Asymptotic Behavior of Colored Jones polynomial and Turaev-Viro Invariant of figure eight knot

In this paper we investigate the asymptotic behavior of the colored Jones polynomials and the Turaev-Viro invariants for the figure eight knot. More precisely, we consider the $M$-th colored Jones polynomials evaluated at $(N+1/2)$-th root of unity with a fixed limiting ratio, $s$, of $M$ and $(N+1/2)$. We find out the asymptotic expansion formula (AEF) of the colored Jones polynomials of the figure eight knot with $s$ close to $1$. Nonetheless, we show that the exponential growth rate of the colored Jones polynomials of the figure eight knot with $s$ close to $1/2$ is strictly less than those with $s$ close to $1$. It is known that the Turaev Viro invariant of the figure eight knot can be expressed in terms of a sum of its colored Jones polynomials. Our results show that this sum is asymptotically equal to the sum of the terms with $s$ close to 1. As an application of the asymptotic behavior of the colored Jones polynomials, we obtain the asymptotic expansion formula for the Turaev-Viro invariants of the figure eight knot. Finally, we suggest a possible generalization of our approach so as to relate the AEF for the colored Jones polynomials and the AEF for the Turaev-Viro invariants for general hyperbolic knots.Comment: 40 pages, 0 figure

A comparison of continuous and bi-level positive airway pressure non-invasive ventilation in patients with acute cardiogenic pulmonary oedema: a meta-analysis

INTRODUCTION: We conducted the present study to investigate the potential beneficial and adverse effects of continuous positive airway pressure (CPAP) compared with bi-level positive airway pressure (BiPAP) noninvasive ventilation in patients with cardiogenic pulmonary oedema. METHOD: We included randomized controlled studies comparing CPAP and BiPAP treatment in patients with cardiogenic pulmonary oedema from the Cochrane Controlled Trials Register (2005 issue 3), and EMBASE and MEDLINE databases (1966 to 1 December 2005), without language restriction. Two reviewers reviewed the quality of the studies and independently performed data extraction. RESULTS: Seven randomized controlled studies, including a total of 290 patients with cardiogenic pulmonary oedema, were considered. The hospital mortality (relative risk [RR] 0.76, 95% confidence interval [CI] 0.32–1.78; P = 0.52; I(2 )= 0%) and risk for requiring invasive ventilation (RR 0.80, 95% CI 0.33–1.94; P = 0.62; I(2 )= 0%) were not significantly different between patients treated with CPAP and those treated with BiPAP. Stratifying studies that used either fixed or titrated pressure during BiPAP treatment and studies involving patients with or without hypercapnia did not change the results. The duration of noninvasive ventilation required until the pulmonary oedema resolved (weighted mean difference [WMD] in hours = 3.65, 95% CI -12.12 to +19.43; P = 0.65, I(2 )= 0%) and length of hospital stay (WMD in days = -0.04, 95% CI -2.57 to +2.48; P = 0.97, I(2 )= 0%) were also not significantly different between the two groups. Based on the limited data available, there was an insignificant trend toward an increase in new onset acute myocardial infarction in patients treated with BiPAP (RR 2.10, 95% CI 0.91–4.84; P = 0.08; I(2 )= 25.3%). CONCLUSION: BiPAP does not offer any significant clinical benefits over CPAP in patients with acute cardiogenic pulmonary oedema. Until a large randomized controlled trial shows significant clinical benefit and cost-effectiveness of BiPAP versus CPAP in patients with acute cardiogenic pulmonary oedema, the choice of modality will depend mainly on the equipment available

The effectiveness of acupuncture on the sleep quality of elderly with dementia: A within-subjects trial

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The Eye4HK Meme and the Construction of an Injustice Frame

