A certain class of Laplace transforms with applications to reaction and reaction-diffusion equations

A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables and the concept of Laplacianness in statistics, alpha-Laplace and Mittag-Leffler stochastic processes, the concepts of infinite divisibility and geometric infinite divisibility problems in probability theory and certain fractional integrals and fractional derivatives. A number of applications are pointed out with special reference to solutions of fractional reaction and reaction-diffusion equations and their generalizations.Comment: LaTeX, 12 pages, corrected typo

Effects of Transport Memory and Nonlinear Damping in a Generalized Fisher's Equation

Memory effects in transport require, for their incorporation into reaction diffusion investigations, a generalization of traditional equations. The well-known Fisher's equation, which combines diffusion with a logistic nonlinearity, is generalized to include memory effects and traveling wave solutions of the equation are found. Comparison is made with alternate generalization procedures.Comment: 6 pages, 4 figures, RevTeX

Reaction-diffusion systems and nonlinear waves

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. The importance of the derived results lies in the fact that numerous results on fractional reaction, fractional diffusion, anomalous diffusion problems, and fractional telegraph equations scattered in the literature can be derived, as special cases, of the results investigated in this article.Comment: LaTeX, 16 pages, corrected typo

Effect of initial conditions on the speed of reaction-diffusion fronts

The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed

Cavity-enhanced direct frequency comb spectroscopy

Cavity-enhanced direct frequency comb spectroscopy combines broad spectral bandwidth, high spectral resolution, precise frequency calibration, and ultrahigh detection sensitivity, all in one experimental platform based on an optical frequency comb interacting with a high-finesse optical cavity. Precise control of the optical frequency comb allows highly efficient, coherent coupling of individual comb components with corresponding resonant modes of the high-finesse cavity. The long cavity lifetime dramatically enhances the effective interaction between the light field and intracavity matter, increasing the sensitivity for measurement of optical losses by a factor that is on the order of the cavity finesse. The use of low-dispersion mirrors permits almost the entire spectral bandwidth of the frequency comb to be employed for detection, covering a range of ~10% of the actual optical frequency. The light transmitted from the cavity is spectrally resolved to provide a multitude of detection channels with spectral resolutions ranging from a several gigahertz to hundreds of kilohertz. In this review we will discuss the principle of cavity-enhanced direct frequency comb spectroscopy and the various implementations of such systems. In particular, we discuss several types of UV, optical, and IR frequency comb sources and optical cavity designs that can be used for specific spectroscopic applications. We present several cavity-comb coupling methods to take advantage of the broad spectral bandwidth and narrow spectral components of a frequency comb. Finally, we present a series of experimental measurements on trace gas detections, human breath analysis, and characterization of cold molecular beams.Comment: 36 pages, 27 figure

The Association of Socioeconomic Status With Hypertension in 76 Low- and Middle-Income Countries.

Effective equity-focused health policy for hypertension in low- and middle-income countries (LMICs) requires an understanding of the condition's current socioeconomic gradients and how these are likely to change in the future as countries develop economically. This cross-sectional study aimed to determine how hypertension prevalence in LMICs varies by individuals' education and household wealth, and how these socioeconomic gradients in hypertension prevalence are associated with a country's gross domestic product (GDP) per capita. We pooled nationally representative household survey data from 76 LMICs. We disaggregated hypertension prevalence by education and household wealth quintile, and used regression analyses to adjust for age and sex. We included 1,211,386 participants in the analysis. Pooling across all countries, hypertension prevalence tended to be similar between education groups and household wealth quintiles. The only world region with a clear positive association of hypertension with education or household wealth quintile was Southeast Asia. Countries with a lower GDP per capita had, on average, a more positive association of hypertension with education and household wealth quintile than countries with a higher GDP per capita, especially in rural areas and among men. Differences in hypertension prevalence between socioeconomic groups were generally small, with even the least educated and least wealthy groups having a substantial hypertension prevalence. Our cross-sectional interaction analyses of GDP per capita with the socioeconomic gradients of hypertension suggest that hypertension may increasingly affect adults in the lowest socioeconomic groups as LMICs develop economically

Diabetes risk and provision of diabetes prevention activities in 44 low-income and middle-income countries: a cross-sectional analysis of nationally representative, individual-level survey data.

