On the Geometry of Rectifiable Sets with Carleson and Poincare-type inequlaities

Thesis (Ph.D.)--University of Washington, 2016-06

Floral structure, breeding system and fruit-set in the threatened sub-shrub Tetratheca juncea Smith (Tremandraceae)

Tetratheca juncea Smith (Tremandraceae) has undergone a range contraction of approx. 50 km in the last 100 years and is now listed as a vulnerable sub-shrub restricted to the central and north coast regions of New South Wales, Australia. There are approx. 250 populations in a 110 km north-south distribution and populations are usually small with fewer than 50 plants/clumps. The reproductive ecology of the species was studied to determine why seed-set is reportedly rare. Flowers are bisexual, odourless and nectarless. Flowers are presented dependentally and there are eight stamens recurved around the pistil. Anthers are poricidal, contain viable pollen and basally contain a deep-red tapetal fluid that is slightly oily. Thus flowers are presented for buzz pollinators, although none were observed at flowers during our study. The species was found to be facultatively xenogamous with only one in 50 glasshouse flowers setting seed autogamously, i.e. without pollinator assistance. Field studies revealed fertile fruit in 24 populations but production varied significantly across sites from exceedingly low (0.6 fruits per plant clump) to low (17 fruits per plant clump). Fruit-set ranged from 0 to 65%, suggesting that pollen vectors exist or that autogamy levels in the field are variable and higher than glasshouse results. Fruit production did not vary with population size, although in three of the five populations in the south-west region more than twice as much fruit was produced as in populations elsewhere. A moderately strong relationship between foliage volume and fruit : flower ratios suggests that bigger plants may be more attractive than smaller plants to pollinators. A review of Tetratheca pollination ecology revealed that several species are poorly fecund and pollinators are rare. The habitat requirements for Tetratheca, a genus of many rare and threatened species, is discussed. (C) 2003 Annals of Botany Company.

Mixed partitions of sets of triples into small planes

We continue our study of partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. We develop further necessary conditions for the existence of partitions of such sets into copies of PG(2, 2) and copies of AG(2, 3), and deal with the cases v = 13, 14, 15 and 17. These partitions, together with those already known for v = 12, 16 and 18, then become starters for recursive constructions of further infinite families of partitions. (C) 2004 Elsevier B.V. All rights reserved.

Generalized Perk-Schultz models: solutions of the Yang-Baxter equation associated with quantized orthosymplectic superalgebras

The Perk-Schultz model may be expressed in terms of the solution of the Yang-Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra U-q (gl(m/n)], with a multiparametric coproduct action as given by Reshetikhin. Here, we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras U-q[osp(m/n)]. In this manner, we obtain generalizations of the Perk-Schultz model.

Automatic segmentation of the knee bones using 3D active shape models

This paper presents an automated segmentation approach for MR images of the knee bones. The bones are the first stage of a segmentation system for the knee, primarily aimed at the automated segmentation of the cartilages. The segmentation is performed using 3D active shape models (ASM), which are initialized using an affine registration to an atlas. The 3D ASMs of the bones are created automatically using a point distribution model optimization scheme. The accuracy and robustness of the segmentation approach was experimentally validated using an MR database of fat suppressed spoiled gradient recall images.

Storia e tragedia. P. Oxy. XXIII 2382: edizione critica e commento

Il lavoro consta di un’introduzione dedicata in primis alla presentazione formale di P. Oxy. XXIII 2382, di cui sono posti in evidenza i legami strutturali e concettuali con il racconto di Hdt. I 8-12. Segue dunque la trattazione dei problemi posti da P. Oxy. 2382, quello del genere letterario di appartenenza (tragedia o novella in versi?) e quello della datazione (età classica o età ellenistica?), finalizzata ad una puntuale definizione dello status quaestionis. Le conclusioni mettono in luce gli elementi a favore dell’ipotesi tragica: la presenza di paragraphoi e il passo di Ach. Tat. I 8 4-7 (corredato da un’appendice relativa alla storia del termine δρᾶμα: se e quando tale termine assume l’accezione di ‘narrazione romanzesca’?), nonché il soggetto storico (con un excursus relativo ai drammi di argomento storico). Si evidenziano infine gli elementi di debolezza contenuti nelle ipotesi avanzate da Cantarella (1952) e Lloyd-Jones (1953), propensi a ritenere P. Oxy. 2382 rispettivamente una novella in versi (il che offre lo spunto per una breve trattazione relativa alle caratteristiche contenutistiche e formali delle novelle milesie) e un giambo archilocheo, di cui il fr. 19 W.2 conserverebbe l’incipit. Quanto alla cronologia, sono enumerati i limiti della datazione alta, nonché gli elementi di affinità di P. Oxy. 2382 con la tragedia ellenistica; infine, pensando ad una possibile attribuzione, si propone, in termini puramente ipotetici, il confronto con l’esperienza della Pleiade alessandrina. Segue dunque un’analisi (laddove le condizioni dei testi, spesso frammentarie, lo consentano) dell’opera di Licofrone di Calcide, Sositeo e Sosifane di Siracusa, esponenti della Pleiade, nonché di Moschione ed Ezechiele, volta ad individuare elementi di continuità con P. Oxy. 2382. Il lavoro si conclude con l’edizione critica e il commento verso per verso di P. Oxy. XXIII 2382, corredati da un’appendice dedicata a P. Oxy. XLIV 3161, testo con notazioni musicali apparentemente affine a P. Oxy. XXIII 2382, costituito da 4 frr. notevolmente accidentati, di cui si fornisce l’edizione critica.

