Selection, Stability and Renormalization

We illustrate how to extend the concept of structural stability through applying it to the front propagation speed selection problem. This consideration leads us to a renormalization group study of the problem. The study illustrates two very general conclusions: (1) singular perturbations in applied mathematics are best understood as renormalized perturbation methods, and (2) amplitude equations are renormalization group equations.Comment: 38 pages, LaTeX, two PostScript figures available by anonymous ftp to gijoe.mrl.uiuc.edu (128.174.119.153) files /pub/front_kkfest_fig

Development of a Portfolio Diet Score and Its Concurrent and Predictive Validity Assessed by a Food Frequency Questionnaire

The Portfolio Diet, a plant-based portfolio of cholesterol-lowering foods, has been shown to reduce low-density lipoprotein cholesterol (LDL-C), and other cardiovascular risk factors, in randomized controlled trials (RCTs). It is not known if these beneficial effects translate to a lower incidence cardiovascular disease (CVD) risk. To support examinations between Portfolio Diet adherence and disease, a Portfolio Diet score (PDS) was developed and its predictive and concurrent validity was assessed within the Toronto Healthy Diet Study, a six-month RCT in overweight adults. Predictive validity was assessed using change in the PDS measured by food frequency questionnaire (FFQ) and concomitant change in LDL-C from baseline to six months using multiple linear regression, adjusted for potential confounders (n = 652). Concurrent validity was assessed in a subset of participants (n = 50) who completed the FFQ and a 7-day diet record (7DDR) at baseline. The PDS determined from each diet assessment method was used to derive correlation coefficients and Bland–Altman plots to assess the between-method agreement. The change in PDS was inversely associated with change in LDL-C (β coefficients: −0.01 mmol/L (95% confidence intervals (CIs): −0.02, −0.002; p = 0.02). The correlation between the PDS from the FFQ and 7DDR was 0.69 (95% CIs: 0.48, 0.85). The Bland–Altman plot showed reasonable agreement between the score from the FFQ and 7DDR. These findings indicate predictive validity of the PDS with lower LDL-C, and reasonable concurrent validity of the PDS as assessed by an FFQ against a 7DDR