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 panel session will highlight collaboration between power systems and education researchers to produce interactive power and energy curriculum materials for upper elementary and middle school students and teachers. The materials are being developed as part of the NSF-funded Trustworthy Cyber Infrastructure for the Power Grid project. We will discuss how the knowledge and expertise of power researchers, curriculum specialists, classroom teachers, and students have been utilized to produce lessons that are both technically and pedagogically sound. Methods of dissemination will also be discussed, such as direct involvement with students and teachers in their classrooms, presentations at conferences for teachers of mathematics and science, and implementation of the materials through teacher workshops.

Collaboration and dissemination efforts related to pre-university power lessons

Effectively communicating the behavior of an electric grid is an important pursuit in education, research, and industrial applications. This paper presents considerations for visual storytelling as a means for interpreting and communicating the behavior of the grid for simulations ranging in duration from seconds to days. By framing the issue of communicating the vast amounts of data associated with wide-area transmission grid operation as a story to tell, those tasked with presenting this data are encouraged to consider what makes an effective story and, in turn, create compelling and understandable stand-alone narratives. Demonstrations are presented for cases of various scales including a 37-bus case, a 2000-bus case, and a 24,000-bus case. Narrative techniques including non-linear time and alternative path storytelling are shown.

Case Study on Design Considerations for Wide-Area Transmission Grid Operation Visual Storytelling

: Effective power system operation requires power system engineers and operators to analyze vast amounts of information. In systems containing thousands, or even tens of thousands of buses, a key challenge is to present this data in a form such that the user can assess the state of the system in an intuitive and quick manner. This paper presents several power system specific visualization techniques to help in this task. These techniques include animation of power system flow values, contouring of various power system values including voltage magnitudes and transmission line percentage loadings, and brief coverage of a data aggregation technique. Results are shown for several large scale power systems.

Visualization of Large Scale Power Systems

Electric transmission infrastructure in the United States is increasingly burdened by bulk power transfers. The system is being utilized at levels beyond those originally envisioned by the designers, with no decrease in demand in sight. Thus, there is great desire to find new ways to transfer even more power over existing lines. This project is examining the system requirements for reactive power support in power transfers and quantifying the impact of this support on transfer capabilities.

Twenty-eighth annual report of the Power Affiliates Program.

Subsection 1221(a) of the Energy Policy Act of 2005 calls for a study to determine national interest electric transmission corridors These corridors are defined as "any geographic area experiencing electric transmission capacity constraints or congestion that adversely affects consumers" This paper presents a method to define a "direct flow" between two hubs using the power transfer distribution factors (PTDFs) With these hubs properly defined, the hope is to be able to assess where these transmission corridors of national significance exist

Thomas J. Overbye

Papers

Collaboration and dissemination efforts related to pre-university power lessons

Case Study on Design Considerations for Wide-Area Transmission Grid Operation Visual Storytelling

Visualization of Large Scale Power Systems

Twenty-eighth annual report of the Power Affiliates Program.

Transmission Corridor Analysis using PTDFs