Information geometric measurements of generalisation

Neural networks can be regarded as statistical models, and can be analysed in a Bayesian framework. Generalisation is measured by the performance on independent test data drawn from the same distribution as the training data. Such performance can be quantified by the posterior average of the information divergence between the true and the model distributions. Averaging over the Bayesian posterior guarantees internal coherence; Using information divergence guarantees invariance with respect to representation. The theory generalises the least mean squares theory for linear Gaussian models to general problems of statistical estimation. The main results are: (1)~the ideal optimal estimate is always given by average over the posterior; (2)~the optimal estimate within a computational model is given by the projection of the ideal estimate to the model. This incidentally shows some currently popular methods dealing with hyperpriors are in general unnecessary and misleading. The extension of information divergence to positive normalisable measures reveals a remarkable relation between the dlt dual affine geometry of statistical manifolds and the geometry of the dual pair of Banach spaces Ld and Ldd. It therefore offers conceptual simplification to information geometry. The general conclusion on the issue of evaluating neural network learning rules and other statistical inference methods is that such evaluations are only meaningful under three assumptions: The prior P(p), describing the environment of all the problems; the divergence Dd, specifying the requirement of the task; and the model Q, specifying available computing resources.

Canonical solution groups of a homomorphism : manipulator kinematics, nonparametric regression and distributed object systems

The kinematic mapping of a rigid open-link manipulator is a homomorphism between Lie groups. The homomorphisrn has solution groups that act on an inverse kinematic solution element. A canonical representation of solution group operators that act on a solution element of three and seven degree-of-freedom (do!) dextrous manipulators is determined by geometric analysis. Seven canonical solution groups are determined for the seven do! Robotics Research K-1207 and Hollerbach arms. The solution element of a dextrous manipulator is a collection of trivial fibre bundles with solution fibres homotopic to the Torus. If fibre solutions are parameterised by a scalar, a direct inverse funct.ion that maps the scalar and Cartesian base space coordinates to solution element fibre coordinates may be defined. A direct inverse pararneterisation of a solution element may be approximated by a local linear map generated by an inverse augmented Jacobian correction of a linear interpolation. The action of canonical solution group operators on a local linear approximation of the solution element of inverse kinematics of dextrous manipulators generates cyclical solutions. The solution representation is proposed as a model of inverse kinematic transformations in primate nervous systems. Simultaneous calibration of a composition of stereo-camera and manipulator kinematic models is under-determined by equi-output parameter groups in the composition of stereo-camera and Denavit Hartenberg (DH) rnodels. An error measure for simultaneous calibration of a composition of models is derived and parameter subsets with no equi-output groups are determined by numerical experiments to simultaneously calibrate the composition of homogeneous or pan-tilt stereo-camera with DH models. For acceleration of exact Newton second-order re-calibration of DH parameters after a sequential calibration of stereo-camera and DH parameters, an optimal numerical evaluation of DH matrix first order and second order error derivatives with respect to a re-calibration error function is derived, implemented and tested. A distributed object environment for point and click image-based tele-command of manipulators and stereo-cameras is specified and implemented that supports rapid prototyping of numerical experiments in distributed system control. The environment is validated by a hierarchical k-fold cross validated calibration to Cartesian space of a radial basis function regression correction of an affine stereo model. Basic design and performance requirements are defined for scalable virtual micro-kernels that broker inter-Java-virtual-machine remote method invocations between components of secure manageable fault-tolerant open distributed agile Total Quality Managed ISO 9000+ conformant Just in Time manufacturing systems.

