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Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields
The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $\\mathbb F_p(t)$, when $p$ is prime and $r\\ge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $\\mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $\\mathbb F_q(t^1/d)$.
eBook
ON A NONCRITICAL SYMMETRIC SQUARE -VALUE OF THE CONGRUENT NUMBER ELLIPTIC CURVES
The congruent number elliptic curves are defined by$E_{d}:y^{2}=x^{3}-d^{2}x$, where$d\\in \\mathbb{N}$. We give a simple proof of a formula for$L(\\operatorname{Sym}^{2}(E_{d}),3)$in terms of the determinant of the elliptic trilogarithm evaluated at some degree zero divisors supported on the torsion points on$E_{d}(\\overline{\\mathbb{Q}})$.
Journal Article
Acclimation and adaptation components of the temperature dependence of plant photosynthesis at the global scale
The temperature response of photosynthesis is one of the key factors determining predicted responses to warming in global vegetation models (GVMs). The response may vary geographically, owing to genetic adaptation to climate, and temporally, as a result of acclimation to changes in ambient temperature. Our goal was to develop a robust quantitative global model representing acclimation and adaptation of photosynthetic temperature responses. We quantified and modelled key mechanisms responsible for photosynthetic temperature acclimation and adaptation using a global dataset of photosynthetic CO2 response curves, including data from 141 C3 species from tropical rainforest to Arctic tundra. We separated temperature acclimation and adaptation processes by considering seasonal and common‐garden datasets, respectively. The observed global variation in the temperature optimum of photosynthesis was primarily explained by biochemical limitations to photosynthesis, rather than stomatal conductance or respiration. We found acclimation to growth temperature to be a stronger driver of this variation than adaptation to temperature at climate of origin. We developed a summary model to represent photosynthetic temperature responses and showed that it predicted the observed global variation in optimal temperatures with high accuracy. This novel algorithm should enable improved prediction of the function of global ecosystems in a warming climate.
Journal Article
Inflectionary Invariants for Isolated Complete Intersection Curve Singularities
We investigate the role played by curve singularity germs in the enumeration of inflection points in families of curves acquiring
singular members. Let
eBook
Higher genus curves in mathematical physics and arithmetic geometry : AMS Special Session Higher Genus Curves and Fibrations in Mathematical Physics and Arithmetic Geometry, January 8, 2016, Seattle, Washington
This volume contains the proceedings of the AMS Special Session on Higher Genus Curves and Fibrations in Mathematical Physics and Arithmetic Geometry, held on January 8, 2016, in Seattle, Washington.Algebraic curves and their fibrations have played a major role in both mathematical physics and arithmetic geometry. This volume focuses on the role of higher genus curves; in particular, hyperelliptic and superelliptic curves in algebraic geometry and mathematical physics.The articles in this volume investigate the automorphism groups of curves and superelliptic curves and results regarding integral points on curves and their applications in mirror symmetry. Moreover, geometric subjects are addressed, such as elliptic $K$3 surfaces over the rationals, the birational type of Hurwitz spaces, and links between projective geometry and abelian functions.
eBook
The precision–recall curve overcame the optimism of the receiver operating characteristic curve in rare diseases
Compare the area under the receiver operating characteristic curve (AUC) vs. the area under the precision–recall curve (AUPRC) in summarizing the performance of a diagnostic biomarker according to the disease prevalence.
A simulation study was performed considering different sizes of diseased and nondiseased groups. Values of a biomarker were sampled with various variances and differences in mean values between the two groups. The AUCs and the AUPRCs were examined regarding their agreement and vs. the positive predictive value (PPV) and the negative predictive value (NPV) of the biomarker.
With a disease prevalence of 50%, the AUC and the AUPRC showed high correlations with the PPV and the NPV (ρ > 0.95). With a prevalence of 1%, small PPV and AUPRC values (<0.2) but high AUC values (>0.9) were found. The AUPRC reflected better than the AUC the discriminant ability of the biomarker; it had a higher correlation with the PPV (ρ = 0.995 vs. 0.724; P < 0.001).
In uncommon and rare diseases, the AUPRC should be preferred to the AUC because it summarizes better the performance of a biomarker.
Journal Article
Algebraic Curves over a Finite Field
This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves.
The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
eBook
4-028 Right ventriculography via a power-injector to guide conduction system pacing: a case series
BackgroundLeft Bundle Branch Area Pacing (LBBAP) is emerging as the preferred Conduction System Pacing (CSP) modality, receiving guideline backing in a number of clinical scenarios. However, there is a considerable learning curve, and, even in experienced hands, success rates are only between 81%-92%. Additional techniques to increase success rates are essential to permit widespread adoption.We aimed to facilitate successful LBBAP by using right ventriculography (RVG) via a power-injector to provide a greater understanding of right ventricular (RV) anatomy.MethodsAll procedures (n=5) were performed by a left axillary approach. A 5F pigtail catheter was guided into the RV. The catheter was connected to a power-injector, with RVG performed with 25ml of contrast delivered at 15ml/s.Images were taken in the left anterior oblique (LAO) and right anterior oblique (RAO) views. SelectSecure 3830 pacing leads (Medtronic, 4.1 F, 69cm) were used via a fixed curve C315-HIS guide (Medtronic).Using the RAO ventriculogram [figure 1a] to identify the tricuspid valve summit, an initial lead position in the basal-mid RV septum (15–20mm from the TVS towards the RV apex) was selected. Using the LAO ventriculogram [figure 2a] the delivery catheter was placed perpendicular to the interventricular septum with the lead oriented 10–40° superiorly to the horizontal plane. The lead was then advanced towards the left ventricle with confirmation of CSP as per the EHRA consensus document.ResultsAll patients underwent successful LBBAP with final lead positions demonstrated in figures 1b and 2b.ConclusionOur series demonstrates how RVG via a power-injector allows total opacification of the RV, providing a greater understanding of the variable RV anatomy which might be useful in facilitating successful LBBAP. It’s particularly useful for training less experienced operators, potentially reducing the learning curve, as well as procedural and fluoroscopic times.
Journal Article