1,768 research outputs found
Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles
In this paper we study the asymptotic behaviour of the spectral function
corresponding to the lower part of the spectrum of the Kodaira Laplacian on
high tensor powers of a holomorphic line bundle. This implies a full asymptotic
expansion of this function on the set where the curvature of the line bundle is
non-degenerate. As application we obtain the Bergman kernel asymptotics for
adjoint semi-positive line bundles over complete Kaehler manifolds, on the set
where the curvature is positive. We also prove the asymptotics for big line
bundles endowed with singular Hermitian metrics with strictly positive
curvature current. In this case the full asymptotics holds outside the singular
locus of the metric.Comment: 71 pages; v.2 is a final update to agree with the published pape
On the stability of equivariant embedding of compact CR manifolds with circle action
We prove the stability of the equivariant embedding of compact strictly
pseudoconvex CR manifolds with transversal CR circle action under circle
invariant perturbations of the CR structures.Comment: 21 pages, final versio
Fast Search for Dynamic Multi-Relational Graphs
Acting on time-critical events by processing ever growing social media or
news streams is a major technical challenge. Many of these data sources can be
modeled as multi-relational graphs. Continuous queries or techniques to search
for rare events that typically arise in monitoring applications have been
studied extensively for relational databases. This work is dedicated to answer
the question that emerges naturally: how can we efficiently execute a
continuous query on a dynamic graph? This paper presents an exact subgraph
search algorithm that exploits the temporal characteristics of representative
queries for online news or social media monitoring. The algorithm is based on a
novel data structure called the Subgraph Join Tree (SJ-Tree) that leverages the
structural and semantic characteristics of the underlying multi-relational
graph. The paper concludes with extensive experimentation on several real-world
datasets that demonstrates the validity of this approach.Comment: SIGMOD Workshop on Dynamic Networks Management and Mining (DyNetMM),
201
A Selectivity based approach to Continuous Pattern Detection in Streaming Graphs
Cyber security is one of the most significant technical challenges in current
times. Detecting adversarial activities, prevention of theft of intellectual
properties and customer data is a high priority for corporations and government
agencies around the world. Cyber defenders need to analyze massive-scale,
high-resolution network flows to identify, categorize, and mitigate attacks
involving networks spanning institutional and national boundaries. Many of the
cyber attacks can be described as subgraph patterns, with prominent examples
being insider infiltrations (path queries), denial of service (parallel paths)
and malicious spreads (tree queries). This motivates us to explore subgraph
matching on streaming graphs in a continuous setting. The novelty of our work
lies in using the subgraph distributional statistics collected from the
streaming graph to determine the query processing strategy. We introduce a
"Lazy Search" algorithm where the search strategy is decided on a
vertex-to-vertex basis depending on the likelihood of a match in the vertex
neighborhood. We also propose a metric named "Relative Selectivity" that is
used to select between different query processing strategies. Our experiments
performed on real online news, network traffic stream and a synthetic social
network benchmark demonstrate 10-100x speedups over selectivity agnostic
approaches.Comment: in 18th International Conference on Extending Database Technology
(EDBT) (2015
Berezin-Toeplitz quantization for lower energy forms
Let be an arbitrary complex manifold and let be a Hermitian
holomorphic line bundle over . We introduce the Berezin-Toeplitz
quantization of the open set of where the curvature on is
non-degenerate. The quantum spaces are the spectral spaces corresponding to
( fixed), of the Kodaira Laplace operator acting on forms
with values in tensor powers . We establish the asymptotic expansion of
associated Toeplitz operators and their composition as and we
define the corresponding star-product. If the Kodaira Laplace operator has a
certain spectral gap this method yields quantization by means of harmonic
forms. As applications, we obtain the Berezin-Toeplitz quantization for
semi-positive and big line bundles.Comment: 44 pages; v.2 is a final update to agree with the published pape
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