1,235 research outputs found

    Computation of the first factor of the class number of cyclotomic fields

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    AbstractWe show how to compute the values of h1(p), the first factor of the class number of the cyclotomic field Q(exp 2iπ/p), for each prime p≤3000, and determine the set of prime divisors for each p≤1000. We confirm, for these values, a number of well known conjectures about h1(p). We give some reasons why we believe that Kummer's conjectured asymptotic estimate for h1(p) is likely to be wrong. We show how an extension of the recent work of Goldfeld, Cross, and Zagier might be used to establish that h1(p) is monotone increasing for all p≥19

    Decoding intentions of self and others from fMRI activity patterns

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    Previous studies using multi-voxel pattern analysis have decoded the content of participants' delayed intentions from patterns of fMRI data. Here we investigate whether this technique can be used to decode not only participants' own intentions, but also their representation of the intentions held by other people. In other words: if Sam is thinking about Hoki, can we decode the content of Hoki's intention by scanning Sam's brain? We additionally distinguished two components of intentions: action-plans versus goals, and included novel control analyses that allowed us to distinguish intending an outcome from simply expecting it to occur or simulating its consequences. Regions of frontal, parietal, and occipital cortex contained patterns from which it was possible to decode intentions of both self and other. Furthermore, crossclasification between self and other was possible, suggesting overlap between the two. Control analyses suggested that these results reflected visuo-spatial processes by which intentions were generated in our paradigm, rather than anything special about intentions per se. There was no evidence for any representation of intentions as mental states distinct from visuospatial processes involved in generating their content and/or simulating their outcomes. These findings suggest that the brain activity patterns decoded in intention-decoding fMRI studies may reflect domain-general processes rather than being intention-specific

    Irregular behaviour of class numbers and Euler-Kronecker constants of cyclotomic fields: the log log log devil at play

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    Kummer (1851) and, many years later, Ihara (2005) both posed conjectures on invariants related to the cyclotomic field Q(ζq)\mathbb Q(\zeta_q) with qq a prime. Kummer's conjecture concerns the asymptotic behaviour of the first factor of the class number of Q(ζq)\mathbb Q(\zeta_q) and Ihara's the positivity of the Euler-Kronecker constant of Q(ζq)\mathbb Q(\zeta_q) (the ratio of the constant and the residue of the Laurent series of the Dedekind zeta function ζQ(ζq)(s)\zeta_{\mathbb Q(\zeta_q)}(s) at s=1s=1). If certain standard conjectures in analytic number theory hold true, then one can show that both conjectures are true for a set of primes of natural density 1, but false in general. Responsible for this are irregularities in the distribution of the primes. With this survey we hope to convince the reader that the apparently dissimilar mathematical objects studied by Kummer and Ihara actually display a very similar behaviour.Comment: 20 pages, 1 figure, survey, to appear in `Irregularities in the Distribution of Prime Numbers - Research Inspired by Maier's Matrix Method', Eds. J. Pintz and M. Th. Rassia

    The Triangulum Extended (TREX) Survey: The Stellar Disk Dynamics of M33 as a Function of Stellar Age

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    Triangulum, M33, is a low mass, relatively undisturbed spiral galaxy that offers a new regime in which to test models of dynamical heating. In spite of its proximity, the dynamical heating history of M33 has not yet been well constrained. In this work, we present the TREX Survey, the largest stellar spectroscopic survey across the disk of M33. We present the stellar disk kinematics as a function of age to study the past and ongoing dynamical heating of M33. We measure line of sight velocities for ~4,500 disk stars. Using a subset, we divide the stars into broad age bins using Hubble Space Telescope and Canada-France-Hawaii-Telescope photometric catalogs: massive main sequence stars and helium burning stars (~80 Myr), intermediate mass asymptotic branch stars (~1 Gyr), and low mass red giant branch stars (~4 Gyr). We compare the stellar disk dynamics to that of the gas using existing HI, CO, and Halpha kinematics. We find that the disk of M33 has relatively low velocity dispersion (~16 km/s), and unlike in the Milky Way and Andromeda galaxies, there is no strong trend in velocity dispersion as a function of stellar age. The youngest disk stars are as dynamically hot as the oldest disk stars and are dynamically hotter than predicted by most M33 like low mass simulated analogs in Illustris. The velocity dispersion of the young stars is highly structured, with the large velocity dispersion fairly localized. The cause of this high velocity dispersion is not evident from the observations and simulated analogs presented here.Comment: 27 pages, 15 figures, 6 table

