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7,804
Critical Power for Asymptotic Connectivity in Wireless Networks
, 1998
"... : In wireless data networks each transmitter's power needs to be high enough to reach the intended receivers, while generating minimum interference on other receivers sharing the same channel. In particular, if the nodes in the network are assumed to cooperate in routing each others ' pack ..."
Abstract

Cited by 548 (19 self)
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as the number of nodes in the network goes to infinity. It is shown that if n nodes are placed in a disc of unit area in ! 2 and each node transmits at a power level so as to cover an area of ßr 2 = (log n + c(n))=n, then the resulting network is asymptotically connected with probability one if and only
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity also carrying over in a similar fashion. Finally we study the significance of these results in a variety of combinatorial optimization problems including the general 01 integer programs, the maximum clique and maximum stable set problems in perfect graphs, the maximum k partite subgraph problem in graphs, and va...
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 766 (29 self)
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Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propose a method to approach this problem by trying to estimate a function f which is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a preliminary theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabelled d...
Large Margin Classification Using the Perceptron Algorithm
 Machine Learning
, 1998
"... We introduce and analyze a new algorithm for linear classification which combines Rosenblatt 's perceptron algorithm with Helmbold and Warmuth's leaveoneout method. Like Vapnik 's maximalmargin classifier, our algorithm takes advantage of data that are linearly separable with large ..."
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Cited by 518 (2 self)
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We introduce and analyze a new algorithm for linear classification which combines Rosenblatt 's perceptron algorithm with Helmbold and Warmuth's leaveoneout method. Like Vapnik 's maximalmargin classifier, our algorithm takes advantage of data that are linearly separable with large margins. Compared to Vapnik's algorithm, however, ours is much simpler to implement, and much more efficient in terms of computation time. We also show that our algorithm can be efficiently used in very high dimensional spaces using kernel functions. We performed some experiments using our algorithm, and some variants of it, for classifying images of handwritten digits. The performance of our algorithm is close to, but not as good as, the performance of maximalmargin classifiers on the same problem, while saving significantly on computation time and programming effort. 1 Introduction One of the most influential developments in the theory of machine learning in the last few years is Vapnik's work on supp...
Capacity of multiantenna Gaussian channels
 EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS
, 1999
"... We investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading. We derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate such form ..."
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Cited by 2878 (6 self)
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We investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading. We derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate such formulas. We show that the potential gains of such multiantenna systems over singleantenna systems is rather large under independence assumptions for the fades and noises at different receiving antennas.
A Probabilistic Approach to Concurrent Mapping and Localization for Mobile Robots
 Machine Learning
, 1998
"... . This paper addresses the problem of building largescale geometric maps of indoor environments with mobile robots. It poses the map building problem as a constrained, probabilistic maximumlikelihood estimation problem. It then devises a practical algorithm for generating the most likely map from ..."
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Cited by 487 (47 self)
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. This paper addresses the problem of building largescale geometric maps of indoor environments with mobile robots. It poses the map building problem as a constrained, probabilistic maximumlikelihood estimation problem. It then devises a practical algorithm for generating the most likely map from data, alog with the most likely path taken by the robot. Experimental results in cyclic environments of size up to 80 by 25 meter illustrate the appropriateness of the approach. Keywords: Bayes rule, expectation maximization, mobile robots, navigation, localization, mapping, maximum likelihood estimation, positioning, probabilistic reasoning 1. Introduction Over the last two decades or so, the problem of acquiring maps in indoor environments has received considerable attention in the mobile robotics community. The problem of map building is the problem of determining the location of entitiesofinterest (such as: landmarks, obstacles), often relative to a global frame of reference (such as ...
Blobworld: Image segmentation using ExpectationMaximization and its application to image querying
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1999
"... Retrieving images from large and varied collections using image content as a key is a challenging and important problem. We present a new image representation which provides a transformation from the raw pixel data to a small set of image regions which are coherent in color and texture. This "B ..."
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Cited by 431 (10 self)
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Retrieving images from large and varied collections using image content as a key is a challenging and important problem. We present a new image representation which provides a transformation from the raw pixel data to a small set of image regions which are coherent in color and texture. This "Blobworld" representation is created by clustering pixels in a joint colortextureposition feature space. The segmentation algorithm is fully automatic and has been run on a collection of 10,000 natural images. We describe a system that uses the Blobworld representation to retrieve images from this collection. An important aspect of the system is that the user is allowed to view the internal representation of the submitted image and the query results. Similar systems do not offer the user this view into the workings of the system; consequently, query results from these systems can be inexplicable, despite the availability of knobs for adjusting the similarity metrics. By finding image regions whi...
The Geometry of Dissipative Evolution Equations: The Porous Medium Equation
"... We show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural. In order to convince the reader that it is mathematically natural, we show the time asymptotic behavior can be easily understood in this framework. We use the intuition and the ..."
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Cited by 413 (11 self)
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and the calculus of Riemannian geometry to quantify this asymptotic behavior. Contents 1 The porous medium equation as a gradient flow 2 1.1 The porous medium equation . . . . . . . . . . . . . . . . . . 2 1.2 Abstract gradient flow . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Two interpretations
Weighted Essentially NonOscillatory Schemes
, 1994
"... In this paper we introduce a new version of ENO (Essentially NonOscillatory) shockcapturing schemes which we call Weighted ENO. The main new idea is that, instead of choosing the "smoothest" stencil to pick one interpolating polynomial for the ENO reconstruction, we use a convex combinati ..."
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Cited by 336 (9 self)
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In this paper we introduce a new version of ENO (Essentially NonOscillatory) shockcapturing schemes which we call Weighted ENO. The main new idea is that, instead of choosing the "smoothest" stencil to pick one interpolating polynomial for the ENO reconstruction, we use a convex combination of all candidates to achieve the essentially nonoscillatory property, while additionally obtaining one order of improvement in accuracy. The resulting Weighted ENO schemes are based on cellaverages and a TVD RungeKutta time discretization. Preliminary encouraging numerical experiments are given.
Bandwidth Sharing: Objectives and Algorithms
 IEEE/ACM Transactions on Networking
, 1999
"... This paper concerns the design of distributed algorithms for sharing network bandwidth resources among contending flows. The classical fairness notion is the socalled maxmin fairness; F. Kelly [8] has recently introduced the alternative proportional fairness criterion; we introduce a third crit ..."
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Cited by 334 (11 self)
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This paper concerns the design of distributed algorithms for sharing network bandwidth resources among contending flows. The classical fairness notion is the socalled maxmin fairness; F. Kelly [8] has recently introduced the alternative proportional fairness criterion; we introduce a third criterion, which is naturally interpreted in terms of the delays experienced by ongoing transfers. We prove that fixed size window control can achieve fair bandwidth sharing according to any of these criteria, provided scheduling at each link is performed in an appropriate manner. We next consider a distributed random scheme where each traffic source varies its sending rate randomly, based on binary feedback information from the network. We show how to select the source behaviour so as to achieve an equilibrium distribution concentrated around the considered fair rate allocations. This stochastic analysis is then used to assess the asymptotic behaviour of deterministic rate adaption proc...
Results 1  10
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7,804