Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

Efficient computation of discrete polynomial transforms

This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )

Computation of discrete cosine transform using Clenshaw's recurence formula

Clenshaw’s recurrenee formula is used to derive recursive algorithms for the discrete cosine transform @CT) and the inverse discrete cosine transform (IDCT). The recursive DCT algorithm presented here requires one fewer delay element per coefficient and one fewer multiply operation per coeflident compared with two recently proposed methods. Clenshaw’s recurrence formula provides a unified development for the recursive DCT and IDCT algorithms. The M v e al gorithms apply to arbitrary lengtb algorithms and are appropriate for VLSI implementation.

ON MARGINALIZED MULTILEVEL MODELS AND THEIR COMPUTATION

Clustered data analysis is characterized by the need to describe both systematic variation in a mean model and cluster-dependent random variation in an association model. Marginalized multilevel models embrace the robustness and interpretations of a marginal mean model, while retaining the likelihood inference capabilities and flexible dependence structures of a conditional association model. Although there has been increasing recognition of the attractiveness of marginalized multilevel models, there has been a gap in their practical application arising from a lack of readily available estimation procedures. We extend the marginalized multilevel model to allow for nonlinear functions in both the mean and association aspects. We then formulate marginal models through conditional specifications to facilitate estimation with mixed model computational solutions already in place. We illustrate this approach on a cerebrovascular deficiency crossover trial.

A Restriction-Centered Theory of Reasoning and Computation to materialize a Web 3.0

Researchers suggest that personalization on the Semantic Web adds up to a Web 3.0 eventually. In this Web, personalized agents process and thus generate the biggest share of information rather than humans. In the sense of emergent semantics, which supplements traditional formal semantics of the Semantic Web, this is well conceivable. An emergent Semantic Web underlying fuzzy grassroots ontology can be accomplished through inducing knowledge from users' common parlance in mutual Web 2.0 interactions [1]. These ontologies can also be matched against existing Semantic Web ontologies, to create comprehensive top-level ontologies. On the Web, if augmented with information in the form of restrictions andassociated reliability (Z-numbers) [2], this collection of fuzzy ontologies constitutes an important basis for an implementation of Zadeh's restriction-centered theory of reasoning and computation (RRC) [3]. By considering real world's fuzziness, RRC differs from traditional approaches because it can handle restrictions described in natural language. A restriction is an answer to a question of the value of a variable such as the duration of an appointment. In addition to mathematically well-defined answers, RRC can likewise deal with unprecisiated answers as "about one hour." Inspired by mental functions, it constitutes an important basis to leverage present-day Web efforts to a natural Web 3.0. Based on natural language information, RRC may be accomplished with Z-number calculation to achieve a personalized Web reasoning and computation. Finally, through Web agents' understanding of natural language, they can react to humans more intuitively and thus generate and process information.