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A Boolean network with only quadratic regulatory functions will be called a strictly quadratic network.
The proposed model is shown to be a convex quadratic network flow problem, for which we design an efficient Variational Inequality algorithm.
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Notice that in a strictly quadratic, bi-quadratic network every variable must have exactly two inputs and two outputs.
By connecting these as in the proof of Theorem 7, we achieve a strictly bi-quadratic network.
Alas, it will not give us all by itself strictly bi-quadratic networks.
Similarly, in strictly bi-quadratic networks, cooperativity does not imply additional bounds on p-c-chaos beyond the previously known bound of c < 10 1 / 4 for c-chaos.
But strictly bi-quadratic networks that are also p-unstable and p-c-chaotic can exist only if c < 3 (see Section 3.2), and we show that this bound is again optimal (Theorem 8).
The protein restraints are described by the quadratic elastic network model.
This paper focuses on the design of the intelligent rate control algorithm via introducing global rate distortion (RD) model constructed by quadratic neural network, by evaluating data-driven pattern analysis rather than rate-distortion mathematical models.
These values appear quite acceptable and indicate that the algorithm scales better than quadratic with network dimension.
While we do not know whether the bounds on α, p, and c in Theorem 6 are optimal, we conjecture that there are some nontrivial bounds on these parameters in bi-quadratic cooperative networks, that is, we conjecture that the analogue of Theorem 5 fails for this class of Boolean networks.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com