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69
Convolution Kernels on Discrete Structures
, 1999
"... We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on an infinite set from kernels involving generators of the set. The family of kernels generated generalizes the fa ..."
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Cited by 506 (0 self)
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We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on an infinite set from kernels involving generators of the set. The family of kernels generated generalizes the family of radial basis kernels. It can also be used to define kernels in the form of joint Gibbs probability distributions. Kernels can be built from hidden Markov random elds, generalized regular expressions, pairHMMs, or ANOVA decompositions. Uses of the method lead to open problems involving the theory of infinitely divisible positive definite functions. Fundamentals of this theory and the theory of reproducing kernel Hilbert spaces are reviewed and applied in establishing the validity of the method.
Design and multiobjective optimization of a linkage for a haptic interface. in Advances in Robot Kinematics
 Preprints of the ISER4, International Symposium on Experimental Robotics
, 1994
"... Abstract A method to carry out the design of linkage for a haptic interface is described. Factors such as size, workspace, intrusion, inertia, response and structural properties are considered in this process. The dependencies of the various criteria are examined and a hierarchical method is applie ..."
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Cited by 43 (15 self)
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Abstract A method to carry out the design of linkage for a haptic interface is described. Factors such as size, workspace, intrusion, inertia, response and structural properties are considered in this process. The dependencies of the various criteria are examined and a hierarchical method is applied. The result is a compact device which is easy to manufacture and which fulfills the requirements demanded by its application. Several quantitative measures designed to capture its principal properties are at the heart the process. I. Introduction and Problem Statement The design of a haptic interface is driven by many requirements. Because a haptic device is essentially a humanmachine interface, it must have the general featmes of an ergonomic design. In particular, it should be compact and the operating workspace should be large in relation to the size of the device itself. It should also cause minimal
Parallel scientific computing in C++ and MPI: a seamless approach to parallel algorithms and their implementation
, 2003
"... Scientific computing is by its very nature a practical subject it requires tools and a lot of practice. To solve realistic problems we need not only fast algorithms but also a combination of good tools and fast computers. This is the subject of the current book, which emphasizes equally all three: ..."
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Cited by 32 (2 self)
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Scientific computing is by its very nature a practical subject it requires tools and a lot of practice. To solve realistic problems we need not only fast algorithms but also a combination of good tools and fast computers. This is the subject of the current book, which emphasizes equally all three: algorithms, tools, and computers. Often times such concepts and tools are taught serially across different courses and different textbooks, and hence the interconnection between them is not immediately apparent. We believe that such a close integration is important from the outset. The book starts with a heavy dosage of C++ and basic mathematical and computational concepts, and it ends emphasizing advanced parallel algorithms that are used in modern simulations. We have tried to make this book fun to read, to somewhat demystify the subject, and thus the style is sometimes informal and personal. It may seem that this happens at the expense of rigor, and indeed we have tried to limit notation and theorem proofing. Instead, we emphasize concepts and useful tricksofthetrade with many code segments, remarks, reminders, and warnings throughout the book. The material of this book has been taught at different times to students in engineering,
The challenges of clustering highdimensional data
 In New Vistas in Statistical Physics: Applications in Econophysics, Bioinformatics, and Pattern Recognition
, 2003
"... Cluster analysis divides data into groups (clusters) for the purposes of summarization or improved understanding. For example, cluster analysis has been used to group related documents for browsing, to find genes and proteins that have similar functionality, or as a means of data compression. While ..."
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Cited by 21 (0 self)
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Cluster analysis divides data into groups (clusters) for the purposes of summarization or improved understanding. For example, cluster analysis has been used to group related documents for browsing, to find genes and proteins that have similar functionality, or as a means of data compression. While clustering has a long history and a large number of clustering techniques have been developed in statistics, pattern recognition, data mining, and other fields, significant challenges still remain. In this chapter we provide a short introduction to cluster analysis, and then focus on the challenge of clustering high dimensional data. We present a brief overview of several recent techniques, including a more detailed description of recent work of our own which uses a conceptbased clustering approach. 1
NONLINEAR DYNAMICAL SYSTEM IDENTIFICATION FROM UNCERTAIN AND INDIRECT MEASUREMENTS
, 2002
"... We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regressio ..."
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Cited by 21 (0 self)
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We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regression approaches, noisy measurements can produce inaccurate parameter estimates. Another problem is that for chaotic systems the cost functions that have to be minimized to estimate states and parameters are so complex that common optimization routines may fail. We show that the inclusion of information about the timecontinuous nature of the underlying trajectories can improve parameter estimation considerably. Two approaches, which take into account both the errorsinvariables problem and the problem of complex cost functions, are described in detail: shooting approaches and recursive estimation techniques. Both are demonstrated on numerical examples.
