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.

Wind Power Plants (WPPs) DTU Orbit (02/11/2019) Power-Hardware-In-the-Loop (PHIL) Test of VSC-based HVDC connection for Offshore Wind Power Plants (WPPs) This paper presents a power-hardware-in-the-loop (PHIL) test for an offshore wind power plant (WPP) interconnected to the onshore grid by a VSC-based HVDC connection. The intention of the PHIL test is to verify the control coordination between the plant side converter of the HVDC connection and the wind turbines within the WPP in order to ensure smooth operation of the WPP under both normal operating condition and operating conditions with grid faults. The PHIL test platform is comprised of a real time digital simulator (RTDS), a Spitzenberger Spies three phase 7.5 kW amplifier, a Danfoss VSC based converter and a chopper. The WPP is simulated in the RTDS which consists of a number of full scale converter wind turbines (FSCWTs). The simulated WPP interacts with the plant side converter through the Spitzenberger Spies amplifier. The interfacing between the RTDS and the Spitzenberger Spies amplifier is done by the analogue I/O card of the RTDS and the input channel of the amplifier. The amplifier scales up the voltages at the point of common coupling (PCC) of the WPP to the voltage level for the converter. The plant side VSC converter supplies power to the chopper. The test results show the successful control coordination between the WPP and the plant side VSC converter of the HVDC connection of the WPP.

Power-Hardware-In-the-Loop (PHIL) Test of VSC-based HVDC connection for Offshore Wind Power Plants (WPPs)

This paper presents the implementation of the IEC generic model of Type 1 wind turbine generator (WTG) in the real time digital simulator (RTDS) environment. The model is based on the IEC 61400 TC88 under wind turbine working group’s standardization efforts are implemented. Several case studies have been carried out to verify the dynamic performance of the IEC generic Type 1 WTG model under both steady state and dynamic conditions. The case study results show that the IEC generic Type 1 WTG model can represent the relevant dynamic behavior of WTG to ensure grid integration compatibility.

/pdf/implementation-of-iec-generic-model-type-1a-using-rtds-29m6pwaf8w.pdf

Implementation of IEC Generic Model Type 1A using RTDS

New Real-Time Market Facilitating Demand-Side Resources for System Balancing

This paper describes the real-time d platform that can be used for power system op and power system modeling. This particular pl operators, planners and researchers the oppor how a power system behaves and can be used modeling, system disturbances of various ty recovery actions, as well as to illustrate compl concepts. The Kundur power system consi symmetrical areas linked together by two 230kV by using RSCAD in order to carry out simulat Various phenomena commonly encountered w the two-area system is studied. Despite its sma very closely the behavior of typical systems in The electromagnetic transient type of simu RSCAD enables the study of fast and detailed single-phase faults in the two-area network and effects on a larger time scale. Also, the case system with 5 generators has been also used an presented.

http://ieeexplore.ieee.org/iel5/5685176/5696950/05696961.pdf

me Simulation Platform er System Operation

The operation of the distribution network willchange in the near future due to increasing size and number ofdistributed energy resources (DER) and demand side resources(DSR). An active distribution network is proposed to addressthe challenges. The normal operation of an active distributionnetwork requires coordination of different values and operationconstraints of various involved actors. This paper proposes amultilevel coordination strategy for congestion management ofdistribution network. Firstly, the scheme of an active distributionnetwork is described. Then, the coordination strategies betweenvarious actors, i.e., distribution system operator (DSO), fleetoperators (FO), and EV owners are discussed. Further, a mathe-matical formulation of the chosen coordination strategies betweenDSO and FOs are presented and some case studies are shownto illustrate the effectiveness of the proposed solutions. Finally,we give the argument and proposal of using multi-agent basedplatform to demonstrate the multilevel coordination solution.Index Terms—Congestion management, Distribution grid,Multilevel coordination, Multiagent systems based platform.

Jacob Østergaard

Papers

Power-Hardware-In-the-Loop (PHIL) Test of VSC-based HVDC connection for Offshore Wind Power Plants (WPPs)

Implementation of IEC Generic Model Type 1A using RTDS

New Real-Time Market Facilitating Demand-Side Resources for System Balancing

me Simulation Platform er System Operation

Multilevel Coordination in Smart Grids for Congestion Management of Distribution Grid