Wavefront and ray-density plots using seventh-order matrices

The optimization of an optical system benefits greatly from a study of its aberrations and an identification of each of its elements' contribution to the overall aberration figures. The matrix formalism developed by one of the authors was the object of a previous paper and allows the expression of image-space coordinates as high-order polynomials of object-space coordinates. In this paper we approach the question of aberrations, both through the evaluation of the wavefront evolution along the system and its departure from the ideal spherical shape and the use of ray density plots. Using seventh-order matrix modeling, we can calculate the optical path between any two points of a ray as it travels along the optical system and we define the wavefront as the locus of the points with any given optical path; the results are presented on the form of traces of the wavefront on the tangential plane, although the formalism would also permit sagital plane plots. Ray density plots are obtained by actual derivation of the seventh-order polynomials.Comment: 15 pages, 5 figure

On the Phases Structure of the Micromaser System

We investigate, in an exact manner, the phase structure of the micromaser system in terms of the physical parameters at hand like the atom cavity transit time, the atom-photon frequency detuning, the number of thermal photons and the probability for a pump atom to be in its excited state. Phase diagrams are mapped out for various values of the physical parameters. At sufficiently large values of the detuning, we find a ``twinkling'' mode of the micromaser system. A correlation length is used to study fluctuations close to the various phase transitions.Comment: 4 pages, 4 figure

Bylaw Governance

This article argues that Delaware corporate law permits shareholders to use bylaws to circumscribe the managerial authority of the board of directors. While shareholders cannot mandate action by the board, they can enact specific prohibitions on its behavior, so long as the board retains enough discretion to implement—in practice, not merely in theory—its managerial policies by other means. The use of such circumscribing bylaws to discourage shirking (or analogous managerial abuses) by the directors or officers resembles the use of negative covenants in debt contracts that seek to prevent the debtor from squandering assets. Bylaw governance thus subtly but significantly reallocates governance power within the corporation, so as to reduce the agency costs of management. Its legal validity should also prompt courts and scholars alike to focus less on the quantity of power wielded by the shareholders, and more on the ways that power can be configured to produce managerial efficiencies

kk-Theory for Banach Algebras I: The Non-Equivariant Case

kk$^{\text{ban}}$ is a bivariant K-theory for Banach algebras that has reasonable homological properties, a product and is Morita invariant in a very general sense. We define it here by a universal property and ensure its existence in a rather abstract manner using triangulated categories. The definition ensures that there is a natural transformation from Lafforgue's theory KK$^{\text{ban}}$ into it so that one can take products of elements in KK$^{\text{ban}}$ that lie in kk$^{\text{ban}}$.Comment: 43 page

Temiar Reduplication in One-Level Prosodic Morphology

Temiar reduplication is a difficult piece of prosodic morphology. This paper presents the first computational analysis of Temiar reduplication, using the novel finite-state approach of One-Level Prosodic Morphology originally developed by Walther (1999b, 2000). After reviewing both the data and the basic tenets of One-level Prosodic Morphology, the analysis is laid out in some detail, using the notation of the FSA Utilities finite-state toolkit (van Noord 1997). One important discovery is that in this approach one can easily define a regular expression operator which ambiguously scans a string in the left- or rightward direction for a certain prosodic property. This yields an elegant account of base-length-dependent triggering of reduplication as found in Temiar.Comment: 9 pages, 2 figures. Finite-State Phonology: SIGPHON-2000, Proceedings of the Fifth Workshop of the ACL Special Interest Group in Computational Phonology, pp.13-21. Aug. 6, 2000. Luxembour

Optimal and fast detection of spatial clusters with scan statistics

We consider the detection of multivariate spatial clusters in the Bernoulli model with $N$ locations, where the design distribution has weakly dependent marginals. The locations are scanned with a rectangular window with sides parallel to the axes and with varying sizes and aspect ratios. Multivariate scan statistics pose a statistical problem due to the multiple testing over many scan windows, as well as a computational problem because statistics have to be evaluated on many windows. This paper introduces methodology that leads to both statistically optimal inference and computationally efficient algorithms. The main difference to the traditional calibration of scan statistics is the concept of grouping scan windows according to their sizes, and then applying different critical values to different groups. It is shown that this calibration of the scan statistic results in optimal inference for spatial clusters on both small scales and on large scales, as well as in the case where the cluster lives on one of the marginals. Methodology is introduced that allows for an efficient approximation of the set of all rectangles while still guaranteeing the statistical optimality results described above. It is shown that the resulting scan statistic has a computational complexity that is almost linear in $N$.Comment: Published in at http://dx.doi.org/10.1214/09-AOS732 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org