Formal Methods in Macro-Biology: First International by François Fages, Carla Piazza (eds.) PDF

By François Fages, Carla Piazza (eds.)

ISBN-10: 3319103970

ISBN-13: 9783319103976

ISBN-10: 3319103989

ISBN-13: 9783319103983

This ebook constitutes the refereed complaints of the 1st foreign convention on Formal tools in Macro-Biology, FMMB 2014, held in Nouméa, New Caledonia, in September 2014.
The 7 revised complete and three brief papers offered including 7 invited displays have been rigorously reviewed and chosen from 17 submissions. The clinical software comprises papers on a large choice of themes, together with ecological platforms, clinical functions, logical frameworks, and discrete non-stop and hybrid versions for the research of organic structures at macroscopic levels.

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Safety property ∀ Ψ. recurrence property ∀ Ψ. stabilisation property ∀ Ψ. We consider a continuous-time system S defined by a semiflow φ : X → (R+ → X) with initial set X0 : K(X), and temporal logic formulae based on an atomic proposition Ψ : X → S. The target property S |= ∀ Ψ translates to ∀x0 ∈ X0 , ∀ξ ∈ φ(x0 ), ∃t ∈ R+ , Ψ(ξ(t)). This is verifiable since the set of all trajectories φ(X0 ) = {φ(x0 ) | x0 ∈ X0 } is a compact subset of X[0,∞) , and path formula Ψ defines a set of valid trajectories {η ∈ X[0,∞) | ∃t ∈ R+ , Ψ(η(t))} which is open in X[0,∞) .

We first need to find a compact subset AX of X which we can guarantee contains the true state x. We then show that the derivative of the projection π(x) satisfies d (π ◦ x) = π (x)x˙ = π (x)f (x, u). dt and hence taking x ˜ = π(x) we have x ˜˙ ∈ F (˜ x) := {π (x)f (x, u) | x ∈ π −1 (˜ x) ∩ AX }. Model-Checking in Systems Biology - From Micro to Macro 13 The resulting system is a differential inclusion for the projection x ˜. Given an approximate reduction x ˜˙ = f˜(˜ x, u), we can alternatively write x˜˙ (t) = f˜(˜ x(t), u(t)) + e˜(t); e˜(t) ∈ E(˜ x(t), u(t)) where the error set E is given by E(˜ x, u) = {π (x)f (x, u) − f˜(π(x), u) | x ∈ π −1 (˜ x) ∩ AX }.

This is natural since open sets are those for which we can approximate from below. A probability measure on X is a valuation P such that P (X) = 1. Valuations are naturally equivalent to integrals of lower-semicontinuous funcn −1 tions ψ : X → H by X ψ dν = sup (pm , ∞]) | (p0 , . . , m=1 (pm − pm−1 ) ν(ψ ∗ pn ) ∈ Q , 0 = p0 < p1 < · · · < pn . The integral of a valuation ν : (X → S) → H is an additive functional (X → H) → H. Conversely, from such a functional, we can define a valuation by ν(U ) = χU .

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Formal Methods in Macro-Biology: First International Conference, FMMB 2014, Nouméa, New Caledonia, September 22-24, 2014. Proceedings by François Fages, Carla Piazza (eds.)


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