The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

The rigidity of periodic body-bar frameworks on the three-dimensional fixed torus

We present necessary and sufficient conditions for the generic rigidity of body-bar frameworks on the three-dimensional fixed torus. These frameworks correspond to infinite periodic body-bar frameworks in $\mathbb{R}^3$ with a fixed periodic lattice.Comment: 31 pages, 12 figure

Optimal Atmospheric Compensation for Anisoplanatism in Adaptive-Optical Systems

Anisoplanatism in adaptive optics (AO) systems is a performance-degrading effect that arises whenever light from the wave-front sensor beacon and light from the object of interest sample different volumes of optical turbulence. This effect occurs if there is either a spatial separation between the object and the beacon, or a spatial separation between the wave-front sensor and phase-compensation aperture, or if both types of separation are present in the AO system. Anisoplanatism results in an increased value of the aperture-averaged residual phase variance after AO compensation, which causes an exponential decrease in system performance. This dissertation offers a theoretical framework in which the most-general form of anisoplanatism can be analyzed

Non-Imaging Infrared Spectral Target Detection

Automatic detection of time-critical mobile targets using spectral-only infrared radiance data is explored. A quantification of the probability of detection, false alarm rate, and total error rate associated with this detection process is provided. A set of classification features is developed for the spectral data, and these features are utilized in a Bayesian classifier singly and in combination to provide target detection. The results of this processing are presented and sensitivity of the class separability to target set, target configuration, diurnal variations, mean contrast, and ambient temperature estimation errors is explored. This work introduces the concept of atmospheric normalization of classification features, in which feature values are normalized using an estimate of the ambient temperature surrounding the target being observed and applying the Plauck radiation law with those estimates. This technique is demonstrated to reduce the total error rate associated with classification processing to less than one-fourth of that observed using non-normalized features. Classification testing of spectral field measurements made on an array of U.S. and foreign military assets reveal a total error rate near 5% with a 95% probability of detection and a concurrent false alarm rate of 4% when a single classification feature is employed. Multiple feature classification on the same data yields detection probabilities near 97% with a concurrent false alarm rate of 2.5%. Sensitivity analysis indicates that the probability of detection is reduced to 70-75% in the hours preceding daylight, and that for the total error rate to be less than 10%, the target-to-background mean contrast must be greater than 0.1. Analysis of the atmospheric normalization technique reveals that in order to keep the total error rate less than 10%, the ambient temperature must be estimated wit

Identification of QuiP, the Product of Gene PA1032, as the Second Acyl-Homoserine Lactone Acylase of Pseudomonas aeruginosa PAO1

The relevance of the acyl homoserine lactone (acyl-HSL) quorum signals N-3-oxododecanoyl-homoserine lactone (3OC12HSL) and N-butanoyl-homoserine lactone to the biology and virulence of Pseudomonas aeruginosa is well investigated. Previously, P. aeruginosa was shown to degrade long-chain, but not short-chain, acyl-HSLs as sole carbon and energy sources (J. J. Huang, J.-I. Han, L.-H. Zhang, and J. R. Leadbetter, Appl. Environ. Microbiol. 69:5941-5949, 2003). A gene encoding an enzyme with acyl-HSL acylase activity, pvdQ (PA2385), was identified, but it was not required for acyl-HSL utilization. This indicated that P. aeruginosa encodes another acyl-HSL acylase, which we identify here. A comparison of total cell proteins of cultures grown with long-acyl acyl-HSLs versus other substrates implicated the involvement of a homolog of PvdQ, the product of gene PA1032, for which we propose the name QuiP. Transposon mutants of quiP were defective for growth when P. aeruginosa was cultured in medium containing decanoyl-HSL as a sole carbon and energy source. Complementation with a functional copy of quiP rescued this growth defect. When P. aeruginosa was grown in buffered lysogeny broth, constitutive expression of QuiP in P. aeruginosa led to decreased accumulations of the quorum signal 3OC12HSL, relative to the wild type. Heterologous expression of QuiP was sufficient to confer long-chain acyl-HSL acylase activity upon Escherichia coli. Examination of gene expression patterns during acyl-HSL-dependent growth of P. aeruginosa further supported the involvement of quiP in signal decay and revealed other genes also possibly involved. It is not yet known under which "natural" conditions quiP is expressed or how P. aeruginosa balances the expression of its quorum-sensing systems with the expression of its acyl-HSL acylase activities

When is a symmetric pin-jointed framework isostatic?

Maxwell's rule from 1864 gives a necessary condition for a framework to be isostatic in 2D or in 3D. Given a framework with point group symmetry, group representation theory is exploited to provide further necessary conditions. This paper shows how, for an isostatic framework, these conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. In particular, it turns out that an isostatic framework in 2D can belong to one of only six point groups. Some conjectures and initial results are presented that would give sufficient conditions (in both 2D and 3D) for a framework that is realized generically for a given symmetry group to be an isostatic framework.Comment: 24 pages, 10 figures; added references, minor changes, revised last paragrap

Nonuniqueness in a minimal model for cell motility

Two–phase flow models have been used previously to model cell motility, however these have rapidly become very complicated, including many physical processes, and are opaque. Here we demonstrate that even the simplest one–dimensional, two–phase, poroviscous, reactive flow model displays a number of behaviours relevant to cell crawling. We present stability analyses that show that an asymmetric perturbation is required to cause a spatially uniform, stationary strip of cytoplasm to move, which is relevant to cell polarization. Our numerical simulations identify qualitatively distinct families of travelling–wave solution that co–exist at certain parameter values. Within each family, the crawling speed of the strip has a bell–shaped dependence on the adhesion strength. The model captures the experimentally observed behaviour that cells crawl quickest at intermediate adhesion strengths, when the substrate is neither too sticky nor too slippy