429 research outputs found
Topological string entanglement
We investigate how topological entanglement of Chern-Simons theory is
captured in a string theoretic realization. Our explorations are motivated by a
desire to understand how quantum entanglement of low energy open string degrees
of freedom is encoded in string theory (beyond the oft discussed classical
gravity limit). Concretely, we realize the Chern-Simons theory as the
worldvolume dynamics of topological D-branes in the topological A-model string
theory on a Calabi-Yau target. Via the open/closed topological string duality
one can map this theory onto a pure closed topological A-model string on a
different target space, one which is related to the original Calabi-Yau
geometry by a geometric/conifold transition. We demonstrate how to uplift the
replica construction of Chern-Simons theory directly onto the closed string and
show that it provides a meaningful definition of reduced density matrices in
topological string theory. Furthermore, we argue that the replica construction
commutes with the geometric transition, thereby providing an explicit closed
string dual for computing reduced states, and Renyi and von Neumann entropies
thereof. While most of our analysis is carried out for Chern-Simons on S^3, the
emergent picture is rather general. Specifically, we argue that quantum
entanglement on the open string side is mapped onto quantum entanglement on the
closed string side and briefly comment on the implications of our result for
physical holographic theories where entanglement has been argued to be crucial
ingredient for the emergence of classical geometry.Comment: 48 pages + appendices, many tikz fgures. v2: added clarification
Tag-Cloud Drawing: Algorithms for Cloud Visualization
Tag clouds provide an aggregate of tag-usage statistics. They are typically
sent as in-line HTML to browsers. However, display mechanisms suited for
ordinary text are not ideal for tags, because font sizes may vary widely on a
line. As well, the typical layout does not account for relationships that may
be known between tags. This paper presents models and algorithms to improve the
display of tag clouds that consist of in-line HTML, as well as algorithms that
use nested tables to achieve a more general 2-dimensional layout in which tag
relationships are considered. The first algorithms leverage prior work in
typesetting and rectangle packing, whereas the second group of algorithms
leverage prior work in Electronic Design Automation. Experiments show our
algorithms can be efficiently implemented and perform well.Comment: To appear in proceedings of Tagging and Metadata for Social
Information Organization (WWW 2007
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Deep Multilevel Graph Partitioning
Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that require parallel processing. While the amount of available cores in parallel architectures has significantly increased in recent years, state-of-the-art graph partitioning algorithms do not work well if the input needs to be partitioned into a large number of blocks. Often currently available algorithms compute highly imbalanced solutions, solutions of low quality, or have excessive running time for this case. This is due to the fact that most high-quality general-purpose graph partitioners are multilevel algorithms which perform graph coarsening to build a hierarchy of graphs, initial partitioning to compute an initial solution, and local improvement to improve the solution throughout the hierarchy. However, for large number of blocks, the smallest graph in the hierarchy that is used for initial partitioning still has to be large.
In this work, we substantially mitigate these problems by introducing deep multilevel graph partitioning and a shared-memory implementation thereof. Our scheme continues the multilevel approach deep into initial partitioning - integrating it into a framework where recursive bipartitioning and direct k-way partitioning are combined such that they can operate with high performance and quality. Our integrated approach is stronger, more flexible, arguably more elegant, and reduces bottlenecks for parallelization compared to existing multilevel approaches. For example, for large number of blocks our algorithm is on average at least an order of magnitude faster than competing algorithms while computing partitions with comparable solution quality. At the same time, our algorithm consistently produces balanced solutions. Moreover, for small number of blocks, our algorithms are the fastest among competing systems with comparable quality
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