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

Measurement-based load model parameter estimation uses measurements from a disturbance on the grid Those measurements can include voltage and/or real and reactive power In this paper, we show that the type of measurements used directly impacts the accuracy of parameter estimation We look at four scenarios With wide-area deployment of voltage sensors, such as PMUs, the resulting parameter estimation is very accurate at high signal-to-noise ratios (SNR), but is very poor at low SNRs, because voltage has low sensitivity to the parameters With only local deployment of complex power sensors, the estimate is worse than the first scenario at all SNRs However, with wide-area deployment of complex power sensors, the estimate becomes very robust to low SNR, because complex power has much higher sensitivity to the parameters Combining wide-area voltage and power measurements produces the best results

Impact of measurement selection on load model parameter estimation

The advent of large-scale power system software packages has made a crucial impact on tasks performed both in industry and research domains. However, additional analysis on the results in an external program is commonly necessitated for a variety of applications. This requires importing and managing the resulting data into an external platform, increasing user effort and rendering the process cumbersome. One of the capabilities of commercial software is an automation server which allows the software to be directly interfaced with an external processing program. This enables automatic retrieval of data without the need to maintain a database manually. This automation would allow for more straightforward algorithms and freedom in design, motivating more innovative data-driven methods with the use of multiple programs in a single environment. In this paper, we will discuss the generic capabilities of such automation servers, their setup, and explore the development of a simulation-based fault location algorithm applying this technique and the subsequent results.

Automation of commercial power system software for data-driven research

Situational awareness is imperative for reactive power management, particularly for interpreting the results of studies evaluating the impact of geomagnetic disturbances or high levels of renewable generation on the grid. This paper introduces a visualization technique, VAR Ready Reserves (VRRs), to provide a novel and useful tool to enhance the situational awareness of users performing and interpreting power system studies. This visualization technique can be adapted to demonstrate the dispatch, injection, and absorption capability of reactive power devices (such as generators, shunts, SVCs) in either a chart view (VRR charts) or with an integrated system view (VRR GDVs) to provide users with the awareness of reactive power capability and dispatch over the duration of a simulation or spatially. This paper reviews industry practices for reactive power management, summarizes existing visualization strategies, and demonstrates the newly-developed VRRs on a 2000-bus case study.

Situational Awareness for Reactive Power Management in Large-Scale Electric Grids

With deregulation in the electric industry the process of siting new generation has changed dramatically. In the previous vertically integrated utility paradigm, the local utility could bundle the cost of new transmission with the costs associated with adding generation. With deregulation, independent generators usually wish to site at locations in which their new generation will not cause any new overloads in the transmission grid. This paper describes a process for systematically determining the impact new generation will have on the transmission system. Emphasis is also placed on the visualization of these transmission system impacts.

Transmission impacts and visualization of new generation

This paper covers the reasons for studying transient behavior of electromechanical disturbances in electric power systems. It motivates the idea of using measurement data from transient events to infer as much as possible about the power system. As a starting point, frequency-domain analysis is explained and utilized. As an extension of the work in [2], two additional faults have been simulated with the 9-bus system and the frequency-domain analysis technique has been utilized to infer knowledge about the system. Frequency measurements from a simulation of an example large-scale interconnected power grid have also been analyzed. Some relevant literature and potentially useful data is highlighted. Lastly, the key take-aways are mentioned.

Thomas J. Overbye

Papers

Impact of measurement selection on load model parameter estimation

Automation of commercial power system software for data-driven research

Situational Awareness for Reactive Power Management in Large-Scale Electric Grids

Transmission impacts and visualization of new generation

Frequency-domain analysis of electromechanical disturbances in electric power systems