1,819 research outputs found
A time series model of CDS sequences in complete genome
A time series model of CDS sequences in complete genome is proposed.
A map of DNA sequence to integer sequence is given. The correlation
dimensions and Hurst exponents of CDS sequences in complete genome of bacteria
are calculated. Using the average of correlation dimensions, some interesting
results are obtained.Comment: 11 pages with 4 figures and one table, Chaos, Solitons and Fractals
(2000)(to appear
Fractal and multifractal properties of a family of fractal networks
In this work, we study the fractal and multifractal properties of a family of
fractal networks introduced by Gallos {\it et al.} ({\it Proc. Natl. Acad. Sci.
U.S.A.}, 2007, {\bf 104}: 7746). In this fractal network model, there is a
parameter which is between and , and allows for tuning the level of
fractality in the network. Here we examine the multifractal behavior of these
networks, dependence relationship of fractal dimension and the multifractal
parameters on the parameter . First, we find that the empirical fractal
dimensions of these networks obtained by our program coincide with the
theoretical formula given by Song {\it et al.} ( {\it Nat. Phys}, 2006, {\bf
2}: 275). Then from the shape of the and curves, we find the
existence of multifractality in these networks. Last, we find that there exists
a linear relationship between the average information dimension and
the parameter .Comment: 12 pages, 7 figures, accepted by J. Stat. Mec
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
The subordinated processes controlled by a family of subordinators and corresponding Fokker-Planck type equations
In this work, we consider subordinated processes controlled by a family of
subordinators which consist of a power function of time variable and a negative
power function of stable random variable. The effect of parameters in
the subordinators on the subordinated process is discussed. By suitable
variable substitutions and Laplace transform technique, the corresponding
fractional Fokker-Planck-type equations are derived. We also compute their mean
square displacements in a free force field. By choosing suitable ranges of
parameters, the resulting subordinated processes may be subdiffusive, normal
diffusive or superdiffusive.Comment: 11 pages, accepted by J. Stat. Mech.: Theor. Ex
One way to Characterize the compact structures of lattice protein model
On the study of protein folding, our understanding about the protein
structures is limited. In this paper we find one way to characterize the
compact structures of lattice protein model. A quantity called Partnum is given
to each compact structure. The Partnum is compared with the concept
Designability of protein structures emerged recently. It is shown that the
highly designable structures have, on average, an atypical number of local
degree of freedom. The statistical property of Partnum and its dependence on
sequence length is also studied.Comment: 10 pages, 5 figure
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