Extending the support of 11- and 22-level densities for cusp form LL-functions under square-root cancellation hypotheses

The Katz-Sarnak philosophy predicts that the behavior of zeros near the central point in families of $L$-functions agrees with that of eigenvalues near 1 of random matrix ensembles. Under GRH, Iwaniec, Luo and Sarnak showed agreement in the one-level densities for cuspidal newforms with the support of the Fourier transform of the test function in $(-2, 2)$. They increased the support further under a square-root cancellation conjecture, showing that a ${\rm GL}(1)$ estimate led to additional agreement between number theory and random matrix theory. We formulate a two-dimensional analog and show it leads to improvements in the two-level density. Specifically, we show that a square-root cancellation of certain classical exponential sums over primes increases the support of the test functions such that the main terms in the $1$- and $2$-level densities of cuspidal newforms averaged over bounded weight $k$ (and fixed level $1$) converge to their random matrix theory predictions. We also conjecture a broad class of such exponential sums where we expect improvement in the case of arbitrary $n$-level densities, and note that the arguments in [ILS] yield larger support than claimed.Comment: 14 pages, to be submitted to Acta Arithmetic

How to Combine Independent Data Sets for the Same Quantity

This paper describes a new mathematical method called conflation for consolidating data from independent experiments that measure the same physical quantity. Conflation is easy to calculate and visualize and minimizes the maximum loss in Shannon information in consolidating several independent distributions into a single distribution. A formal mathematical treatment of conflation has recently been published. For the benefit of experimenters wishing to use this technique, in this paper we derive the principal basic properties of conflation in the special case of normally distributed (Gaussian) data. Examples of applications to measurements of the fundamental physical constants and in high energy physics are presented, and the conflation operation is generalized to weighted conflation for cases in which the underlying experiments are not uniformly reliable. When different experiments are designed to measure the same unknown quantity, how can their results be consolidated in an unbiased and optimal way? Given data from experiments made at different times, in different locations, with different methodologies, and perhaps differing even in underlying theory, is there a straightforward, easily applied method for combining the results from all of the experiments into a single distribution? This paper describes a new mathematical method called conflation for consolidating data from independent experiments that measure the same physical quantity

Compartment-based reconstruction of acquisition-weighted 31P cardiac MRSI reduces sensitivity to cardiac motion and scan planning

Motivation:31P magnetic resonance spectroscopic imaging (31P MRSI) is a powerful technique for investigating the metabolic effects of treatments for heart failure in vivo, allowing a better understanding of their mechanism of action in patient cohorts. Unfortunately, cardiac 31P MRSI is fundamentally limited by low SNR, which leads to compromises in acquisition, such as no cardiac or respiratory gating or low spatial resolution, in order to achieve reasonable scan times. Spectroscopy with linear algebra modeling (SLAM) reconstruction may be able to address these challenges and therefore improve repeatability by incorporating a segmented localizer into the reconstruction.Methods: Six healthy volunteers were scanned twice in a test–retest procedure to allow quantification of repeatability. Each scan consisted of anatomical localizers and two acquisition-weighted (AW) 31P MRSI acquisitions, which were acquired with and without cardiac gating. Five patients with heart failure with a preserved ejection fraction were then scanned with the same 31P MRSI sequence without cardiac gating. All 31P MRSI datasets were reconstructed with both conventional Fourier transform (FT)-based reconstruction and SLAM reconstruction, which were compared statistically. The effect of shifting the 31P MRSI acquisition field of view was also investigated.Results: In the healthy volunteer cohort, the spectral fit of the SLAM reconstructions had significantly improved Cramer–Rao lower bounds (CRLBs) compared to the FT-based reconstruction of non-cardiac gated data, as well as improved coefficients of variability and repeatability. The SLAM reconstruction found a significant difference in the PCr/ATP ratio between the healthy volunteer and patient cohorts, which the FT-based reconstruction did not find. Furthermore, the SLAM reconstruction was less influenced by the placement of the field of view (FOV) of the 31P MRSI acquisition in post hoc analysis.Discussion: The experimental benefits of the SLAM reconstruction for AW data were demonstrated by the improvements in fit confidence and repeatability seen in the healthy volunteer cohort and post hoc FOV analysis. The benefit of SLAM reconstruction of AW data for clinical studies was then illustrated by the patient cohort, which suggested improved sensitivity to clinically significant changes in the PCr/ATP ratio

Development of the preterm infant gut microbiome: a research priority.

