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 presents a methodology and set of validation criteria for the systematic creation of synthetic power system test cases The synthesized grids do not correspond to any real grid and are, thus, free from confidentiality requirements The cases are built to match statistical characteristics found in actual power grids First, substations are geographically placed on a selected territory, synthesized from public information about the underlying population and generation plants A clustering technique is employed, which ensures the synthetic substations meet realistic proportions of load and generation, among other constraints Next, a network of transmission lines is added This paper describes several structural statistics to be used in characterizing real power system networks, including connectivity, Delaunay triangulation overlap, dc power flow analysis, and line intersection rate The paper presents a methodology to generate synthetic line topologies with realistic parameters that satisfy these criteria Then, the test cases can be augmented with additional complexities to build large, realistic cases The methodology is illustrated in building a 2000 bus public test case that meets the criteria specified

Grid Structural Characteristics as Validation Criteria for Synthetic Networks

State estimation is an important power system application that is used to estimate the state of the power transmission networks using (usually) a redundant set of sensor measurements and network topology information. Many power system applications such as contingency analysis rely on the output of the state estimator. Until recently it was assumed that the techniques used to detect and identify bad sensor measurements in state estimation can also thwart malicious sensor measurement modification. However, recent work by Liu et al. [1] demonstrated that an adversary, armed with the knowledge of network configuration, can inject false data into state estimation that uses DC power flow models without being detected. In this work, we explore the detection of false data injection attacks of [1] by protecting a strategically selected set of sensor measurements and by having a way to independently verify or measure the values of a strategically selected set of state variables. Specifically, we show that it is necessary and sufficient to protect a set of basic measurements to detect such attacks.

/pdf/detecting-false-data-injection-attacks-on-dc-state-3ormqqgezs.pdf

Detecting False Data Injection Attacks on DC State Estimation

Although phasor measurement units (PMUs) have become increasingly widespread throughout power networks, the buses monitored by PMUs still constitute a very small percentage of the total number of system buses. Our research explores methods to derive useful information from PMU data in spite of this limited coverage. In particular, we have developed an algorithm which uses known system topology information, together with PMU phasor angle measurements, to detect system line outages. In addition to determining the outaged line, the algorithm also provides an estimate of the pre-outage flow on the outaged line. To demonstrate the effectiveness of our approach, the algorithm is demonstrated using simulated and real PMU data from two systems - a 37-bus study case and the TVA control area.

Line Outage Detection Using Phasor Angle Measurements

The paper examines the tradeoffs between using a full ac model versus the less exact, but much faster, dc power flow model for LMP-based market calculations. The paper first provides a general discussion of the approximations associated with using a dc model, with an emphasis on the impact these approximations will have on security constrained OPF (SCOPF) results and LMP values. Then, since the impact of the approximations can be quite system specific, the paper provides case studies using both a small 37 bus system and a somewhat larger 12,965 bus model of the Midwest U.S. transmission grid. Results are provided comparing both the accuracy and the computational requirements of the two models. The general conclusion is that while there is some loss of accuracy using the dc approximation, the results actually match fairly closely with the full ac solution.

A comparison of the AC and DC power flow models for LMP calculations

Electricity markets involve suppliers (generators) and sometimes consumers (loads) bidding for MWhr generation and consumption. In this market model, a central operator selves an optimal power flow (OPF) based on the maximization of social welfare to determine the generation and load dispatch and system spot prices. In this structure, market participants will choose their bids in order to maximize their profits. This presents a two-level optimization problem in which participants try to maximize their profit under the constraint that their dispatch and price are determined by the OPF. This paper presents an efficient numerical technique, using price and dispatch sensitivity information available from the OPF solution, to determine how a market participant should vary its bid portfolio in order to maximize its overall profit. The paper further demonstrates the determination of Nash equilibrium when all participants are trying to maximize their profit in this manner.

Thomas J. Overbye

Papers

Grid Structural Characteristics as Validation Criteria for Synthetic Networks

Detecting False Data Injection Attacks on DC State Estimation

Line Outage Detection Using Phasor Angle Measurements

A comparison of the AC and DC power flow models for LMP calculations

A two-level optimization problem for analysis of market bidding strategies