Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

The transtheoretical model in weight management: Validation of the Processes of Change Questionnaire

Objective: The processes of change implied in weight management remain unclear. The present study aimed to identify these processes by validating a questionnaire designed to assess processes of change (the P-Weight) in line with the transtheoretical model. The relationship of processes of change with stages of change and other external variables is also examined. Methods: Participants were 723 people from community and clinical settings in Barcelona. Their mean age was 32.07 (SD = 14.55) years; most of them were women (75.0%), and their mean BMI was 26.47 (SD = 8.52) kg/m2. They all completed the P-Weight and the stages of change questionnaire (SWeight), both applied to weight management, as well as two subscales from the Eating Disorders Inventory-2 and Eating Attitudes Test-40 questionnaires about the concern with dieting. Results: A 34-item version of the PWeight was obtained by means of a refinement process. The principal components analysis applied to half of the sample identified four processes of change. A confirmatory factor analysis was then carried out with the other half of the sample, revealing that the model of four freely correlated first-order factors showed the best fit (GFI = 0.988, AGFI = 0.986, NFI = 0.986, and SRMR = 0.0559). Corrected item-total correlations (0.322-0.865) and Cronbach"s alpha coefficients (0.781-0.960) were adequate. The relationship between the P-Weight and the S-Weight and the concern with dieting measures from other questionnaires supported the validity of the scale. Conclusion: The study identified processes of change involved in weight management and reports the adequate psychometric properties of the P-Weight. It also reveals the relationship between processes and stages of change and other external variables.