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

Interest in promoting innovation for large, highvoltage power grids has driven recent efforts to reproduce actual system properties in synthetic electric grids, which are fictitious datasets designed to be large, complex, realistic, and totally public. This paper presents new techniques based on system planning sensitivities, integrated into a synthesis methodology to mimic the constraints used in designing actual grids. This approach improves on previous work by explicitly quantifying each candidate transmission line’s contribution to contingency robustness, balancing that with geographic and topological metrics. Example synthetic grids built with this method are compared to actual transmission grids, showing that the emulated careful design also achieves observed complex network properties. The results shed light on how the underlying graph structure of power grids reflects the engineering requirements of their design. Moreover, the datasets synthesized here provide researchers in many fields with public power system test cases that are detailed and realistic.

/pdf/planning-sensitivities-for-building-contingency-robustness-2maws2eawl.pdf

Planning Sensitivities for Building Contingency Robustness and Graph Properties into Large Synthetic Grids

Synthetic power grids, that is, test cases designed to match realistic structural and statistical characteristics of actual grids, are useful for research, development, and demonstration of innovations, since the cases are fictitious and thus free from data confidentiality issues. Building on previous work, this paper addresses a couple of related problems in the transmission network synthesis process. These issues appear as created cases become larger and involve multiple areas and overlapping nominal voltage levels. A fast, scalable hierarchical clustering is designed to assign voltage levels to substations considering the needs of the system, the specific constraints of the area, and smooth interconnections between neighboring areas with different voltage levels. A line topology generation framework is considered that is appropriate for many networks of different voltage levels, constructed together for a useful, realistic grid. These methods are demonstrated in a new 2000 bus test case, validated and publicly released.

/pdf/building-synthetic-power-transmission-networks-of-many-5b453mk6fz.pdf

Building Synthetic Power Transmission Networks of Many Voltage Levels, Spanning Multiple Areas

Power system dynamic simulation demands substantial computation due to extensive interconnection among power systems. Traditionally, the computational burden has been reduced by using dynamic equivalent methodologies, such as modal, coherency and measurement-based. Measurement-based method replaces an external system with a simple equivalent and estimates its parameters through optimization method with measurement. However, the conventional method does not clearly present the model structure for the external equivalent. This ambiguity, then, may lead to poor performance of the equivalent. The proposed method uses generator equivalent model and shows how to choose a proper number of generators for the equivalent model structure using coherency concept. The approach preserves relevant modes from the external and thus enhances the simulation performance of the dynamic equivalent. Test results of a simple power system are presented and show a high level of accuracy of the proposed method.

Enhanced measurement-based dynamic equivalence using coherency identification

Embedding the modeling and simulation of geomagnetically induced currents, GIC, into power flow simulation software allows the study of sensitivity and transient stability of the North American bulk power system under the distress of a geomagnetic storm. Modeling the interaction between the auroral electrojets and the Earth's atmosphere is a crucial step in determining the geoelectric field induced by the geomagnetic storm. Geomagnetic storms interact with the Earth's magnetic field, inducing damaging currents into the power grid, which have proven to be harmful to high voltage transformers and the overall stability of the power grid.

Power flow studies in the presence of geomagnetically induced currents

One viable option for the visualization of bus-based power system data is contouring. As contouring research progresses, more computationally efficient methods must be developed. A new algorithm presented here uses the concept of creating a unique influence distance for each bus. The distance is based on the closest g number of buses, instead of previous methods that use the same influence distance for each bus. The improvement in speed, along with the overall accuracy and pictorial quality of the images produced by this algorithm are examined in this paper

/pdf/adaptive-influence-distance-algorithm-for-contouring-bus-41pgfsvv42.pdf

Thomas J. Overbye

Papers

Planning Sensitivities for Building Contingency Robustness and Graph Properties into Large Synthetic Grids

Building Synthetic Power Transmission Networks of Many Voltage Levels, Spanning Multiple Areas

Enhanced measurement-based dynamic equivalence using coherency identification

Power flow studies in the presence of geomagnetically induced currents

Adaptive Influence Distance Algorithm for Contouring Bus-Based Power System Data