Download An Introduction to Systems Biology: Design Principles of by Uri Alon PDF

By Uri Alon

Thorough and obtainable, this ebook offers the layout ideas of organic platforms, and highlights the habitual circuit parts that make up organic networks. It presents an easy mathematical framework which might be used to appreciate or even layout organic circuits. The textavoids expert phrases, focusing as an alternative on a number of well-studied organic platforms that concisely show key rules. An advent to structures Biology: layout ideas of organic Circuits builds a superb starting place for the intuitive realizing of basic ideas. It encourages the reader to invite why a process is designed in a selected means after which proceeds to respond to with simplified versions.

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Extra info for An Introduction to Systems Biology: Design Principles of Biological Circuits (Chapman & Hall CRC Mathematical & Computational Biology)

Sample text

Note however that the projected state is generally not error–free since the symmetric subspace contains states which are not of the simple product form | Ψ | Ψ . . | Ψ . Nevertheless it has been shown that the error probability will be suppressed by a factor of 1/R [39]. More recently projections on symmetric subspaces were replaced by more complicated projections on carefully selected subspaces. These projections, proposed by Shor [40], Calderbank and Shor [41], Steane [42] and others [43, 44, 45, 46, 47], are constructed on the basis of classical error-correcting methods but represent intrinsically new quantum error-correction and stabilisation schemes; they are the subject of much current study.

H. Zurek, Phys. Rev. Lett. 77, 198 (1996). [45] D. Gottesman, Phys. Rev. A 54, 1862 (1996). R. M. W. A. Sloane, Phys. Rev. Lett. 78, 405 (1997). [47] E. Knill and R. Laflamme, e-print quant-ph/9608012 (1996). W. P. W. Shor, Phys. Rev. Lett. 77, 3260 (1996). Solovay, “Lie groups and quantum circuits”, preprint 1999.

X1 x0 mxn−1 ... | mx1 | mx0 = | x | Mx , (107) where xi ∈ {0, 1}. Then a superposition α | x + β | y evolves as (α | x + β | y ) | M → α | x | Mx + β | y | My , (108) but now the scalar product Mx | My which reduces the off-diagonal elements of the density operator of the whole register and which affects the probabilities in the interference experiment is given by Mx | My = mx0 | my0 mx1 | my1 ... e. g. the Hamming distance between 101101 and 111101 is 1 because the two binary string differ only in the second binary place).

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