The detailed algebra of three-state Markov models taking de novo carcinoma into account is presented in Appendix A. Due to the Markov property that assumes that the next transition is dependent on the current transition but independent of the previous transition, annual transition rate follows an exponential distribution.
An abnormal spatial distribution of transition rate is observed in samples prepared with a two-step crystallization approach, in which samples crystallized at high temperature and then were quenched to low temperatures for further crystallization.
We estimated σ and δ using nonlinear mixed-effects models in R 2.1.1 [48]–[49] assuming a constant transition rate, which produces an exponential distribution of the proportion infected: where rate denotes the transition rates σ or δ.
The posterior distribution for transition rate α (I to R) was symmetric, but for the transition rate β (S to I) and ν (R to I), the posterior distributions were asymmetric.
This required deconvoluting the intrinsic distribution from the distribution arising from a finite value for n, and then determining the distribution in the f values that might arise from a distribution in the transition rate constants (see Appendix).
The Avrami index decreases to n < 1 for Ttr < 283 K, indicating a broadened distribution of the transition rate caused by the spatial heterogeneity of the amorphous state at low temperatures near the glass transition.
By fully exploiting the properties of 2-D cumulative distribution function and transition rate matrices, together with the convexification of uncertain domains, a sufficient condition for H∞ performance analysis is firstly derived, and then both the mode-dependent and mode-independent filter synthesis are developed, respectively.
Breeding in homogeneous habitats and uniform distribution patterns were identified as probable ancestral states in Ciconiiformes, but there was a significant transition rate from uniform to central-periphery distributions in species occupying homogeneous habitats.
That approach allows for a general model of evolutionary change to be used, however branch lengths, transition rates, and nucleotide distributions at the root must be estimated or integrated out.
From its current α value a cell adopts a new value α' with a transition rate R. α' is drawn from a Gaussian distribution p, centred around α with standard deviation σ.
