Second-order bounds on the domain of attraction and the rate ofconvergence of nonlinear dynamical systems and neural networks

We present a method for analyzing the convergence properties of nonlinear dynamical systems yielding second-order bounds on the domain of attraction of an asymptotically stable equilibrium point and on the time of convergence in the estimated domain. We show that under certain conditions on the system, there exists an analytic solution to the corresponding optimization problem. The method is applied in analyzing the dynamics of a neural network model.     

Velocity-Guided Tracking of Deformable Contours in Three Dimensional Space

This paper presents a 3D active contour model for boundary detection and tracking of non-rigid objects, which applies stereo vision and motion analysis to the class of energy-minimizing deformable contour models, known as snakes. The proposed contour evolves in three-dimensional space in reaction to a 3D potential function, which is derived by projecting the contour onto the 2D stereo images. The potential function is augmented by a kinetic term, which is related to the velocity field along the contour. This term is used to guide the inter-image contour displacement. The incorporation of inter-frame velocity estimates in the tracking algorithm is especially important for contours which evolve in 3D space, where the added freedom of motion can easily result in loss of tracking. The proposed scheme incorporates local velocity information seamlessly in the snake model, with little computational overhead, and does not require exogenous computation of the optical flow or related quantities in each image. The resulting algorithm is shown to provide good tracking performance with only one iteration per frame, which provides a considerable advantage for real time operation.     

Nonuniform image representation in area-of-interest systems

This paper is concerned with image representation by data distributed nonuniformly and in particular with a representation scheme suitable for "area-of-interest" imaging. The class of signals under consideration, whose information density varies with position, can be represented according to a nonuniform sampling scheme. Position-varying projection operators are presented as simple low-pass filtering operations in a Fourier-like domain. Sequential projections are used for pyramidal representation of nonuniformly sampled images. It is shown that irregular random sampling, prevents, under certain mild restrictions, aliasing effects.     

Variations in the composition of spinal anesthetic solutions: the effects of drug addition order and preparation methods

Adjuvants such as opioids or epinephrine are commonly added in small volumes to multicomponent spinal anesthetic solutions. In this study, we tested the hypothesis that final adjuvant concentrations vary depending on the devices and techniques used to prepare the anesthetic solution. We compared two aspiration devices, the filter needle and the filter straw, in a laboratory study. Two techniques for drawing up and estimating adjuvant volumes were assessed, as was variation in the composition of a model spinal anesthetic solution resulting from intra- and interindividual variability. A model hyperbaric anesthetic solution consisting of tetracaine, dextrose, and methylene blue (MB) as a small-volume tracer solution was studied. The components were drawn up into a syringe through one of two commercially supplied aspiration devices, a filter straw or a filter needle. The effect of the order of aspiration of the components into the syringe was measured by determining the MB concentration in the final solution by optical absorbance. Ten experienced anesthesiologists then prepared samples of the test solution using one of two different techniques to estimate tracer volume in the aspiration syringe. In comparison studies, the MB tracer was added to the hyperbaric solution with a tuberculin syringe. The order of aspiration of the solution components had a large effect on the final concentration of the MB tracer in the ultimate mixture. Variation in the MB concentration was on the order of four- to fivefold. Effects were larger for the filter straw compared with the filter needle. A comparison of 10 anesthesiologists revealed large intra- and interindividual variations in the final composition of the model anesthetic solution. The concentration of tracer added to the mixture with a tuberculin syringe approximated the planned yield. We conclude that the devices and techniques used to prepare mixtures of drugs for delivery to the cerebrospinal fluid may influence the concentrations of drugs in the anesthetic and, thus, the dose supplied to the patient receiving spinal anesthesia. Variation in clinical effects of spinal anesthetics may be attributable, in part, to variation in the composition of the anesthetic. IMPLICATIONS: This laboratory study demonstrates the potential for large variation in the composition of spinal anesthetic mixtures.     

On the distinction between clinical process and clinical content theories.

Draws a distinction between clinical process theory, which refers to the method of investigation, and clinical content theory, which refers to the findings of an investigation. It is suggested that psychoanalysts attend to the process and attempt to specify and microanalyze it in its naturalistic context. The problem of clinical evidence is perhaps the most neglected topic in psychoanalytic therapy. The significance of broad-based mental models of human experience in understanding the therapeutic process is discussed. It is suggested that psychoanalytic therapy should be viewed as an early craft that is not yet a science. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Robust tracking of position and velocity with Kalman snakes

A new Kalman-filter based active contour model is proposed for tracking of nonrigid objects in combined spatio-velocity space. The model employs measurements of gradient-based image potential and of optical-flow along the contour as system measurements. In order to improve robustness to image clutter and to occlusions an optical-flow based detection mechanism is proposed. The method detects and rejects spurious measurements which are not consistent with previous estimation of image motion     

The Velocity Snake: Deformable Contour for Tracking in Spatio-Velocity Space

We present a new active contour model for boundary tracking and position prediction of nonrigid objects, which results from applying a velocity control to the class of elastodynamical contour models, known as snakes. The proposed control term minimizes an energy dissipation function which measures the difference between the contour velocity and the apparent velocity of the image. Treating the image video-sequence as continuous measurements along time, it is shown that the proposed control results in robust tracking. This is in contrast to the original snake model which is proven to have tracking errors relative to image (object) velocity, thus resulting in high sensitivity to image clutter. The motion estimation further allows for position prediction of nonrigid boundaries. Based on the proposed control approach, we propose a new class of real time tracking contours, varying from models with batch-mode control estimation to models with real time adaptive controllers.     

Trajectory Control of Convergent Networks

We present a class of feedback control functions which increase the convergence rates of nonlinear dynamical systems. A simple sign function is used to obtain convergence in finite time. We describe a trajectory learning procedure which preserves the convergence property of the system. Based on the proposed feedback, we developed a new neural network model which converges in finite time.     

Convergence analysis of nonlinear dynamical systems by nestedLyapunov functions

A method for estimating the domain of attraction of an asymptotically stable equilibrium point of a nonlinear dynamical system and for deriving an upper bound on the time of convergence in the estimated domain is presented. It is based on a set of Lyapunov functions. Defined on nested regions in the state space. The estimated domain, obtained as the union of a subset of these regions, is based on a local Lyapunov-like condition for the convergence of the solution in each region to its inner boundary. A bound on the time of convergence within the estimated domain is given by the sum of the local bounds. This concept is implemented using a class of regions whose boundaries are described by Fourier series     

The impact of condom availability [correction of distribution] in Seattle schools on sexual behavior and condom use

OBJECTIVES: Ten Seattle high schools made condoms available through vending machines, baskets in school clinics, or both. This study measured the number of condoms that students obtained and subsequent changes in sexual behavior and condom use. METHODS: Schoolwide surveys were administered in spring 1993 and in spring 1995, before and during the condom availability program. These data were compared with data from nationally representative surveys administered at the same time. RESULTS: Seattle students obtained an average of 4.6 condoms per year, the vast majority from baskets and very few from vending machines. Relative to the national samples, the percentage of Seattle students who had ever had sex remained stable after the program began; current sexual activity decreased significantly; and the percentage of sexually experienced students who used a condom the last time they had sex decreased significantly, particularly in the 5 schools with baskets of condoms in clinics. CONCLUSIONS: Making condoms available in Seattle schools enabled students to obtain relatively large numbers of condoms but did not lead to increases in either sexual activity or condom use.