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

Measuring the changes to the earth's magnetic field during geomagnetic disturbance (GMD) events provides valuable insights which can be used to better understand potential impacts of GMDs on the electrical power grid and develop mitigating measures. This paper analyzes variations in the magnetic field measurement data captured from 17 magnetometers placed across the United States over the course of a strong GMD event that occurred in early November 2021. Various correlation analyses are performed based on the magnetic field measurements and time-shifted signals during four distinct scenarios (pre-storm, early-storm, peak-storm, and post-storm). The results provide a better understanding of the changes in magnetic field patterns, which can lead to a more accurate assessment of the induced electric field on the grid.

Analysis of Magnetometer Data from a Strong G3 Geomagnetic Disturbance

With deregulation in the electric industry the process of siting new generation has changed dramatically. In the previous vertically integrated utility paradigm, the local utility could bundle the cost of new transmission with the costs associated with adding generation. With deregulation, independent generators usually wish to site at locations in which their new generation will not cause any new overloads in the transmission grid. This paper describes a process for systematically determining the impact new generation will have on the transmission system. Emphasis is also placed on the visualization of these transmission system impacts.

Transmission impacts and visualization of new generation

A sensitivity analysis is applied to the mode and mode shape calculations of the Matrix Pencil method, in order to measure the robustness of the results. The methodology has been proven to work quickly and accurately when identifying modes, but there has not been testing regarding the ability of the MP method to operate under different time windows and sampling frequencies. A variety of signals are used for testing, including both signals with known and unknown modes in conjunction with the moving time windows and sampling frequencies.

Sensitivity of Modes from Modal Analysis of Electric Grids

A key challenge to Geomagnetic Disturbance (GMD) studies is the scarcity of severe geomagnetic field data available to researchers due to its low event occurrence. This study aims to address this challenge by first creating realistic “synthetic” data that represents the geomagnetic field fluctuations caused by recent GMD events. This paper utilizes a machine-learning approach to generate synthetic geomagnetic field data. Specifically, the application and preliminary results of a modified form of the generative adversarial network (GAN) to create time-series synthetic geomagnetic field data of three different severities are described here. The purpose of this paper is to document the first step towards creating severe synthetic geomagnetic field data to advance power system research. Future studies beyond this paper will extend on this work to generate data representing severe GMD storms.

Synthetic Geomagnetic Field Data Creation for Geomagnetic Disturbance Studies using Time-series Generative Adversarial Networks

As the electricity industry becomes increasingly competitive, knowledge concerning the capacity, constraints and reliability of the electric system will become a commodity of great value. Electricity markets can be fast changing; understanding the implications of these changes before others can give an important competitive advantage. Power systems, however, are characterized by extremely large sets of data that cover spatial, temporal and contingent dimensions. Therefore the focus of this mini-track is on the management and visualization of the information associated with power markets and power systems. This year there were four accepted papers. The first paper, “Visualization and Animation of Inverter-Driven Induction Motor Operations” addresses power system visualization at the component level. Power systems are characterized by devices with many different characteristics and widely varying time frames of response. In some situations, understanding the response of the entire system requires having a detailed knowledge of the individual components. The first paper presents an overview of a component-based virtual power system simulation and visualization environment. The paper then demonstrates these concepts with the example of an inverter-driven induction motor. The second paper, “Real-time Data Retrieval and New Visualization Techniques for the Energy Industry”, moves from a micro to a macro view of the power system. Rather than providing detailed visualizations of the individual components, the second paper presents some innovative methods for providing a visualization of the high level operation of the power grid. The paper makes a very useful contribution in providing some case study results

Thomas J. Overbye

Papers

Analysis of Magnetometer Data from a Strong G3 Geomagnetic Disturbance

Transmission impacts and visualization of new generation

Sensitivity of Modes from Modal Analysis of Electric Grids

Synthetic Geomagnetic Field Data Creation for Geomagnetic Disturbance Studies using Time-series Generative Adversarial Networks

Information management and visualization in electric power systems