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.

Vehicle to Grid (V2G) in Denmark-Feasibility Study

A method that exploits Thevenin equivalent representation for obtaining post-contingency steady-state nodal voltages is integrated with a method of detecting post-contingency aperiodic small-signal instability. The task of integrating stability assessment with contingency assessment is challenged by the cases of unstable post-contingency conditions. For unstable postcontingency conditions there exists no credible steady-state which can be used for basis of a stability assessment. This paper demonstrates how Thevenin Equivalent methods can be applied in algebraic representation of such bifurcation points which may be used in assessment of post-contingency aperiodic small-signal stability. The assessment method is introduced with a numeric example.

/pdf/thevenin-equivalent-method-for-dynamic-contingency-2nzgibk56n.pdf

Thevenin equivalent method for dynamic contingency assessment

HVDC Connection of Off-shore Wind Power Plants

Application of MV/LV Transformers with OLTC for Increasing the PV Hosting Capacity of LV Grids

This paper presents a Particle Swarm Optimization (PSO) based on multi-agent controller. Real-time digital simulator (RTDS) is used for modelling the power system, while a PSO based multi-agent LFC algorithm is developed in JAVA for communicating with resource agents and determines the scenario to stabilize the frequency and voltage after the system enters into the islanding operation mode. The proposed algorithm is based on the formulation of an optimization problem using agent based PSO. The modified IEEE 9-bus system is employed to illustrate the performance of the proposed controller via RTDS to verify its practical efficacy. Case studies are presented under different operating conditions.

/pdf/agent-based-particle-swarm-optimization-for-load-frequency-51cyn0mdys.pdf

Jacob Østergaard

Papers

Vehicle to Grid (V2G) in Denmark-Feasibility Study

Thevenin equivalent method for dynamic contingency assessment

HVDC Connection of Off-shore Wind Power Plants

Application of MV/LV Transformers with OLTC for Increasing the PV Hosting Capacity of LV Grids

Agent based Particle Swarm Optimization for load frequency control of distribution grid