Download PDF by Tan Wai-Yuan: Stochastic Models with Applications to Genetics, Cancers,

By Tan Wai-Yuan

ISBN-10: 9810248687

ISBN-13: 9789810248680

ISBN-10: 9812777962

ISBN-13: 9789812777966

Show description

Read Online or Download Stochastic Models with Applications to Genetics, Cancers, AIDS and Other Biomedical Systems (Series on Concrete and Applicable Mathematics, Volume 4) PDF

Similar mathematics books

Download e-book for iPad: The Math Book: From Pythagoras to the 57th Dimension, 250 by Clifford A. Pickover

Math’s countless mysteries and wonder spread during this follow-up to the best-selling The technology publication. starting thousands of years in the past with old “ant odometers” and relocating via time to our modern day quest for brand new dimensions, it covers 250 milestones in mathematical heritage. one of the a number of delights readers will know about as they dip into this inviting anthology: cicada-generated major numbers, magic squares from centuries in the past, the invention of pi and calculus, and the butterfly impact.

Download PDF by Remigijus Paulavičius, Julius Žilinskas: Simplicial Global Optimization

Simplicial international Optimization is based on deterministic masking tools partitioning possible zone through simplices. This booklet appears into some great benefits of simplicial partitioning in worldwide optimization via functions the place the quest house should be considerably diminished whereas taking into consideration symmetries of the target functionality by way of surroundings linear inequality constraints which are controlled through preliminary partitioning.

Additional info for Stochastic Models with Applications to Genetics, Cancers, AIDS and Other Biomedical Systems (Series on Concrete and Applicable Mathematics, Volume 4)

Sample text

T, A(t)}'. Then under some general conditions, {X(t),t G T = ( 0 , 1 , . . ,oo)} is a multi-dimensional Markov chain with discrete time. This type of Markov chains in HIV epidemic has been developed by Tan and his associates in terms of chain binomial and chain multinomial distributions; see [7-12]. 2. }. Then the random behavior and properties of this Markov chain is characterized by the transition probabilities which is defined by pij(s,t) = P{X(t) = j\X(s) = i} for t > s. Prom these transition The Transition Probabilities and Computation 39 probabilities, obviously, we have: pij(s,s) = 5^, where 5^ is the Kronecker's 6 defined by da = 1 and S^ — 0 if i ^ j .

Let {S(t),I(u,t)} denote the numbers of S people and of I(u) people at the ith month respectively and A(t) the total number of AIDS cases including those died from AIDS by the ith month. Put X(t) = {S(t),I(u,t),u = 0 , 1 , . . ,t, A(t)}'. Then under some general conditions, {X(t),t G T = ( 0 , 1 , . . ,oo)} is a multi-dimensional Markov chain with discrete time. This type of Markov chains in HIV epidemic has been developed by Tan and his associates in terms of chain binomial and chain multinomial distributions; see [7-12].

The Transition Probabilities and Computation 43 The characteristic function (x) of Q is 4>{x) = \Q- xl4\ = (-x) ^ [ - - x \~X 1 I 8 V2 \ \ \ - X = -G-^)fG^)(i-)-fnG^)} =iG_:c)G":c)(4x2~2x~i)=oHence the eigenvalues of Q are {Ai = ^,A2 = \,\3 = \(1 + V§) = ^ei,A 4 = ^(1 — y/5) = 162}- Since all eigenvalues are real and distinct, Q can be expressed in terms of spectral expansion. The spectrum matrices of Q are: Ei = 1 (Q - X2I4)(Q - X3I4)(Q - A4/4) (Ax - A2)(A! - A3)(A! ) 4 V 4 2 / X 1 i / 4 £1 4 £1 4 1 J and £4 = -(Q-A1/4)(Q-A274)(Q-A3/4) (A 4 -A 1 )(A 4 -A 2 )(A 4 -A 3 )' 1 l(' + !

Download PDF sample

Stochastic Models with Applications to Genetics, Cancers, AIDS and Other Biomedical Systems (Series on Concrete and Applicable Mathematics, Volume 4) by Tan Wai-Yuan


by Robert
4.1

Rated 4.89 of 5 – based on 3 votes