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 behaviour of a diode pumped figure-of-eight ytterbium/erbium-doped fibre laser which generates subpicosecond pulses is described. This laser is observed to mode-lock simultaneously in two orthogonal polarisation states with distinct temporal and spectral characteristics.

Simultaneous dual polarisation operation of a diode pumped femtosecond fibre laser

Simultaneous modulation of several WDM channels using a single electro-absorption modulator

The effect of diazepam on spatial visualization was studied using a double-blind crossover design. Diazepam 10 mg (or placebo) was given orally to 12 healthy young men at bedtime, followed again by 10 mg (or placebo) the next morning. One hour after the administration of the morning dose, the subjects performed a mental rotation task. Diazepam effects were analyzed in terms of an information processing model previously constructed to account for performance of the task. Using this method, the slope and intercept parameters of a linear function relating reaction time to task condition (i.e., angular difference in orientation between two identical stimulus figures) were computed for diazepam and placebo conditions. Diazepam significantly increased the slope and intercept of the mental rotation function (P<0.05). These results suggest that diazepam impairs spatial visualization ability.

Effect of diazepam on the speed of mental rotation.

Recent investigations have shown that the self- Raman interaction in optical fibers causes pulses to shift In frequency as they propagate.1–3 The combination of the Kerr nonlinearity and stimulated Raman scattering produces ultrashort pulses, a process known as soliton-Raman pulse generation.4 These pulses, however, copropagate with the pump over many kilometers without an accompanying shift in frequency. We present both experimental and theoretical results to explain this discrepancy. We show that the presence of the pump wave is responsible for the suppression of the self-frequency shift by including an extra term in the nonlinear Schrodinger equation to account for the frequency-dependent gain of the pump wave.

Suppression of the soliton self-frequency shift

Previous extensions of the stability criterion of Popov [1] for systems with a stable linear time-invariant plant $G(s)$ followed by a nonlinear time-varying gain $k(t)f( \cdot )$ entailed the definition of nonlinearity classes $[ f( \cdot ) \in N]$ and corresponding frequency domain multipliers $Z_N (s)$ Then, defining a measure of nonlinearity \[ F_{\min } \equiv \mathop {\min }\limits_x \{ \frac{{xf( x)}}{{\int_0^x {f( z )dz} }} \} \] stability is ensured if $Z(s) \in Z_N (s)$ exists, such that (i) $G(s)Z(s)$ is strictly positive real, (ii) $Z(s - \Lambda ) \in Z_N (s)$ and (iii)\[\frac{1}{k}\frac{{dk}}{{dt}}\leqq \Lambda F_{\min } \quad ( {\text{see [ 5 ]}})\]In this paper, the point by point requirement of (iii) is replaced by an integral criterion In many cases the constraints on $k(t)$ predicated by the integral inequality are substantially less strict than those of (iii) above As (iii) is a special case of the integral relation, the results are never more strictThe development here will be li

James Taylor

Papers

Simultaneous dual polarisation operation of a diode pumped femtosecond fibre laser

Simultaneous modulation of several WDM channels using a single electro-absorption modulator

Effect of diazepam on the speed of mental rotation.

Suppression of the soliton self-frequency shift

The Corduneanu-Popov Approach to the Stability of Nonlinear Time-Varying Systems