ordering rate for lung cancer. Prostate cancers harbored 148 unique alterations affecting 63 distinct genes. No two patients had an identical molecular portfolio. The median number of characterized genomic alterations per patient was 3 (range, 1 to 9). Fifty-six of 67 patients (84%) had ≥ 1 potentially actionable alteration. TMPRSS2 fusions affected 28.4% of patients. Genomic aberrations were most frequently detected in TP53 (55.2% of patients), PTEN (29.9%), MYC (17.9%), PIK3CA (13.4%), APC (9.0%), BRCA2 (9.0%), CCND1 (9.0%), and RB1 genes (9.0%). The PI3K (52.2% of patients), WNT (13.5%), DNA repair (17.9%), cell cycle (19.4%), and MAPK (14.9%) machinery were commonly impacted. A minority of patients harbored BRAF, NTRK, ERBB2, or mismatch repair gene abnormalities, which are highly druggable in some cancers. Only ~ 10% of prostate cancer trials (clinicaltrials.gov, year 2017) applied a (non-hormone) biomarker before intervention. In conclusion, though use of clinical-grade NGS is relatively low and only a minority of trials deploy DNA-based biomarkers, many prostate cancer-associated molecular alterations may be pharmacologically tractable with genomcially targeted therapy or, in the case of mismatch repair anomalies, with checkpoint inhibitor immunotherapy

Genomic landscape of salivary gland tumors.

Effective treatment options for advanced salivary gland tumors are lacking. To better understand these tumors, we report their genomic landscape. We studied the molecular aberrations in 117 patients with salivary gland tumors that were, on physician request, tested in a Clinical Laboratory Improvement Amendments (CLIA) laboratory (Foundation Medicine, Cambridge, MA) using next-generation sequencing (182 or 236 genes), and analyzed by N-of-One, Inc. (Lexington, MA). There were 354 total aberrations, with 240 distinct aberrations identified in this patient population. Only 10 individuals (8.5%) had a molecular portfolio that was identical to any other patient (with four different portfolios amongst the ten patients). The most common abnormalities involved the TP53 gene (36/117 [30.8% of patients]), cyclin pathway (CCND1, CDK4/6 or CDKN2A/B) (31/117 [26.5%]) and PI3K pathway (PIK3CA, PIK3R1, PTEN or AKT1/3) (28/117 [23.9%]). In multivariate analysis, statistically significant co-existing aberrations were observed as follows: TP53 and ERBB2 (p = 0.01), cyclin pathway and MDM2 (p = 0.03), and PI3K pathway and HRAS (p = 0.0001). We were able to identify possible cognate targeted therapies in most of the patients (107/117 [91.5%]), including FDA-approved drugs in 80/117 [68.4%]. In conclusion, salivary gland tumors were characterized by multiple distinct aberrations that mostly differed from patient to patient. Significant associations between aberrations in TP53 and ERBB2, the cyclin pathway and MDM2, and HRAS and the PI3K pathway were identified. Most patients had actionable alterations. These results provide a framework for tailored combinations of matched therapies

Transverse Optical Mode Patterns for an RF Excited Ar-He-Xe Laser

Transverse optical modes for an RF excited Ar-He-Xe laser are studied both experimentally and theoretically. A diffraction model for a waveguide with a nonsaturable gain and refractive index gradients placed between two plane mirrors is formulated. The effects of gain and diffraction index gradients and of diffraction in free space are evaluated for typical experimental conditions. A direct comparison between theoretical mode patterns and experimentally measured ones at distances of 17 and 114 cm from the output mirror demonstrated a satisfactory agreement for various laser wavelengths and gas mixture composition

Asymptotic analysis and analytical solutions of a model of cardiac excitation.

