592 research outputs found
An introduction to Graph Data Management
A graph database is a database where the data structures for the schema
and/or instances are modeled as a (labeled)(directed) graph or generalizations
of it, and where querying is expressed by graph-oriented operations and type
constructors. In this article we present the basic notions of graph databases,
give an historical overview of its main development, and study the main current
systems that implement them
Two-dimensional models as testing ground for principles and concepts of local quantum physics
In the past two-dimensional models of QFT have served as theoretical
laboratories for testing new concepts under mathematically controllable
condition. In more recent times low-dimensional models (e.g. chiral models,
factorizing models) often have been treated by special recipes in a way which
sometimes led to a loss of unity of QFT. In the present work I try to
counteract this apartheid tendency by reviewing past results within the setting
of the general principles of QFT. To this I add two new ideas: (1) a modular
interpretation of the chiral model Diff(S)-covariance with a close connection
to the recently formulated local covariance principle for QFT in curved
spacetime and (2) a derivation of the chiral model temperature duality from a
suitable operator formulation of the angular Wick rotation (in analogy to the
Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational
chiral theories. The SL(2,Z) modular Verlinde relation is a special case of
this thermal duality and (within the family of rational models) the matrix S
appearing in the thermal duality relation becomes identified with the
statistics character matrix S. The relevant angular Euclideanization'' is done
in the setting of the Tomita-Takesaki modular formalism of operator algebras.
I find it appropriate to dedicate this work to the memory of J. A. Swieca
with whom I shared the interest in two-dimensional models as a testing ground
for QFT for more than one decade.
This is a significantly extended version of an ``Encyclopedia of Mathematical
Physics'' contribution hep-th/0502125.Comment: 55 pages, removal of some typos in section
Efficient and Effective Query Auto-Completion
Query Auto-Completion (QAC) is an ubiquitous feature of modern textual search
systems, suggesting possible ways of completing the query being typed by the
user. Efficiency is crucial to make the system have a real-time responsiveness
when operating in the million-scale search space. Prior work has extensively
advocated the use of a trie data structure for fast prefix-search operations in
compact space. However, searching by prefix has little discovery power in that
only completions that are prefixed by the query are returned. This may impact
negatively the effectiveness of the QAC system, with a consequent monetary loss
for real applications like Web Search Engines and eCommerce. In this work we
describe the implementation that empowers a new QAC system at eBay, and discuss
its efficiency/effectiveness in relation to other approaches at the
state-of-the-art. The solution is based on the combination of an inverted index
with succinct data structures, a much less explored direction in the
literature. This system is replacing the previous implementation based on
Apache SOLR that was not always able to meet the required
service-level-agreement.Comment: Published in SIGIR 202
On The Effect of Hyperedge Weights On Hypergraph Learning
Hypergraph is a powerful representation in several computer vision, machine
learning and pattern recognition problems. In the last decade, many researchers
have been keen to develop different hypergraph models. In contrast, no much
attention has been paid to the design of hyperedge weights. However, many
studies on pairwise graphs show that the choice of edge weight can
significantly influence the performances of such graph algorithms. We argue
that this also applies to hypegraphs. In this paper, we empirically discuss the
influence of hyperedge weight on hypegraph learning via proposing three novel
hyperedge weights from the perspectives of geometry, multivariate statistical
analysis and linear regression. Extensive experiments on ORL, COIL20, JAFFE,
Sheffield, Scene15 and Caltech256 databases verify our hypothesis. Similar to
graph learning, several representative hyperedge weighting schemes can be
concluded by our experimental studies. Moreover, the experiments also
demonstrate that the combinations of such weighting schemes and conventional
hypergraph models can get very promising classification and clustering
performances in comparison with some recent state-of-the-art algorithms
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