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.

This paper presents the details of a new real-time stability assessment method. The method assesses a particular mechanism of stability: each generator's capability to generate sufficient steady state electromechanical torque. The lack of sufficient steady state torque causes aperiodic increase in rotor angle and a loss of synchronism, referred to as aperiodic small signal instability. The paper provides the theoretical background of the method and an analytical assessment criterion. Furthermore, a mathematical mapping of the generators' operating points that enables informative visualization of multiple operating points is derived in the paper. Finally, results from timedomain simulation of instability scenarios in the Nordic32 test system are presented and results used for testing the assessment method. The results illustrate the method's capability to efficiently identify the location of the emerging problem and to quantify margins to stability boundary.

/pdf/wide-area-assessment-of-aperiodic-small-signal-rotor-angle-vwm3l44ukp.pdf

Wide-area assessment of aperiodic small signal rotor angle stability in real-time

High temperature superconducting (HTS) cables for use in electric ac power systems are under development around the world today. There are two main constructions under development: the room temperature dielectric design and the cryogenic dielectric design. However, theoretical studies have shown that the insertion of these cables in the network is not without problems. The network stability requirements may impose severe constraints on the actual obtainable length of superconducting cables. Load flow considerations show that it may be difficult to use these high current cables to their full extent. Short circuits in the network may require a special protection system.

https://iopscience.iop.org/article/10.1088/0953-2048/13/5/315/pdf

Power applications for superconducting cables

The paper introduces an approach to investigate voltage sags, which are caused by large generator rotor swings following a transient disturbance. Therefore, the method exploits sensitivities derived from the algebraic network equations. These provide information on the impact of a generator on the voltage magnitude at a load bus and the effect of load variation on the generator's power injection. It is shown that these sensitivities give valuable information to identify critical generator-load pairs and locations for applying preventive control measures.

/pdf/sensitivity-based-assessment-of-transient-voltage-sags-2k4vb6d19o.pdf

Sensitivity based assessment of transient voltage sags caused by rotor swings

Bornholm is a Danish island situated south of Sweden, having the Oestkraft Company as the Distribution System Operator (DSO) and comprising 60 kV, 10 kV and 0.4 kV distribution systems with cables, overhead lines and transformers. Through a 60 kV submarine cable and a transformer, the island is connected to the 135 kV Swedish transmission system. The production capacity comprises thermal generation, being diesel and steam turbines, and on-land wind turbines. Wind power corresponds to 32% of the electric power load of the island having the maximum of 55 MW (in 2007). The power system of Bornholm reminds the Danish power system with a significant share of wind power. Regarding the area, population and electricity consumption, Bornholm corresponds to 1% of Denmark. The ability to go into planned island operation makes it suitable for research, education and demonstration of grid-integration, control and management of power systems with a significant share of wind power. Grid-connection of additional 70 to 100 MW offshore wind power is under consideration. This paper presents the determination of load-flow operational regimes with comparison to the measurements, i.e. state-estimation, being a necessary step for any other following research and demonstration activities including more wind power integration.

https://orbit.dtu.dk/files/5017028/WWEC-2009-FullPaper-vers04-20090417-final-aspresented.pdf

Wind power system of the Danish island of Bornholm: Model set-up and determination of operation regimes

https://backend.orbit.dtu.dk/ws/files/255811012/A_Complementarity_Model_for_Electric_Power_Transmission_Distribution_Coordination_Under_Uncertainty.pdf

Jacob Østergaard

Papers

Wide-area assessment of aperiodic small signal rotor angle stability in real-time

Power applications for superconducting cables

Sensitivity based assessment of transient voltage sags caused by rotor swings

Wind power system of the Danish island of Bornholm: Model set-up and determination of operation regimes

A Complementarity Model for Electric Power Transmission-Distribution Coordination Under Uncertainty