Geometric Properties of AR(q) Nonlinear Regression Models

This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].

CONFIDENCE REGIONS IN TERMS OF STATISTICAL CURVATURE FOR AR(q) NONLINEAR REGRESSION MODELS

This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence regions for parameters and parameter subsets in terms of statistical curvatures are given based on the likelihood ratio statistics and score statistics. Several previous results, such as [1] and [2] are extended to AR(q) nonlinear regression models.

Cross inhibition improves activity selection when switching incurs time costs

We consider a behavioural model of an animal choosing between two activities, based on positive feedback, and exa- mine the effect of introducing cross inhibition between the motivations for the two activities. While cross-inhibition has pre- viously been included in models of decision making, the question of what benefit it may provide to an animal＇s activity selection behaviour has not previously been studied. In neuroscience and in collective behaviour cross-inhibition, and other equivalent means of coupling evidence-accumulating pathways, have been shown to approximate statistically-optimal decision-making and to adaptively break deadlock, thereby improving decision performance. Switching between activities is an ongoing decision process yet here we also find that cross-inhibition robustly improves its efficiency, by reducing the frequency of costly switches between behaviours .

Low-protein diet accelerates wound healing in mice post-acute injury

Background:Wound healing processes are influenced by macronutrient intake(protein,carbohydrate and fat).The most favourable diet for cutaneous wound healing is not known,although highprotein diets are currently favoured clinically.This experimental study investigates the optimal macronutrient balance for cutaneous wound healing using a mouse model and the Geometric Framework,a nutrient modelling method,capable of analyzing the individual and interactive effects of a wide spectrum of macronutrient intake.Methods:Two adjacent and identical full-thickness skin excisions(1 cm^(2))were surgically created on the dorsal area of male C57BL/6 mice.Mice were then allocated to one of 12 high-energy diets that varied in protein,carbohydrate and fat content.In select diets,wound healing processes,cytokine expression,energy expenditure,body composition,muscle and fat reserves were assessed.Results:Using the Geometric Framework,we show that a low-protein intake,coupled with a balanced intake of carbohydrate and fat is optimal for wound healing.Mice fed a low-protein diet progressed quickly through wound healing stages with favourable wound inflammatory cytokine expression and significantly accelerated collagen production.These local processes were associated with an increased early systemic inflammatory response and a higher overall energy expenditure,related to metabolic changes occurring in key macronutrient reserves in lean body mass and fat depots.Conclusions:The results suggest that a low-protein diet may have a greater potential to accelerate wound healing than the current clinically used high-protein diets.