From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two areas was first observed through Montgomery's work on the pair correlation of zeros of the Riemann zeta function. As its generalizations and consequences have motivated much of the following work, and to this day remains one of the most important outstanding conjectures in the field, it occupies a central role in our discussion below. We describe some of the many techniques and results from the past sixty years, especially the important roles played by numerical and experimental investigations, that led to the discovery of the connections and progress towards understanding the behaviors. In our survey of these two areas, we describe the common mathematics that explains the remarkable universality. We conclude with some thoughts on what might lie ahead in the pair correlation of zeros of the zeta function, and other similar quantities.Comment: Version 1.1, 50 pages, 6 figures. To appear in "Open Problems in Mathematics", Editors John Nash and Michael Th. Rassias. arXiv admin note: text overlap with arXiv:0909.491

Exposure to ambient particulate matter is associated with accelerated functional decline in idiopathic pulmonary fibrosis

BACKGROUND: Idiopathic pulmonary fibrosis (IPF), a progressive disease with an unknown pathogenesis, may be due in part to an abnormal response to injurious stimuli by alveolar epithelial cells. Air pollution and particulate inhalation of matter evoke a wide variety of pulmonary and systemic inflammatory diseases. We therefore hypothesized that increased average ambient particulate matter (PM) concentrations would be associated with an accelerated rate of decline in FVC in IPF. METHODS: We identified a cohort of subjects seen at a single university referral center from 2007 to 2013. Average concentrations of particulate matter < 10 and < 2.5 μg/m3 (PM10 and PM2.5, respectively) were assigned to each patient based on geocoded residential addresses. A linear multivariable mixed-effects model determined the association between the rate of decline in FVC and average PM concentration, controlling for baseline FVC at first measurement and other covariates. RESULTS: One hundred thirty-five subjects were included in the final analysis after exclusion of subjects missing repeated spirometry measurements and those for whom exposure data were not available. There was a significant association between PM10 levels and the rate of decline in FVC during the study period, with each μg/m3 increase in PM10 corresponding with an additional 46 cc/y decline in FVC (P = .008). CONCLUSIONS: Ambient air pollution, as measured by average PM10 concentration, is associated with an increase in the rate of decline of FVC in IPF, suggesting a potential mechanistic role for air pollution in the progression of disease

The Role of CT Scanning in Multidimensional Phenotyping of COPD

BackgroundCOPD is a heterogeneous disease characterized by airflow obstruction and diagnosed by lung function. CT imaging is emerging as an important, noninvasive tool in phenotyping COPD. However, the use of CT imaging in defining the disease heterogeneity above lung function is not fully known.MethodsSeventy-five patients with COPD (58 men, 17 women) were studied with CT imaging and with measures of airway inflammation. Airway physiology and health status were also determined.ResultsThe presence of emphysema (EM), bronchiectasis (BE), and bronchial wall thickening (BWT) was found in 67%, 27%, and 27% of subjects, respectively. The presence of EM was associated with lower lung function (mean difference % FEV1, −20%; 95% CI, −28 to −11; P < .001). There was no difference in airway inflammation, exacerbation frequency, or bacterial load in patients with EM alone or with BE and/or BWT ± EM. The diffusing capacity of the lung for carbon monoxide/alveolar volume ratio was the most sensitive and specific parameter in identifying EM (area under the receiver operator characteristic curve, 0.87; 95% CI, 0.79-0.96). Physiologic cluster analysis identified three clusters, two of which were EM predominant and the third characterized by a heterogeneous combination of EM and BE.ConclusionsThe application of CT imaging can be useful as a tool in the multidimensional approach to phenotyping patients with COPD

Effect of cadence on locomotor–respiratory coupling during upper-body exercise

Introduction: Asynchronous arm-cranking performed at high cadences elicits greater cardiorespiratory responses compared to low cadences. This has been attributed to increased postural demand and locomotor–respiratory coupling (LRC), and yet, this has not been empirically tested. This study aimed to assess the effects of cadence on cardiorespiratory responses and LRC during upper-body exercise. Methods: Eight recreationally-active men performed arm-cranking exercise at moderate and severe intensities that were separated by 10 min of rest. At each intensity, participants exercised for 4 min at each of three cadences (50, 70, and 90 rev min−1) in a random order, with 4 min rest-periods applied in-between cadences. Exercise measures included LRC via whole- and half-integer ratios, cardiorespiratory function, perceptions of effort (RPE and dyspnoea), and diaphragm EMG using an oesophageal catheter. Results: The prevalence of LRC during moderate exercise was highest at 70 vs. 50 rev min−1 (27 ± 10 vs. 13 ± 9%, p = 0.000) and during severe exercise at 90 vs. 50 rev min−1 (24 ± 7 vs. 18 ± 5%, p = 0.034), with a shorter inspiratory time and higher mean inspiratory flow (p < 0.05) at higher cadences. During moderate exercise, (Formula presented.) and fC were higher at 90 rev min−1 (p < 0.05) relative to 70 and 50 rev min−1 ((Formula presented.) 1.19 ± 0.25 vs. 1.05 ± 0.21 vs. 0.97 ± 0.24 L min−1; fC 116 ± 11 vs. 101 ± 13 vs. 101 ± 12 b min−1), with concomitantly elevated dyspnoea. There were no discernible cadence-mediated effects on diaphragm EMG. Conclusion: Participants engage in LRC to a greater extent at moderate-high cadences which, in turn, increase respiratory airflow. Cadence rate should be carefully considered when designing aerobic training programmes involving the upper-limbs

Normalization of Voltage-Sensitive Dye Signal with Functional Activity Measures

In general, signal amplitude in optical imaging is normalized using the well-established ΔF/F method, where functional activity is divided by the total fluorescent light flux. This measure is used both directly, as a measure of population activity, and indirectly, to quantify spatial and spatiotemporal activity patterns. Despite its ubiquitous use, the stability and accuracy of this measure has not been validated for voltage-sensitive dye imaging of mammalian neocortex in vivo. In this report, we find that this normalization can introduce dynamic biases. In particular, the ΔF/F is influenced by dye staining quality, and the ratio is also unstable over the course of experiments. As methods to record and analyze optical imaging signals become more precise, such biases can have an increasingly pernicious impact on the accuracy of findings, especially in the comparison of cytoarchitechtonic areas, in area-of-activation measurements, and in plasticity or developmental experiments. These dynamic biases of the ΔF/F method may, to an extent, be mitigated by a novel method of normalization, ΔF/ΔFepileptiform. This normalization uses as a reference the measured activity of epileptiform spikes elicited by global disinhibition with bicuculline methiodide. Since this normalization is based on a functional measure, i.e. the signal amplitude of “hypersynchronized” bursts of activity in the cortical network, it is less influenced by staining of non-functional elements. We demonstrate that such a functional measure can better represent the amplitude of population mass action, and discuss alternative functional normalizations based on the amplitude of synchronized spontaneous sleep-like activity. These findings demonstrate that the traditional ΔF/F normalization of voltage-sensitive dye signals can introduce pernicious inaccuracies in the quantification of neural population activity. They further suggest that normalization-independent metrics such as waveform propagation patterns, oscillations in single detectors, and phase relationships between detector pairs may better capture the biological information which is obtained by high-sensitivity imaging