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It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators.
An interesting observation that can be made from the similarities between the receptive field families derived by necessity from the assumptions and receptive profiles found by cell recordings in biological vision is that receptive fields in the retina, LGN, and V1 of higher mammals are very close to ideal in view of the stated structural requirements/symmetry properties.
A main theoretical argument is that idealized models for linear receptive fields can be derived by necessity given a small set of symmetry requirements that reflect properties of the world that one may naturally require an idealized vision system to be adapted to.
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The necessity condition of optimal control is derived by using the first order Gâteaux derivative of cost functional and adjoint equation.
The necessity condition of optimal control is derived by using the first order Gâteaux derivative of the cost functional and the adjoint equation.
Necessity of the condition follows by taking the test function in (4.2) and observing that for those and which satisfy the conditions and (see also [31, Theorem 6.6.1, page 418] for the similar arguments) while necessity of the condition can be derived by choosing the test function and taking into account the estimate for and.
Thus, the non-specific binding observed for any binder selected appears to be intrinsic to just that sdAb, however it points out the necessity to critically evaluate specificity for binders derived by this or similar methods.
However, optimal solution derived by solving the MDP is also 5% better than heuristic solutions suggesting the necessity to develop better heuristics in future.
Thus pacifism is usually derived by negation.
BY necessity, venture capitalists are trend predictors.
Her pictures are talismans of mystical devotion derived from inner necessity, conceived as teaching tools for lost souls.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com