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

As power systems become more heavily loaded, there will be an increase in the number of situations where the power flow equations have no real solution, particularly in contingency analysis and planning applications. Since these cases can represent the most severe threats to viable system operation, it is important that a computationally efficient technique be developed to both quantify the degree of unsolvability, and to provide optimal recommendations of the parameters to change to return to a solvable solution. Such an algorithm is developed in the paper. The distance in parameter space between the desired operating point and the closest solvable operating point provides a measure of the degree of unsolvability, with the difference between these two points providing the optimal system parameter changes. The algorithm is based upon a Newton-Raphson power flow algorithm, which provides both computational efficiency and compatibility with existing security analysis techniques. The method is demonstrated on systems of up to 118 buses. >

A power flow measure for unsolvable cases

Existing and forthcoming devices at the residential level have the ability to provide reactive power support. Inverters which connect distributed generation such as solar panels and pluggable hybrid electric vehicles (PHEVs) to the grid are an example. Such devices are not currently utilized by the power system. We investigate the integration of these end-user reactive-power-capable devices to provide voltage support to the grid via a secure communications infrastructure. We determine effective locations in the transmission system and show how reactive power resources connected at those buses can be controlled. Buses belong to reactive support groups which parallel the regions of the secure communications architecture that is presented. Ultimately, our goal is to present how the smart grid can enable the utilization of available end-user devices as a resource to mitigate power system problems such as voltage collapse.

An Authenticated Control Framework for Distributed Voltage Support on the Smart Grid

New technologies are increasing the vulnerability of the power system to cyber security threats. Dealing with these threats and determining vulnerabilities is an important task for utilities. This paper presents the development of a testbed designed to assess the vulnerabilities introduced by using public networks for communication.

/pdf/scada-cyber-security-testbed-development-3paxmak7jk.pdf

SCADA Cyber Security Testbed Development

Preserving the availability and integrity of the power grid critical infrastructures in the face of fast-spreading intrusions requires advances in detection techniques specialized for such large-scale cyber-physical systems. In this paper, we present a security-oriented cyber-physical state estimation (SCPSE) system, which, at each time instant, identifies the compromised set of hosts in the cyber network and the maliciously modified set of measurements obtained from power system sensors. SCPSE fuses uncertain information from different types of distributed sensors, such as power system meters and cyber-side intrusion detectors, to detect the malicious activities within the cyber-physical system. We implemented a working prototype of SCPSE and evaluated it using the IEEE 24-bus benchmark system. The experimental results show that SCPSE significantly improves on the scalability of traditional intrusion detection techniques by using information from both cyber and power sensors. Furthermore, SCPSE was able to detect all the attacks against the control network in our experiments.

SCPSE: Security-Oriented Cyber-Physical State Estimation for Power Grid Critical Infrastructures

A security measure is defined to indicate vulnerability to voltage collapse based on an energy function for system models that includes voltage variation and reactive loads. The system dynamic model, the energy function, and the security measure are first illustrated in a simple radial system. Application of the security measure and its computational aspects are then examined in a standard 30-bus example (New England System). The security measure captures nonlinear effects such as VAR limits on generators that can influence the systems vulnerability to collapse. The behavior of the index with respect to network load increases is nearly linear over a wide range of load variation, facilitating prediction of the onset of collapse. >

/pdf/an-energy-based-security-measure-for-assessing-vulnerability-5613pvppf2.pdf

Thomas J. Overbye

Papers

A power flow measure for unsolvable cases

An Authenticated Control Framework for Distributed Voltage Support on the Smart Grid

SCADA Cyber Security Testbed Development

SCPSE: Security-Oriented Cyber-Physical State Estimation for Power Grid Critical Infrastructures

An energy based security measure for assessing vulnerability to voltage collapse