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Adaptive Multilevel Methods in Three Space Dimensions
 Int. J. Numer. Methods Eng
, 1993
"... this paper to collect wellknown results on 3D mesh refinement ..."
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Cited by 56 (13 self)
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this paper to collect wellknown results on 3D mesh refinement
New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function
, 1996
"... Dedicated to the memory of GianCarlo Rota who encouraged me to write this paper in the present style Abstract. In this paper we derive many infinite families of explicit exact formulas involving either squares or triangular numbers, two of which generalize Jacobi’s 4 and 8 squares identities to 4n ..."
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Cited by 45 (1 self)
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Dedicated to the memory of GianCarlo Rota who encouraged me to write this paper in the present style Abstract. In this paper we derive many infinite families of explicit exact formulas involving either squares or triangular numbers, two of which generalize Jacobi’s 4 and 8 squares identities to 4n 2 or 4n(n + 1) squares, respectively, without using cusp forms. In fact, we similarly generalize to infinite families all of Jacobi’s explicitly stated degree 2, 4, 6, 8 Lambert series expansions of classical theta functions. In addition, we extend Jacobi’s special analysis of 2 squares, 2 triangles, 6 squares, 6 triangles to 12 squares, 12 triangles, 20 squares, 20 triangles, respectively. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results, depending on new expansions for powers of various products of classical theta functions, arise in the setting of Jacobi elliptic functions, associated continued fractions, regular Cfractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. The Schur function form of these infinite families of identities are analogous to the ηfunction identities of Macdonald. Moreover, the powers 4n(n + 1), 2n 2 + n, 2n 2 − n that appear in Macdonald’s work also arise at appropriate places in our analysis. A special case of our general methods yields a proof of the two Kac–Wakimoto conjectured identities involving representing
Optimal Wiresizing for Interconnects with Multiple Sources
 ACM Trans. on Design Automation of Electronics Systems
, 1996
"... this paper, we study the optimal wiresizing problem for nets with multiple sources under the RC tree model and the Elmore delay model. We decompose the routing tree for a multisource net into the source subtree (SST) and a set of loading subtrees (LSTs), and show that the optimal wiresizing solution ..."
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Cited by 42 (18 self)
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this paper, we study the optimal wiresizing problem for nets with multiple sources under the RC tree model and the Elmore delay model. We decompose the routing tree for a multisource net into the source subtree (SST) and a set of loading subtrees (LSTs), and show that the optimal wiresizing solution satisfies a number of interesting properties, including: the LST separability, the LST monotone property, the SST local monotone property, and the dominance property. Furthermore, we study the optimal wiresizing problem using a variable segmentdivision rather than an a priori fixed segmentdivision as in all previous works and reveal the bundled refinement property. These properties lead to efficient algorithms to compute the optimal solutions. We have tested our algorithm on nets extracted from the multilayer layout for a highperformance Intel microprocessor. Accurate SPICE simulation shows that our methods reduce the average delay by up to 23.5% and the maximum delay by up to 37.8%, respectively, for the submicron CMOS technology when compared to the minimal wire width solution. In addition, the algorithm based on the variable segmentdivision yields a speedup of over 1003 time and does not lose any accuracy, when compared with the algorithm based on the a priori fixed segmentdivision
MultiWay Partitioning Via Geometric Embeddings, Orderings, and Dynamic Programming
 Orderings, and Dynamic Programming’, in IEEE Trans. on CAD
, 1995
"... This paper presents effective algorithms for multiway partitioning. Confirming ideas originally due to Hall [27], we demonstrate that geometric embeddings of the circuit netlist can lead to highquality kway partitionings. The netlist embeddings are derived via the computation of d eigenvectors o ..."
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Cited by 20 (1 self)
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This paper presents effective algorithms for multiway partitioning. Confirming ideas originally due to Hall [27], we demonstrate that geometric embeddings of the circuit netlist can lead to highquality kway partitionings. The netlist embeddings are derived via the computation of d eigenvectors of the Laplacian for a graph representation of the netlist. As [27] did not specify how to partition such geometric embeddings, we explore various geometric partitioning objectives and algorithms, and find that they are limited because they do not integrate topological information from the netlist. Thus, we also present a new partitioning algorithm that exploits both the geometric embedding and netlist information, as well as a Restricted Partitioning formulation that requires each cluster of the kway partitioning to be contiguous in a given linear ordering. We begin with a ddimensional spectral embedding and construct a heuristic 1dimensional ordering of the modules (combining spacefillin...
