By Kazem Mahdavi, Rebecca Culshaw, John Boucher

ISBN-10: 9812700153

ISBN-13: 9789812700155

ISBN-10: 9812706798

ISBN-13: 9789812706799

This quantity is a suite of papers on a number of components of present curiosity in mathematical biology, corresponding to epidemic affliction modeling, together with the consequences of vaccination and pressure substitute; immunology, corresponding to T-Cell dynamics and the mechanism of phagocytosis; knot conception; DNA computation; and Boolean networks.

**Read or Download Current Developments in Mathematical Biology: Proceedings of the Conference on Mathematical Biology and Dynamical Systems, the University of Texas at Tyler, ... 2005 (Series on Knots and Everything) PDF**

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**Additional resources for Current Developments in Mathematical Biology: Proceedings of the Conference on Mathematical Biology and Dynamical Systems, the University of Texas at Tyler, ... 2005 (Series on Knots and Everything)**

**Example text**

An ∈ ZZ− {0} and n even or odd, the numerical continued fraction F (T ) = F ([[a1 ], [a2 ], . . , [an ]]) = [a1 , a2 , . . , an ] 1 := a1 + , a2 + · · · + a 1+ 1 n−1 an If a rational tangle T changes by an isotopy, the associated continued fraction form may also change. However, the fraction is a topological invariant of T and does not change. For example, [2, −2, 3] = [1, 2, 2] = 75 , see Figure 7. The fraction characterizes the isotopy class of T . For the isotopy type of a rational tangle T with fraction pq we shall use the notation [ pq ].

Having chosen these children, we next assign Boolean functions to them. Independently, for each child w of τ (us ), let φi be assigned to it. This event has probability pi , and for j = 1, . . , mi , the probability that τ (us ) is the jth in-gate of w is 1/n. Summing over all i, we get the probability that τ (us ) directly 2nd Reading November 21, 2006 17:57 B-455 Current Developments in Mathematical Biology Trim Size: 9in x 6in Dynamics of Random Boolean Networks ch02 29 aﬀects w: ∞ mi pi i=1 pr(τ (us )is the jth in-gate of w, the initial state is x, x∈{ 0,1 }mi j=1 and us directly aﬀects w on input x | fw = φi ) ∞ = i=1 = pi n γ(φi , x)aυ(x) (1 − a)mi −υ(x) x∈{ 0,1 }mi λ .

Let u, v ∈ { 1, . . , n } and x ∈ { 0, 1 }n. We say that v aﬀects u at time t on input x if But (x) = But (xv ). We put At+ (v, x) = { u ∈ V : v aﬀects u at time t on input x } At− (v, x) and = { u ∈ V : u aﬀects v at time t on input x }. 5. , B t (x) = B t (xv ). Note that if v is t-ineﬀective for some t, then it is weak. In analyzing the robustness of Boolean networks, we will estimate the number of t-ineﬀective gates, for suitable t, since this appears more tractable than estimating the number of weak gates.

### Current Developments in Mathematical Biology: Proceedings of the Conference on Mathematical Biology and Dynamical Systems, the University of Texas at Tyler, ... 2005 (Series on Knots and Everything) by Kazem Mahdavi, Rebecca Culshaw, John Boucher

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