    Right ventricular shape and function: cardiovascular magnetic resonance reference morphology and biventricular risk factor morphometrics in UK Biobank

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    Background The associations between cardiovascular disease (CVD) risk factors and the biventricular geometry of the right ventricle (RV) and left ventricle (LV) have been difficult to assess, due to subtle and complex shape changes. We sought to quantify reference RV morphology as well as biventricular variations associated with common cardiovascular risk factors. Methods A biventricular shape atlas was automatically constructed using contours and landmarks from 4329 UK Biobank cardiovascular magnetic resonance (CMR) studies. A subdivision surface geometric mesh was customized to the contours using a diffeomorphic registration algorithm, with automatic correction of slice shifts due to differences in breath-hold position. A reference sub-cohort was identified consisting of 630 participants with no CVD risk factors. Morphometric scores were computed using linear regression to quantify shape variations associated with four risk factors (high cholesterol, high blood pressure, obesity and smoking) and three disease factors (diabetes, previous myocardial infarction and angina). Results The atlas construction led to an accurate representation of 3D shapes at end-diastole and end-systole, with acceptable fitting errors between surfaces and contours (average error less than 1.5 mm). Atlas shape features had stronger associations than traditional mass and volume measures for all factors (p < 0.005 for each). High blood pressure was associated with outward displacement of the LV free walls, but inward displacement of the RV free wall and thickening of the septum. Smoking was associated with a rounder RV with inward displacement of the RV free wall and increased relative wall thickness. Conclusion Morphometric relationships between biventricular shape and cardiovascular risk factors in a large cohort show complex interactions between RV and LV morphology. These can be quantified by z-scores, which can be used to study the morphological correlates of disease

    Maintaining Fluoroquinolone Class Efficacy: Review of Influencing Factors

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    Previous experience with antimicrobial resistance has emphasized the importance of appropriate stewardship of these pharmacotherapeutic agents. The introduction of fluoroquinolones provided potent new drugs directed primarily against gram-negative pathogens, while the newer members of this class demonstrate more activity against gram-positive species, including Streptococcus pneumoniae. Although these agents are clinically effective against a broad range of infectious agents, emergence of resistance and associated clinical failures have prompted reexamination of their use. Appropriate use revolves around two key objectives: 1) only prescribing antimicrobial therapy when it is beneficial and 2) using the agents(s) with optimal activity against the expected pathogens(s). Pharmacodynamic principles and properties can be applied to achieve the latter objective when prescribing agents belonging to the fluoroquinolone class. A focused approach emphasizing “correct-spectrum” coverage may reduce development of antimicrobial resistance and maintain class efficacy

    Health-related quality of life after treatment for bladder cancer in England

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    Background Little is known about quality of life after bladder cancer treatment. This common cancer is managed using treatments that can affect urinary, sexual and bowel function. Methods To understand quality of life and inform future care, the Department of Health (England) surveyed adults surviving bladder cancer 1–5 years after diagnosis. Questions related to disease status, co-existing conditions, generic health (EQ-5D), cancer-generic (Social Difficulties Inventory) and cancer-specific outcomes (Functional Assessment of Cancer Therapy—Bladder). Results In total, 673 (54%) patients responded; including 500 (74%) men and 539 (80%) with co-existing conditions. Most respondents received endoscopic treatment (60%), while 92 (14%) and 99 (15%) received radical cystectomy or radiotherapy, respectively. Questionnaire completion rates varied (51–97%). Treatment groups reported ≥1 problem using EQ-5D generic domains (59–74%). Usual activities was the most common concern. Urinary frequency was common after endoscopy (34–37%) and radiotherapy (44–50%). Certain populations were more likely to report generic, cancer-generic and cancer-specific problems; notably those with co-existing long-term conditions and those treated with radiotherapy. Conclusion The study demonstrates the importance of assessing patient-reported outcomes in this population. There is a need for larger, more in-depth studies to fully understand the challenges patients with bladder cancer face
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