We survey the problem of comparing labeled trees based on simple local operations of deleting, inserting and relabeling nodes. These operations lead to the tree edit distance, alignment distance and inclusion problem. For each problem we review the results available and present, in detail, one or more of the central algorithms for solving the problem.

A 2-distance k-coloring of a graph G is a mapping from V (G) to the set of colors {1, . . . , k} such that every two vertices at distance at most 2 receive distinct colors. The 2-distance chromatic number χ2(G) of G is then the mallest k for which G admits a 2-distance k-coloring. For any finite set of positive integers D = {d1, . . . , dk}, the integer distance graph G = G(D) is the infinite g...

For many educators, the phrase ‘from distance education to e-learning’ conjures up the view of an ‘evolutionary’ progression beginning with correspondence study and developed through more sophisticated technologies to its current identification with computers, the Internet, and the World Wide Web. For others, particularly those with little knowledge or experience of (and often equally little in...

Euclidean distance matrix completion problem aims at reconstructing the low dimensional geometry structure of nodes given only a few pairwise distances between nodes [1]. This problem arises in many applications including networks and machine learning where much information of points is laking. For instance, in sensor networks, due to the constraints of energy and communication radius, sensor n...

Tutor Marked Assignments (TMAs) are the major mechanism by which Open University (OU) students receive feedback on their academic progress. This paper shows how the OU has used ICT to improve both the quality of feedback and speed of response to student work, reduce feelings of isolation and make the university seem less remote. The paper examines the system for online submission and return of ...

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficents can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counter-terms. We a...

Classic linear dimensionality reduction (LDR) methods, such as principal component analysis (PCA) and linear discriminant analysis (LDA), are known not to be robust against outliers. Following a systematic analysis of the multi-class LDR problem in a unified framework, we propose a new algorithm, called minimal distance maximization (MDM), to address the non-robustness issue. The principle behi...

Distance relays are used to protect EHV and HV Transmission lines. Over the past decades many algorithms have emerged for digital distance relays. These are based on the calculation of the transmission line impedance from the relaying to fault points. In this paper a novel method for digital distance relaying is proposed. In the method the tracking procedure is implemented. The method uses the ...

A set of vertices $S$ in a connected graph $G$ is a different-distance set if, for any vertex $w$ outside $S$, no two vertices in $S$ have the same distance to $w$.The lower and upper different-distance number of a graph are the order of a smallest, respectively largest, maximal different-distance set.We prove that a different-distance set induces either a special type of path or an independent...