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

Over the past 5 years there have been many new technologies that have been developed or adapted for use in viticulture. While these technologies provide a large amount of extra information on the production system, this information is only valuable if it can be translated into a decision. This decision support system facet of Precision Agriculture is the least understood and researched part of the precision agriculture management philosophy. As a result of this, the adoption of many technologies has been hindered by an inability to confidently act on the information gathered. Conversely, the uptake of technologies with minimal decision support requirements, for example tractor guidance/auto steer, has been very strong as producers are a lot clearer on the actual benefits and opportunities associated with the technology. The pre-eminent question in viticulture (and agriculture generally) is how to incorporate this new information into viticultural (agronomic) practices to improve production and the understanding of the production system. This paper gives a brief overview of the technologies currently available and then focuses on how these are being used and where there is a knowledge or technology gap to be addressed. While disparities between ‚Old World™ (France, Europe) and ‚New World™ (Australia, South and North America) production systems exist the authors have tried to address concerns from both perspectives.

Bottling Good Information: Mixing Tradition and Technology in vineyards

Picosecond pulse generation in a passively mode-locked green dye laser

Multi-siting and mode locking in a Yb3+:CS-FAP laser

Earlier research in the modeling and simulation of hybrid systems led to the development of a general hybrid systems modeling language (HSML). Effort is underway to implement this concept in software. The standard MATLAB model framework and integration algorithms have been extended to support state-event handling in continuous-time components and to handle embedded discrete-time components. In this paper we overview the algorithmic implementation of the HSML language constructs for dealing with state events and embedded discrete-time modules in MATLAB. An extensive example of an electro-mechanical pointing system with stiction under discrete-time control is presented to demonstrate the efficacy of these extensions.

Rigorous hybrid systems simulation of an electro-mechanical pointing system with discrete-time control

Highly efficient generation of 130fs pulses at 1.5 μm, through a single-pass cascade Raman soliton-like compression-amplification process in a single-mode fibre, is described. The dispersion-shifted fibre, with a zero-dispersion wavelength at 1.46μm, was pumped by the lOOps pulses from a CW mode-locked Nd : YAG laser operated at 1.32 μm.

James Taylor

Papers

Bottling Good Information: Mixing Tradition and Technology in vineyards

Picosecond pulse generation in a passively mode-locked green dye laser

Multi-siting and mode locking in a Yb3+:CS-FAP laser

Rigorous hybrid systems simulation of an electro-mechanical pointing system with discrete-time control

Femtosecond single-pass cascade Raman soliton generation at 1.5 μm