Optimal Estimation of Several Linear Parameters in the Presence of Lorentzian Thermal Noise

In a previous article we developed an approach to the optimal (minimum variance, unbiased) statistical estimation technique for the equilibrium displacement of a damped, harmonic oscillator in the presence of thermal noise. Here, we expand that work to include the optimal estimation of several linear parameters from a continuous time series. We show that working in the basis of the thermal driving force both simplifies the calculations and provides additional insight to why various approximate (not optimal) estimation techniques perform as they do. To illustrate this point, we compare the variance in the optimal estimator that we derive for thermal noise with those of two approximate methods which, like the optimal estimator, suppress the contribution to the variance that would come from the irrelevant, resonant motion of the oscillator. We discuss how these methods fare when the dominant noise process is either white displacement noise or noise with power spectral density that is inversely proportional to the frequency ($1/f$ noise). We also construct, in the basis of the driving force, an estimator that performs well for a mixture of white noise and thermal noise. To find the optimal multi-parameter estimators for thermal noise, we derive and illustrate a generalization of traditional matrix methods for parameter estimation that can accommodate continuous data. We discuss how this approach may help refine the design of experiments as they allow an exact, quantitative comparison of the precision of estimated parameters under various data acquisition and data analysis strategies.Comment: 16 pages, 10 figures. Accepted for publication in Classical and Quantum Gravit

Effect of casing treatment of overall performance of axial-flow transonic fan stage with pressure ratio of 1.75 and tip solidity of 1.5

The effect of a number of casing treatments on the overall performance of a 1.75-pressure-ratio, 423-m/sec-tip-speed fan stage was evaluated. The skewed slot configuration with short-open slots over the midportion of the rotor had a stall margin of 23.5 percent, while the solid casing had a stall margin of 15.0 percent. The skewed slot configuration with long open slots extending ahead of and over portion of rotor displaced the stall line to the lowest flow at all speeds tested. At design speed, the peak efficiency for the long, forward open slots was 1 point less than that for the short midopen slots and 3 points less than that for the solid casing

Effects of tip clearance on overall performance of transonic fan stage with and without casing treatment

The overall performance of a transonic fan stage is presented for various tip clearances, with and without casing treatment. The stage was tested with a solid casing, and with open skewed slots and closed skewed slots in the casing over the rotor blade tips. Four nominal nonrotating rotor blade tip clearances from 0.061 to 0.178 centimeter were used. For all three casings, the pressure ratio and efficiency decreased with increasing tip clearance. The stall margin for a given casing also decreased with increasing clearance. At design speed and a given tip clearance, the highest stall margin was obtained with the open-slot casing, and the lowest stall margin was obtained with the solid casing

Influence of Dislocations in Thomson's Problem

We investigate Thomson's problem of charges on a sphere as an example of a system with complex interactions. Assuming certain symmetries we can work with a larger number of charges than before. We found that, when the number of charges is large enough, the lowest energy states are not those with the highest symmetry. As predicted previously by Dodgson and Moore, the complex patterns in these states involve dislocation defects which screen the strains of the twelve disclinations required to satisfy Euler's theorem.Comment: 9 pages, 4 figures in gif format. Original PS files can be obtained in http://fermi.fcu.um.es/thomso

Reinforcement Learning: A Survey

This paper surveys the field of reinforcement learning from a computer-science perspective. It is written to be accessible to researchers familiar with machine learning. Both the historical basis of the field and a broad selection of current work are summarized. Reinforcement learning is the problem faced by an agent that learns behavior through trial-and-error interactions with a dynamic environment. The work described here has a resemblance to work in psychology, but differs considerably in the details and in the use of the word ``reinforcement.'' The paper discusses central issues of reinforcement learning, including trading off exploration and exploitation, establishing the foundations of the field via Markov decision theory, learning from delayed reinforcement, constructing empirical models to accelerate learning, making use of generalization and hierarchy, and coping with hidden state. It concludes with a survey of some implemented systems and an assessment of the practical utility of current methods for reinforcement learning.Comment: See http://www.jair.org/ for any accompanying file

Planning Guide Outdoor Recreation Facilities

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Is sea-basing a viable method of providing logistic support to the UK amphibious force?

Maritime power has traditionally been a central part of the UK’s defence planning and is well suited to supporting a wide range of military operations. The littoral area has always created problems for naval planners as most landings historically have had to endure a tactical separation of the naval and land components, and hence an artificial seam between the Navy and the Marines. With the end of the Cold War, amphibious operations are going to be more difficult to conduct than in the past, and amphibious forces are going to have to adopt manoeuvre warfare capabilities in order to successfully complete their missions. It is very likely that amphibious forces will have to conduct operations against a numerically superior enemy, who is on his own terrain, and be surrounded by a neutral, if not hostile populace. As such, the concept of Operational Manoeuvre From The Sea (OMFTS) whereby the sea is used as a manoeuvre space, and command and control is fast enough to cope with large amounts of information, but at the same time allow subordinates maximum flexibility to use their initiative, is increasingly attractive. It will be important not only for the combat elements to be able to use this new concept, but the Combat Service Support (CSS) elements as well

Performance of a transonic fan stage designed for a low meridional velocity ratio

The aerodynamic performance and design parameters of a transonic fan stage are presented. The fan stage was designed for a meridional velocity ratio of 0.8 across the tip of the stage, a pressure ratio of 1.57, a flow of 29.5 kilograms per second, and a tip speed of 426 meters per second. Radial surveys were obtained over the stable operating range from 50 to 100 percent of design speed. The measured, peak efficiency (0.81) of the stage occurred at a pressure ratio of 1.58 and a flow of 28.7 kilograms per second