A Bayesian perspective on stochastic neurocontrol

Control design for stochastic uncertain nonlinear systems is traditionally based on minimizing the expected value of a suitably chosen loss function. Moreover, most control methods usually assume the certainty equivalence principle to simplify the problem and make it computationally tractable. We offer an improved probabilistic framework which is not constrained by these previous assumptions, and provides a more natural framework for incorporating and dealing with uncertainty. The focus of this paper is on developing this framework to obtain an optimal control law strategy using a fully probabilistic approach for information extraction from process data, which does not require detailed knowledge of system dynamics. Moreover, the proposed control method framework allows handling the problem of input-dependent noise. A basic paradigm is proposed and the resulting algorithm is discussed. The proposed probabilistic control method is for the general nonlinear class of discrete-time systems. It is demonstrated theoretically on the affine class. A nonlinear simulation example is also provided to validate theoretical development.

Reciprocating power generation in a chemically driven synthetic muscle

A scalable synthetic muscle has been constructed that transducts nanoscale molecular shape changes into macroscopic motion. The working material, which deforms affinely in response to a pH stimulus, is a self-assembled block copolymer comprising nanoscopic hydrophobic domains in a weak polyacid matrix. A device has been assembled where the muscle does work on a cantilever and the force generated has been measured. When coupled to a chemical oscillator this provides a free running chemical motor that generates a peak power of 20 mW kg 1 by the serial addition of 10 nm shape changes that scales over 5 orders of magnitude. It is the nanostructured nature of the gel that gives rise to the affine deformation and results in a robust working material for the construction of scalable muscle devices.

Antagonistic triblock polymer gels powered by pH oscillations

A study was conducted to create a pH-responsive layer, in which a small change in the individual polyacid or polybase gel length was transferred into a larger motion that curls up the gel. It was observed that the transfer of motion from a linear displacement into a curved displacement through the geometric design effectively increases the displacement rate. A robust, reversible, and chemically driven mechanical actuator was was produced that demonstrated its response over many pH oscillations. The affine nature of the triblock copolymers, demonstrated for for the polyacid and polybase indicated that the effect will also function at some smaller length scales, which is appropriate for a working biomimetic and soft nanotechnology device. The study also demonstrated the potential applicability of these polymeric gels and suggested the fabrication of related molecular machines and devices based on the principles of soft nanotechnology.

Autonomous volume transitions of a polybase triblock copolymer gel in a chemically driven pH-oscillator

A pH-responsive ABA triblock copolymer, comprising poly(methyl methacrylate)-b/ock-poly(2-(diethylamino)ethyl methacrylate)-block-poly(methyl methacrylate) [PMMA-b-PDEA-b-PMMA], has been cast Into thin films with a well-defined microstructure. Small Angle X-ray Scattering (SAXS) and Atomic Force Microscopy (AFM) studies confirm that this copolymer forms a hydrogel consisting of PMMA spheres embedded within a polybase PDEA matrix, with the PMMA domains acting as physical cross-links. The hydrogel has a pH-reversible coil-globule transition at around pH 4.5. This responsive physical property was exploited by immersing a sample of copolymer hydrogel in an aqueous solution containing a cyclic pH-oscillating reaction, whereby the pH was continuously oscillated above and below the transition pH so as to induce autonomous volume transitions. The changes in microscopic and macroscopic length scales correlate closely during (de)swelling cycles, with affine behaviour occurring over five orders of magnitude. Copyright © 2007 WILEY-VCH Verlag GmbH & Co. KGaA,.

A probabilistic indirect adaptive control for systems with input-dependent noise

A probabilistic indirect adaptive controller is proposed for the general nonlinear multivariate class of discrete time system. The proposed probabilistic framework incorporates input–dependent noise prediction parameters in the derivation of the optimal control law. Moreover, because noise can be nonstationary in practice, the proposed adaptive control algorithm provides an elegant method for estimating and tracking the noise. For illustration purposes, the developed method is applied to the affine class of nonlinear multivariate discrete time systems and the desired result is obtained: the optimal control law is determined by solving a cubic equation and the distribution of the tracking error is shown to be Gaussian with zero mean. The efficiency of the proposed scheme is demonstrated numerically through the simulation of an affine nonlinear system.

CAPS in Z(2,n)

We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small n.