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

On epilepsy and epileptiform convulsions

We present long-term timing observations of four millisecond radio pulsars with the 305 m Arecibo and the 100 m Effelsberg radiotelescopes. Our analysis of the combined pulse time-of-arrival data from the two telescopes has led to improvements of the precision of timing parameter determination for all the four pulsars. A new, much more significant measurement of a third-order spin frequency derivative of PSR B1257+12 adds to the existing evidence that a fourth, distant planet may orbit this pulsar. Proper motions have been measured for PSR J1640+2224, PSR B1953+29, and PSR J2229+2643. The derived low transverse velocities of these objects agree with the kinematic characteristics of the observed millisecond pulsar population. Exceptionally low spindown rates of PSR J1640+2224 and PSR J2229+2634 have been used to derive useful limits on the initial spin periods of these objects and on the variation of the gravitational constant G.

Timing Observations of Four Millisecond Pulsars with the Arecibo and Effelsberg Radio Telescopes

Air-cored, photonic band-gap crystal fibers exhibiting low nonlinearity and anomalous chromatic dispersion in spectral ranges inaccessible to conventional fibers can be used in the realization of all-fiber-format pulse compressors with unprecedented peak powers and wavelength diversity. Linear compression of inherently chirped and prestretched pulses by factors ranging from 20 to 80 around 1.0 and 1.5 microm have allowed generation of pulses as short as 163 fs. The results show that totally integrated femtosecond fiber laser sources can be realized throughout the visible and near-infrared and point to the possibility of megawatt peak and tens of watt average in-fiber power levels.

All-Fiber Format Compression of Frequency Chirped Pulses in Air-Guiding Photonic Crystal Fibers

We report on generation of 850fs mode-locked pulses at 1065nm in a completely fiber integrated format. The figure-of-eight, fiber laser source incorporates anomalous dispersion compensation by using a holey fiber and a short length, high gain, double-clad Yb-fiber amplifier.

Totally fiber integrated, figure-of-eight, femtosecond source at 1065 nm.

A soliton spectral tunnelling effect (SSTE) is predicted. This is characterised in the spectral domain by the passage of a femtosecond soliton through a potential barrier-like spectral inhomogeneity of group velocity dispersion (GVD), including the forbidden band of positive GVD.

James Taylor

Papers

On epilepsy and epileptiform convulsions

Timing Observations of Four Millisecond Pulsars with the Arecibo and Effelsberg Radio Telescopes

All-Fiber Format Compression of Frequency Chirped Pulses in Air-Guiding Photonic Crystal Fibers

Totally fiber integrated, figure-of-eight, femtosecond source at 1065 nm.

Soliton spectral tunnelling effect