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380
A tutorial on support vector machines for pattern recognition
 Data Mining and Knowledge Discovery
, 1998
"... The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SV ..."
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Cited by 2942 (12 self)
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The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very large (even infinite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization performance is guaranteed for SVMs, there are several arguments which support the observed high accuracy of SVMs, which we review. Results of some experiments which were inspired by these arguments are also presented. We give numerous examples and proofs of most of the key theorems. There is new material, and I hope that the reader will find that even old material is cast in a fresh light.
Modelchecking algorithms for continuoustime Markov chains
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 2003
"... Continuoustime Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steadystate and transientstate probabilities. This paper introduces a branching temporal logic for expressing realt ..."
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Cited by 210 (43 self)
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Continuoustime Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steadystate and transientstate probabilities. This paper introduces a branching temporal logic for expressing realtime probabilistic properties on CTMCs and presents approximate model checking algorithms for this logic. The logic, an extension of the continuous stochastic logic CSL of Aziz et al., contains a timebounded until operator to express probabilistic timing properties over paths as well as an operator to express steadystate probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steadystate operator) and a Volterra integral equation system (for timebounded until). We then show that the problem of modelchecking timebounded until properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows the verification of probabilistic timing properties by efficient techniques for transient analysis for CTMCs such as uniformization. Finally, we show that a variant of lumping equivalence (bisimulation), a wellknown notion for aggregating CTMCs, preserves the validity of all formulas in the logic.
Automated 3D Extraction of Inner and Outer Surfaces of Cerebral Cortex from MRI
 NEUROIMAGE
, 2000
"... Automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging (MRI) is greatly aided by deformable models, which are used to extract, identify, and quantify specific neuroanatomic structures. A general method of deforming polyhedra is presented h ..."
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Cited by 160 (16 self)
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Automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging (MRI) is greatly aided by deformable models, which are used to extract, identify, and quantify specific neuroanatomic structures. A general method of deforming polyhedra is presented here, with two novel features. First, explicit prevention of selfintersecting surface geometries is provided, unlike conventional deformable models, which use regularization constraints to discourage but not necessarily prevent such behavior. Second, deformation of multiple surfaces with intersurface proximity constraints allows each surface to help guide other surfaces into place using modelbased constraints such as expected thickness of an anatomic surface. These two features are used advantageously to identify automatically the total surface of the outer and inner boundaries of cerebral cortical gray matter from normal human MR images, accurately locating the depths of the sulci, even where noise and partial volume artifacts in the image obscure the visibility of sulci. The extracted surfaces are enforced to be simple twodimensional manifolds (having the topology of a sphere), even though the data may have topological holes. This automatic 3D cortex segmentation technique has been applied to 150 normal subjects, simultaneously extracting both the gray/white and gray/cerebrospinal fluid interface from each individual. The collection of surfaces has been used to create a spatial map of the mean and standard deviation for the location and the thickness of cortical gray matter. Three alternative criteria for defining cortical thickness at each cortical location were developed and compared. These results are shown to corroborate published postmortem and in vivo measurements of cortical thickness.
Approximate symbolic model checking of continuoustime Markov chains (Extended Abstract)
, 1999
"... . This paper presents a symbolic model checking algorithm for continuoustime Markov chains for an extension of the continuous stochastic logic CSL of Aziz et al [1]. The considered logic contains a timebounded untiloperator and a novel operator to express steadystate probabilities. We show that t ..."
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Cited by 148 (24 self)
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. This paper presents a symbolic model checking algorithm for continuoustime Markov chains for an extension of the continuous stochastic logic CSL of Aziz et al [1]. The considered logic contains a timebounded untiloperator and a novel operator to express steadystate probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steady stateoperator) and a Volterra integral equation system for timebounded until. We propose a symbolic approximate method for solving the integrals using MTDDs (multiterminal decision diagrams), a generalisation of MTBDDs. These new structures are suitable for numerical integration using quadrature formulas based on equallyspaced abscissas, like trapezoidal, Simpson and Romberg integration schemes. 1 Introduction The mechanised verification of a given (usually) finitestate model against a property expressed in some temporal logic is known as model checking. For probabilistic...
Characterizing the hemodynamic response: Effects of presentation rate, sampling procedure, and the possibility of ordering brain activity based on relative timing
 NEUROIMAGE 11: 735–759
, 2000
"... Rapidpresentation eventrelated functional MRI (ERfMRI) allows neuroimaging methods based on hemodynamics to employ behavioral task paradigms typical of cognitive settings. However, the sluggishness of the hemodynamic response and its variance provide constraints on how ERfMRI can be applied. In ..."
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Cited by 129 (10 self)
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Rapidpresentation eventrelated functional MRI (ERfMRI) allows neuroimaging methods based on hemodynamics to employ behavioral task paradigms typical of cognitive settings. However, the sluggishness of the hemodynamic response and its variance provide constraints on how ERfMRI can be applied. In a series of two studies, estimates of the hemodynamic response in or near the primary visual and motor cortices were compared across various paradigms and sampling procedures to determine the limits of ERfMRI procedures and, more generally, to describe the behavior of the hemodynamic response. The temporal profile of the hemodynamic response was estimated across overlapping events by solving a set of linear equations within the general linear model. No
ObjectCentered Surface Reconstruction: Combining MultiImage Stereo and Shading
 International Journal of Computer Vision
, 1995
"... Our goal is to reconstruct both the shape and reflectance properties of surfaces from multiple images. We argue that an objectcentered representation is most appropriate for this purpose because it naturally accommodates multiple sources of data, multiple images (including motion sequences of a rig ..."
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Cited by 127 (19 self)
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Our goal is to reconstruct both the shape and reflectance properties of surfaces from multiple images. We argue that an objectcentered representation is most appropriate for this purpose because it naturally accommodates multiple sources of data, multiple images (including motion sequences of a rigid object), and selfocclusions. We then present a specific objectcentered reconstruction method and its implementation. The method begins with an initial estimate of surface shape provided, for example, by triangulating the result of conventional stereo. The surface shape and reflectance properties are then iteratively adjusted to minimize an objective function that combines information from multiple input images. The objective function is a weighted sum of stereo, shading, and smoothness components, where the weight varies over the surface. For example, the stereo component is weighted more strongly where the surface projects onto highly textured areas in the images, and less strongly othe...
The Surface Energy Balance System (SEBS) for estimation of turbulent heat fluxes
 Hydrology and Earth System Sciences
, 2002
"... heat fluxes ..."
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CONTRAfold: RNA secondary structure prediction without physicsbased models
 Bioinformatics
, 2006
"... doi:10.1093/bioinformatics/btl246 ..."
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Articulated soft objects for videobased body modeling
 In ICCV
, 2001
"... We develop a framework for 3–D shape and motion recovery of articulated deformable objects. We propose a formalism that incorporates the use of implicit surfaces into earlier robotics approaches that were designed to handle articulated structures. We demonstrate its effectiveness for human body mode ..."
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Cited by 74 (10 self)
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We develop a framework for 3–D shape and motion recovery of articulated deformable objects. We propose a formalism that incorporates the use of implicit surfaces into earlier robotics approaches that were designed to handle articulated structures. We demonstrate its effectiveness for human body modeling from video sequences. Our method is both robust and generic. It could easily be applied to other shape and motion recovery problems. 1.
The hiball tracker: highperformance widearea tracking for virtual and augmented environments
 In VRST ’99: Proceedings of the ACM symposium on Virtual reality software and technology
, 1999
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