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

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

An Introduction to MultiAgent Systems.

The increasing amount of distributed generation (DG) in today's highly complex restructured power networks gives more options for distribution system operators (DSOs) under contingency conditions. A low voltage distribution network with a large amount of DG can be operated as an islanded system if the distribution system is disconnected from the main grid due to the contingency. The control and management of the islanded distribution system are important, and the overall network synchronism must be maintained in the islanded distribution system. In this paper, a multi-agent based controller is proposed to stabilize the frequency and voltages of an active distribution system after it enters into the islanding operation mode. The modified IEEE 9-bus system was used to illustrate the dynamic and steady state performance of the active distribution system during islanding operation with the proposed multi-agent based controller. Case studies have been carried out using the RealTime Digital Simulator (RTDS). Case study results show that the proposed multi-agent controller can efficiently help stabilize the frequency and voltages of active distribution systems after switching to islanding operation.

Multi-agent based controller for islanding operation of active distribution networks with distributed generation (DG)

A method for superimposing voltage sources is sought optimized by using a sparse triangular solver and multiprocessing. A revision to the method is suggested which exploits Schur’s complement of the network admittance matrix and optimal re-use of computations. The algorithm is implemented and parallelized for shared memory multiprocessing. The proposed algorithm is tested on a collection of large test systems and performance is found to be significantly better than the reference method. The algorithm will thereby facilitate a speed-up of methods relying on Thevenin equivalent representation such as the Thevenin equivalent method for contingency assessment.

/pdf/super-positioning-of-voltage-sources-for-fast-assessment-of-5kfm0g9j1o.pdf

Super-Positioning of Voltage Sources for Fast Assessment of Wide-Area Thévenin Equivalents

The necessity for smart electrical systems having minimum technical loss and environmental impact is providing impetus to go for Distributed Generations (DGs) which may offer several other advantages such as reduced transmission and distribution system resources, increased reliability, better power quality, etc. However, depending on the system configuration and management, these advantages may not be true. Moreover, due to structural and managerial changes in the electricity supply industry motivated with introduction of completion, the role of small generations distributed in the low/medium voltage network has gained importance. This paper adopts a systematic approach by focusing on the most important research areas related to the distributed generations. Various DG technologies are described and penetration of DGs in the Indian system has been discussed. This paper also highlights the key issues in the DG integration in power systems.

Distributed Generation in Power Systems: An Overview and Key Issues

Classical spot pricing theory is based on multipliers of the primal problem of an optimal market dispatch, i.e., the solution of the dual problem. However, the dual problem of market dispatch may yield multiple solutions. In these circumstances, spot pricing or any standard pricing practice based on multipliers cannot generate a unique clearing price. Although such situations are rare, they can cause significant uncertainties and complexities in market dispatch. In practice, this situation is solved through simple empirical methods, which may cause additional operations or biased allocation. Based on a strict extension of the principles of spot pricing and surplus allocation, we propose a new pricing methodology that can yield unique, impartial, and robust solution. The new method has been analyzed and compared with other pricing approaches in accordance with spot pricing theory. Case studies support the results of the theoretical analysis, and further demonstrate that the method performs effectively in both uniform-pricing and nodal-pricing markets.

Spot Pricing When Lagrange Multipliers Are Not Unique

This paper first presents the Hopf bifurcation analysis for a vector-controlled doubly fed induction generator (DFIG) which is widely used in wind power conversion systems. Using three-phase back-to-back pulse-width-modulated (PWM) converters, DFIG can keep stator frequency constant under variable rotor speed and provide independent control of active and reactive power output. The oscillatory instability of the DFIG has been observed by simulation study. The detailed mathematical model of the DFIG closed-loop system is derived and used to analyze the observed bifurcation phenomena. The loci of the Jacobian's eigenvalues are computed and the analysis shows that the system loses stability via a Hopf bifurcation. The eigenvalue sensitivity analysis with respect to machine and control parameters are performed to assess the impact of parameters upon system stability. Moreover, the Hopf bifurcation boundaries of the key parameters are also given that can facilitate the tuning of those parameters to ensure stable operation.

Jacob Østergaard

Papers

Multi-agent based controller for islanding operation of active distribution networks with distributed generation (DG)

Super-Positioning of Voltage Sources for Fast Assessment of Wide-Area Thévenin Equivalents

Distributed Generation in Power Systems: An Overview and Key Issues

Spot Pricing When Lagrange Multipliers Are Not Unique

Hopf bifurcation and eigenvalue sensitivity analysis of doubly fed induction generator wind turbine system