Advanced Methods of Physiological System Modeling: Volume 2 by Vasilis Z. Marmarelis (auth.), Vasilis Z. Marmarelis (eds.)

By Vasilis Z. Marmarelis (auth.), Vasilis Z. Marmarelis (eds.)

This quantity is the second one in a sequence of guides subsidized by means of the Biomedical Simulations source (BMSR) on the collage of Southern California that document on fresh learn advancements within the quarter of physiological platforms modeling and anal­ ysis of physiological signs. As within the first quantity of this sequence, the paintings said herein is anxious with the improvement of complex methodologies and their novel program to difficulties of biomedical curiosity, with emphasis on nonlinear elements of physiological functionality. The time period "advanced methodologies" is used to point that the scope of this paintings extends past the normal form of research utilized by so much investigators during this zone, that's constrained essentially within the linear area. because the im­ portance of nonlinearities in realizing the advanced mechanisms of physiological functionality is more and more famous, the necessity for powerful and functional methodolo­ gies that tackle the problem of nonlinear dynamics in existence sciences turns into a growing number of urgent. The ebook of those volumes and the workshops, geared up via the BMSR at the comparable topic, are key actions in our efforts to advertise and accentuate examine during this sector, foster interplay and collaboration between investigators, and disseminate contemporary effects during the biomedical community.

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The case of oscillatory behavior due to large sigmoid negative feedback is not covered by the Volterra-Wiener analysis presented in the previous section. It is, however, of great interest in physiology because of the numerous and functionally important physiological oscillators. It is a subject worthy of further exploration, albeit outside the scope of this article. We return to the study of the sigmoid feedback for small values of e. The effect of varying the slope of the sigmoid nonlinearity is demonstrated in Fig.

The obtained first-order Wiener kernel estimates for GWN input power level P = 1, 16, 256 and 4096 are shown in Fig. 46 (with appropriate offsets to allow easier visual inspection). The FFT magnitudes of these kernels are shown in Fig. 47, and they exhibit decreasing resonance frequency and broadening of the "tuning curve" as P increases. This transition pattern is similar to the one observed in auditory nerve fibers. Second-order kernels of some nonlinear feedback systems Our examples so far have employed nonlinear feedback with odd symmetry (cubic and sigmoid) and our attention has focused on first-order Wiener kernels of the resulting systems.

When the aj come from a Poisson process and the Aj are constant, the process has long been called shot noise, ego Weiss (1977). One could build a full stochastic model for the data by assuming some specific distribution for the Aj and aj' ego Poisson and gamma, and then seek maximum likelihood estimates of the unknown parameters. These estimates would be efficient in some sense. In what follows it will be assumed that the process M has increments satisfying cov (dM(t+u),dM(t)} = a 20(u)dtdu and cum (dM(t+u),dM(t+v),dM(t)} = ')'CJ3 0(u)0(v)dtdudv as would follow if the process M had independent increments and in particular for the A j independent and {aj} a Poisson process.

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