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Exemption from Particular Classes Policy
"... A. For all students to achieve all planned educational outcomes B. For students to be part of the school community and to form cohesive class groups C. To respect beliefs of individual families D. To cater for individual capabilities and interests II. Principles A. As much as possible we wish all st ..."
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grounds for exemption, however if it can be shown that an alternative individual program would be in the best interests of the student and could be achieved without undue hardship to the teacher and the class, it will be considered. This is particularly relevant for extension work. E. Exemptions may
Generating particular classes of connected graphs
, 2009
"... We present an algorithm to generate all connected graphs in a recursive and efficient manner. This algorithm is restricted subsequently to 1particle irreducible graphs and to connected graphs without selfloops. The recursions proceed by loop order and vertex number. The main result of [1] is a recu ..."
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We present an algorithm to generate all connected graphs in a recursive and efficient manner. This algorithm is restricted subsequently to 1particle irreducible graphs and to connected graphs without selfloops. The recursions proceed by loop order and vertex number. The main result of [1] is a recursion formula to generate all tree graphs. The underlying structure is a Hopf algebraic representation of graphs defined in the context of quantum field theory. This recursion formula is generalized to all connected graphs in [2]. In both cases, graphs are generated together with weight factors, which correspond to the inverses of their symmetry factors as considered in [3, 4]. In this paper, we reformulate that recursion formula to generate all connected graphs, in terms of abstract graphs. In addition, we restrict this result successively to 1PI graphs and to connected graphs without selfloops. Crucially, as in [1, 2], the correct weights of graphs are obtained. The (double) recursions proceed by loop order and vertex number. Our method is based on three basic operations on graphs, which are suitable to produce graphs with, say, e internal edges from a graph with e−1 internal edges. Namely, attaching a selfloop to a vertex; connecting a pair of adjacent vertices with an edge; and splitting a vertex in two, distributing
Designing Reusable Classes.
 Journal of Object Oriented Programming
, 1988
"... Abstract Objectoriented programming is as much a different way of designing programs as it is a different way of designing programming languages. This paper describes what it is like to design systems in Smalltalk. In particular, since a major motivation for objectoriented programming is software ..."
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Cited by 614 (9 self)
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Abstract Objectoriented programming is as much a different way of designing programs as it is a different way of designing programming languages. This paper describes what it is like to design systems in Smalltalk. In particular, since a major motivation for objectoriented programming
On the Solution Sets of Particular Classes of Linear Interval Systems
 J. Comput. Appl. Math
, 1996
"... We characterize the solution set S of real linear systems Ax = b by a set of inequalities if b lies between some given bounds b; b and if the n × n coefficient matrix A varies similarly between two bounds A and A. In addition, we restrict A to a particular class of matrices, for instance t ..."
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Cited by 9 (1 self)
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We characterize the solution set S of real linear systems Ax = b by a set of inequalities if b lies between some given bounds b; b and if the n × n coefficient matrix A varies similarly between two bounds A and A. In addition, we restrict A to a particular class of matrices, for instance
On the Solution Sets of Particular Classes of Linear Systems
, 1996
"... We characterize the solution set S of real linear systems Ax = b by a set of inequalities if b lies between some given bounds b; b and if the n × n coefficient matrix A varies similarly between two bounds A and A. In addition, we restrict A to a particular class of matrices, for instance t ..."
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Cited by 2 (0 self)
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We characterize the solution set S of real linear systems Ax = b by a set of inequalities if b lies between some given bounds b; b and if the n × n coefficient matrix A varies similarly between two bounds A and A. In addition, we restrict A to a particular class of matrices, for instance
ClassBased ngram Models of Natural Language
 Computational Linguistics
, 1992
"... We address the problem of predicting a word from previous words in a sample of text. In particular we discuss ngram models based on calsses of words. We also discuss several statistical algoirthms for assigning words to classes based on the frequency of their cooccurrence with other words. We find ..."
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Cited by 986 (5 self)
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We address the problem of predicting a word from previous words in a sample of text. In particular we discuss ngram models based on calsses of words. We also discuss several statistical algoirthms for assigning words to classes based on the frequency of their cooccurrence with other words. We
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
, 1997
"... We develop a face recognition algorithm which is insensitive to gross variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a highdimensional space. We take advantage of the observation that the images ..."
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Cited by 2310 (17 self)
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of a particular face, under varying illumination but fixed pose, lie in a 3D linear subspace of the high dimensional image space  if the face is a Lambertian surface without shadowing. However, since faces are not truly Lambertian surfaces and do indeed produce selfshadowing, images will deviate
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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Cited by 474 (3 self)
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The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological
DecisionTheoretic Planning: Structural Assumptions and Computational Leverage
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 1999
"... Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control theory and economics. While the assumptions and perspectives ..."
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Cited by 515 (4 self)
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related methods, showing how they provide a unifying framework for modeling many classes of planning problems studied in AI. It also describes structural properties of MDPs that, when exhibited by particular classes of problems, can be exploited in the construction of optimal or approximately optimal policies
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