Suppose x is an unknown vector in Ropfm (a digital image or signal); we plan to measure n general linear functionals of x and then reconstruct. If x is known to be compressible by transform coding with a known transform, and we reconstruct via the nonlinear procedure defined here, the number of measurements n can be dramatically smaller than the size m. Thus, certain natural classes of images with m pixels need only n=O(m1/4log5/2(m)) nonadaptive nonpixel samples for faithful recovery, as opposed to the usual m pixel samples. More specifically, suppose x has a sparse representation in some orthonormal basis (e.g., wavelet, Fourier) or tight frame (e.g., curvelet, Gabor)-so the coefficients belong to an lscrp ball for 0<ples1. The N most important coefficients in that expansion allow reconstruction with lscr2 error O(N1/2-1p/). It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients. Moreover, a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing. The nonadaptive measurements have the character of "random" linear combinations of basis/frame elements. Our results use the notions of optimal recovery, of n-widths, and information-based complexity. We estimate the Gel'fand n-widths of lscrp balls in high-dimensional Euclidean space in the case 0<ples1, and give a criterion identifying near- optimal subspaces for Gel'fand n-widths. We show that "most" subspaces are near-optimal, and show that convex optimization (Basis Pursuit) is a near-optimal way to extract information derived from these near-optimal subspaces

Compressed sensing

The fat content of the human body has physiological and medical importance. It may influence morbidity and mortality, it may aIter the effectiveness of drugs and anaesthetics, and it may affect the ability to withstand exposure to cold and starvation. Thus the measurement of the total body fat provides useful information. In many people, but by no means everyone, a moderately satisfactory estimate of the body fat content can be obtained from the height and weight. However, for more precise evaluation several methods are available which give a reasonably accurate measure of body fat both in normal subjects and in individuals with unusual body builds. Most of these methods are based on the assumption that the body can be considered to consist of two compartments of relatively constant composition but which are distinctly different; these compartments are: (I) the body fat, which includes the entire content of chemical fat or lipids in the body, and (2) the fat-free mass (FFM), which includes all the rest of the body apart from fat. The body fat compartment is anhydrous, contains no potassium and has a fairly constant density of about 0.90 x 103 kg/m3. The fat-free compartment on the other hand probably has a fairly constant density of about 1.10 x 103 kg/m3, a potassium content of about 68 mequiv./kg in males (about 10% less in females) and a water content of about 720 g/kg. Thus measurement of body density or of total body K or of total body water allows a calculation of the relative proportion of these two compartments in the body and therefore also of the total fat content. The accuracy of these measures, however, is limited by the variability of the composition and density of the fat-free compartment in different individuals. In particular, individuals with a relatively high or

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Body fat assessed from total body density and its estimation from skinfold thickness: measurements on 481 men and women aged from 16 to 72 years

Background Childhood obesity increases the risk of obesity in adulthood, but how parental obesity affects the chances of a child's becoming an obese adult is unknown. We investigated the risk of obesity in young adulthood associated with both obesity in childhood and obesity in one or both parents. Methods Height and weight measurements were abstracted from the records of 854 subjects born at a health maintenance organization in Washington State between 1965 and 1971. Their parents' medical records were also reviewed. Childhood obesity was defined as a body-mass index at or above the 85th percentile for age and sex, and obesity in adulthood as a mean body-mass index at or above 27.8 for men and 27.3 for women. Results In young adulthood (defined as 21 to 29 years of age), 135 subjects (16 percent) were obese. Among those who were obese during childhood, the chance of obesity in adulthood ranged from 8 percent for 1- or 2-year-olds without obese parents to 79 percent for 10-to-14-year-olds with at least on...

https://www.nejm.org/doi/pdf/10.1056/NEJM199709253371301

Predicting Obesity in Young Adulthood from Childhood and Parental Obesity

Ten per cent of the world’s school-aged children are estimated to be carrying excess body fat (Fig. 1), with an increased risk for developing chronic disease. Of these overweight children, a quarter are obese, with a significant likelihood of some having multiple risk factors for type 2 diabetes, heart disease and a variety of other co-morbidities before or during early adulthood. The prevalence of overweight is dramatically higher in economically developed regions, but is rising significantly in most parts of the world. In many countries the problem of childhood obesity is worsening at a dramatic rate. Surveys during the 1990s show that in Brazil and the USA, an additional 0.5% of the entire child population became overweight each year. In Canada, Australia and parts of Europe the rates were higher, with an additional 1% of all children becoming overweight each year. The burden upon the health services cannot yet be estimated. Although childhood obesity brings a number of additional problems in its train – hyperinsulinaemia, poor glucose tolerance and a raised risk of type 2 diabetes, hypertension, sleep apnoea, social exclusion and depression – the greatest health problems will be seen in the next generation of adults as the present childhood obesity epidemic passes through to adulthood. Greatly increased rates of heart disease, diabetes, certain cancers, gall bladder disease, osteoarthritis, endocrine disorders and other obesityrelated conditions will be found in young adult populations, and their need for medical treatment may last for their remaining life-times. The costs to the health services, the losses to society and the burdens carried by the individuals involved will be great. The present report has been written to focus attention on the issue and to urge policy-makers to consider taking action before it is too late. Specifically, the report:

