253,845 research outputs found
Web ontology representation and reasoning via fragments of set theory
In this paper we use results from Computable Set Theory as a means to
represent and reason about description logics and rule languages for the
semantic web.
Specifically, we introduce the description logic \mathcal{DL}\langle
4LQS^R\rangle(\D)--admitting features such as min/max cardinality constructs
on the left-hand/right-hand side of inclusion axioms, role chain axioms, and
datatypes--which turns out to be quite expressive if compared with
\mathcal{SROIQ}(\D), the description logic underpinning the Web Ontology
Language OWL. Then we show that the consistency problem for
\mathcal{DL}\langle 4LQS^R\rangle(\D)-knowledge bases is decidable by
reducing it, through a suitable translation process, to the satisfiability
problem of the stratified fragment of set theory, involving variables
of four sorts and a restricted form of quantification. We prove also that,
under suitable not very restrictive constraints, the consistency problem for
\mathcal{DL}\langle 4LQS^R\rangle(\D)-knowledge bases is
\textbf{NP}-complete. Finally, we provide a -translation of rules
belonging to the Semantic Web Rule Language (SWRL)
Elementary construction of Lusztig's canonical basis
In this largely expository article we present an elementary construction of
Lusztig's canonical basis in type ADE. The method, which is essentially
Lusztig's original approach, is to use the braid group to reduce to rank two
calculations. Some of the wonderful properties of the canonical basis are
already visible; that it descends to a basis for every highest weight
integrable representation, and that it is a crystal basis.Comment: 12 page
DUDE-Seq: Fast, Flexible, and Robust Denoising for Targeted Amplicon Sequencing
We consider the correction of errors from nucleotide sequences produced by
next-generation targeted amplicon sequencing. The next-generation sequencing
(NGS) platforms can provide a great deal of sequencing data thanks to their
high throughput, but the associated error rates often tend to be high.
Denoising in high-throughput sequencing has thus become a crucial process for
boosting the reliability of downstream analyses. Our methodology, named
DUDE-Seq, is derived from a general setting of reconstructing finite-valued
source data corrupted by a discrete memoryless channel and effectively corrects
substitution and homopolymer indel errors, the two major types of sequencing
errors in most high-throughput targeted amplicon sequencing platforms. Our
experimental studies with real and simulated datasets suggest that the proposed
DUDE-Seq not only outperforms existing alternatives in terms of
error-correction capability and time efficiency, but also boosts the
reliability of downstream analyses. Further, the flexibility of DUDE-Seq
enables its robust application to different sequencing platforms and analysis
pipelines by simple updates of the noise model. DUDE-Seq is available at
http://data.snu.ac.kr/pub/dude-seq
Combinatorial descriptions of the crystal structure on certain PBW bases (extended abstract)
Lusztig's theory of PBW bases gives a way to realize the infinity crystal for
any simple complex Lie algebra where the underlying set consists of Kostant
partitions. In fact, there are many different such realizations, one for each
reduced expression for the longest element of the Weyl group. There is an
algorithm to calculate the actions of the crystal operators, but it can be
quite complicated. For ADE types, we give conditions on the reduced expression
which ensure that the corresponding crystal operators are given by simple
combinatorial bracketing rules. We then give at least one reduced expression
satisfying our conditions in every type except , and discuss the resulting
combinatorics. Finally, we describe the relationship with more standard
tableaux combinatorics in types A and D.Comment: Extended abstract to appear in proceedings for FPSAC 201
Discovering Implicational Knowledge in Wikidata
Knowledge graphs have recently become the state-of-the-art tool for
representing the diverse and complex knowledge of the world. Examples include
the proprietary knowledge graphs of companies such as Google, Facebook, IBM, or
Microsoft, but also freely available ones such as YAGO, DBpedia, and Wikidata.
A distinguishing feature of Wikidata is that the knowledge is collaboratively
edited and curated. While this greatly enhances the scope of Wikidata, it also
makes it impossible for a single individual to grasp complex connections
between properties or understand the global impact of edits in the graph. We
apply Formal Concept Analysis to efficiently identify comprehensible
implications that are implicitly present in the data. Although the complex
structure of data modelling in Wikidata is not amenable to a direct approach,
we overcome this limitation by extracting contextual representations of parts
of Wikidata in a systematic fashion. We demonstrate the practical feasibility
of our approach through several experiments and show that the results may lead
to the discovery of interesting implicational knowledge. Besides providing a
method for obtaining large real-world data sets for FCA, we sketch potential
applications in offering semantic assistance for editing and curating Wikidata
Young tableaux, canonical bases and the Gindikin-Karpelevich formula
A combinatorial description of the crystal B(infinity) for finite-dimensional
simple Lie algebras in terms of certain Young tableaux was developed by J. Hong
and H. Lee. We establish an explicit bijection between these Young tableaux and
canonical bases indexed by Lusztig's parametrization, and obtain a
combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum
over the set of Young tableaux.Comment: 19 page
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