The geometry of Sloppiness

The use of mathematical models in the sciences often involves the estimation of unknown parameter values from data. Sloppiness provides information about the uncertainty of this task. In this paper, we develop a precise mathematical foundation for sloppiness as initially introduced and define rigorously key concepts, such as `model manifold', in relation to concepts of structural identifiability. We redefine sloppiness conceptually as a comparison between the premetric on parameter space induced by measurement noise and a reference metric. This opens up the possibility of alternative quantification of sloppiness, beyond the standard use of the Fisher Information Matrix, which assumes that parameter space is equipped with the usual Euclidean metric and the measurement error is infinitesimal. Applications include parametric statistical models, explicit time dependent models, and ordinary differential equation models

Granulomatous reaction - a histopathological study: a retrospective and prospective study of 5 years

Background:The present study was done to investigate the prevalence of granulomatous infection among the patients. The study was conducted from the time period of July 2008 to June 2013. The study was conducted at the histopathology laboratory, pathology department, P. D. U. government medical college, Rajkot (Gujarat, India).Methods:In the present study, total 300 cases were studied. Specimens for study were received from various departments like surgery, ENT, medicine, pediatrics etc. from July 2008 to June 2013. The sections of these specimens were taken & slides were prepared by staining with Hematoxylin & Eosin (H&E) for microscopic examination.Results: In present study, most the common granulomatous reaction was tuberculosis and majority of cases were found in among young Hindu males specially in the lower socioeconomical class of rural areas.Conclusion:Our study confirms that the most common granulomatous reaction is tuberculosis, mainly found in skin and more common among the population of lower socioeconomic class & rural population, signifying increasing incidence of granulomation infection. The present study is a comprehensive comparative study of granulomatous reactions done in correlation with the age, sex, involved sites and clinical profile of the patients. This information is valuable in policy formation for the control & specific treatment and outcome of granulomatous infection.

Women and Informal Employment: An Analysis of Socio-Economic and Health Conditions of Women Home-Based Workers in Chennai, India

This study seeks to analyse the socio-economic and health status of women workers in the informal sector in Chennai, India. Informal employment consists of various kinds of micro-enterprises offering commodities and services and home-based work. Of all these different types of work in the informal sector, home-based work is associated with women because of its nature and characteristic features. Home-based work is piecework for remuneration that is completed in the premises of the worker’s choice rather than the workplace of the employer. Women homeworkers face many issues such as long hours of work, low wages, meagre rates per piece, lack of social security and lack of union or organizational support. More importantly, their conditions of work and health are deplorable. The present study has followed the descriptive research method to carry out the survey. The data for this study has been collected directly using the field survey method. A formally structured questionnaire was prepared and circulated among the target sample for this purpose. The questions were formulated using the variables taken from the literature review and research gap. A stratified random sampling method was adopted for the survey. The sample size was justified on the calculation of secondary data and by applying the appropriate formula to collect data from 150 sample respondents in the study area. As the study focuses on female home-based workers, a direct survey was conducted among women workers. The data collected relates to the socio-economic and work conditions of women workers. The findings reveal that 59.2 percent of the home-based women workers are in the age group 25 to 35 years, and the average wage is low at Rs.164.7 per day, based on a fixed piece rate. Further analysis of the data shows that 35.5 percent of the respondents earn Rs.100 per day, which is significantly below the minimum wage. Therefore, the findings reveal that female home-based workers are subject to multiple forms of exploitation such as low wages, delayed and irregular payments and sporadic work. In conclusion, the researcher states that despite these problems, home-based work is the most suitable avenue for poverty alleviation and employment generation among urban women. However, low wages, lack of micro-capital for entrepreneurial ventures and non-payment of dues on time are serious issues that these workers face

Histopathological study of nasal lesions: 2 years study

ackground: Majority of the nasal lesions are polypoid. It is difficult to comment upon the nature of the nasal lesion- whether neoplastic or non-neoplastic. Hence histopathological examination is essential for both ENT surgeons as well as pathologists. Aim to study the incidence of different nasal lesion. Also, to find out frequency of inflammatory, benign and malignant conditions of nasal lesions and to compare various histopathological lesions of nasal mass in relation to age, sex and site distribution.Methods: The present study was undertaken in histopathology laboratory of Department of Pathology, P.D.U. medical college and hospital, Rajkot for period of 2 years from October 2013 to September 2015. A histopathological study of total 100 cases of nasal lesions was done. Tissue were processed and studied.Results: Out of 100 cases, 59 were males and 41 were females. Male to Female ratio was 1.44:1. Maximum numbers of nasal lesions were detected in age group of 11-20 years with 24 (24.00%) cases. Out of these 100 cases, 80 (80.00%) were non neoplastic and 20 (20.00%) were of neoplastic origin. In neoplastic lesions, 12(12.00%) were benign, 1 (1.00%) was borderline and 7 (7.00%) were malignant nasal lesions. Non neoplastic lesions were composed of the majority of cases followed by benign neoplastic lesions.Conclusions: Most of malignant neoplastic lesions were occurs after 40 years of age. Incidence of malignant neoplastic lesions was increase with advanced age

The geometry of sloppiness

The use of mathematical models in the sciences often involves the estimation of unknown parameter values from data. Sloppiness provides information about the uncertainty of this task. In this paper, we develop a precise mathematical foundation for sloppiness as initially introduced and define rigorously key concepts, such as `model manifold', in relation to concepts of structural identifiability. We redefine sloppiness conceptually as a comparison between the premetric on parameter space induced by measurement noise and a reference metric. This opens up the possibility of alternative quantification of sloppiness, beyond the standard use of the Fisher Information Matrix, which assumes that parameter space is equipped with the usual Euclidean metric and the measurement error is infinitesimal. Applications include parametric statistical models, explicit time dependent models, and ordinary differential equation models

Derivative moments in turbulent shear flows

We propose a generalized perspective on the behavior of high-order derivative moments in turbulent shear flows by taking account of the roles of small-scale intermittency and mean shear, in addition to the Reynolds number. Two asymptotic regimes are discussed with respect to shear effects. By these means, some existing disagreements on the Reynolds number dependence of derivative moments can be explained. That odd-order moments of transverse velocity derivatives tend not vanish as expected from elementary scaling considerations does not necessarily imply that small-scale anisotropy persists at all Reynolds numbers.Comment: 11 pages, 7 Postscript figure