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

This paper describes the design of power grid operational scenarios that can enable students or professionals to experience operating the grid. The scenarios are created using complex and realistic grid systems of varying sizes, and range from normal daily operations to extreme events. They can involve one or multiple participants based on the objectives of the training exercise, complexity of the system and tasks, etc. The main objective is to use these scenarios towards effective grid operations training, and research applications. The scenarios created include, 1) a voltage control scenario to simulate normal operations, 2) a geomagnetic disturbance (GMD) simulation to experience operating a simple grid model under a GMD, and 3) a multi-user scenario to simulate normal operations while communicating with a team. The paper introduces the simulation environment used, and describes the scenario design process including the learning objective, system variation, and the user interface and controls.

Design Considerations for Operational Power System Simulation Scenarios

An Overview of Modeling Geomagnetic Disturbances in Power Systems

While the operation of much of the electric power grid is automated, the human operators and engineers are still very much “in the loop.” During times of emergency operation, when the system may be close to instability and collapse, having access to timely, pertinent information about a potentially rapidly changing system state could prove crucial in preventing major blackouts. This chapter examines the role power system visualization can play in providing this information to access the margin to system instability. The focus of the chapter is on techniques for the rapid analysis and display of information, based primarily on Supervisory Control and Data Acquisition (SCADA) data, which will allow operators and engineers to quickly assess the state of a large power grid, and then take effective control actions. It also examines how visualization can be used to provide an early warning as a secure power system state gradually approaches the system stability boundary.

The Role of Power System Visualization in Enhancing Power System Security

The impact of geomagnetic disturbances (GMDs) on the high voltage electric grid can result in severe damage by producing geomagnetically induced currents (GICs). Protection against GMD therefore necessitates the accurate estimation of the GICs. GIC estimation can be challenging since they depend in part upon the substation grounding resistances, which are not always well known. To address this issue the paper proposes an algorithm to calculate the sensitivity of the GICs at any substation to these resistances. The method is demonstrated on several power grid models.

Geomagnetically induced current sensitivity to multiple substation grounding resistances

Geomagnetically induced currents (GICs) can cause transformer half cycle saturation and consequently affect the power grid with harmonic currents and increased reactive power loss. This paper focuses on using transformer neutral GIC measurements to help validate the GIC models. A linear GIC model is presented that relates the geoelectric field input to the transformer neutral GICs. To validate this model, a temporal GIC matrix model is introduced and the singular value decomposition (SVD) is used for estimating the geoelectric field. The effectiveness of the approach is shown using a 20 bus test case. Finally, the GIC model is extended to account for nonuniform electric field and its accuracy is evaluated through SVD.

Thomas J. Overbye

Papers

Design Considerations for Operational Power System Simulation Scenarios

An Overview of Modeling Geomagnetic Disturbances in Power Systems

The Role of Power System Visualization in Enhancing Power System Security

Geomagnetically induced current sensitivity to multiple substation grounding resistances

Singular value decomposition in geomagnetically induced current validation