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11,902
Equivalence Classes of Direction Objects and Applications
, 1999
"... Direction is an important spatial relationship that is used in many fields such as geographic information systems(GIS) and image interpretation. It is also frequently used as a selection condition in spatial queries. In our recent work we have described a novel viewpoint to model direction as a `spa ..."
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Cited by 4 (4 self)
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classes. By defining an algebra on equivalence classes we provide a framework to model semantics of direction predicates for qualitative spatial reasoning. We then proceed to extrapolate the definition of direction equivalence classes to define `path' equivalence classes with an application
Enhancing equivalence class formation by pretraining of other equivalence classes
 The Psychological Record
, 1997
"... This study investigated how the learning of one set of equivalence classes enhances the learning of new equivalence classes. Fiftytwo undergraduate students were divided into four groups. Subjects in Group 1 received no pretraining. Using the simpletocomplex procedure followed by incremental expa ..."
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Cited by 11 (2 self)
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This study investigated how the learning of one set of equivalence classes enhances the learning of new equivalence classes. Fiftytwo undergraduate students were divided into four groups. Subjects in Group 1 received no pretraining. Using the simpletocomplex procedure followed by incremental
Counting equivalence classes of irreducible representations
"... Abstract. Let n be a positive integer, and let R be a (possibly infinite dimensional) finitely presented algebra over a computable field of characteristic zero. We describe an algorithm for deciding (in principle) whether R has at most finitely many equivalence classes of ndimensional irreducible r ..."
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Abstract. Let n be a positive integer, and let R be a (possibly infinite dimensional) finitely presented algebra over a computable field of characteristic zero. We describe an algorithm for deciding (in principle) whether R has at most finitely many equivalence classes of ndimensional irreducible
Verification by State Spaces with Equivalence Classes
"... . This paper demonstrates the potential of verification based on state spaces reduced by equivalence relations. The basic observation is that quite often, some states of a system are similar, i.e., they induce similar behaviours. Similarity can be formally expressed by defining equivalence relations ..."
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relations on the set of states and the set of actions of a system under consideration. A state space can be constructed, in which the nodes correspond to equivalence classes of states and the arcs correspond to equivalence classes of actions. Such a state space is often much smaller than the ordinary full
Triangle surfaces with discrete equivalence classes
 Proceedings of SIGGRAPH 2010
, 2010
"... triangles optimized to 10 unique polygons (only 0.3 % of the total polygons) using our method. Left shows a closeup of the tessellation of the surface. We propose a technique that takes a triangulated surface as input and outputs a surface with the same topology but altered geometry such that each ..."
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Cited by 21 (0 self)
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polygon falls into a set of discrete equivalence classes. We begin by describing an error function that measures how close the polygons are to satisfying this criteria. To optimize this error function, we first cluster triangles into discrete sets such that the assignment of sets minimizes our error. We
Differential Ktheory as equivalence classes . . .
"... We construct a model of differential Ktheory, using the geometrically defined Chern forms, whose cocycles are certain equivalence classes of maps into the Grassmannians and unitary groups. In particular, we produce the circleintegration maps for these models using classical homotopytheoretic con ..."
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We construct a model of differential Ktheory, using the geometrically defined Chern forms, whose cocycles are certain equivalence classes of maps into the Grassmannians and unitary groups. In particular, we produce the circleintegration maps for these models using classical homotopy
Equivalence classes of latin squares and nets
 in CP 2
"... Abstract. The fundamental combinatorial structure of a net in CP2 is its associated set of mutually orthogonal Latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in CP2. Then we count these equivalence classes ..."
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Abstract. The fundamental combinatorial structure of a net in CP2 is its associated set of mutually orthogonal Latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in CP2. Then we count these equivalence classes
The Complexity of Identifying Large Equivalence Classes
, 1998
"... We prove that at least  O(k) equivalence tests and no more than + O(n) equivalence tests are needed in the worst case to identify the equivalence classes with at least k members in set of n elements. The upper bound is an improvement by a factor 2 compared to known results. For k = 3 we give tighte ..."
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Cited by 2 (0 self)
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We prove that at least  O(k) equivalence tests and no more than + O(n) equivalence tests are needed in the worst case to identify the equivalence classes with at least k members in set of n elements. The upper bound is an improvement by a factor 2 compared to known results. For k = 3 we give
Age Differences in the Formation of Equivalence Classes
"... In order to investigate the relationship between stimulus equivalence class formation and age differences, two groups of elderly (ages 6281) and young (ages 1922) adult men and women mastered a series of simple and conditional discriminations. Subsequently, they were administered a test for the em ..."
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In order to investigate the relationship between stimulus equivalence class formation and age differences, two groups of elderly (ages 6281) and young (ages 1922) adult men and women mastered a series of simple and conditional discriminations. Subsequently, they were administered a test
Equivalence Classes of Operators on B(H)
"... Let L(B(H)) be the algebra of all linear operators on B(H) and P be a property on B(H). For φ1, φ2 ∈ L(B(H)) we say that φ1∼Pφ2 whenever φ1(T) has property P if and only if φ2(T) has this property. In particular, if I is the identity map on B(H) then φ∼PI means that φ preserves property P in both di ..."
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directions. Each property P produces an equivalence class on L(B(H)). We study the relation between equivalence classes with respect to different properties.
Results 11  20
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11,902