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37,533
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira– Spencer theory, which may be viewed as the closed string analog of the Chern–Simon theory. Using the mirror map this leads to computation of the ‘number ’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2 theory. Relations with c = 1 strings are also pointed out.
Unified analysis of discontinuous Galerkin methods for elliptic problems
 SIAM J. Numer. Anal
, 2001
"... Abstract. We provide a framework for the analysis of a large class of discontinuous methods for secondorder elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment ..."
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Cited by 519 (31 self)
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Abstract. We provide a framework for the analysis of a large class of discontinuous methods for secondorder elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment of elliptic problems.
View Interpolation for Image Synthesis
"... Imagespace simplifications have been used to accelerate the calculation of computer graphic images since the dawn of visual simulation. Texture mapping has been used to provide a means by which images may themselves be used as display primitives. The work reported by this paper endeavors to carry t ..."
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Cited by 605 (0 self)
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Imagespace simplifications have been used to accelerate the calculation of computer graphic images since the dawn of visual simulation. Texture mapping has been used to provide a means by which images may themselves be used as display primitives. The work reported by this paper endeavors to carry this concept to its logical extreme by using interpolated images to portray threedimensional scenes. The specialeffects technique of morphing, which combines interpolation of texture maps and their shape, is applied to computing arbitrary intermediate frames from an array of prestored images. If the images are a structured set of views of a 3D object or scene, intermediate frames derived by morphing can be used to approximate intermediate 3D transformations of the object or scene. Using the view interpolation approach to synthesize 3D scenes has two main advantages. First, the 3D representation of the scene may be replaced with images. Second, the image synthesis time is independent of the scene complexity. The correspondence between images, required for the morphing method, can be predetermined automatically using the range data associated with the images. The method is further accelerated by a quadtree decomposition and a viewindependent visible priority. Our experiments have shown that the morphing can be performed at interactive rates on today’s highend personal computers. Potential applications of the method include virtual holograms, a walkthrough in a virtual environment, imagebased primitives and incremental rendering. The method also can be used to greatly accelerate the computation of motion blur and soft shadows cast by area light sources.
Compressive sampling
, 2006
"... Conventional wisdom and common practice in acquisition and reconstruction of images from frequency data follow the basic principle of the Nyquist density sampling theory. This principle states that to reconstruct an image, the number of Fourier samples we need to acquire must match the desired res ..."
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Cited by 1427 (15 self)
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Conventional wisdom and common practice in acquisition and reconstruction of images from frequency data follow the basic principle of the Nyquist density sampling theory. This principle states that to reconstruct an image, the number of Fourier samples we need to acquire must match the desired resolution of the image, i.e. the number of pixels in the image. This paper surveys an emerging theory which goes by the name of “compressive sampling” or “compressed sensing,” and which says that this conventional wisdom is inaccurate. Perhaps surprisingly, it is possible to reconstruct images or signals of scientific interest accurately and sometimes even exactly from a number of samples which is far smaller than the desired resolution of the image/signal, e.g. the number of pixels in the image. It is believed that compressive sampling has far reaching implications. For example, it suggests the possibility of new data acquisition protocols that translate analog information into digital form with fewer sensors than what was considered necessary. This new sampling theory may come to underlie procedures for sampling and compressing data simultaneously. In this short survey, we provide some of the key mathematical insights underlying this new theory, and explain some of the interactions between compressive sampling and other fields such as statistics, information theory, coding theory, and theoretical computer science.
Least angle regression
 Ann. Statist
"... The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to s ..."
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Cited by 1308 (43 self)
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The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to select a parsimonious set for the efficient prediction of a response variable. Least Angle Regression (LARS), a new model selection algorithm, is a useful and less greedy version of traditional forward selection methods. Three main properties are derived: (1) A simple modification of the LARS algorithm implements the Lasso, an attractive version of ordinary least squares that constrains the sum of the absolute regression coefficients; the LARS modification calculates all possible Lasso estimates for a given problem, using an order of magnitude less computer time than previous methods. (2) A different LARS modification efficiently implements Forward Stagewise linear regression, another promising
Exokernel: An Operating System Architecture for ApplicationLevel Resource Management
, 1995
"... We describe an operating system architecture that securely multiplexes machine resources while permitting an unprecedented degree of applicationspecific customization of traditional operating system abstractions. By abstracting physical hardware resources, traditional operating systems have signifi ..."
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Cited by 724 (24 self)
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We describe an operating system architecture that securely multiplexes machine resources while permitting an unprecedented degree of applicationspecific customization of traditional operating system abstractions. By abstracting physical hardware resources, traditional operating systems have significantly limited the performance, flexibility, and functionality of applications. The exokernel architecture removes these limitations by allowing untrusted software to implement traditional operating system abstractions entirely at applicationlevel. We have implemented a prototype exokernelbased system that includes Aegis, an exokernel, and ExOS, an untrusted applicationlevel operating system. Aegis defines the lowlevel interface to machine resources. Applications can allocate and use machine resources, efficiently handle events, and participate in resource revocation. Measurements show that most primitive Aegis operations are 10–100 times faster than Ultrix,a mature monolithic UNIX operating system. ExOS implements processes, virtual memory, and interprocess communication abstractions entirely within a library. Measurements show that ExOS’s applicationlevel virtual memory and IPC primitives are 5–50 times faster than Ultrix’s primitives. These results demonstrate that the exokernel operating system design is practical and offers an excellent combination of performance and flexibility. 1
String theory and noncommutative geometry
 JHEP
, 1999
"... We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from ..."
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Cited by 801 (8 self)
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We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary DiracBornInfeld theory with its noncommutative counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its Tduality, and Morita equivalence. We also discuss the D0/D4 system, the relation to Mtheory in DLCQ, and a possible noncommutative version of the sixdimensional (2, 0) theory. 8/99
Results 1  10
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37,533