Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles

This thesis analyzes the Chow motives of 3 types of smooth projective varieties: the desingularized elliptic self fiber product, the Fano surface of lines on a cubic threefold and an ample hypersurface of an Abelian variety. For the desingularized elliptic self fiber product, we use an isotypic decomposition of the motive to deduce the Murre conjectures. We also prove a result about the intersection product. For the Fano surface of lines, we prove the finite-dimensionality of the Chow motive. Finally, we prove that an ample hypersurface on an Abelian variety possesses a Chow-Kunneth decomposition for which a motivic version of the Lefschetz hyperplane theorem holds.

Finite mixture distributions, sequential likelihood and the EM algorithm

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log-likelihood function. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.

Ptolemaic Mummy Stuffings, 2: A Comic Fragment and Grammatical Text in the Yale Collection (P. CtYBR inv. 5019, 5043)

This is the second installment of a three-part project to publish a group of ten Ptolemaic papyri purchased by Yale’s Beinecke Library in 1998 (acquisition “1998b”), which came to the Beinecke as three hard wads that were apparently the stuffing from the stomach cavity of a mummified animal. This article publishes: (1) P.CtYBR inv. 5019, a fragment of line ends in iambic tetrameter catalectic meter from an unknown comedy; the format suggests that this is a further example of certain type of Ptolemaic writing exercise. (2) P.CtYBR inv. 5043, a fragmentary grammatical text of uncertain import.