14,716 research outputs found
Two Approaches to Sidorenko's Conjecture
Sidorenko's conjecture states that for every bipartite graph on
, holds, where is the
Lebesgue measure on and is a bounded, non-negative, symmetric,
measurable function on . An equivalent discrete form of the conjecture
is that the number of homomorphisms from a bipartite graph to a graph
is asymptotically at least the expected number of homomorphisms from to the
Erd\H{o}s-R\'{e}nyi random graph with the same expected edge density as . In
this paper, we present two approaches to the conjecture. First, we introduce
the notion of tree-arrangeability, where a bipartite graph with bipartition
is tree-arrangeable if neighborhoods of vertices in have a
certain tree-like structure. We show that Sidorenko's conjecture holds for all
tree-arrangeable bipartite graphs. In particular, this implies that Sidorenko's
conjecture holds if there are two vertices in such that each
vertex satisfies or ,
and also implies a recent result of Conlon, Fox, and Sudakov \cite{CoFoSu}.
Second, if is a tree and is a bipartite graph satisfying Sidorenko's
conjecture, then it is shown that the Cartesian product of and
also satisfies Sidorenko's conjecture. This result implies that, for all , the -dimensional grid with arbitrary side lengths satisfies
Sidorenko's conjecture.Comment: 20 pages, 2 figure
Sidorenko's conjecture for higher tree decompositions
This is a companion note to our paper 'Some advances on Sidorenko's
conjecture', elaborating on a remark in that paper that the approach which
proves Sidorenko's conjecture for strongly tree-decomposable graphs may be
extended to a broader class, comparable to that given in work of Szegedy,
through further iteration.Comment: 7 pages, unpublished not
Probing TeV scale Top-Philic Resonances with Boosted Top-Tagging at the High Luminosity LHC
We investigate the discovery potential of singly produced top-philic
resonances at the high luminosity (HL) LHC in the four-top final state. Our
analysis spans over the fully-hadronic, semi-leptonic, and same-sign dilepton
channels where we present concrete search strategies adequate to a boosted
kinematic regime and high jet-multiplicity environments. We utilize the
Template Overlap Method (TOM) with newly developed template observables for
tagging boosted top quarks, a large-radius jet variable and customized
b-tagging tactics for background discrimination. Our results show that the
same-sign dilepton channel gives the best sensitivity among the considered
channels, with an improvement of significance up to 10%-20% when combined with
boosted-top tagging. Both the fully-hadronic and semi-leptonic channels yield
comparable discovery potential and contribute to further enhancements in the
sensitivity by combining all channels. Finally, we show the sensitivity of a
top-philic resonance at the LHC and HL-LHC by showing the exclusion
limit and discovery reach, including a combination of all three
channels.Comment: 19 pages, 14 figure
Boosted Event Topologies from TeV Scale Light Quark Composite Partners
We propose a new search strategy for quark partners which decay into a
boosted Higgs and a light quark. As an example, we consider phenomenologically
viable right handed up-type quark partners of mass TeV in composite
pseudo-Nambu-Goldstone-boson Higgs models within the context of flavorful
naturalness. Our results show that and signal significance of is achievable at TeV LHC with 35 of
integrated luminosity, sufficient to claim discovery of a new particle. A
combination of a multi-dimensional boosted Higgs tagging technique, kinematics
of pair produced heavy objects and -tagging serves to efficiently diminish
the large QCD backgrounds while maintaining adequate levels of signal
efficiency. We present the analysis in the context of effective field theory,
such that our results can be applied to any future search for pair produced
vector-like quarks with decay modes to Higgs and a light jet.Comment: 18 pages, 7 figures, 5 tables, v2: short discussion added in Sec. 2,
references added, corresponds to version published in JHE
Processing SPARQL queries with regular expressions in RDF databases
Background: As the Resource Description Framework (RDF) data model is widely used for modeling and sharing a lot of online bioinformatics resources such as Uniprot (dev.isb-sib.ch/projects/uniprot-rdf) or Bio2RDF (bio2rdf.org), SPARQL - a W3C recommendation query for RDF databases - has become an important query language for querying the bioinformatics knowledge bases. Moreover, due to the diversity of users' requests for extracting information from the RDF data as well as the lack of users' knowledge about the exact value of each fact in the RDF databases, it is desirable to use the SPARQL query with regular expression patterns for querying the RDF data. To the best of our knowledge, there is currently no work that efficiently supports regular expression processing in SPARQL over RDF databases. Most of the existing techniques for processing regular expressions are designed for querying a text corpus, or only for supporting the matching over the paths in an RDF graph.
Results: In this paper, we propose a novel framework for supporting regular expression processing in SPARQL query. Our contributions can be summarized as follows. 1) We propose an efficient framework for processing SPARQL queries with regular expression patterns in RDF databases. 2) We propose a cost model in order to adapt the proposed framework in the existing query optimizers. 3) We build a prototype for the proposed framework in C++ and conduct extensive experiments demonstrating the efficiency and effectiveness of our technique.
Conclusions: Experiments with a full-blown RDF engine show that our framework outperforms the existing ones by up to two orders of magnitude in processing SPARQL queries with regular expression patterns.X113sciescopu
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