1,501 research outputs found
On Characterization of Inverse Data in the Boundary Control Method
We deal with a dynamical system
\begin{align*} & u_{tt}-\Delta u+qu=0 && {\rm in}\,\,\,\Omega \times (0,T)\\
& u\big|_{t=0}=u_t\big|_{t=0}=0 && {\rm in}\,\,\,\overline \Omega\\ &
\partial_\nu u = f && {\rm in}\,\,\,\partial\Omega \times [0,T]\,,
\end{align*} where is a bounded domain, a real-valued function, the outward normal to , a solution. The input/output correspondence is realized
by a response operator
and its relevant extension by hyperbolicity . Ope\-rator is
determined by , where . The inverse problem is: Given to
recover in . We solve this problem by the boundary control method
and describe the {\it ne\-ces\-sary and sufficient} conditions on ,
which provide its solvability.Comment: 33 pages, 1 figur
Tropical geometries and dynamics of biochemical networks. Application to hybrid cell cycle models
We use the Litvinov-Maslov correspondence principle to reduce and hybridize
networks of biochemical reactions. We apply this method to a cell cycle
oscillator model. The reduced and hybridized model can be used as a hybrid
model for the cell cycle. We also propose a practical recipe for detecting
quasi-equilibrium QE reactions and quasi-steady state QSS species in
biochemical models with rational rate functions and use this recipe for model
reduction. Interestingly, the QE/QSS invariant manifold of the smooth model and
the reduced dynamics along this manifold can be put into correspondence to the
tropical variety of the hybridization and to sliding modes along this variety,
respectivelyComment: conference SASB 2011, to be published in Electronic Notes in
Theoretical Computer Scienc
Flexible and robust networks
We consider networks with two types of nodes. The v-nodes, called centers,
are hyper- connected and interact one to another via many u-nodes, called
satellites. This central- ized architecture, widespread in gene networks,
possesses two fundamental properties. Namely, this organization creates
feedback loops that are capable to generate practically any prescribed
patterning dynamics, chaotic or periodic, or having a number of equilib- rium
states. Moreover, this organization is robust with respect to random
perturbations of the system.Comment: Journal of Bioinformatics and Computational Biology, in pres
- …