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589
Testing halfspaces
 IN PROC. 20TH ANNUAL SYMPOSIUM ON DISCRETE ALGORITHMS (SODA
, 2009
"... This paper addresses the problem of testing whether a Booleanvalued function f is a halfspace, i.e. a function of the form f(x) = sgn(w ·x−θ). We consider halfspaces over the continuous domain R n (endowed with the standard multivariate Gaussian distribution) as well as halfspaces over the Boolean ..."
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Cited by 33 (15 self)
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other ingredients. These include “crossconsistency ” versions of the results mentioned above for pairs of halfspaces with the same weights but different thresholds; new structural results relating the largest degree1 Fourier coefficient and the largest weight in unbalanced halfspaces; and algorithmic
Fast Scenariobased Decision Making in Unbalanced Distribution Networks
"... Abstract—In this paper we consider the problem faced by a distribution network operator that is required to guarantee, with high probability, the satisfaction of operational constraints of the grid in the presence of stochastic disturbances caused by fluctuating loads and intermittent microgeneratio ..."
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Cited by 1 (1 self)
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Abstract—In this paper we consider the problem faced by a distribution network operator that is required to guarantee, with high probability, the satisfaction of operational constraints of the grid in the presence of stochastic disturbances caused by fluctuating loads and intermittent microgeneration. We formulate this problem as a chanceconstrained decision problem, and we employ a scenariobased approach in order to convert it into a largescale deterministic decision problem. In order to make this latter problem computationally tractable, we approximate the nonlinear power flow equations via a sparse, implicit linear model. This approach results in an accurate and fast decision making strategy, that we validate in simulations on the IEEE13 threephase test feeder. I.
Fluid Dynamics Averaging over Fast Gravity Waves for Geophysical Flows with Unbalanced Initial Data1
, 1997
"... Abstract. Various facets of recent mathematical theories for averaging over fast gravity waves on advective time scales for geophysical flows with unbalanced initial data are presented here including nonlinear Rossby adjustment and simplified reduced dynamics. This work is presented within the conte ..."
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Abstract. Various facets of recent mathematical theories for averaging over fast gravity waves on advective time scales for geophysical flows with unbalanced initial data are presented here including nonlinear Rossby adjustment and simplified reduced dynamics. This work is presented within
Multicategory proximal support vector machine classifiers
 Machine Learning
, 2001
"... Abstract. Given a dataset, each element of which labeled by one of k labels, we construct by a very fast algorithm, a kcategory proximal support vector machine (PSVM) classifier. Proximal support vector machines and related approaches (Fung & Mangasarian, 2001; Suykens & Vandewalle, 1999) c ..."
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Cited by 29 (0 self)
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with this onefromtherest approach. The resulting twoclass problems are often very unbalanced, leading in some cases to poor performance. We propose balancing the k classes and a novel Newton refinement modification to PSVM in order to deal with this problem. Computational results indicate that these two
2003), Coulomb stress accumulation along the San Andreas Fault system
 J. Geophys. Res
"... [1] Stress accumulation rates along the primary segments of the San Andreas Fault system are computed using a threedimensional (3D) elastic halfspace model with realistic fault geometry. The model is developed in the Fourier domain by solving for the response of an elastic halfspace due to a poi ..."
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Cited by 18 (2 self)
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[1] Stress accumulation rates along the primary segments of the San Andreas Fault system are computed using a threedimensional (3D) elastic halfspace model with realistic fault geometry. The model is developed in the Fourier domain by solving for the response of an elastic halfspace due to a
Small weak epsilonnets in three dimensions
 In Proceedings of the 18th Canadian Conference on Computational Geometry
, 2006
"... We study the problem of finding small weak εnets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak εnet of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R3. 1 ..."
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Cited by 5 (0 self)
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We study the problem of finding small weak εnets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak εnet of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R3. 1
Small Weak EpsilonNets in Three Dimensions
"... We study the problem of finding small weak εnets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak εnet of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R 3. 1 ..."
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We study the problem of finding small weak εnets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak εnet of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R 3. 1
Linear Size Binary Space Partitions for Uncluttered Scenes
 Algorithmica
, 1998
"... We describe a new and simple method for constructing binary space partitions in arbitrary dimensions. We also introduce the concept of uncluttered scenes, which are scenes with a certain property that we suspect many realistic scenes exhibit, and we show that our method constructs a BSP of size O ..."
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Cited by 33 (9 self)
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We describe a new and simple method for constructing binary space partitions in arbitrary dimensions. We also introduce the concept of uncluttered scenes, which are scenes with a certain property that we suspect many realistic scenes exhibit, and we show that our method constructs a BSP of size O(n) for an uncluttered scene consisting of n objects. The construction time is O(n log n). Because any set of disjoint fat objects is uncluttered, our result implies an efficient method to construct a linear size BSP for fat objects. We use our BSP to develop a data structure for point location in uncluttered scenes. The query time of our structure is O(log n), and the amount of storage is O(n). This result can in turn be used to perform range queries with nottoosmall ranges in scenes consisting of disjoint fat objects or, more generally, in socalled lowdensity scenes. 1 Introduction Many geometric problems can be solved more easily if a decomposition of the space of interest in...
Exhausting, pneumatic transport
"... Abstract: The contribution describes frequent functional problems of exhausting devices, caused by no observing of essential rules of fluid mechanics. For instance, due to the unbalanced tubing system of several branches the medium flows in individual connections and their relevant energy transports ..."
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Abstract: The contribution describes frequent functional problems of exhausting devices, caused by no observing of essential rules of fluid mechanics. For instance, due to the unbalanced tubing system of several branches the medium flows in individual connections and their relevant energy
Active zones in CSG for accelerating boundary evaluation, redundancy elimination, interference detection, and shading algorithms
 ACM Transactions on Graphics
, 1989
"... Solids defined by Boolean combinations of solid primitives may be represented in constructive solid geometry (CSG) as binary trees. Most CSGbased algorithms (e.g., for boundary evaluation, graphic shading, interference detection) do various forms of setmembership classification by traversing the t ..."
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Cited by 29 (9 self)
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Solids defined by Boolean combinations of solid primitives may be represented in constructive solid geometry (CSG) as binary trees. Most CSGbased algorithms (e.g., for boundary evaluation, graphic shading, interference detection) do various forms of setmembership classification by traversing the tree associated with the solid. These algorithms usually generate intermediate results that do not contribute to the final result, and hence may be regarded as redundant and a source of inefficiency. To reduce such inefficiencies, we associate with each primitive A in a tree S an active zone 2 that represents the region of space where changes to A affect the solid represented by S, and we use a representation of 2 instead of S for setmembership classification. In the paper we develop a mathematical theory of active zones, prove that they correspond to the intersection of certain nodes of the original trees, and show how they lead to efficient new algorithms for boundary evaluation, for detecting and eliminating redundant nodes in CSG trees, for interference (nullset) detection, and for graphic shading.
Results 1  10
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589