Systems Biology (Methods in Molecular Biology)

then it is called stable equilibrium point. As in scalar equations, by expanding the Taylor’s series forf(x,y) andg(x,y); u_¼x_¼ ...

l Stable (or neutrally stable). Each trajectory move about the critical point within a finite range of distance. l Definition(Hy ...

J¼ ∂f 1 ∂x ∂f 1 ∂y ∂f 2 ∂x ∂f 2 ∂y 0 B B @ 1 C C A ð^34 Þ A.5 Hopf Bifurcation Using the following procedure it is possible to c ...

A.7 Singular Value Decomposition EveryA, matrixmn,mncan be decomposed as A¼UΣVT ð 39 Þ where (.)Tdenotes the transposed matrix ...

A.9 Stochastic Resonance Since several times the system shows a bistability one can consider the following stochastic equation: ...

produced is a stochastic version of the trajectory that would be obtained by solving the corresponding stochastic differential e ...

l Inverse problem solving tools for solving inverse problems. An open-source Python library for modelling and inversion in geoph ...

Guzzi R (2012) Introduction to inverse meth- ods with applications to geophysics and remote sensing (in Italian). Earth science ...

Chapter 7 Systems Biology Approach and Mathematical Modeling for Analyzing Phase-Space Switch During Epithelial-Mesenchymal Tran ...

entropyvalues [1]. By analogy, in biological systems, among the most reliable potential functions which describe such transition ...

feedback and feedforward loops that give rise to complex dynamics, it is difficult to elucidate cell behavior from these regulat ...

the very specific nonlinear dynamics to which the different system components are subjected. In Biology, the mesoscopic level us ...

similar at all scales of physical observation [18]. Order parameters, like the physical observables, thus enable in capturing th ...

allowing such polarized cells to undergo multiple biochemical and/or structural changes that enable them to assume a mesenchy- m ...

Modeling may ultimately help recognizing critical factors and steps in promoting tumor reversal. Two methodological directions a ...

the healthy (stable) equilibrium (see Fig. 1b). It is worthwhile stressing that a stable dynamics should not be confused with a ...

suitable numerical implementations [29]. By means of numerical algorithms, mathematical models so complex that they are not amen ...

step towards full transformation into fibrosis or an even worse (cancer) phenotype [31]. On the other hand, EMT is still a rever ...

The cell density should also be considered an “environmental” constraint. Indeed, experiments performed at different densities t ...

Moreover, the fractal dimension epitomizes themorphologi- cal complexityof the overall cell system, by referring to the minimal ...