A theoretical justification for the random vector version of the functional-link (RVFL) net is presented in this paper, based on a general approach to adaptive function approximation. The approach consists of formulating a limit-integral representation of the function to be approximated and subsequently evaluating that integral with the Monte-Carlo method. Two main results are: (1) the RVFL is a universal approximator for continuous functions on bounded finite dimensional sets, and (2) the RVFL is an efficient universal approximator with the rate of approximation error convergence to zero of order O(C/ radicaln), where n is number of basis functions and with C independent of n. Similar results are also obtained for neural nets with hidden nodes implemented as products of univariate functions or radial basis functions. Some possible ways of enhancing the accuracy of multivariate function approximations are discussed.

Double-quantum light scattering by a system of molecules is discussed in this paper. Expressions have been obtained for the scattered light intensity considering both the coherent and incoherent contributions. In that coherent contributions are also considered in this treatment, it goes beyond the scope of previous studies. It is shown that, for molecules of low symmetry, elliptically polarized light must be used in order to determine five independent quadratic forms in the 18 symmetric components (βijk+βikj). According to the present results, the apparent discrepancy between the observed value of ⅓ for the depolarization ratio for CCl4 and the value to be expected from theory may be due to the fact that the coherent contribution had been neglected in previous theoretical considerations. In general, orientational correlation is essential if there is to be appreciable contribution from coherent scattering. For macromolecules, this constitutes a major difference between single- and double-quantum scattering, and additional information may be expected if the latter is investigated experimentally.

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A major problem in studying biological traits is understanding how genes work together to provide organismal structures and functions. Conventional reductionist paradigms attribute functions to particular proteins, motifs, and amino acids. An equally important but harder problem involves the synthesis of data at fundamental levels of biological systems to understand functionality at higher levels. We used subtle, naturally occurring, multigenic variation of cardiovascular (CV) properties in a panel of genetically randomized strains that are derived from the A/J and C57BL/6J strains of mice to perturb CV functions in nonpathologic ways. In this proof-of-concept study, computational analysis correctly identified the known relations among CV properties and revealed functionality at higher levels of the CV system. The network was then used to account for pleiotropies and homeostatic responses in single gene mutant mice and in mice treated with a pharmacologic agent (anesthesia). The CV network accounted for functional dependencies in complementary ways to the insights obtained from genetic networks and biochemical pathways. These networks are therefore an important approach for defining and characterizing functional relations in complex biological systems in health and disease.