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

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

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or

Principles of Neural Science

1. Introduction. Control System Design Steps. Adaptive Control. A Brief History. 2. Models for Dynamic Systems. Introduction. State-Space Models. Input/Output Models. Plant Parametric Models. Problems. 3. Stability. Introduction. Preliminaries. Input/Output Stability. Lyapunov Stability. Positive Real Functions and Stability. Stability of LTI Feedback System. Problems. 4. On-Line Parameter Estimation. Introduction. Simple Examples. Adaptive Laws with Normalization. Adaptive Laws with Projection. Bilinear Parametric Model. Hybrid Adaptive Laws. Summary of Adaptive Laws. Parameter Convergence Proofs. Problems. 5. Parameter Identifiers and Adaptive Observers. Introduction. Parameter Identifiers. Adaptive Observers. Adaptive Observer with Auxiliary Input. Adaptive Observers for Nonminimal Plant Models. Parameter Convergence Proofs. Problems. 6. Model Reference Adaptive Control. Introduction. Simple Direct MRAC Schemes. MRC for SISO Plants. Direct MRAC with Unnormalized Adaptive Laws. Direct MRAC with Normalized Adaptive Laws. Indirect MRAC. Relaxation of Assumptions in MRAC. Stability Proofs in MRAC Schemes. Problems. 7. Adaptive Pole Placement Control. Introduction. Simple APPC Schemes. PPC: Known Plant Parameters. Indirect APPC Schemes. Hybrid APPC Schemes. Stabilizability Issues and Modified APPC. Stability Proofs. Problems. 8. Robust Adaptive Laws. Introduction. Plant Uncertainties and Robust Control. Instability Phenomena in Adaptive Systems. Modifications for Robustness: Simple Examples. Robust Adaptive Laws. Summary of Robust Adaptive Laws. Problems. 9. Robust Adaptive Control Schemes. Introduction. Robust Identifiers and Adaptive Observers. Robust MRAC. Performance Improvement of MRAC. Robust APPC Schemes. Adaptive Control of LTV Plants. Adaptive Control for Multivariable Plants. Stability Proofs of Robust MRAC Schemes. Stability Proofs of Robust APPC Schemes. Problems. Appendices. Swapping Lemmas. Optimization Techniques. Bibliography. Index. License Agreement and Limited Warranty.

Robust adaptive control

For strict-feedback nonlinear systems, this paper shows that it is impossible to reduce to zero the optimal cost in the regulation of more states than the number of control inputs in the system, even using unrestricted control effort. By constructing a near optimal cheap control law, we characterise the infimum value of the optimal regulation cost as the optimal value of a reduced-order regulator problem where the states with lower relative degree drive those with higher relative degree. We illustrate our results with two examples of practical interest: the optimal regulation of the rotational motion of a free rigid body, and the optimal control of a magnetic suspension system.

Cheap control performance of a class of non-right-invertible nonlinear systems

It is shown how some classes of symmetric bidirectional heterogeneous vehicle strings can be modelled using a Hamiltonian framework. Hamiltonian systems theory is applied to show stability and string stability of certain vehicle strings. We also indicate how this analysis might be extended to classes of nonlinear controllers.

Energy-based control of bidirectional vehicle strings

This paper addresses the issue of global stabilization of an important class of nonlinear systems, namely, a cascade of a linear, controllable system with a nonlinear system which is asymptotically (even exponentially) stable. Such systems arise as the normal form of "minimum phase" nonlinear systems. Local stabilizability results have been known for some time for such systems. Global stabilizability results have also been obtained in some cases. However, it is also known, that when the linear "connection" to the nonlinear system is nonminimum phase, then global or semiglobal stabilizability may be impossible. Indeed, it has been shown that for any nonminimum phase linear subsystem, there exists a nonlinear asymptotically stable subsystem, for which the cascade cannot be globally stabilized. We expand on the understanding of this area by establishing, for a broader class of systems, conditions under which global or semiglobal stabilization is impossible for linear and nonlinear feedbacks.

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Global and semiglobal stabilizability in certain cascade nonlinear systems

The increasing demand for data in mobile applications has created a need for better communications systems. To satisfy this growing data demand next generation wireless systems are planned to use millimetre wave carrier frequencies. At these frequencies, radio shadowing is severe. To compensate for shadowing, incoming data flows must therefore be split and sent over several radio interfaces, that may have different delay properties. This paper analyses the stability properties of a MIMO data splitter that controls the delay skew between the data paths. The stability analysis is performed using IQC stability theory.

/pdf/stability-properties-of-a-mimo-data-flow-controller-56cpmher5d.pdf

Stability properties of a MIMO data flow controller

Studies robustness and sensitivity properties of a sampled-data feedback system with a generalized sampled-data hold function (GSHF). The authors argue that shifting nonminimum phase zeros using GSHF control can lead to robustness difficulties unless the zero is outside the closed loop bandwidth. >

/pdf/robustness-of-zero-shifting-via-generalized-sampled-data-4y5ubdmy2t.pdf

Richard H. Middleton

Papers

Cheap control performance of a class of non-right-invertible nonlinear systems

Energy-based control of bidirectional vehicle strings

Global and semiglobal stabilizability in certain cascade nonlinear systems

Stability properties of a MIMO data flow controller

Robustness of zero-shifting via generalized sampled-data hold functions