In this paper, these concepts are defined in algebraic terms, using morphisms, functors and natural transformations. It is argued that inference on the basis of a model is not possible unless the model admits a natural extension that includes the domain for which inference is required., When there is only one covariate, p = 1, we simply write x1 = x11; : : : ; xn = xn1. The the picture below illustrates the logistic regression model, where the red points correspond to the data values (x1; Y1); : : : ; (xn; Yn) of the covariate and response, and the black curve shows the probability function p(x) = e 0+ 1x 1+e 0+ 1x :, Model theory is the branch of logic that deals with mathematical structures and the formal languages they interpret. First order logic is the most important formal language and its model theory is a rich and interesting subject with significant applications to the main body of mathematics., The CAPM can be used to price an asset. In order to see how this is done consider an asset that is purchased for the price P and later sold at the price Q. We model the sale price Q as a random variable with mean μQ. The rate of return and expected rate of return for this asset are P = r P − Q and μQ − P μr = . P, Model Predictive Control linear convex optimal control finite horizon approximation model predictive control fast MPC implementations supply chain management, .