8,010 research outputs found
Determination of multifractal dimensions of complex networks by means of the sandbox algorithm
Complex networks have attracted much attention in diverse areas of science
and technology. Multifractal analysis (MFA) is a useful way to systematically
describe the spatial heterogeneity of both theoretical and experimental fractal
patterns. In this paper, we employ the sandbox (SB) algorithm proposed by
T\'{e}l et al. (Physica A, 159 (1989) 155-166), for MFA of complex networks.
First we compare the SB algorithm with two existing algorithms of MFA for
complex networks: the compact-box-burning (CBB) algorithm proposed by Furuya
and Yakubo (Phys. Rev. E, 84 (2011) 036118), and the improved box-counting (BC)
algorithm proposed by Li et al. (J. Stat. Mech.: Theor. Exp., 2014 (2014)
P02020) by calculating the mass exponents tau(q) of some deterministic model
networks. We make a detailed comparison between the numerical and theoretical
results of these model networks. The comparison results show that the SB
algorithm is the most effective and feasible algorithm to calculate the mass
exponents tau(q) and to explore the multifractal behavior of complex networks.
Then we apply the SB algorithm to study the multifractal property of some
classic model networks, such as scale-free networks, small-world networks, and
random networks. Our results show that multifractality exists in scale-free
networks, that of small-world networks is not obvious, and it almost does not
exist in random networks.Comment: 17 pages, 2 table, 10 figure
Multifractal analysis of weighted networks by a modified sandbox algorithm
Complex networks have attracted growing attention in many fields. As a
generalization of fractal analysis, multifractal analysis (MFA) is a useful way
to systematically describe the spatial heterogeneity of both theoretical and
experimental fractal patterns. Some algorithms for MFA of unweighted complex
networks have been proposed in the past a few years, including the sandbox (SB)
algorithm recently employed by our group. In this paper, a modified SB
algorithm (we call it SBw algorithm) is proposed for MFA of weighted
networks.First, we use the SBw algorithm to study the multifractal property of
two families of weighted fractal networks (WFNs): "Sierpinski" WFNs and "Cantor
dust" WFNs. We also discuss how the fractal dimension and generalized fractal
dimensions change with the edge-weights of the WFN. From the comparison between
the theoretical and numerical fractal dimensions of these networks, we can find
that the proposed SBw algorithm is efficient and feasible for MFA of weighted
networks. Then, we apply the SBw algorithm to study multifractal properties of
some real weighted networks ---collaboration networks. It is found that the
multifractality exists in these weighted networks, and is affected by their
edge-weights.Comment: 15 pages, 6 figures. Accepted for publication by Scientific Report
ProtoEM: A Prototype-Enhanced Matching Framework for Event Relation Extraction
Event Relation Extraction (ERE) aims to extract multiple kinds of relations
among events in texts. However, existing methods singly categorize event
relations as different classes, which are inadequately capturing the intrinsic
semantics of these relations. To comprehensively understand their intrinsic
semantics, in this paper, we obtain prototype representations for each type of
event relation and propose a Prototype-Enhanced Matching (ProtoEM) framework
for the joint extraction of multiple kinds of event relations. Specifically,
ProtoEM extracts event relations in a two-step manner, i.e., prototype
representing and prototype matching. In the first step, to capture the
connotations of different event relations, ProtoEM utilizes examples to
represent the prototypes corresponding to these relations. Subsequently, to
capture the interdependence among event relations, it constructs a dependency
graph for the prototypes corresponding to these relations and utilized a Graph
Neural Network (GNN)-based module for modeling. In the second step, it obtains
the representations of new event pairs and calculates their similarity with
those prototypes obtained in the first step to evaluate which types of event
relations they belong to. Experimental results on the MAVEN-ERE dataset
demonstrate that the proposed ProtoEM framework can effectively represent the
prototypes of event relations and further obtain a significant improvement over
baseline models.Comment: Work in progres
A well-balanced lattice Boltzmann model for binary fluids based on the incompressible phase-field theory
