this paper to collect well--known results on 3--D mesh refinement

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 segment-division rather than an a priori fixed segment-division 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 high-performance 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 segment-division yields a speedup of over 1003 time and does not lose any accuracy, when compared with the algorithm based on the a priori fixed segment-division

Dedicated to the memory of Gian-Carlo 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 C-fractions, 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 η-function 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

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.

This paper presents effective algorithms for multi-way partitioning. Confirming ideas originally due to Hall [27], we demonstrate that geometric embeddings of the circuit netlist can lead to high-quality k-way 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 k-way partitioning to be contiguous in a given linear ordering. We begin with a d-dimensional spectral embedding and construct a heuristic 1-dimensional ordering of the modules (combining spacefillin...

Zusammenfassung Data Structures and Concepts for Adaptive Finite Element Methods. The administration of strongly nonuniform, adaptively generated finite element meshes requires specialized techniques and data structures. A special data structure of this kind is described in this paper. It relies on points, edges and triangles as basic structures and is especially well suited for the realization of iterative solvers like the hierarchical basis or the multilevel nodal basis method. AMS Subject Classifications: 65N50, 65Y99, 65N30, 65N55, 65F10 Key words: Data structures, adaptive finite element methods. Datenstrukturen und Strategien fur adaptive Finite Elemente. Fur die Verwaltung von extrem nichtuniformen, adaptiv erzeugten Finite Element Gittern benotigt man spezielle Techniken und Datenstrukturen. Eine Datenstruktur dieser Art wird in diesem Artikel beschrieben. Basisstrukturen sind Punkte, Kanten und Dreiecke. Die Datenstruktur ist besonders zugeschnitten auf iterative Loser wie die hierarchische Basis oder die "multilevel nodal basis" Methode. 1.

This paper demonstrates that "social network collaborative filtering " (SNCF), wherein user-selected like-minded alters are used to make predictions, can rival traditional user-to-user 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 by-user average rating; generic friends often are not like-minded. However, SNCF using "ally " alters is competitive with CF. These results are significant because SNCF is tremendously more computationally efficient than traditional user-user CF and may be implemented in large-scale 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 like-minded 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:

In recent torsional oscillator experiments by Kim and Chan (KC), a decrease of rotational inertia has been observed in solid 4 He in porous materials 1,2 and in a bulk annular channel 3. This observation strongly suggests the existence of “ non-classical rotational inertia ” (NCRI), i.e. superflow, in solid 4 He. In order to study such a possible “ supersolid ” phase, we perform torsional oscillator experiments for cylindrical solid 4 He samples. We have observed decreases of rotational inertia below 200 mK for two solid samples (pressures P = 4.1 and 3.0 MPa). The observed NCRI fraction at 70 mK is 0.14 %, which is about 1/3 of the fraction observed in the annulus by KC. Our observation is the first experimental confirmation of the possible supersolid finding by KC. PACS numbers: 67.80.-s 1.

Optical model potentials for elastic nucleon nucleus scattering are calculated for a number of target nuclides from a full-folding integral of two different realistic target density matrices together with full off-shell nucleonnucleon t-matrices derived from two different Bonn meson exchange models. Elastic proton and neutron scattering observables calculated from these full-folding optical potentials are compared to those obtained from ‘optimum factorized ’ approximations in the energy regime between 65 and 400 MeV projectile energy. The optimum factorized form is found to provide a good approximation to elastic scattering observables obtained from the full-folding optical potentials, although the potentials differ somewhat in the structure of their nonlocality.