A randomsurfer webgraph model
 In ANALCO ’06: Proceedings of the 3rd Workshop on Analytic Algorithmics and Combinatorics
, 2006
"... In this paper we provide theoretical and experimental results on a randomsurfer model for construction of a random graph. In this model, a new node connects to the existing graph by choosing a start node uniformly at random and then performing a short random walk. We show that in certain formulatio ..."
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Cited by 19 (0 self)
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In this paper we provide theoretical and experimental results on a randomsurfer model for construction of a random graph. In this model, a new node connects to the existing graph by choosing a start node uniformly at random and then performing a short random walk. We show that in certain formulations, this results in the same distribution as the preferentialattachment randomgraph model, and in others we give a direct analysis of powerlaw distribution of degrees or “virtual degrees ” of the resulting graphs. We also present experimental results for a number of settings of parameters that we are not able to analyze mathematically. 1
Image Subband Coding Artifacts: Analysis And Remedies
, 1993
"... This thesis deals with SubBand Coding (SBC) of still images at low bit rates, where the emphasis is on designing the SBC to be robust in the sense that the perceived image quality degrades gracefully as the bit rate is reduced. At low bit rates the subband data are coarsely approximated, and this re ..."
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Cited by 17 (1 self)
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This thesis deals with SubBand Coding (SBC) of still images at low bit rates, where the emphasis is on designing the SBC to be robust in the sense that the perceived image quality degrades gracefully as the bit rate is reduced. At low bit rates the subband data are coarsely approximated, and this results in visible distortions in the reconstructed image. The distortion characteristics depend on the filter bank applied. Blocking effects and ringing noise are the artifacts experienced using the Discrete Cosine Transform (DCT) and classical SBC, respectively. More recent filter banks, such as the Lapped Orthogonal Transforms (LOTs), utilize relatively short filter lengths. The noise characteristics are a cross between that of DCT and SBC: Less ringing noise than SBC, and smoother blocking artifacts than DCT. Much work has been done to develop clever quantization strategies for reducing the noise's influence on the reconstructed image. In this work we adopt a different strategy: Design the...
Simultaneous Water Filling in Mutually Interfering Systems
 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS
, 2004
"... In this paper we investigate properties of simultaneous water filling for a wireless system with two mutually interfering transmitters and receivers with noncooperative coding strategies. This is slightly different from the traditional interference channel problem which assumes that transmitters co ..."
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Cited by 14 (0 self)
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In this paper we investigate properties of simultaneous water filling for a wireless system with two mutually interfering transmitters and receivers with noncooperative coding strategies. This is slightly different from the traditional interference channel problem which assumes that transmitters cooperate in their respective coding strategies, and that interference cancellation can be performed at the receivers. In this noncooperative setup, greedy capacity optimization by individual transmitters through various algorithms leads to simultaneous water filling fixed points where the spectrum of the transmit covariance matrix of one user water fills over the spectrum of its corresponding interferenceplusnoise covariance matrix, and in our paper we study the properties of these fixed points. We show that at a simultaneous water filling point the eigenvectors of transmit covariance matrices at each receiver are aligned, and identify three regimes which correspond to simultaneous water filling that depend on the interference gains: a) complete spectral overlap, b) partial spectral overlap, and c) spectral segregation. These imply that the transmit covariance matrices will be white in regions of both overlap and segregation, but not necessarily white overall. We also consider performance as a function of interference gain and show that complete spectral overlap is a strongly suboptimal solution over a wide range of gains. Overall,
Relaxations of the Satisfiability Problem using Semidefinite Programming
, 2000
"... We derive a semidefinite relaxation of the satisfiability (SAT) problem and discuss its strength. We give both the primal and dual formulation of the relaxation. The primal formulation is an eigenvalue optimization problem, while the dual formulation is a semidefinite feasibility problem. It is s ..."
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Cited by 14 (2 self)
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We derive a semidefinite relaxation of the satisfiability (SAT) problem and discuss its strength. We give both the primal and dual formulation of the relaxation. The primal formulation is an eigenvalue optimization problem, while the dual formulation is a semidefinite feasibility problem. It is shown that using the relaxation, the notorious pigeon hole and mutilated chessboard problems are solved in polynomial time. As a byproduct we find a new `sandwich' theorem that is similar to Lov'asz' famous #function. Furthermore, using the semidefinite relaxation 2SAT problems are solved. By adding an objective function to the dual formulation, a specific class of polynomially solvable 3SAT instances can be identified. We conclude with discussing how the relaxation can be used to solve more general SAT problems and some empirical observations. 1 Introduction The satisfiability problem of propositional logic (SAT) is the original NP complete problem [5]. Many algorithms for SAT have ...