Estimation of time- and state-dependent delays and other parameters in functional differential equations

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay

Estimation of discontinuous coefficients and boundary parameters for hyperbolic systems

The problem of estimating discontinuous coefficients, including locations of discontinuities, that occur in second order hyperbolic systems typical of those arising in I-D surface seismic problems is discussed. In addition, the problem of identifying unknown parameters that appear in boundary conditions for the system is treated. A spline-based approximation theory is presented, together with related convergence findings and representative numerical examples

Computational methods for estimation of parameters in hyperbolic systems

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized

Estimation of coefficients and boundary parameters in hyperbolic systems

Semi-discrete Galerkin approximation schemes are considered in connection with inverse problems for the estimation of spatially varying coefficients and boundary condition parameters in second order hyperbolic systems typical of those arising in 1-D surface seismic problems. Spline based algorithms are proposed for which theoretical convergence results along with a representative sample of numerical findings are given

The Rocketdyne Multifunction Tester. Part 2: Operation of a Radial Magnetic Bearing as an Excitation Source

The operation of the magnetic bearing used as an excitation source in the Rocketdyne Multifunction Tester is described. The tester is scheduled for operation during the summer of 1990. The magnetic bearing can be used in two control modes: (1) open loop mode, in which the magnetic bearing operates as a force actuator; and (2) closed loop mode, in which the magnetic bearing provides shaft support. Either control mode can be used to excite the shaft; however, response of the shaft in the two control modes is different due to the alteration of the eigenvalues by closed loop mode operation. A rotordynamic model is developed to predict the frequency response of the tester due to excitation in either control mode. Closed loop mode excitation is shown to be similar to the excitation produced by a rotating eccentricity in a conventional bearing. Predicted frequency response of the tester in the two control modes is compared, and the maximum response is shown to be the same for the two control modes when synchronous unbalance loading is not considered. The analysis shows that the response of this tester is adequate for the extraction of rotordynamic stiffness, damping, and inertia coefficients over a wide range of test article stiffnesses

Investigating the Effects of Finite Resolution on Observed Transverse Jet Profiles

Both the emission properties and evolution of Active Galactic Nuclei (AGN) radio jets are dependent on the magnetic fields that thread them. Faraday Rotation gradients are a very important way of investigating these magnetic fields, and can provide information on the orientation and structure of the magnetic field in the immediate vicinity of the jet; for example, a toroidal or helical field component should give rise to a systematic gradient in the observed Faraday rotation across the jet, as well as characteristic intensity and polarization profiles. However, real observed radio images have finite resolution, usually expressed via convolution with a Gaussian beam whose size corresponds to the central lobe of the point source response function. This will tend to blur transverse structure in the jet profile, raising the question of how well resolved a jet must be in the transverse direction in order to reliably detect transverse structure associated with a helical jet magnetic field. We present results of simulated intensity, polarization and Faraday rotation images designed to directly and empirically investigate the effect of finite resolution on observed transverse jet structures

Ayahuasca’s ‘afterglow’: improved mindfulness and cognitive flexibility in ayahuasca drinkers

Rationale: There is a growing body of evidence demonstrating the therapeutic potential of ayahuasca for treating depression and anxiety. However, the mechanisms of action involved in ayahuasca’s therapeutic effects are unclear. Mindfulness and cognitive flexibility may be two possible psychological mechanisms. Like other classic psychedelics, ayahuasca also leads to an 'afterglow' effect of improved subjective wellbeing that persists after the acute effects have subsided. This period may offer a window of increased therapeutic potential. Objective: to explore changes in mindfulness and cognitive flexibility before, and within 24 hours after ayahuasca use. Methods: Forty-eight participants (54% female) were assessed on measures of mindfulness (Five Facets Mindfulness Questionnaire, FFMQ), decentering (Experiences Questionnaire, EQ) and cognitive flexibility (Cognitive Flexibility Scale, CFS), and completed the Stroop and Wisconsin Picture Card Sorting Task (WPCST) before drinking ayahuasca, and again within 24-hours. Results: Mindfulness (FFMQ total scores and four of the five mindfulness facets; Observe, Describe, Act with Awareness and Non-reactivity) and decentering (EQ) significantly increased in the 24 hours after ayahuasca use. Cognitive flexibility (CFS and WPCST) significantly improved in the 24 hours after ayahuasca use. Changes in both mindfulness and cognitive flexibility were not influenced by prior ayahuasca use. Conclusions: The present study supports ayahuasca’s ability to enhance mindfulness and further reports changes in cognitive flexibility in the 'afterglow' period occur, suggesting both could be possible psychological mechanisms concerning the psychotherapeutic effects of ayahuasca. Given psychological gains occurred regardless of prior ayahuasca use suggests potentially therapeutic effects for both naïve and experienced ayahuasca drinkers

Do Economic Restrictions Improve Forecasts?

A previous study showed that imposing economic restrictions improves the forecasting ability of food demand systems, thus warranting their use even when rejected in-sample. This study attempts to determine whether this is due solely to the fact that restrictions improve degrees of freedom. Results indicate that restrictions improve forecasting ability even when not derived from economic theory, but theoretical restrictions forecast best.Demand and Price Analysis,