By Smirnov V.
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E. 33786. 068. 691). e. 23722. These defining ranges as evaluated above will however depend on the parameters of the utility function and will therefore be different for different investors according to the values assigned to his or her utility indices corresponding to the expected excess equity. 44 In general, if we have a parabolic utility function u (x) = a + bx – cx2, where c > 0 ensures concavity, then we have u’ (x) = b – 2cx and u’’ (x) = -2c. The Arrow-Pratt measure is given by λ (x) = 2c /(b–2cx).
Though benign tumors are usually not directly life threatening, some of the benign types do have the capability of becoming malignant. Therefore, viewed a stochastic process, a purely benign growth should approach some critical steady-state mass whereas any growth that subsequently becomes cancerous would fail to approach such a steady-state mass. One of the underlying premises of our model then is that cell population growth takes place according to the basic Markov chain rule such that the observed tumor mass in time tj+1 is dependent on the mass in time tj.
A neural network having no hidden layers at all basically becomes a linear classifier and is therefore statistically indistinguishable from the general linear regression model. Model premises: (1) The function governing the biochemical dynamics of cell population growth is inherently non-linear (2) The sudden and rapid degeneration of a benign cell growth to a malignant one may be attributed to an underlying chaotic attractor (3) Given adequate training data, a non-linear binary classification technique such as that of Artificial Neural Networks can learn to detect this underlying chaotic attractor and thereby prove useful in predicting whether a benign cell growth may subsequently turn cancerous Model structure: We propose a nested approach where we treat the output generated by an earlier phase as an input in a latter phase.