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.

/pdf/linear-matrix-inequalities-in-system-and-control-theory-2q5cf0pqm2.pdf

Linear Matrix Inequalities in System and Control Theory

The development of mechanistic models for predicting growth of various crops (including potatoes) has continued for several decades, and new applications of such models are increasingly becoming available. Despite the benefits of this development, it may be difficult for the user to decide which models are suitable for a specific purpose (such as decision making in potato farming). In this chapter, we try to provide insights that would help the potential user to better understand the benefits and limitations of various types of models. First, we present some ideas of the general principles of mechanistic modelling and potential applications of crop models. Then we briefly describe the main physiological processes of potato growth and how they have been handled in mechanistic models. Finally, we provide examples of the recent applications of potato models and discuss the future use of the models for new applications, mainly in precision farming.

https://www.eprints.ncl.ac.uk/file_store/production/237989/F8472029-9C9F-4DEC-9DD5-159BE4625C67.pdf

Modelling potato growth

A retarding‐field differential‐output energy prefilter has been optically matched to a quadrupole mass spectrometer to produce a high‐performance secondary ion quadrupole mass spectrometer. The sample area was designed to be field free to allow for sample charge compensation and to prevent secondary ion trajectories from being affected by electric fields. Design considerations for optically matching the energy prefilter to the quadrupole mass filter (QMF) are discussed. The overall transmission of the instrument was 1.8×10−4 at a mass resolution of 100 M/ΔM (1–100 amu range) for copper and 1.7×10−5 at a mass resolution of 400 M/ΔM (10–250 amu range) for tungsten.

Retarding‐field differential‐output energy prefilter for high‐performance secondary ion mass spectrometry

* Abbreviations:
 HR — : hazard ratio
 TSB — : total serum bilirubin

It is axiomatic that for every treatment there are associated adverse events. For many medical conditions, the risk/benefit assessment of treatment is trivial, with an example being antibiotics for patients with bacterial meningitis. Even the risk of therapies leading to serious adverse events may be outweighed by the potential benefit, such as chemotherapy for a child with leukemia. However, the calculus becomes more difficult when the likelihood of an adverse outcome without treatment is small and/or the patients receiving the treatment are not sick but healthy.

Such is the case with phototherapy. In this issue of Pediatrics , Newman et al1 analyzed data from a large and rich database and found an increased risk of subsequent seizures in newborns treated with phototherapy. Although the increased risk was small, with an adjusted hazard ratio (HR) of 1.22, and only truly apparent in boys, the results are troubling. Phototherapy is a common therapy for newborns; in the data evaluated by Newman et al,1 ∼8% of ∼500 000 newborns received this treatment for hyperbilirubinemia. Most of the infants who … 

Address correspondence to James A. Taylor, MD, Department of Pediatrics, University of Washington, Box 354920, Seattle, WA 98195. E-mail: uncjat{at}uw.edu

https://pediatrics.aappublications.org/content/pediatrics/142/4/e20182241.full.pdf

Phototherapy and Seizures: Should We Change Practice?

Data-Driven Supervisor Design for Cace Package Integration

A simple, compact, fully fibre integrated source of /spl sim/100 fs pulses at a wavelength of 1.1 /spl mu/m is reported. 4 ps pulses at 1063 nm from a modelocked fibre laser were amplified to 23 mW in a ytterbium-doped fibre amplifier and subsequently propagated through 62 m of holey fibre with a zero dispersion wavelength at 1040 nm. Soliton formation, breakup and self frequency shift resulted in the formation of /spl sim/100 fs pulses at 1.1 /spl mu/m. Wavelength tunability from 1113 to 1220 nm is demonstrated.

James Taylor

Papers

Modelling potato growth

Retarding‐field differential‐output energy prefilter for high‐performance secondary ion mass spectrometry

Phototherapy and Seizures: Should We Change Practice?

Data-Driven Supervisor Design for Cace Package Integration

Compact fully fibre integrated source of 100 fs pulses at 1.1 [micro sign]m based on compression in holey fibre