Sphere partition functions and quantum de Sitter thermodynamics

Driven by a tiny positive cosmological constant, our observable universe asymptotes into a casual patch in de Sitter space in the distant future. Due to the exponential cosmic expansion, a static observer in a de Sitter space is surrounded by a horizon. A semi-classical gravity analysis by Gibbons and Hawking implies that the de Sitter horizon has a temperature and entropy, obeying laws of thermodynamics. Understanding the statistical origin of these thermodynamic quantities requires a precise microscopic model for the de Sitter horizon. With the vision of narrowing the search of such a model with quantum-corrected macroscopic data, we aim to exactly compute the leading quantum (1-loop) corrections to the Gibbons-Hawking entropy, mathematically defined as the logarithm of the effective field theory path integral expanded around the round sphere saddle, i.e. sphere partition functions. This thesis discusses sphere partition functions and their relations to de Sitter (dS) thermodynamics. It consists of three main parts: The first part addresses the subtleties of 1-loop partition functions for totally symmetric tensor fields on ^{d⁺¹, and generalizes all known results to arbitrary spin ≥ 0 in arbitrary dimensions ≥ 1. Starting from a manifestly covariant and local path integral on the sphere, we carry out a detailed analysis for any massive, shift-symmetric, massless, and partially massless fields. For any field with spin ≥ 1, we find a finite contribution from longitudinal modes; for any massless and partially massless fields, there is a residual group volume factor due to modes generating constant gauge transformations; for any massless and partially massless fields with spin ≥ 2, we derive the phase factor resulted from Wick-rotating negative conformal modes, generalizing the phase factor first obtained by Polchinski for the case of massless spin 2 to arbitrary spins. The second part presents a novel formalism for studying 1-loop quantum de Sitter thermodynamics. We first argue that the Harish-Chandra character for the de Sitter group (1,+1) provides a manifestly de Sitter-invariant regularization for normal mode density of states in the static patch, without introducing boundary ambiguities as in the traditional brick wall approach. These characters encode quasinormal mode spectrums in the static patch. With these, we write down a simple integral formula for the thermal (quasi)canonical partition function, which straightforwardly generalizes to arbitrary spin representations. Then, we derive a universal formula for 1-loop sphere partition functions in terms of the (1,+1)$ characters. We find a precise relation between these and the (quasi)canonical partition function mentioned earlier: they are equal for scalars and spinors; for any fields with spin ≥ 1, they differ by ``edge'' degrees of freedom living on the de Sitter horizon. This formalism allows us to efficiently compute the exact 1-loop corrected de Sitter horizon entropy, which as we argue provides non-trivial constraints on microscopic models for the de Sitter horizon. In three dimensions, higher-spin gravity can be alternatively formulated as an sl() Chern-Simons theory, which as we show possesses an exponentially large landscape of de Sitter vacua. For each vacuum, we obtain the all-loop exact sphere partition function, given by the absolute value squared of a topological string partition function. Finally, our formalism elegantly proves the relations between generic dS, AdS, and conformal higher-spin partition functions. The last part extends our studies in the previous part to grand (quasi)canonical partition functions on the dS static patch, where we generalize the (quasi)canonical partition functions by allowing non-zero chemical potentials in some of the angular directions. For these, we derive a generalized character integral formula in terms of the full (1,+1) characters. In three dimensions, we relate them to path integrals on Lens spaces. Similar to its sphere counterpart, the Lens space path integral exhibits a ``bulk-edge'' structure

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Outcome and risk factor analysis of patients who underwent open infrarenal aortic aneurysm repair

The aim of this study was to evaluate the short- and long-term outcomes in patients who underwent open infrarenal aortic aneurysm repair. Consecutive patients who underwent open repair of infrarenal aortic aneurysms at our institution from July 1st 1990 to June 30th 2012 were reviewed from a prospective collected departmental database. Short-term outcomes included 30-day mortality and peri-operative complications. Independent risk factors to predict 30-day mortality were identified. Long-term survival and secondary interventions were also reported. Three hundred and eighty-three patients (317 males, median age 72 years with a range of 15–90 years) underwent open infrarenal aortic aneurysm repair during the period, of whom 266 (69.5%) were elective, 18 (4.7%) were urgent for symptomatic but nonruptured cases, and 99 (25.8%) were emergency procedures for ruptured aneurysms. Mean aneurysm size was 6.5 cm (ranging from 2.5 cm to15 cm). All patients were followed up for at least 24 months with a mean follow up period 163 months. Overall 30-day mortality was 11.0% (36.4% for ruptured cases, 11.1% for symptomatic cases, and 1.5% for elective cases, p < 0.001). Preexisting renal disease and ruptured aneurysms were independent risk factors for 30-day mortality (p = 0.001 and p = 0.006 respectively). Systemic complications included 50 cardiac events, 52 respiratory events, six renal events, three cerebral vascular accidents, and one deep vein thrombosis/pulmonary embolism. Local complications included two anastomotic/graft hemorrhage, 10 distal thrombosis/embolisms, five bowel ischemias, one spinal cord ischemia, and 17 wound complications. The ruptured group presented survival rates of 53.5%, 50.5%, 47.5%, 42.3%, 38.0%, 21.9%, and 12.5% at 1 year, 2 years, 3 years, 4 years, 5 years, 10 years, and 15 years, respectively, while nonruptured survival rates were 91.5%, 88.0%, 83.7%, 78.3%, 73.0%, 43.0%, and 25.3%, respectively (log rank p < 0.001). For those who died 30 days after the operation, only six patients (1.8%) died from aneurysm related mortality. A total of three (0.9%) patients underwent late re-interventions, one for late aorto-enteric fistulae and two for anastomotic pseudoaneurysms. In the current era of endovascular repair, open infrarenal aneurysm repair is effective and durable, and has very low secondary interventions rates