Efficient Algorithms for Line and Curve Segment Intersection Using Restricted Predicates
, 1999
"... We consider whether restricted sets of geometric predicates support efficient algorithms to solve line and curve segment intersection problems in the plane. Our restrictions are based on the notion of algebraic degree, proposed by Preparata and others as a way to guide the search for efficient al ..."
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Cited by 17 (3 self)
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We consider whether restricted sets of geometric predicates support efficient algorithms to solve line and curve segment intersection problems in the plane. Our restrictions are based on the notion of algebraic degree, proposed by Preparata and others as a way to guide the search for efficient algorithms that can be implemented in more realistic computational models than the Real RAM.
Social network collaborative filtering
"... This paper demonstrates that "social network collaborative filtering " (SNCF), wherein userselected likeminded alters are used to make predictions, can rival traditional usertouser collaborative filtering (CF) in predictive accuracy. Using a unique data set from an online community whe ..."
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This paper demonstrates that "social network collaborative filtering " (SNCF), wherein userselected likeminded alters are used to make predictions, can rival traditional usertouser collaborative filtering (CF) in predictive accuracy. Using a unique data set from an online community where users rated items and also created social networking links specifically intended to represent likeminded “allies, ” we use SNCF and traditional CF to predict ratings by networked users. We find that SNCF using generic "friend " alters is moderately worse than the better CF techniques, but outperforms benchmarks such as byitem or byuser average rating; generic friends often are not likeminded. However, SNCF using "ally " alters is competitive with CF. These results are significant because SNCF is tremendously more computationally efficient than traditional useruser CF and may be implemented in largescale web commerce and social networking communities. It is notoriously difficult to distinguish the contributions of social influence (where allies influence users) and "social” selection (where users are simply effective at selecting likeminded people as their allies). Nonetheless, comparing similarity over time, we do show no evidence of strong social influence among allies or friends. Categories and Subject Descriptors:
noaa NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION National Ocean Service Office of Response and Restoration
, 2001
"... NOAA is responsible for protecting and restoring marine and coastal environments impacted by spills and hazardous substance releases. The Office of Response and Restoration (OR&R) is the focal point for NOAA’s spill preparedness, emergency response, and restoration programs. OR&R’s Hazardous ..."
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Cited by 1 (0 self)
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NOAA is responsible for protecting and restoring marine and coastal environments impacted by spills and hazardous substance releases. The Office of Response and Restoration (OR&R) is the focal point for NOAA’s spill preparedness, emergency response, and restoration programs. OR&R’s Hazardous Materials Response Division and its contingent of onscene Scientific Support Coordinators have earned a wide reputation for delivering scientifically valid solutions to the Federal OnScene Coordinator (the U.S. Coast Guard in the coastal zone, or EPA in inland areas). OR&R’s Coastal Protection and Restoration Division and Damage Assessment Center are critic al components of NOAA's natural resource trusteeship responsibilities. The CPR Division works closely with the U.S. Environmental Protection Agency to redress the environmental effects of hazardous waste sites across the United States. Coastal Resource Coordinators provide sitespecific technical expertise in ecological risk assessment and coastal remediation issues. This expertise ranges from physical science to ecology, marine biology, and oceanography. In their NOAA trusteeship role, CRCs assess the longerterm risks to coastal resources (including threatened and endangered species) from Superfundsite contamination, support decisionmaking for site remedies and habitat restoration, and negotiate protective remedies with the responsible parties to ensure that cleanup, restoration, and recovery are appropriate and fully monitored. While the HAZMAT and CPR divisions work to prevent and minimize injury to natural resources during spill response and waste site remediation activities, the Damage Assessment Center focuses on addressing the injury that remains after the cleanup or response. DAC’s Rapid Assessment Program goes onscene at oil or hazardous materials releases to assess damages to NOAA trust resources, including National Marine Sanctuaries
SUMMARY
"... We consider the approximate solution of selfadjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly nonuniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method ..."
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We consider the approximate solution of selfadjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly nonuniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner. Here, the accuracy of the iterative solution is coupled with the discretization error. As the performance of hierarchical bases preconditioners deteriorates in three space dimensions, the BPX preconditioner is used, taking special care of an efficient implementation. Reliable o posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements. To illustrate the theoretical results, we consider a familiar model problem involving reentrant corners and a reallife problem arising from hyperthermia, a recent clinical method for cancer therapy. 1.