There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Using Multivariate Statistics

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

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Linear Matrix Inequalities in System and Control Theory

The authors demonstrate silica-fibre Raman amplifiers with gain bandwidths of up to 114 nm and peak small-signal gains of up to 41.5 dB. Cascaded Raman fibre lasers operating at wavelengths of 1423, 1455 and 1480 nm have been used to simultaneously pump these amplifiers.

Triple wavelength pumped silica-fibre Raman amplifiers with 114 nm bandwidth

Dual-wavelength-pumped silica-fibre Raman amplifiers operating at wavelengths around 1.55 /spl mu/m and with gain bandwidths around 60 nm have been constructed. An experimental comparison is made between dual and single stage configurations and the spectral gain tilt due to inhomogeneous saturation under large signal conditions has been characterised.

Gain and saturation characteristics of dual-wavelength-pumped silica-fibre Raman amplifiers

The authors report a novel 1.3 /spl mu/m actively modelocked semiconductor ring laser which generates near transform-limited pulses as short as 1.9 ps at a repetition rate of 10 GHz. The laser is constructed from discrete fibre pigtailed components and an electroabsorption modulator is used as the modelocking element.

10 GHz 1.9 ps actively modelocked fibre integrated ring laser at 1.3 [micro sign]m

The application of optimal reactive power flow (ORPF) to the New Brunswick (NB) power system is presented. The potential benefits and the real-time implementation problems of ORPF are discussed. Some important issues of real-time implementation on ORPF, such as frequency of running, the number of activated control variables, and the order of adjustment of different controls, are discussed. The application of ORPF on the NB power network has shown two major benefits: (1) an improvement in the voltage profile and voltage stability, and (2) a saving in active power loss. The improvement in the voltage profile can cause fewer violations and a more stable system from the voltage point of view. A reduction in active power loss gained from ORPF can save a significant amount of money. The total ideal savings for the year 1997 predicted in the study was in excess of $900000, however, only 10 to 30% of this amount is realistically obtainable due to operational and other constraints. These savings can be gained simultaneously with the improvement of the voltage profiles.

Real-time implementation of optimal reactive power flow

A periodically-poled MgO-doped stoichiometric lithium tantalate crystal is applied for single-pass, 67% peak-power efficient, 7.05W average power second-harmonic generation of a single-mode Yb-doped all-fiber fundamental source. Reduced photorefraction and green-induced infrared absorption of the material allowed to maintain a low M2 value of the high-average-power 532nm beam.

James Taylor

Papers

Triple wavelength pumped silica-fibre Raman amplifiers with 114 nm bandwidth

Gain and saturation characteristics of dual-wavelength-pumped silica-fibre Raman amplifiers

10 GHz 1.9 ps actively modelocked fibre integrated ring laser at 1.3 [micro sign]m

Real-time implementation of optimal reactive power flow

7 W average power, high-beam-quality green generation in MgO-doped stoichiometric periodically poled lithium tantalate