Spurious velocities arising from the imperfect offset of the undesired term
at the discrete level are frequently observed in numerical simulations of
equilibrium multiphase flow systems using the lattice Boltzmann equation (LBE)
method. To capture the physical equilibrium state of two-phase fluid systems
and eliminate spurious velocities, a well-balanced LBE model based on the
incompressible phase-field theory is developed. In this model, the equilibrium
distribution function for the Cahn-Hilliard (CH) equation is designed by
treating the convection term as a source to avoid the introduction of undesired
terms, enabling achievement of possible discrete force balance. Furthermore,
this approach allows for the attainment of a divergence-free velocity field,
effectively mitigating the impact of artificial compression effects and
enhancing numerical stability. Numerical tests, including a flat interface
problem, a stationary droplet, and the coalescence of two droplets, demonstrate
the well-balanced properties and improvements in the stability of the present
model
(1-Oxo-2,6,7-trioxa-1-phosphabicyclo[2.2.2]octan-4-yl)methyl 4-methylbenzenesulfonate
In the title compound, C12H15O7PS, the P atom has a distorted tetrahedral environment. The P—O—C—C torsion angles deviate significantly from zero [average = 12.0 (3)°], indicating that the bicyclic OP(OCH2)3C cage is strained. In the crystal, weak C—H⋯O interactions consolidate the packing
A computationally-efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes
Multifractal analysis (MFA) is a useful tool to systematically describe the
spatial heterogeneity of both theoretical and experimental fractal patterns.
One of the widely used methods for fractal analysis is box-covering. It is
known to be NP-hard. More severely, in comparison with fractal analysis
algorithms, MFA algorithms have much higher computational complexity. Among
various MFA algorithms for complex networks, the sandbox MFA algorithm behaves
with the best computational efficiency. However, the existing sandbox algorithm
is still computationally expensive. It becomes challenging to implement the MFA
for large-scale networks with tens of millions of nodes. It is also not clear
whether or not MFA results can be improved by a largely increased size of a
theoretical network. To tackle these challenges, a computationally-efficient
sandbox algorithm (CESA) is presented in this paper for MFA of large-scale
networks. Our CESA employs the breadth-first search (BFS) technique to directly
search the neighbor nodes of each layer of center nodes, and then to retrieve
the required information. Our CESA's input is a sparse data structure derived
from the compressed sparse row (CSR) format designed for compressed storage of
the adjacency matrix of large-scale network. A theoretical analysis reveals
that the CESA reduces the time complexity of the existing sandbox algorithm
from cubic to quadratic, and also improves the space complexity from quadratic
to linear. MFA experiments are performed for typical complex networks to verify
our CESA. Finally, our CESA is applied to a few typical real-world networks of
large scale.Comment: 19 pages, 9 figure
An In-Context Schema Understanding Method for Knowledge Base Question Answering
The Knowledge Base Question Answering (KBQA) task aims to answer natural
language questions based on a given knowledge base. As a kind of common method
for this task, semantic parsing-based ones first convert natural language
questions to logical forms (e.g., SPARQL queries) and then execute them on
knowledge bases to get answers. Recently, Large Language Models (LLMs) have
shown strong abilities in language understanding and may be adopted as semantic
parsers in such kinds of methods. However, in doing so, a great challenge for
LLMs is to understand the schema of knowledge bases. Therefore, in this paper,
we propose an In-Context Schema Understanding (ICSU) method for facilitating
LLMs to be used as a semantic parser in KBQA. Specifically, ICSU adopts the
In-context Learning mechanism to instruct LLMs to generate SPARQL queries with
examples. In order to retrieve appropriate examples from annotated
question-query pairs, which contain comprehensive schema information related to
questions, ICSU explores four different retrieval strategies. Experimental
results on the largest KBQA benchmark, KQA Pro, show that ICSU with all these
strategies outperforms that with a random retrieval strategy significantly
(from 12\% to 78.76\% in accuracy)
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