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

http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

미국의 “전국 수학 교사 협의회”(National Council of Teachers of Mathematics, NCTM)는 1989년부터 〈학교 수학의 교육과정과 평가 규준〉(1989), 〈수학 가르침(교수)의 전문성 규준〉(1991), 〈학교 수학의 평가(시험) 규준〉(NCTM, 1995), 〈학교 수학의 원리와 규준〉(2000)을 출판하여 미국의 수학 교육 의 전망(목표, 나아갈 길)과 규준(실행 지침)을 제시하였다. 수학 교사들로 구성된 미국의 NCTM은 학생, 학부모, 학교 행정가 등 많은 사람들과 힘을 합하여 모든 학생들에게 수준 높은 수학 교육을 받을 수 있는 여건(환경, 기회)을 조성하는 데 구심점의 역할을 하였다. 한편 많은 관련 단체들은 여러 배경과 능력을 가진 학생들이 전문성을 지닌 교사(특수 교사를 일컫는 밀이 아니다. 수학 교과를 이해하고 수학의 전문성과 특수성을 가르칠 수 있는 일반 교사를 일컫는 말이다.)로부터 미래를 대비해 평등하고, 진취적이며, 지원이 잘 이루어지고, 공학 도구(IT)가 잘 갖춰진 환경에서 중요한 수학적 아이디어를 이해하면서 학습할 수 있는 수학 교실(미국에서는 우리나라처럼 수학 교사가 수학 시간에 학생의 방(교실: Homeroom)에 찾아가지 않고 학생들이 선생의 방(수학 교실: Classroom)을 찾아온다. 전형적인 수학 교실의 사진은 2쪽에 나와 있다.)을 만들기 위해 함께 힘썼다. NCTM에서 출간한 여러 규준들은 우리나라의 제6차와 제7차 교육과정에도 큰 영향을 미쳤다. 이 글에서는 NCTM(2000)에서 제시한 학습 원리를 간단히 살펴본 다음 이를 중심으로 현재 미국 수학 교육의 교수ㆍ학습 이론의 동향을 살펴본다.

미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론

In spite of the challenges associated with obtaining actual PMU measurements for research purposes and analytic methods testing, it remains crucial that experimental input data exhibits similar quality features of real measurements for proper grid assessment and planning. The objective of this paper is to generate and validate large sets of synthetic, but realistic, PMU datasets obtained from complex grid models. A study of different variability components in PMU measurements is first presented followed by the proposed steps in generating synthetic datasets. Random variations of resource inputs are used in a simulation platform to generate prior voltage data from a synthetic 2,000-bus system, followed by a data modification process to infuse further realism into the dataset. The validation process used to assess the accuracy of the generated voltage dataset utilizes a variability metric to determine the level of inherent variations in individual measurements, and further applies a dimension reduction technique to identify the extent of electrical dynamics retained in the overall synthetic dataset.

Large-Scale Generation and Validation of Synthetic PMU Data

One of the most challenging aspects of engineering education is to give students an intuitive feel for the systems they are studying. Historically, engineering schools have excelled at providing their undergraduate students with a strong background in the basic sciences and the theoretical fundamentals of engineering. Such a background has been, and continues to be, crucial. But while paper and pencil exercises can be quite useful for highlighting these fundamentals, they often fall short in imparting the desired intuitive system insight. Yet such insight can be crucial, particularly as a new engineer moves from straightforward analysis into the domain of design. To help, this article provides a case study example of how a design project can be used to provide such intuitive insight into both basic power system operation involving power flow and contingency analysis as well as more advanced topics involving an hourly locational marginal price (LMP) power market. This design project is based upon one developed by the author that is included in the Power System Analysis and Design textbook (third edition), and it is solved using the PowerWorld Simulator software.

Fostering intuitive minds for power system design

This paper presents a hybrid approach with AC and DC power flow models for power flow analysis. Power flow problems are solved with the AC model in a part of system, whereas with the DC model in other parts. The proposed methodology can obtain benefits from both AC (non-linear) and DC (linear) models. In other words, this approach formulates both nonlinear and linear algebraic equations, and deals with tradeoff issues between accuracy of the AC model and faster solution of the DC model. A case study with an IEEE 14-bus system is provided to compare accuracy between the proposed and the DC model. It is shown that the hybrid approach can be used for applications requiring more accuracy than DC model allows.

Hybrid power flow analysis: Combination of AC and DC models

This paper presents a modified method for power system transient stability analysis, allowing the reduction of the computational requirements while retaining important system dynamics. The approach formulates the power balance equations depending on the area of interest. The detailed ac model, including full real and reactive power equations, is used for the area in which high accuracy is required, while the simpler dc model, including linear real power equation, is used for more remote areas where real power dynamics dominate. A high level of accuracy can be achieved using the ac model in the area of interest, and computational complexity can be reduced with the less detailed dc model in the remainder of the system. In order to prevent the loss of simulation accuracy, this paper proposes a way to compensate line losses neglected using the dc model. Case studies with the IEEE 118-bus system are provided to validate the performance of the proposed method.

Mixed Transient Stability Analysis Using AC and DC Models

High quality synchrophasor data ensure that mission-critical applications produce trustworthy results during grid monitoring. Hence, there is a need for risk assessment activities to screen incoming data for errors, and decide if erroneous portions of data be either rejected or passed on to the dependent-applications. Visualization of prototyped PMU data errors provides a means for better identifying and understanding error mechanisms in real-life PMU data. The objective of this work is to develop a framework for the simulation of prototype PMU data errors within an emulation environment. In this work, two errors have been simulated: error due to a time skew, and error due to mislabeled flag bits during a leap second transition.

Thomas J. Overbye

Papers

Large-Scale Generation and Validation of Synthetic PMU Data

Fostering intuitive minds for power system design

Hybrid power flow analysis: Combination of AC and DC models

Mixed Transient Stability Analysis Using AC and DC Models

An emulation environment for prototyping PMU data errors