Outcome and risk factor analysis of patients who underwent open infrarenal aortic aneurysm repair

Introduction: The aim of this study was to evaluate the short- and long-term outcomes in patients who underwent open infrarenal aortic aneurysm repair. Methods: Consecutive patients who underwent open repair of infrarenal aortic aneurysms at our institution from July 1st 1990 to June 30th 2012 were reviewed from a prospective collected departmental database. Short-term outcomes included 30-day mortality and peri-operative complications. Independent risk factors to predict 30-day mortality were identified. Long-term survival and secondary interventions were also reported. Results: Three hundred and eighty-three patients (317 males, median age 72 years with a range of 15–90 years) underwent open infrarenal aortic aneurysm repair during the period, of whom 266 (69.5%) were elective, 18 (4.7%) were urgent for symptomatic but nonruptured cases, and 99 (25.8%) were emergency procedures for ruptured aneurysms. Mean aneurysm size was 6.5 cm (ranging from 2.5 cm to15 cm). All patients were followed up for at least 24 months with a mean follow up period 163 months. Overall 30-day mortality was 11.0% (36.4% for ruptured cases, 11.1% for symptomatic cases, and 1.5% for elective cases; p < 0.001). Preexisting renal disease and ruptured aneurysms were independent risk factors for 30-day mortality (p = 0.001 and p = 0.006 respectively). Systemic complications included 50 cardiac events, 52 respiratory events, six renal events, three cerebral vascular accidents, and one deep vein thrombosis/pulmonary embolism. Local complications included two anastomotic/graft hemorrhage, 10 distal thrombosis/embolisms, five bowel ischemias, one spinal cord ischemia, and 17 wound complications. The ruptured group presented survival rates of 53.5%, 50.5%, 47.5%, 42.3%, 38.0%, 21.9%, and 12.5% at 1 year, 2 years, 3 years, 4 years, 5 years, 10 years, and 15 years, respectively; while nonruptured survival rates were 91.5%, 88.0%, 83.7%, 78.3%, 73.0%, 43.0%, and 25.3%, respectively (log rank p < 0.001). For those who died 30 days after the operation, only six patients (1.8%) died from aneurysm related mortality. A total of three (0.9%) patients underwent late re-interventions, one for late aorto-enteric fistulae and two for anastomotic pseudoaneurysms. Conclusion: In the current era of endovascular repair, open infrarenal aneurysm repair is effective and durable, and has very low secondary interventions rates

Global economic burden of unmet surgical need for appendicitis

Background There is a substantial gap in provision of adequate surgical care in many low- and middle-income countries. This study aimed to identify the economic burden of unmet surgical need for the common condition of appendicitis. Methods Data on the incidence of appendicitis from 170 countries and two different approaches were used to estimate numbers of patients who do not receive surgery: as a fixed proportion of the total unmet surgical need per country (approach 1); and based on country income status (approach 2). Indirect costs with current levels of access and local quality, and those if quality were at the standards of high-income countries, were estimated. A human capital approach was applied, focusing on the economic burden resulting from premature death and absenteeism. Results Excess mortality was 4185 per 100 000 cases of appendicitis using approach 1 and 3448 per 100 000 using approach 2. The economic burden of continuing current levels of access and local quality was US $92 492 million using approach 1 and$73 141 million using approach 2. The economic burden of not providing surgical care to the standards of high-income countries was $95 004 million using approach 1 and$75 666 million using approach 2. The largest share of these costs resulted from premature death (97.7 per cent) and lack of access (97.0 per cent) in contrast to lack of quality. Conclusion For a comparatively non-complex emergency condition such as appendicitis, increasing access to care should be prioritized. Although improving quality of care should not be neglected, increasing provision of care at current standards could reduce societal costs substantially

Global economic burden of unmet surgical need for appendicitis

Background There is a substantial gap in provision of adequate surgical care in many low- and middle-income countries. This study aimed to identify the economic burden of unmet surgical need for the common condition of appendicitis. Methods Data on the incidence of appendicitis from 170 countries and two different approaches were used to estimate numbers of patients who do not receive surgery: as a fixed proportion of the total unmet surgical need per country (approach 1); and based on country income status (approach 2). Indirect costs with current levels of access and local quality, and those if quality were at the standards of high-income countries, were estimated. A human capital approach was applied, focusing on the economic burden resulting from premature death and absenteeism. Results Excess mortality was 4185 per 100 000 cases of appendicitis using approach 1 and 3448 per 100 000 using approach 2. The economic burden of continuing current levels of access and local quality was US $92 492 million using approach 1 and$73 141 million using approach 2. The economic burden of not providing surgical care to the standards of high-income countries was $95 004 million using approach 1 and$75 666 million using approach 2. The largest share of these costs resulted from premature death (97.7 per cent) and lack of access (97.0 per cent) in contrast to lack of quality. Conclusion For a comparatively non-complex emergency condition such as appendicitis, increasing access to care should be prioritized. Although improving quality of care should not be neglected, increasing provision of care at current standards could reduce societal costs substantially