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

High-gain monolithic cascaded Raman fiber amplifier operating at 1.3 µm

There has been increased interest in the use and manipulation of optical fields to address challenging problems that have traditionally been approached with microwave electronics. Some examples that benefit from the low transmission loss, agile modulation and large bandwidths accessible with coherent optical systems include signal distribution, arbitrary waveform generation, and novel imaging. We extend these advantages to demonstrate a microwave generator based on a high-Q optical resonator and a frequency comb functioning as an optical-to-microwave divider. This provides a 10 GHz electrical signal with fractional frequency instability <8e-16 at 1 s, a value comparable to that produced by the best microwave oscillators, but without the need for cryogenic temperatures. Such a low-noise source can benefit radar systems, improve the bandwidth and resolution of communications and digital sampling systems, and be valuable for large baseline interferometry, precision spectroscopy and the realization of atomic time.

Photonic Generation of Ultrastable Microwave Signals

This paper proposes value-at risk (VaR) estimation methods that are a synthesis of conditional autoregressive value at risk (CAViaR) time series models and implied volatility. The appeal of this proposal is that it merges information from the historical time series and the different information supplied by the market's expectation of risk. Forecast-combining methods, with weights estimated using quantile regression, are considered. We also investigate plugging implied volatility into the CAViaR models—a procedure that has not been considered in the VaR area so far. Results for daily index returns indicate that the newly proposed methods are comparable or superior to individual methods, such as the standard CAViaR models and quantiles constructed from implied volatility and the empirical distribution of standardised residuals. We find that the implied volatility has more explanatory power as the focus moves further out into the left tail of the conditional distribution of S&P 500 daily returns.

Using Implied Volatility with CAViaR Models for Value at Risk Estimation

Predictions of call center arrivals are a key input to staff scheduling models It is, therefore, surprising that simplistic forecasting methods dominate practice, and that the research literature on forecasting arrivals is so small In this paper, we evaluate univariate time series methods for forecasting intraday arrivals for lead times from one half-hour ahead to two weeks ahead We analyze five series of intraday arrivals for call centers operated by a retail bank in the United Kingdom A notable feature of these series is the presence of both an intraweek and an intraday seasonal cycle The methods considered include seasonal autoregressive integrated moving average (ARIMA) modeling; periodic autoregressive modeling; an extension of Holt-Winters exponential smoothing for the case of two seasonal cycles; robust exponential smoothing based on exponentially weighted least absolute deviations regression; and dynamic harmonic regression, which is a form of unobserved component state-space modeling Our results indicate strong potential for the use of seasonal ARIMA modeling and the extension of Holt-Winters for predicting up to about two to three days ahead and that, for longer lead times, a simplistic historical average is difficult to beat We find a similar ranking of methods for call center data from an Israeli bank

A Comparison of Time Series Methods for Forecasting Intraday Arrivals at a Call Center

Erratum: Cocaine-induced proliferation of dendritic spines in nucleus accumbens is dependent on the activity of cyclin-dependent kinase-5 (Neuroscience 116: 1 (19-22) PII: S0306452202005602)

James Taylor

Papers

High-gain monolithic cascaded Raman fiber amplifier operating at 1.3 µm

Photonic Generation of Ultrastable Microwave Signals

Using Implied Volatility with CAViaR Models for Value at Risk Estimation

A Comparison of Time Series Methods for Forecasting Intraday Arrivals at a Call Center

Erratum: Cocaine-induced proliferation of dendritic spines in nucleus accumbens is dependent on the activity of cyclin-dependent kinase-5 (Neuroscience 116: 1 (19-22) PII: S0306452202005602)