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Previous studies have suggested that the intake of trans-fatty acids (TFA) plays a role in the development of obesity. The proportions of adipose tissue fatty acids not synthesised endogenously in humans, such as TFA, usually correlate well with the dietary intake. Hence, the use of these biomarkers may provide a more accurate measure of habitual TFA intake than that obtained with dietary questionnaires. The objective of the present study was to investigate the associations between the proportions of specific TFA in adipose tissue and subsequent changes in weight and waist circumference (WC). The relative content of fatty acids in adipose tissue biopsies from a random sample of 996 men and women aged 50–64 years drawn from a Danish cohort study was determined by GC. Baseline data on weight, WC and potential confounders were available together with information on weight and WC 5 years after enrolment. The exposure measures were total trans-octadecenoic acids (18 : 1t), 18 : 1 Δ6-10t, vaccenic acid (18 : 1 Δ11t) and rumenic acid (18 : 2 Δ9c, 11t). Data were analysed using multiple regression with cubic spline modelling. The median proportion of total adipose tissue 18 : 1t was 1·52 % (90 % central range 0·98, 2·19) in men and 1·47 % (1·01, 2·19) in women. No significant associations were observed between the proportions of total 18 : 1t, 18 : 1 Δ6-10t, vaccenic acid or rumenic acid and changes in weight or WC. The present study suggests that the proportions of specific TFA in adipose tissue are not associated with subsequent changes in weight or WC within the exposure range observed in this population.
A way to honour A.W.H. Phillips is to describe the continuing influence of one of his enduring contributions to economic dynamics, his remarkable essay (chapter 42) about how discrete time observations can be used to restrict a continuous time linear model. That chapter precisely described what later came to be known as the problem of ‘aggregation over time ’, set forth a framework for studying it, and achieved useful characterisations of it. Chapter 42 partly shared the destiny of John F. Muth's (1960, 1961) papers about rational expectations. It took years for other economists to recognise how much more could be done with their ideas. In 1960, both Phillips and Muth were far ahead of most other economists in their understanding of the technicalities of time series analysis, and their appreciation of its potential applications to economic dynamics. Economists were not to take up the inquiry from the point left off by Phillips until the early 1970s, when Rex Bergstrom, Christopher Sims, Peter Phillips and others returned to the problem of aggregation over time.
Phillips assumed that observations on a vector of data are generated by a continuous time vector stochastic process with a rational spectral density matrix. Continuous time processes with rational spectral densities form a natural environment for studying the effects of aggregation over time, for several interrelated reasons that Phillips described and exploited.
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