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467-789X.2004.00133.x

Obesity in children and young people: a crisis in public health.

Assessment of fracture risk and its application to screening for postmenopausal osteoporos

Three limitations of the body mass index

BY intent and by design, the Ten-State Nutrition Survey (TSNS) of 1968-1970 was concerned with both undernutrition and overnutrition. One concern was caloric and nutrient insufficiency and the effects of inadequate nutrition on growth and development. A second concern was caloric excess, as reflected by the level of fatness, and especially the prevalence of obesity, in different socioeconomic groupings and in different population segments. In the design of the TSNS, it was obvious that weight alone—or even weight relative to height—was an inadequate measure of fatness. A child might be "overweight," yet of less than average fatness; another child or adult might be underweight, yet actually obese. Accordingly, two fatfold measurements (commonly but improperly called "skinfolds") were incorporated into the anthropometric program. One benefit of the TSNS may be seen in the fact that we now have nine-decade triceps or subscapular fatfold data on more than 40,000 individuals; nearly one half of them are American Negro ( i.e. , black), for whom scant data were previously available. A second benefit is that these new data are sufficient in scope to describe lifelong changes in fatness, including some phases not previously known in detail. A third benefit is the socioeconomic partitioning of fatness, showing both an economic-related fatness increase in the male at all ages and an economic "reversal" of fatness in the female at adolescence and beyond. The TSNS was conducted on a household and family-line basis, including both parents and their children. 1 So we have the opportunity to compare true family-lines, parents and their children, brothers and sisters, and husbands with wives.

https://pediatrics.aappublications.org/content/pediatrics/57/4/443.full.pdf

Trends in Fatness and the Origins of Obesity

The existence of sexual dimorphism in the size of the permanent teeth is a well-known attribute of primates, particularly so for the canine teeth, in which the magnitude of the sex difference in the mesiodistal crown diameter may equal 50 percent or even more. However, little attention has been given until recently to the extent of sexual dimorphism in the remaining teeth of various primates and to variations in the magnitude of sexual dimorphism and the patterning of sexual dimorphism in permanent tooth size in various contemporary populations.1\"2 In man, one would postulate either of two conditions for tooth size dimorphism in various populations, the first being identity in patterning but differences in level or variability and the second being variability in patterning as well as variability in magnitude or level. One would also postulate relatively simple genetic control of sexual dimorphism in tooth size, such that the magnitude of difference in the size of the teeth of brothers and sisters would exhibit strong family-line resemblances. One might further postulate a relationship between the magnitude of sexual dimorphism in tooth size and of sexual dimorphism in body size, also best shown by the analysis of brother-sister pairs. Testing these various hypotheses would enable us to go beyond the simple computation of sexual dimorphism in tooth size and beyond population and species comparisons to the analysis of factors controlling the

Genetic Control of Sexual Dimorphism in Tooth Size

Excerpt The disease most frequently associated with an abnormal uric acid metabolism is gout.1, 2This association is based upon deposits of uric acid in the joints and connective tissue of gouty pa...

Serum uric acid in relation to age and physique in health and in coronary heart disease

useful in their own right, fail to explain the extent to which size and timing are dependent upon endogenous and exogenous factors, respectively. For such work, particular research designs must be selected. Nutrition can be explained within a population where one or more nutritional parameters can be quantified. Genetic factors can be investigated both between populations (if nutritional status is known) and within populations, using sibling and twin comparisons and correcting for attenuation due to measurement error. Sex-specific sibling comparisons (sister-sister, brother-brother) and parentchild comparisons (father-daughter, father-son, etc.) help to uncover Xand Y-linked genetic mediation. S. M. G.

Stanley M. Garn

Papers

Three limitations of the body mass index

Trends in Fatness and the Origins of Obesity

Genetic Control of Sexual Dimorphism in Tooth Size

Serum uric acid in relation to age and physique in health and in coronary heart disease

Genetic, Nutritional, and Maturational Correlates of Dental Development