Least-squares integration of one-dimensional codistributions with application to approximate feedback linearization

We study the problem of approximating one-dimensional nonintegrable codistributions by integrable ones and apply the resulting approximations to approximate feedback linearization of single-input systems. The approach derived in this paper allows a linearizable nonlinear system to be found that is close to the given system in a least-squares (L ₂) sense. A linearly controllable single-input affine nonlinear system is feedback linearizable if and only if its characteristic distribution is involutive (hence integrable) or, equivalently, any characteristic one-form (a one-form that annihilates the characteristic distribution) is integrable. We study the problem of finding (least-squares approximate) integrating factors that make a fixed characteristic one-form close to being exact in anL ₂ sense. A given one-form can be decomposed into exact and inexact parts using the Hodge decomposition. We derive an upper bound on the size of the inexact part of a scaled characteristic one-form and show that a least-squares integrating factor provides the minimum value for this upper bound. We also consider higher-order approximate integrating factors that scale a nonintegrable one-form in a way that the scaled form is closer to being integrable inL ₂ together with some derivatives and derive similar bounds for the inexact part. This allows a linearizable nonlinear system that is close to the given system in a least-squares (L ₂) sense together with some derivatives to be found. The Sobolev embedding techniques allow us to obtain an upper bound on the uniform (L _∞) distance between the nonlinear system and its linearizable approximation. This research was supported in part by NSF under Grant PYI ECS-9396296, by AFOSR under Grant AFOSR F49620-94-1-0183, and by a grant from the Hughes Aircraft Company.     

Semantic priming after severe closed head trauma: Automatic and attentional processes.

The 2-process theory of semantic priming (J. H. Neely, 1977; M. I. Posner and C. R. Snyder, 1975) was used to determine the maintenance of automatic processes after severe closed head injury (CHI) and to determine whether processes that demand attention suffer a deficit. Ss with severe CHI (N?=?18,?>?2 yrs postinjury) and 18 matched control Ss completed a lexical decision task in which a category prime was followed by a target. Automatic and attentional priming were determined by orthogonally varying prime–target relatedness, expectancy, and stimulus onset asynchrony. Although the CHI Ss had slower reaction times (RTs) overall, there were no significant group differences in the magnitude of either the automatic or attentional component of semantic priming. The present results indicate the integrity of semantic processes and normal semantic priming in long-term patients with severe CHI. The results are discussed in relation to an attentional resource hypothesis. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Accelerating entry into supported employment for persons with severe psychiatric disabilities.

Tested the hypothesis that Ss with severe mental illnesses would achieve better vocational outcomes with an accelerated approach to supported employment (AASE), as compared to gradual approaches (GA) with prevocational training. 86 Ss (mean age 35.1 yrs) with a diagnosis of a serious mental illness, were randomly assigned to either the AASE, or the GA, which included a minimum of 4 mo prevocational training. Data were obtained on indicators of vocational outcomes over 2 yrs, and for a limited number of Ss (n=36), during the 4th yr of inception into the program. Initially, only 5% of Ss preferred prevocational training. After 1 yr, AASE Ss showed better outcomes for a range of indicators, including achievement of competitive employment, duration of employment and mean earnings. During the 4th yr, 59% of these Ss were competitively employed, as compared to only 6% of GA Ss. Rehabilitation is more effective using AASE than GA. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Compile-time copy elimination

Single-assignment and functional languages have value semantics that do not permit side-effects. This lack of side-effects makes automatic detection of parallelism and optimization for data locality in programs much easier. However, the same property poses a challenge in implementing these languages efficiently. This paper describes an optimizing compiler system that solves the key problem of aggregate copy elimination. The methods developed rely exclusively on compile-time algorithms, including interprocedural analysis, that are applied to an intermediate data flow representation. By dividing the problem into update-in-place and build-in-place analysis, a small set of relatively simple techniques—edge substitution, graph pattern matching, substructure sharing and substructure targeting—was found to be very powerful. If combined properly and implemented carefully, the algorithms eliminate unnecessary copy operations to a very high degree. No run-time overhead is imposed on the compiled programs.     

Enhanced direct stiffness method for finite element analysis of textile composites

Traditional homogenization techniques are not useful when the microstructural scale of a material is of the same order of magnitude as the structural scale of a component. Such is the case for many textile composites. Since discrete modeling of the microstructure throughout a component is prohibitively expensive, continuum finite elements are needed which account for the microstructure within a single element. This paper describes a simple substructuring technique for formulating these special elements.     

Probing the early stages of polymerization of ethylene on a model chromium/silica catalyst by Fourier transform infrared spectroscopy

The nature of the interaction of monomer, and the early stages of growth of oligomers of ethylene on a rather more uniform surface of Cr/SiO₂ catalyst than hitherto studied has been investigated by differenceFTIR spectroscopy using C₂D₄ and C₂H₄ as reactants both with and without subsequent treatment of the catalyst with CO andTHF. The active catalyst was prepared by reaction of vapour phase CrO₂Cl₂ with the vicinal hydroxyls of the silica surface. Three distinct kinds of methylene groups were detected. Arguments are given for assigning the peaks at 2935 and 2860 cm^–1 to CH₂ groups directly bound to the active site and those at 2920 and 2850 to CH₂s in the growing chain well removed from the Cr. The peaks at 2160 and 2165 cm^–1 are attributed to CD₂ groups hydrogen bonded to surface hydroxyls.