1,637 research outputs found
Unextendible Product Basis for Fermionic Systems
We discuss the concept of unextendible product basis (UPB) and generalized
UPB for fermionic systems, using Slater determinants as an analogue of product
states, in the antisymmetric subspace \wedge^ N \bC^M. We construct an
explicit example of generalized fermionic unextendible product basis (FUPB) of
minimum cardinality for any . We also show that any
bipartite antisymmetric space \wedge^ 2 \bC^M of codimension two is spanned
by Slater determinants, and the spaces of higher codimension may not be spanned
by Slater determinants. Furthermore, we construct an example of complex FUPB of
with minimum cardinality . In contrast, we show that a real FUPB
does not exist for . Finally we provide a systematic construction for
FUPBs of higher dimensions using FUPBs and UPBs of lower dimensions.Comment: 17 pages, no figure. Comments are welcom
A High-Performance Triple Patterning Layout Decomposer with Balanced Density
Triple patterning lithography (TPL) has received more and more attentions
from industry as one of the leading candidate for 14nm/11nm nodes. In this
paper, we propose a high performance layout decomposer for TPL. Density
balancing is seamlessly integrated into all key steps in our TPL layout
decomposition, including density-balanced semi-definite programming (SDP),
density-based mapping, and density-balanced graph simplification. Our new TPL
decomposer can obtain high performance even compared to previous
state-of-the-art layout decomposers which are not balanced-density aware, e.g.,
by Yu et al. (ICCAD'11), Fang et al. (DAC'12), and Kuang et al. (DAC'13).
Furthermore, the balanced-density version of our decomposer can provide more
balanced density which leads to less edge placement error (EPE), while the
conflict and stitch numbers are still very comparable to our
non-balanced-density baseline
TopoSZ: Preserving Topology in Error-Bounded Lossy Compression
Existing error-bounded lossy compression techniques control the pointwise
error during compression to guarantee the integrity of the decompressed data.
However, they typically do not explicitly preserve the topological features in
data. When performing post hoc analysis with decompressed data using
topological methods, preserving topology in the compression process to obtain
topologically consistent and correct scientific insights is desirable. In this
paper, we introduce TopoSZ, an error-bounded lossy compression method that
preserves the topological features in 2D and 3D scalar fields. Specifically, we
aim to preserve the types and locations of local extrema as well as the level
set relations among critical points captured by contour trees in the
decompressed data. The main idea is to derive topological constraints from
contour-tree-induced segmentation from the data domain, and incorporate such
constraints with a customized error-controlled quantization strategy from the
classic SZ compressor.Our method allows users to control the pointwise error
and the loss of topological features during the compression process with a
global error bound and a persistence threshold
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