Machine learning and automated theorem proving by Bridge, James P

By Bridge, James P

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Indeed the minimum (or the minima; uniqueness is not proved) lies on the boundary of the closed cone of the non-negative vectors and, as a result, minima must have several zero values. This effect appears in the use of iterative methods converging to these minima and is known as checkerboarding effect. From these remarks one can draw the conclusion that, if one defines a set of approximate solutions as (24), then this set is too broad. Indeed, it contains both the minima of the Csiszár I-divergence and the correct solution (if is correctly chosen) and therefore it contains very different objects.

We conclude this section with a generalization and refinement of the previous model. In the case of fluorescence microscopy where photons are detected by means of a Charge-Coupled Device (CCD), in addition to photon noise, described above, one should also take into account so-called Read-Out Noise (RON) [64]. This is a white additive Gaussian noise and is statistically independent of the photon noise, so that we have a combination of the two types of noise described above. Since each Gm is the sum of two independent RVs, one with a Poisson distribution and the other with a Gaussian one, it follows that the probability density of the detected signals is given by M +∞ PG (g|f) = e−(Af)m m=1 k=0 (Af)km PRON (gm − k), k!

SIAM Rev. : Electrode models for electric current computed tomography. IEEE Trans. Biomed. Engr. : Recent developments in inverse acoustic scattering theory. SIAM Rev. : The linear sampling method in inverse electromagnetic scattering theory. : A simple method for solving inverse scattering problems in the resonance region. Inverse Problems. : Inverse acoustic and electromagnetic scattering theory. 2nd ed. : A linear sampling method for the detection of leukemia by using microwaves. SIAM J. Appl.

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