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Static Scheduling of Synchronous Data Flow Programs for Digital Signal Processing
 IEEE TRANSACTIONS ON COMPUTERS
, 1987
"... Large grain data flow (LGDF) programming is natural and convenient for describing digital signal processing (DSP) systems, but its runtime overhead is costly in real time or costsensitive applications. In some situations, designers are not willing to squander computing resources for the sake of pro ..."
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Cited by 592 (37 self)
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Large grain data flow (LGDF) programming is natural and convenient for describing digital signal processing (DSP) systems, but its runtime overhead is costly in real time or costsensitive applications. In some situations, designers are not willing to squander computing resources for the sake of programmer convenience. This is particularly true when the target machine is a programmable DSP chip. However, the runtime overhead inherent in most LGDF implementations is not required for most signal processing systems because such systems are mostly synchronous (in the DSP sense). Synchronous data flow (SDF) differs from traditional data flow in that the amount of data produced and consumed by a data flow node is specified a priori for each input and output. This is equivalent to specifying the relative sample rates in signal processing system. This means that the scheduling of SDF nodes need not be done at runtime, but can be done at compile time (statically), so the runtime overhead evaporates. The sample rates can all be different, which is not true of most current datadriven digital signal processing programming methodologies. Synchronous data flow is closely related to computation graphs, a special case of Petri nets. This selfcontained paper develops the theory necessary to statically schedule SDF programs on single or multiple processors. A class of static (compile time) scheduling algorithms is proven valid, and specific algorithms are given for scheduling SDF systems onto single or multiple processors.
The selfduality equations on a Riemann surface
 Proc. Lond. Math. Soc., III. Ser
, 1987
"... In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled 'instanton ..."
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Cited by 524 (6 self)
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In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled 'instantons'. The same equations may be
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 800 (26 self)
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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 fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can 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.
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
HOMOGENIZATION AND TWOSCALE CONVERGENCE
, 1992
"... Following an idea of G. Nguetseng, the author defines a notion of "twoscale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A corrector ..."
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Cited by 445 (14 self)
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Following an idea of G. Nguetseng, the author defines a notion of "twoscale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A correctortype theorem (i.e., which permits, in some cases, replacing a sequence by its "twoscale " limit, up to a strongly convergent remainder in L2(12)) is also established. These results are especially useful for the homogenization of partial differential equations with periodically oscillating coefficients. In particular, a new method for proving the convergence of homogenization processes is proposed, which is an alternative to the socalled energy method of Tartar. The power and simplicity of the twoscale convergence method is demonstrated on several examples, including the homogenization of both linear and nonlinear secondorder elliptic equations.
Random walks for image segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2006
"... Abstract—A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with userdefined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach on ..."
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Cited by 385 (21 self)
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Abstract—A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with userdefined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a highquality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs. Index Terms—Image segmentation, interactive segmentation, graph theory, random walks, combinatorial Dirichlet problem, harmonic functions, Laplace equation, graph cuts, boundary completion. Ç 1
What memory is for
 Behavioral and Brain Sciences
, 1997
"... What working memory is for Citation for published version: Logie, RH 1997, 'What working memory is for ' Behavioral and Brain Sciences, vol 20, no. 1, pp. 28. Link: Link to publication record in Edinburgh Research Explorer ..."
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Cited by 379 (5 self)
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What working memory is for Citation for published version: Logie, RH 1997, 'What working memory is for ' Behavioral and Brain Sciences, vol 20, no. 1, pp. 28. Link: Link to publication record in Edinburgh Research Explorer
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