MODEL SELECTION METHOD BASED ON MAXIMAL INFORMATION COEFFICIENT OF RESIDUALS

The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this ar- ticle, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coe^cient （MIC）, a recently proposed dependence measure, captures a wide range of associ- ations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient （PMIC） is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given.

A much better replacement of the Michaelis—Menten equation and its application

Michaelis-Menten equation is a basic equation of enzyme kinetics and gives acceptable approximations of real chemical reaction processes.Analyzing the derivation of this equation yields the fact that its good performance of approximating real reaction processes is due to Michaelis-Menten curve(8).This curve is derived from Quasi-Steady-State Assumption(QSSA),which has been proved always true and called Quasi-Steady-State Law by Banghe Li et al.[Quasi-steady state laws in enzyme kinetics,J.Phys.Chem.A 112(11)(2008)2311-2321].Here,we found a polynomial equation with total degree of four A(S,E)= 0(14),which gives more accurate approximation of the reaction process in two aspects:during the quasi-steady-state of the reaction,Michaelis-Menten curve approximates the reaction well,while our equation A(S,E)= 0 gives better approximation;near the end of the reaction,our equation approaches the end of the reaction with a tangent line the same to that of the reaction process trajectory simulated by mass action,while MicheielisMenten curve does not.In addition,our equation A(S,E)= 0 differs to Michaelis-Menten curve less than the order of 1/S^3 as S approaches +∞.By considering the above merits of A(S,E)= 0,we suggest it as a replacement of Michaelis-Menten curve.Intuitively,this new equation is more complex and harder to understand.But,just because of its complexity,it provides more information about the rate constants than Michaelis-Menten curve does.Finally,we get a better replacement of the Michaelis-Menten equation by combing 4(S,E)= 0 and the equation dP/dt = k2C(t).