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257
Extending the Regular Restriction of Resolution to NonLinear Subdeductions
 In Proceedings of the Fourteenth National Conference on Artificial Intelligence
, 1997
"... A binary resolution proof, represented as a binary tree, is irregular if some atom is resolved away and reappears on the same branch. We develop an algorithm, linear in the size of the tree, which detects whether reordering the resolutions in a given proof will generate an irregular proof. If so, th ..."
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Cited by 4 (2 self)
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clause containing that literal. That is, both steps should not be in the same branch (or linear subdeduction) of the proof tree. We extend this restriction so that it applies steps to that are not on one branch, but can be made linear by rotating edges of the tree, as long as those rotations do
Extending the Regular Restriction of Resolution to NonLinear Subdeductions
 In Proceedings of the Fourteenth National Conference on Artificial Intelligence
, 1997
"... A binary resolution proof, represented as a binary tree, is irregular if some atom is resolved away and reappears on the same branch. We develop an algorithm, linear in the size of the tree, which detects whether reordering the resolutions in a given proof will generate an irregular proof. If s ..."
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to deduce a clause containing that literal. That is, both steps should not be in the same branch (or linear subdeduction) of the proof tree. We extend this restriction so that it applies steps to that are not on one branch, but can be made linear by rotating edges of the tree, as long as those rotations do
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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to noise a SENSE reconstructed image may be impaired by errors of systematic nature. Errors in sample values may be due, e.g., to tissue motion, main field inhomogeneity, eddy currents, or gradient nonlinearity. The related artifacts are well known in standard imaging. A potential problem specific
Efficient Algorithms to Detect and Restore Minimality, an Extension of the Regular Restriction of Resolution
"... . A given binary resolution proof, represented as a binary tree, is said to be minimal if the resolutions cannot be reordered to generate an irregular proof. Minimality extends Tseitin's regularity restriction and still retains completeness. A linear time algorithm is introduced to decide wheth ..."
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. A given binary resolution proof, represented as a binary tree, is said to be minimal if the resolutions cannot be reordered to generate an irregular proof. Minimality extends Tseitin's regularity restriction and still retains completeness. A linear time algorithm is introduced to decide
Exponential Separations between Restricted Resolution and Cutting Planes Proof Systems
, 1998
"... We prove an exponential lower bound for treelike Cutting Planes refutations of a set of clauses which has polynomial size resolution refutations. This implies an exponential separation between treelike and daglike proofs for both CuttingPlanes and resolution; in both cases only superpolynomial se ..."
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Cited by 24 (5 self)
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like) regular resolution proofs. In fact, the refutation provided to give the upper bound respects the stronger restriction of being a DavisPutnam resolution proof. This extends the corresponding superpolynomial separation of [30]. Finally, we prove an exponential separation between DavisPutnam resolution
Analysis of resolution and noise properties of nonquadratically regularized image reconstruction methods for PET
 IEEE Trans. Med. Imaging
, 2008
"... Abstract—We present accurate and efficient methods for estimating the spatial resolution and noise properties of nonquadratically regularized image reconstruction for positron emission tomography (PET). It is well known that quadratic regularization tends to oversmooth sharp edges. Many types of ed ..."
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Cited by 13 (4 self)
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of edgepreserving nonquadratic penalties have been proposed to overcome this problem. However, there has been little research on the quantitative analysis of nonquadratic regularization due to its nonlinearity. In contrast, quadratically regularized estimators are approximately linear and are well
Linearity and Regularity with Negation Normal Form ∗
"... Proving completeness of NCresolution under a linear restriction has been elusive; it is proved here for formulas in negation normal form. The proof uses a generalization of the AndersonBledsoe excess literal argument, which was developed for resolution. That result is extended to NCresolution wit ..."
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Cited by 1 (0 self)
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Proving completeness of NCresolution under a linear restriction has been elusive; it is proved here for formulas in negation normal form. The proof uses a generalization of the AndersonBledsoe excess literal argument, which was developed for resolution. That result is extended to NCresolution
LINEAR RESOLUTIONS OF QUADRATIC MONOMIAL IDEALS
"... Abstract. We study the minimal free resolution of a quadratic monomial ideal in the case where the resolution is linear. First, we focus on the squarefree case, namely that of an edge ideal. We provide an explicit minimal free resolution under the assumption that the graph associated with the edge i ..."
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Cited by 4 (0 self)
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ideal satisfies specific combinatorial conditions. In addition, we construct a regular cellular structure on the resolution. Finally, we extend our results to nonsquarefree ideals by means of polarization. 1.
Completeness for Linear Regular Negation Normal Form Inference Systems
, 1997
"... . Completeness proofs that generalize the AndersonBledsoe excess literal argument are developed for calculi other than resolution. A simple proof of the completeness of regular, connected tableaux for formulas in conjunctive normal form (CNF) is presented. These techniques also provide completeness ..."
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Cited by 7 (3 self)
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completeness results for some inference mechanisms that do not rely on clause form. In particular, the completeness of regular, connected tableaux for formulas in negation normal form (NNF), and the completeness of NCresolution under a linear restriction, are established. Keywords: Logic for Artificial
Instabilities in spatially extended
"... predatorprey systems: Spatiotemporal patterns in the neighborhood of TuringHopf bifurcations ..."
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predatorprey systems: Spatiotemporal patterns in the neighborhood of TuringHopf bifurcations
Results 1  10
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257