The territory-wide protest in Hong Kong in 2019, originated from a proposed amendment bill on the extradition of fugitives to China which triggered massive protests. In an incident, the police shot a female medic in the eye which outraged the public. A Korean celebrity initiated an online movement by uploading a selfie covering his right eye to Twitter showing solidarity with the victim. The eye-covered image signifies the girl who lost her eye as a political victim, gaining wide sympathy. The sub-campaign constructed an image of resistance against police brutality which strengthened the wider movement in Hong Kong and helped to win support in other parts of the world. The campaign also linked the emotions of the two places by recalling Koreans’ memory of their historical struggle for democracy. The sub-campaign generated symbolic resources accumulating through the production and reproduction process online and subsequently benefited the wider social movement for political change

Effects of risk assessment and management programme for hypertension on clinical outcomes and cardiovascular disease risks after 12 months: a population-based matched cohort study

Objectives: This study evaluated the effectiveness of a structured multidisciplinary risk assessment and management programme for patients with hypertension (RAMP-HT) who were managed in public primary care clinics but had suboptimal blood pressure (BP) control in improving BP, LDL-cholesterol (LDL-C) and predicted 10-year cardiovascular disease (CVD) risk after 12 months of intervention. Methods: A total of 10 262 hypertension patients with suboptimal BP despite treatment, aged less than 80 years and without existing CVD were enrolled in RAMP-HT between October 2011 and March 2012 from public general out-patient clinics in Hong Kong. Their clinical outcomes and predicted 10-year CVD risk were compared with a matched cohort of hypertension patients who were receiving usual care in general out-patient clinics without any RAMP-HT intervention by propensity score matching. Multivariable linear and logistic regressions were used to determine the independent effectiveness of RAMP-HT after adjusting for potential confounding variables. Results: Compared with the usual care group after 12 months, significantly greater proportions of RAMP-HT participants achieved target BP (i.e. BP 20%) (OR = 1.13, P < 0.01). RAMP-HT participants also had significantly greater reduction in predicted 10-year CVD risk by 0.44% (coefficient = -0.44, P < 0.01). Conclusion: The structured multidisciplinary RAMP-HT was more effective than usual care in achieving target BP, LDL-C and reducing predicted 10-year CVD risk in public primary care patients with suboptimal hypertension control after 12 months of intervention. A long-term follow-up should be conducted to confirm whether the improvement in clinical outcomes can be translated into actual reductions in CVD complications and mortalities and whether such approach is cost-effective.published_or_final_versio

Detection and Monitoring of Marine Pollution Using Remote Sensing Technologies

Recently, the marine habitat has been under pollution threat, which impacts many human activities as well as human life. Increasing concerns about pollution levels in the oceans and coastal regions have led to multiple approaches for measuring and mitigating marine pollution, in order to achieve sustainable marine water quality. Satellite remote sensing, covering large and remote areas, is considered useful for detecting and monitoring marine pollution. Recent developments in sensor technologies have transformed remote sensing into an effective means of monitoring marine areas. Different remote sensing platforms and sensors have their own capabilities for mapping and monitoring water pollution of different types, characteristics, and concentrations. This chapter will discuss and elaborate the merits and limitations of these remote sensing techniques for mapping oil pollutants, suspended solid concentrations, algal blooms, and floating plastic waste in marine waters

Wearable and flexible thin film thermoelectric module for multi-scale energy harvesting

Developing a thermoelectric generator(TEG) with shape conformable geometry for sustaining low-thermal impedance and large temperature gradient (ΔT) is fundamental for wearable and multi-scale energy harvesting applications. Here we demonstrate a flexible architectural design, with efficient thin film thermoelectric generator as a solution for this problem. This approach not only decreases the thermal impedance but also multiplies the temperature gradient, thereby increasing the power conversion efficiency (PCE) as comparable to bulk TEG. Intact thin films of Tin telluride (p-type) and Lead Telluride (n-type) are deposited on flexible substrate through physical vapor deposition and a thermoelectric module possessing a maximum output power density of 8.4 mW/cm2 is fabricated. We have demonstrated the performance of p-SnTe/n-PbTe based TEG as a flexible wearable power source for electronic gadgets, as a thermal touch sensor for real-time switching and temperature monitoring for exoskeleton applications