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

With the integration of renewable energy, system inertia may have a trend of decreasing in recent years, which increases the likelihood of transient instability. Inertia has impacts on voltage profiles and such impacts vary by location. After the system is subject to faults on buses or on transmission lines, bus voltages change differently as sum of inertia varies in sites that are either near or far away from violation locations. Critical clearing time (CCT) is a metric assessing condition of system stability. This paper displays how inertia changes affect CCT and how such impacts are location-dependent. An insightful preliminary study is carried out to reveal how inertia comes into play in bus voltage levels. Two case sets considering different oscillations are presented to verify inertia’s locational impacts on CCT.

Locational Dependence of Inertia’s Impacts on Critical Clearing Time

This paper looks at the decision-making involved with taking any snapshot from a dynamic simulation, and re-initializing the power flow from that snapshot. This is particularly important in educational and training contexts, which gives students and engineers the ability to make informed decisions when handling contingencies. A motivating example is provided, followed by an analysis of the most important models to consider when re-initializing a power flow. The analysis is supplemented by computational examples with regards to the models.

Considerations in the Initialization of Power Flow Solutions from Dynamic Simulation Snapshots

Geomagnetically induced currents (GICs) cause half cycle saturation of transformers, which increases harmonic currents and reactive powers in the grid. This paper presents the least-squares (LS) estimation of the geoelectric field using the GIC measurements for model validation purposes. To account for more realistic noise scenarios, a general probabilistic GIC measurement model has been developed. Using the proposed model, the accuracy of the LS estimator and its reliability in assessing the geoelectric field are available analytically. The analytical results are verified through numerical simulations using a practical 20-bus test case.

Probabilistic modeling and reliability analysis for validating geomagnetically induced current data

Natural disasters have long posed a threat to electric grids. This paper considers how islanding can be used to improve electric grid resiliency to such events. Specifically the paper provides an example of undergraduate research applying the concept of islanding to a Texas-sized synthetic grid. The results show that islanding the synthetic grid successfully protects it from a complete blackout, and maintains full functionality for all portions of the electric grid in the absence of an event.

Using Large Scale Synthetic Systems for Undergraduate Research in Electric Grid Islanding

It is common knowledge that the power flow can have multiple solutions; one is the normal (desired) solution while the others are alternative solutions, which are sometimes characterized by low voltages. Usually these alternative solutions represent erroneous or unstable operation conditions. The paper presents a method for quickly assessing whether the power flow has likely converged to an alternative solution by considering, on a bus by bus basis, the sensitivity of the bus voltage magnitude to a change in the bus's reactive power injection, coupled with whether the bus is closely connected with negative reactance branches. Sparse vector methods are used to calculate these sensitivities quickly even for large systems with 10,000+ buses. The paper shows that these solutions can be particularly problematic when assessing voltage stability impacts of geomagnetic disturbances on the grid, and uses the method to identify problematic areas of a system under a GMD event.

Thomas J. Overbye

Papers

Locational Dependence of Inertia’s Impacts on Critical Clearing Time

Considerations in the Initialization of Power Flow Solutions from Dynamic Simulation Snapshots

Probabilistic modeling and reliability analysis for validating geomagnetically induced current data

Using Large Scale Synthetic Systems for Undergraduate Research in Electric Grid Islanding

Computationally Efficient Identification of Power Flow Alternative Solutions with Application to Geomagnetic Disturbance Analysis