Correlation spatiotemporal

Masuda, A., Ushdia, K and Okamoto, T. (2005) New fluorescence correlation spectroscopy enabbng direct observation of spatiotemporal dependence of diffusion constants as an evidence of anomalous transport in extracellular matrices. Biophys.J., 88, 3584—3591. 

This section is devoted to biological order, organization, and evolution. We have already seen in Appendix F that constructive integration of quantum and thermal correlations under appropriate conditions lead to a so-called CDS, i.e., an optimal spatiotemporal structure formed by the precise relations between time, size, and temperature scales. CDS suggests microscopic selforganization including Godel-like self-referential traits. 

Despite the strong evidence ofthe antioxidant properties of flavonoids, demonstrated under in vitro conditions, the putative in-planta function remains unclear (Hernandez et al, 2009). Experimental data suggests that flavonols and flavan-3-ols, may act as antioxidants in plants, but the chemical diversity and complex biochemistry has hindered efforts to establish an unequivocal correlation between the spatiotemporal localization of flavonoids and oxidative stress reactions (Hernandez et al, 2009). 

Hebert B, Costantino S, Wiseman PW. Spatiotemporal image correlation spectroscopy (STICS) theory, verification, and application to protein velocity mapping in living CHO cells. Biophys. J. 2005 88 3601-3614. 

There are many reports on the regulation of FGFs and their mRNAs in the injured spinal cord and in the pathologic brain. Experimentally induced demyelina-tion of the spinal cord leads to an increase in FGF-1 which correlates with the beginning of remyelination.89 Spinal cord injury was also found to increase the expression of FGF-1 and FGF-2 in a differential spatiotemporal pattern.64 65 Elevated levels of the FGF-2 protein correlate with an increase of cellular (glial) and interstitial FGF-2 immunoreactivity.65 FGF-1 immunoreactivity present in ventral motoneurons is amplified after destruction of the spinal cord.64 These results imply that FGF-1 and FGF-2 subserve distinct roles following spinal cord lesion. 

Direct observation of spatiotemporal dependence of anomalous diffusion in inhomogeneous fluid by sampling-volume-controlled fluorescence correlation spectroscopy. Phys. Rev. E, 72, 060101. 

Taking the hard sphere colloids as a reference state, the mean-square displacement (MSD) in dilute suspensions is associated with the particle self-diffusion whereas at finite volume fractions the onset of interactions marks the alteration of the dynamics. The latter can be probed by the intermediate scattering function C(, t) which measures the spatiotemporal correlations of the thermal volume fraction fluctuations [91]. Figure depicts two representations (lower inset and main plot) of the non-exponential for a nondilute hard sphere colloidal... 

Computational techniques are centrally important at every stage of investigation of nonlinear dynamical systems. We have reviewed the main theoretical and computational tools used in studying these problems among these are bifurcation and stability analysis, numerical techniques for the solution of ordinary differential equations and partial differential equations, continuation methods, coupled lattice and cellular automata methods for the simulation of spatiotemporal phenomena, geometric representations of phase space attractors, and the numerical analysis of experimental data through the reconstruction of phase portraits, including the calculation of correlation dimensions and Lyapunov exponents from the data. 

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