Associate Professor Turnover at America’s Public and Private Institutions of Higher Education

This paper uses data from the American Association of University Professors annual salary survey to compute continuation rates for associate professors at American colleges and universities during the 1996-97 to 2001-2002 period. Findings demonstrate that average continuation rates are higher for private academic institutions than for public academic institutions in bachelors-level, masters-level and doctoral-level institutions. Multivariate analyses indicate that the average level of faculty compensation at an institution is an important predictor of the continuation rate. All other things held equal, institutions with higher average faculty compensation have higher continuation rates. However, the magnitude of this relationship is not sufficiently large enough to warrant change in compensation policies at academic institutions, particularly between public and private institutions. The benefits associated with raising average faculty compensation to increase the tenured faculty’s continuation rates at public universities are unlikely to match or exceed the costs of doing so

Weyl-type hybrid subconvexity bounds for twisted LL-functions and Heegner points on shrinking sets

We prove a Weyl-type subconvexity bound for the central value of the $L$-function of a Hecke-Maass form or a holomorphic Hecke eigenform twisted by a quadratic Dirichlet character, uniform in the archimedean parameter as well as the twisting parameter. A similar hybrid bound holds for quadratic Dirichlet $L$-functions, improving on a result of Heath-Brown. As a consequence of these new bounds, we obtain explicit estimates for the number of Heegner points of large odd discriminant in shrinking sets.Comment: 27 pages. v2: Numerous improvements to the exposition. v3: refereed version with further improvement

The Computable Universe Hypothesis

When can a model of a physical system be regarded as computable? We provide the definition of a computable physical model to answer this question. The connection between our definition and Kreisel's notion of a mechanistic theory is discussed, and several examples of computable physical models are given, including models which feature discrete motion, a model which features non-discrete continuous motion, and probabilistic models such as radioactive decay. We show how computable physical models on effective topological spaces can be formulated using the theory of type-two effectivity (TTE). Various common operations on computable physical models are described, such as the operation of coarse-graining and the formation of statistical ensembles. The definition of a computable physical model also allows for a precise formalization of the computable universe hypothesis--the claim that all the laws of physics are computable.Comment: 33 pages, 0 figures; minor change

Vibration-based damage detection in an aircraft wing scaled model using principal component analysis and pattern recognition

This study deals with vibration-based fault detection in structures and suggests a viable methodology based on principal component analysis (PCA) and a simple pattern recognition (PR) method. The frequency response functions (FRFs) of the healthy and the damaged structure are used as initial data. A PR procedure based on the nearest neighbour principle is applied to recognise between the categories of the damaged and the healthy wing data. A modified PCA method is suggested here, which not only reduces the dimensionality of the FRFs but in addition makes the PCA transformed data from the two categories more differentiable. It is applied to selected frequency bands of FRFs which permits the reduction of the PCA transformed FRFs to two new variables, which are used as damage features. In this study, the methodology is developed and demonstrated using the vibration response of a scaled aircraft wing simulated by a finite element (FE) model. The suggested damage detection methodology is based purely on the analysis of the vibration response of the structure. This makes it quite generic and permits its potential development and application for measured vibration data from real aircraft wings as well as for other real and complex structures