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

A 3.5 W fiber-based laser source at 772 nm is demonstrated by using quasiphase-matched second-harmonic generation of a 40 dBm seeded ytterbium–erbium fiber amplifier in PPKTP. A 40% conversion efficiency is achieved across the entire output power range of the EDFA. No optical damage has been observed in the PPKTP over long-term high-power exposure.

3.5 W frequency-doubled fiber-based laser source at 772 nm

A diode-pumped mode-locked Cr:LiSAF laser is demonstrated for what is to our knowledge the first time. Active mode locking, with an acousto-optic modulator, and resonant passive mode locking, with a multiple-quantum-well absorber in an external cavity, have both yielded cw trains of picosecond pulses.

Mode-locked all-solid-state diode-pumped Cr:LiSAF laser.

Recent research in the area of describing function approaches (both random-input and sinusoidal-input) has laid the foundation for a systematic approach to designing controllers for nonlinear plants. This paper provides an overview of one school of thought in this area, typified by the following key ideas: 1. Quasilinear models of the nonlinear system that account for the operating range of system variables must be more realistic than conventional linear models. 2. A staged design approach that applies more power to "difficult" nonlinear plants than to "easy" ones is more sensible than a single design method. 3. The designer should be led to a nonlinear controller design if and only if it is really required. These points will be developed, illustrated and justified in this presentation.

A Systematic Nonlinear Controller Design Approach based on Quasilinear System Models

The 8/9 normalization coefficient for the nonlinear refractive index in nonpolarization-maintaining optical fibers is confirmed directly by measurement of the ratio of the self- and cross-phase modulation coefficients for two orthogonal polarizations. The nonlinear phase shift is accurately measured with a dual-frequency beat signal as a pump source.

Measurement of normalization factor of n(2) for random polarization in optical fibers.

To determine the association between parental health beliefs and the immunization status of their children, parents of children seen in two private pediatric practices completed a questionnaire on attitudes about immunizations. Five components of health beliefs were surveyed: perceived benefits of immunizations, susceptibility to diseases prevented by immunizations, severity of those diseases, parental feelings of self-efficacy in promoting their child's health, and barriers to immunization. Responses to the health-beliefs statements were transformed to an ordinal scale between 1 and 6, with ‘6’ corresponding to strongly positive feelings about immunizations. Immunization data were abstracted from practice medical records. Overall, 162/194 (83.3%) study children were fully immunized. There were no significant differences between parents of fully immunized children and those of under-immunized children in total health-beliefs score or for the benefits, susceptibility, severity, or barriers components. Self...

James Taylor

Papers

3.5 W frequency-doubled fiber-based laser source at 772 nm

Mode-locked all-solid-state diode-pumped Cr:LiSAF laser.

A Systematic Nonlinear Controller Design Approach based on Quasilinear System Models

Measurement of normalization factor of n(2) for random polarization in optical fibers.

The association between parental health beliefs and immunization status among children followed by private pediatricians.