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Exact Representations of and Computability on Real
"... This master's thesis explores computability of real functions via representations of real numbers. ..."
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This master's thesis explores computability of real functions via representations of real numbers.
Exact Representation and Operations on Spherical Maps
"... . We develop exact algorithms for geometric operations on general circles and circular arcs on the sphere, using integer homogeneous coordinates. The algorithms include testing a point against a circle, computing the intersection of two circles, and ordering three arcs out of the same point. Thes ..."
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. We develop exact algorithms for geometric operations on general circles and circular arcs on the sphere, using integer homogeneous coordinates. The algorithms include testing a point against a circle, computing the intersection of two circles, and ordering three arcs out of the same point
Exact Representation and Operations on Spherical Maps
, 1997
"... We develop exact algorithms for geometric operations on general circles and circular arcs on the sphere, using integer homogeneous coordinates. The algorithms include testing a point against a circle, computing the intersection of two circles, and ordering three arcs out of the same point. These ope ..."
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We develop exact algorithms for geometric operations on general circles and circular arcs on the sphere, using integer homogeneous coordinates. The algorithms include testing a point against a circle, computing the intersection of two circles, and ordering three arcs out of the same point
Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have bee ..."
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Cited by 770 (3 self)
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random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linearGaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from
Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ¹ minimization
 PROC. NATL ACAD. SCI. USA 100 2197–202
, 2002
"... Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered ..."
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Cited by 633 (38 self)
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considered the special case where D is an overcomplete system consisting of exactly two orthobases, and has shown that, under a condition of mutual incoherence of the two bases, and assuming that S has a sufficiently sparse representation, this representation is unique and can be found by solving a convex
Exact Representations from FeedForward Networks
, 1999
"... An algorithm to extract representations from feedforward perceptron networks (threshold) is outlined. The representation is based on polytopic decision regions in the input space{ and is exact not an approximation. Multiple example networks are analyzed. Some consequences of the representation are ..."
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Cited by 2 (1 self)
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An algorithm to extract representations from feedforward perceptron networks (threshold) is outlined. The representation is based on polytopic decision regions in the input space{ and is exact not an approximation. Multiple example networks are analyzed. Some consequences of the representation
EXACT REPRESENTATION OF TRUNCATED VARIATION OF BROWNIAN MOTION
"... Abstract. In the recent papers [8, 9, 10] the truncated variation has been introduced, characterized and studied in various stochastic settings. In this note we uncover an intimate link to the Skorokhod problem. Further, we exploit it to give an explicit representation of the truncated variation of ..."
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Abstract. In the recent papers [8, 9, 10] the truncated variation has been introduced, characterized and studied in various stochastic settings. In this note we uncover an intimate link to the Skorokhod problem. Further, we exploit it to give an explicit representation of the truncated variation
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 819 (28 self)
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all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
OBBTree: A hierarchical structure for rapid interference detection
 PROC. ACM SIGGRAPH, 171–180
, 1996
"... We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal and curved models. It precomputes a hierarchical representation of models using tightfitting oriented bo ..."
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Cited by 845 (53 self)
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We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal and curved models. It precomputes a hierarchical representation of models using tightfitting oriented
Results 1  10
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5,309