A class of generalized Lévy Laplacians in infinite dimensional calculus

A class of generalized Lévy Laplacians which contain as a special case the ordinary Lévy Laplacian are considered. Topics such as limit average of the second order functional derivative with respect to a certain equally dense (uniformly bounded) orthonormal base, the relations with Kuo’s Fourier transform and other infinite dimensional Laplacians are studied.

Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

Generalized ocean color inversion model for retrieving marine inherent optical properties

Ocean color measured from satellites provides daily, global estimates of marine inherent optical properties (IOPs). Semi-analytical algorithms (SAAs) provide one mechanism for inverting the color of the water observed by the satellite into IOPs. While numerous SAAs exist, most are similarly constructed and few are appropriately parameterized for all water masses for all seasons. To initiate community-wide discussion of these limitations, NASA organized two workshops that deconstructed SAAs to identify similarities and uniqueness and to progress toward consensus on a unified SAA. This effort resulted in the development of the generalized IOP (GIOP) model software that allows for the construction of different SAAs at runtime by selection from an assortment of model parameterizations. As such, GIOP permits isolation and evaluation of specific modeling assumptions, construction of SAAs, development of regionally tuned SAAs, and execution of ensemble inversion modeling. Working groups associated with the workshops proposed a preliminary default configuration for GIOP (GIOP-DC), with alternative model parameterizations and features defined for subsequent evaluation. In this paper, we: (1) describe the theoretical basis of GIOP; (2) present GIOP-DC and verify its comparable performance to other popular SAAs using both in situ and synthetic data sets; and, (3) quantify the sensitivities of their output to their parameterization. We use the latter to develop a hierarchical sensitivity of SAAs to various model parameterizations, to identify components of SAAs that merit focus in future research, and to provide material for discussion on algorithm uncertainties and future emsemble applications.

Analytically continued generalized continuum distorted waves

The continuum distorted-wave eikonal-initial-state (CDW-EIS) theory of Crothers and McCann (Crothers DSF and McCann JF, 1983 J. Phys. B: At. Mol. Opt. Phys. 16 3229 ) used to describe ionization in ion-atom collisions is generalized (G) to GCDW-EIS, to incorporate the azimuthal ange dependence into the final-state wavefunction. This is accomplished by the analytic continuation of hydrogenic-like wavefunctions from below to above threshold, using parabolic coordinates and quantum numbers including magnetic quantum numbers, thus providing a more complete set of states. At impact energies lower than 25 ke V u^{-1}, the total CDW-EIS ionization cross section falls off, with decreasing energy, too quickly in comparison with experimental data by Crothers and McCann. The idea behind and motivation for the GCDW-EIS model is to improve the theory with respect to experiment, by including contributions from non-zero magnetic quantum numbers. We also therefore incidentally provide a new derivation of the theory of continuum distorted waves for zero magnetic quantum numbers while simultaneously generalizing it.

Generalized compound transport of charged particles in turbulent magnetized plasmas

The transport of charged particles in partially turbulent magnetic systems is investigated from first principles. A generalized compound transport model is proposed, providing an explicit relation between the mean-square deviation of the particle parallel and perpendicular to a magnetic mean field, and the mean-square deviation which characterizes the stochastic field-line topology. The model is applied in various cases of study, and the relation to previous models is discussed.

A comprehensive comparison between generalized incidence calculus and Dempster-Shafer theory of evidence.

Dealing with uncertainty problems in intelligent systems has attracted a lot of attention in the AI community. Quite a few techniques have been proposed. Among them, the Dempster-Shafer theory of evidence (DS theory) has been widely appreciated. In DS theory, Dempster's combination rule plays a major role. However, it has been pointed out that the application domains of the rule are rather limited and the application of the theory sometimes gives unexpected results. We have previously explored the problem with Dempster's combination rule and proposed an alternative combination mechanism in generalized incidence calculus. In this paper we give a comprehensive comparison between generalized incidence calculus and the Dempster-Shafer theory of evidence. We first prove that these two theories have the same ability in representing evidence and combining DS-independent evidence. We then show that the new approach can deal with some dependent situations while Dempster's combination rule cannot. Various examples in the paper show the ways of using generalized incidence calculus in expert systems.