The very low birth weight (VLBW) infant is at great risk for marked dysbiosis of the gut microbiome due to multiple factors, including physiological immaturity and prenatal/postnatal influences that disrupt the development of a normal gut flora. However, little is known about the developmental succession of the microbiota in preterm infants as they grow and mature. This review provides a synthesis of our understanding of the normal development of the infant gut microbiome and contrasts this with dysbiotic development in the VLBW infant. The role of human milk in normal gut microbial development is emphasized, along with the role of the gut microbiome in immune development and gastroenteric health. Current research provides evidence that the gut microbiome interacts extensively with many physiological systems and metabolic processes in the developing infant. However, to the best of our knowledge, there are currently no studies prospectively mapping the gut microbiome of VLBW infants through early childhood. This knowledge gap must be filled to inform a healthcare system that can provide for the growth, health, and development of VLBW infants. The paper concludes with speculation about how the VLBW infants' gut microbiome might function through host-microbe interactions to contribute to the sequelae of preterm birth, including its influence on growth, development, and general health of the infant host

A Better Definition of the Kilogram

This article reviews several recent proposed redefinitions of the kilogram, and compares them with respect to practical realizations, uncertainties (estimated standard deviations), and educational aspects.Comment: 10 pages, no figure

A 3D-Hybrid-Shot Spiral Sequence for Hyperpolarized 13^{13}C Imaging

Purpose: Hyperpolarized imaging experiments have conflicting requirements of high spatial, temporal, and spectral resolution. Spectral-Spatial RF excitation has been shown to form an attractive magnetization-efficient method for hyperpolarized imaging, but the optimum readout strategy is not yet known. Methods: In this work we propose a novel 3D hybrid-shot spiral sequence which features two constant density regions that permit the retrospective reconstruction of either high spatial or high temporal resolution images post hoc, (adaptive spatiotemporal imaging) allowing greater flexibility in acquisition and reconstruction. Results: We have implemented this sequence, both via simulation and on a pre-clinical scanner, to demonstrate its feasibility, in both a 1H phantom and with hyperpolarized 13C pyruvate in vivo. Conclusion: This sequence forms an attractive method for acquiring hyperpolarized imaging datasets, providing adaptive spatiotemporal imaging to ameliorate the conflict of spatial and temporal resolution, with significant potential for clinical translation

Cluster Winds Blow along Supercluster Axes

Within Abell galaxy clusters containing Wide-Angle Tailed radio sources, there is evidence of a ``prevailing wind'' which directs the WAT jets. We study the alignment of nine WAT jets and nearby clusters to test the idea that this wind may be a fossil of drainage along large-scale filaments. We also test this idea with a study of the alignment of WAT jets and filament axes. Statistical tests indicate no significant alignment of WAT jets towards nearest neighbour clusters, but a highly significant alignment with the long axis of the supercluster in which the cluster lies

Prospective evaluation of prognostic factors in operable breast cancer.

In 215 patients with operable breast cancer (T1-T3, N0-1, M0) and no other or previous cancer, presenting to a single breast unit, sufficient tumour was available for the prospective determination of four putative biochemical markers of prognosis: oestrogen receptor (ER) activity, cathepsin D (cath D), epidermal growth factor receptor (EGFR) activity and cyclic AMP-binding proteins (c-AMP-b). There were significant inter-relationships between ER and EGFR (r = -0.26), c-AMP-b and cath D (r = +0.32) and ER and c-AMP-b (r = +0.14). After follow-up (median 36.2 months), a total of 55 recurrences (18 locoregional only) and 35 deaths were recorded. By univariate analysis, up to 10 of 18 biochemical, clinical and histopathological variables of potential prognostic value were significantly related to disease-free interval or death, but by multivariate analysis only oestrogen receptor concentration and node status contributed significantly to risk of both distant recurrence/death; in addition, tumour size made a small contribution to the risk for a distant recurrence only. Only two parameters, tumour grade and ER concentration, were significantly related to risk of locoregional recurrence by univariate analysis, but by multivariate analysis, only tumour grade was important. It is concluded that tumour ER concentration, axillary nodal status and tumour grade remain as the most important prognostic factors in the early years after presentation of operable breast cancer, with a minor influence of tumour size. At this time, the prognostic significance of quantitative measurements of ER concentration, carefully controlled for the quality of both assay and tumour specimen, is probably greater than is generally appreciated. We have yet to identify other factors, which add significantly to the short-term prognostic value of these key features