The original publication is available at www.springerlink.com - http://link.springer.com/article/10.1007/s11538-007-9267-0Journal ArticleCopyright © SpringerWe describe an asymptotic approach to gated ionic models of single-cell cardiac excitability. It has a form essentially different from the Tikhonov fast-slow form assumed in standard asymptotic reductions of excitable systems. This is of interest since the standard approaches have been previously found inadequate to describe phenomena such as the dissipation of cardiac wave fronts and the shape of action potential at repolarization. The proposed asymptotic description overcomes these deficiencies by allowing, among other non-Tikhonov features, that a dynamical variable may change its character from fast to slow within a single solution. The general asymptotic approach is best demonstrated on an example which should be both simple and generic. The classical model of Purkinje fibers (Noble in J. Physiol. 160:317-352, 1962) has the simplest functional form of all cardiac models but according to the current understanding it assigns a physiologically incorrect role to the Na current. This leads us to suggest an "Archetypal Model" with the simplicity of the Noble model but with a structure more typical to contemporary cardiac models. We demonstrate that the Archetypal Model admits a complete asymptotic solution in quadratures. To validate our asymptotic approach, we proceed to consider an exactly solvable "caricature" of the Archetypal Model and demonstrate that the asymptotic of its exact solution coincides with the solutions obtained by substituting the "caricature" right-hand sides into the asymptotic solution of the generic Archetypal Model. This is necessary, because, unlike in standard asymptotic descriptions, no general results exist which can guarantee the proximity of the non-Tikhonov asymptotic solutions to the solutions of the corresponding detailed ionic model

Validity of the diagnosis of pneumonia in hospitalised patients with COPD.

Rationale: Exacerbations of chronic obstructive pulmonary disease (COPD) and pneumonia are two of the most common reasons for acute hospital admissions. Acute exacerbations and pneumonia present with similar symptoms in COPD patients, representing a diagnostic challenge with a significant impact on patient outcomes. The objectives of this study were to compare the prevalence of radiographic consolidation with the discharge diagnoses of hospitalised COPD patients. Methods: COPD patients admitted to three UK hospitals over a 3-year period were identified. Participants were included if they were admitted with an acute respiratory illness, COPD was confirmed by spirometry and a chest radiograph was performed within 24 h of admission. Pneumonia was defined as consolidation on chest radiograph reviewed by two independent observers. Results: There were 941 admissions in 621 patients included in the final analysis. In 235 admissions, consolidation was present on chest radiography and there were 706 admissions without consolidation. Of the 235 admissions with consolidation, only 42.9% had a discharge diagnosis of pneumonia; 90.7% of patients without consolidation had a discharge diagnosis of COPD exacerbation. The presence of consolidation was associated with increased rate of high-dependency care admission, increased mortality and prolonged length of stay. Inhaled corticosteroid use was associated with recurrent pneumonia. Conclusions: Pneumonia is underdiagnosed in patients with COPD. Radiographic consolidation is associated with worse outcomes and prolonged length of stay. Incorrect diagnosis could result in inappropriate use of inhaled corticosteroids. Future guidelines should specifically address the diagnosis and management of pneumonia in COPD

Evaluation of a possible association between estradiol and progesterone levels and ectopic pregnancy in low risk women undergoing IVF/ICSI

Introduction: Several independent risk factors of Ectopic Pregnancy (EP) have been described to date. Nevertheless, estradiol and progesterone have not been related to ectopic pregnancy, although there is biological rationale to think about them as possible candidates. Our aim was to correlate the incidence of EP with levels of estradiol (E2) and progesterone (P4), measured on two days (hCG day, and seven days later (hCG+7)), including the differences and ratios of these concentrations, between the two time-points. Material and methods: Retrospective cohort study of 578 patients undergoing fresh embryo transfer after IVF (100 cycles), ICSI (508 cycles) and IVF/ICSI (64 cycles) without risk of EP, between January 2005 and December 2015. We evaluated EP incidence (10 ectopic pregnancies) in fresh embryo transfers according to estradiol and progesterone levels on hCG day (hCGd) and seven days later (hCG+7) and their variation between both. The proportions were compared using the chi-square test or Fisher's exact test and the means were compared using T-test or ANOVA. To determine the accuracy of each studied variable receiver-operating curves were built. Results: We identified a trend towards an increased risk of EP as progesterone levels rose on hCGd (p=0.020) and an association of progesterone values >1.89ng/ml on hCGd with EP (OR 6.8). An increased risk of EP when the difference of estradiol between hCGd and hCG+7 was either 745pg/mL (p=0.001) was also found. ROC analysis only resulted significant for a moderate/good predictive ability for progesterone values on hCGd (AUC: 0.694). Discussion: We conclude that these measurements are sufficient to identify patients at a high risk of EP. These hormone levels on specific days, leading us to define proper strategies to prevent EP risks in IVF. Further studies should design to prove this hypothesis