The global burden of diabetes is rising rapidly, yet there is little evidence on individual-level diabetes prevention activities undertaken by health systems in low-income and middle-income countries (LMICs). Here we describe the population at high risk of developing diabetes, estimate diabetes prevention activities, and explore sociodemographic variation in these activities across LMICs. We performed a pooled, cross-sectional analysis of individual-level data from nationally representative, population-based surveys conducted in 44 LMICs between October, 2009, and May, 2019. Our sample included all participants older than 25 years who did not have diabetes and were not pregnant. We defined the population at high risk of diabetes on the basis of either the presence of impaired fasting glucose (or prediabetes in countries with a haemoglobin A <sub>1c</sub> available) or overweight or obesity, consistent with the WHO Package of Essential Noncommunicable Disease Guidelines for type 2 diabetes management. We estimated the proportion of survey participants that were at high risk of developing diabetes based on this definition. We also estimated the proportion of the population at high risk that reported each of four fundamental diabetes prevention activities: physical activity counselling, weight loss counselling, dietary counselling, and blood glucose screening, overall and stratified by World Bank income group. Finally, we used multivariable Poisson regression models to evaluate associations between sociodemographic characteristics and these activities. The final pooled sample included 145 739 adults (86 269 [59·2%] of whom were female and 59 468 [40·4%] of whom were male) across 44 LMICs, of whom 59 308 (40·6% [95% CI 38·5-42·8]) were considered at high risk of diabetes (20·6% [19·8-21·5] in low-income countries, 38·0% [37·2-38·9] in lower-middle-income countries, and 57·5% [54·3-60·6] in upper-middle-income countries). Overall, the reach of diabetes prevention activities was low at 40·0% (38·6-41·4) for physical activity counselling, 37·1% (35·9-38·4) for weight loss counselling, 42·7% (41·6-43·7) for dietary counselling, and 37·1% (34·7-39·6) for blood glucose screening. Diabetes prevention varied widely by national-level wealth: 68·1% (64·6-71·4) of people at high risk of diabetes in low-income countries reported none of these activities, whereas 49·0% (47·4-50·7) at high risk in upper-middle-income countries reported at least three activities. Educational attainment was associated with diabetes prevention, with estimated increases in the predicted probability of receipt ranging between 6·5 (3·6-9·4) percentage points for dietary fruit and vegetable counselling and 21·3 (19·5-23·2) percentage points for blood glucose screening, among people with some secondary schooling compared with people with no formal education. A large proportion of individuals across LMICs are at high risk of diabetes but less than half reported receiving fundamental prevention activities overall, with the lowest receipt of these activities among people in low-income countries and with no formal education. These findings offer foundational evidence to inform future global targets for diabetes prevention and to strengthen policies and programmes to prevent continued increases in diabetes worldwide. Harvard T H Chan School of Public Health McLennan Fund: Dean's Challenge Grant Program and the EU's Research and Innovation programme Horizon 2020

Diabetes Prevalence and Its Relationship With Education, Wealth, and BMI in 29 Low- and Middle-Income Countries.

Diabetes is a rapidly growing health problem in low- and middle-income countries (LMICs), but empirical data on its prevalence and relationship to socioeconomic status are scarce. We estimated diabetes prevalence and the subset with undiagnosed diabetes in 29 LMICs and evaluated the relationship of education, household wealth, and BMI with diabetes risk. We pooled individual-level data from 29 nationally representative surveys conducted between 2008 and 2016, totaling 588,574 participants aged ≥25 years. Diabetes prevalence and the subset with undiagnosed diabetes was calculated overall and by country, World Bank income group (WBIG), and geographic region. Multivariable Poisson regression models were used to estimate relative risk (RR). Overall, prevalence of diabetes in 29 LMICs was 7.5% (95% CI 7.1-8.0) and of undiagnosed diabetes 4.9% (4.6-5.3). Diabetes prevalence increased with increasing WBIG: countries with low-income economies (LICs) 6.7% (5.5-8.1), lower-middle-income economies (LMIs) 7.1% (6.6-7.6), and upper-middle-income economies (UMIs) 8.2% (7.5-9.0). Compared with no formal education, greater educational attainment was associated with an increased risk of diabetes across WBIGs, after adjusting for BMI (LICs RR 1.47 [95% CI 1.22-1.78], LMIs 1.14 [1.06-1.23], and UMIs 1.28 [1.02-1.61]). Among 29 LMICs, diabetes prevalence was substantial and increased with increasing WBIG. In contrast to the association seen in high-income countries, diabetes risk was highest among those with greater educational attainment, independent of BMI. LMICs included in this analysis may be at an advanced stage in the nutrition transition but with no reversal in the socioeconomic gradient of diabetes risk