4,562 research outputs found
Properties of Bipolar Fuzzy Hypergraphs
In this article, we apply the concept of bipolar fuzzy sets to hypergraphs
and investigate some properties of bipolar fuzzy hypergraphs. We introduce the
notion of tempered bipolar fuzzy hypergraphs and present some of their
properties. We also present application examples of bipolar fuzzy hypergraphs
Term-Specific Eigenvector-Centrality in Multi-Relation Networks
Fuzzy matching and ranking are two information retrieval techniques widely used in web search. Their application to structured data, however, remains an open problem. This article investigates how eigenvector-centrality can be used for approximate matching in multi-relation graphs, that is, graphs where connections of many different types may exist. Based on an extension of the PageRank matrix, eigenvectors representing the distribution of a term after propagating term weights between related data items are computed. The result is an index which takes the document structure into account and can be used with standard document retrieval techniques. As the scheme takes the shape of an index transformation, all necessary calculations are performed during index tim
Towards Quantum Dielectric Branes: Curvature Corrections in Abelian Beta Function and Nonabelian Born-Infeld Action
We initiate a programme to compute curvature corrections to the nonabelian BI
action. This is based on the calculation of derivative corrections to the
abelian BI action, describing a maximal brane, to all orders in F. An exact
calculation in F allows us to apply the SW map, reducing the maximal abelian
point of view to a minimal nonabelian point of view (replacing 1/F with [X,X]
at large F), resulting in matrix model equations of motion. We first study
derivative corrections to the abelian BI action and compute the 2-loop beta
function for an open string in a WZW (parallelizable) background. This beta
function is the first step in the process of computing string equations of
motion, which can be later obtained by computing the Weyl anomaly coefficients
or the partition function. The beta function is exact in F and computed to
orders O(H,H^2,H^3) (H=dB and curvature is R ~ H^2) and O(DF,D^2F,D^3F). In
order to carry out this calculation we develop a new regularization method for
2-loop graphs. We then relate perturbative results for abelian and nonabelian
BI actions, by showing how abelian derivative corrections yield nonabelian
commutator corrections, at large F. We begin the construction of a matrix model
describing \a' corrections to Myers' dielectric effect. This construction is
carried out by setting up a perturbative classification of the relevant
nonabelian tensor structures, which can be considerably narrowed down by the
constraint of translation invariance in the action and the possibility for
generic field redefinitions. The final matrix action is not uniquely determined
and depends upon two free parameters. These parameters could be computed via
further calculations in the abelian theory.Comment: JHEP3.cls, 64 pages, 3 figures; v2: added references; v3: more
references, final version for NP
Gauge Theories on Deformed Spaces
The aim of this review is to present an overview over available models and
approaches to non-commutative gauge theory. Our main focus thereby is on gauge
models formulated on flat Groenewold-Moyal spaces and renormalizability, but we
will also review other deformations and try to point out common features. This
review will by no means be complete and cover all approaches, it rather
reflects a highly biased selection.Comment: v2 references added; v3 published versio
A similarity-based community detection method with multiple prototype representation
Communities are of great importance for understanding graph structures in
social networks. Some existing community detection algorithms use a single
prototype to represent each group. In real applications, this may not
adequately model the different types of communities and hence limits the
clustering performance on social networks. To address this problem, a
Similarity-based Multi-Prototype (SMP) community detection approach is proposed
in this paper. In SMP, vertices in each community carry various weights to
describe their degree of representativeness. This mechanism enables each
community to be represented by more than one node. The centrality of nodes is
used to calculate prototype weights, while similarity is utilized to guide us
to partitioning the graph. Experimental results on computer generated and
real-world networks clearly show that SMP performs well for detecting
communities. Moreover, the method could provide richer information for the
inner structure of the detected communities with the help of prototype weights
compared with the existing community detection models
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