677 research outputs found
Role of fractal dimension in random walks on scale-free networks
Fractal dimension is central to understanding dynamical processes occurring
on networks; however, the relation between fractal dimension and random walks
on fractal scale-free networks has been rarely addressed, despite the fact that
such networks are ubiquitous in real-life world. In this paper, we study the
trapping problem on two families of networks. The first is deterministic, often
called -flowers; the other is random, which is a combination of
-flower and -flower and thus called hybrid networks. The two
network families display rich behavior as observed in various real systems, as
well as some unique topological properties not shared by other networks. We
derive analytically the average trapping time for random walks on both the
-flowers and the hybrid networks with an immobile trap positioned at an
initial node, i.e., a hub node with the highest degree in the networks. Based
on these analytical formulae, we show how the average trapping time scales with
the network size. Comparing the obtained results, we further uncover that
fractal dimension plays a decisive role in the behavior of average trapping
time on fractal scale-free networks, i.e., the average trapping time decreases
with an increasing fractal dimension.Comment: Definitive version published in European Physical Journal
Scaling of mean first-passage time as efficiency measure of nodes sending information on scale-free Koch networks
A lot of previous work showed that the sectional mean first-passage time
(SMFPT), i.e., the average of mean first-passage time (MFPT) for random walks
to a given hub node (node with maximum degree) averaged over all starting
points in scale-free small-world networks exhibits a sublinear or linear
dependence on network order (number of nodes), which indicates that hub
nodes are very efficient in receiving information if one looks upon the random
walker as an information messenger. Thus far, the efficiency of a hub node
sending information on scale-free small-world networks has not been addressed
yet. In this paper, we study random walks on the class of Koch networks with
scale-free behavior and small-world effect. We derive some basic properties for
random walks on the Koch network family, based on which we calculate
analytically the partial mean first-passage time (PMFPT) defined as the average
of MFPTs from a hub node to all other nodes, excluding the hub itself. The
obtained closed-form expression displays that in large networks the PMFPT grows
with network order as , which is larger than the linear scaling of
SMFPT to the hub from other nodes. On the other hand, we also address the case
with the information sender distributed uniformly among the Koch networks, and
derive analytically the entire mean first-passage time (EMFPT), namely, the
average of MFPTs between all couples of nodes, the leading scaling of which is
identical to that of PMFPT. From the obtained results, we present that although
hub nodes are more efficient for receiving information than other nodes, they
display a qualitatively similar speed for sending information as non-hub nodes.
Moreover, we show that the location of information sender has little effect on
the transmission efficiency. The present findings are helpful for better
understanding random walks performed on scale-free small-world networks.Comment: Definitive version published in European Physical Journal
Distinguishable RGE running effects between Dirac neutrinos and Majorana neutrinos with vanishing Majorana CP-violating phases
In a novel parametrization of neutrino mixing and in the approximation of
-lepton dominance, we show that the one-loop renormalization-group
equations (RGEs) of Dirac neutrinos are different from those of Majorana
neutrinos even if two Majorana CP-violating phases vanish. As the latter can
keep vanishing from the electroweak scale to the typical seesaw scale, it makes
sense to distinguish between the RGE running effects of neutrino mixing
parameters in Dirac and Majorana cases. The differences are found to be quite
large in the minimal supersymmetric standard model with sizable ,
provided the masses of three neutrinos are nearly degenerate or have an
inverted hierarchy.Comment: 12 pages, 5 figure
Mean first-passage time for random walks on undirected networks
In this paper, by using two different techniques we derive an explicit
formula for the mean first-passage time (MFPT) between any pair of nodes on a
general undirected network, which is expressed in terms of eigenvalues and
eigenvectors of an associated matrix similar to the transition matrix. We then
apply the formula to derive a lower bound for the MFPT to arrive at a given
node with the starting point chosen from the stationary distribution over the
set of nodes. We show that for a correlated scale-free network of size with
a degree distribution , the scaling of the lower bound is
. Also, we provide a simple derivation for an eigentime
identity. Our work leads to a comprehensive understanding of recent results
about random walks on complex networks, especially on scale-free networks.Comment: 7 pages, no figures; definitive version published in European
Physical Journal
Topologies and Laplacian spectra of a deterministic uniform recursive tree
The uniform recursive tree (URT) is one of the most important models and has
been successfully applied to many fields. Here we study exactly the topological
characteristics and spectral properties of the Laplacian matrix of a
deterministic uniform recursive tree, which is a deterministic version of URT.
Firstly, from the perspective of complex networks, we determine the main
structural characteristics of the deterministic tree. The obtained vigorous
results show that the network has an exponential degree distribution, small
average path length, power-law distribution of node betweenness, and positive
degree-degree correlations. Then we determine the complete Laplacian spectra
(eigenvalues) and their corresponding eigenvectors of the considered graph.
Interestingly, all the Laplacian eigenvalues are distinct.Comment: 7 pages, 1 figures, definitive version accepted for publication in
EPJ
Random Sierpinski network with scale-free small-world and modular structure
In this paper, we define a stochastic Sierpinski gasket, on the basis of
which we construct a network called random Sierpinski network (RSN). We
investigate analytically or numerically the statistical characteristics of RSN.
The obtained results reveal that the properties of RSN is particularly rich, it
is simultaneously scale-free, small-world, uncorrelated, modular, and maximal
planar. All obtained analytical predictions are successfully contrasted with
extensive numerical simulations. Our network representation method could be
applied to study the complexity of some real systems in biological and
information fields.Comment: 7 pages, 9 figures; final version accepted for publication in EPJ
Degree-distribution Stability of Growing Networks
In this paper, we abstract a kind of stochastic processes from evolving
processes of growing networks, this process is called growing network Markov
chains. Thus the existence and the formulas of degree distribution are
transformed to the corresponding problems of growing network Markov chains.
First we investigate the growing network Markov chains, and obtain the
condition in which the steady degree distribution exists and get its exact
formulas. Then we apply it to various growing networks. With this method, we
get a rigorous, exact and unified solution of the steady degree distribution
for growing networks.Comment: 12 page
Theoretical study of the two-proton halo candidate Ne including contributions from resonant continuum and pairing correlations
With the relativistic Coulomb wave function boundary condition, the energies,
widths and wave functions of the single proton resonant orbitals for Ne
are studied by the analytical continuation of the coupling constant (ACCC)
approach within the framework of the relativistic mean field (RMF) theory.
Pairing correlations and contributions from the single-particle resonant
orbitals in the continuum are taken into consideration by the resonant
Bardeen-Cooper-Schrieffer (BCS) approach, in which constant pairing strength is
used. It can be seen that the fully self-consistent calculations with NL3 and
NLSH effective interactions mostly agree with the latest experimental
measurements, such as binding energies, matter radii, charge radii and
densities. The energy of 2s orbital is slightly higher than that
of orbital, and the occupation probability of the
2s orbital is about 20%, which are in accordance with the
shell model calculation and three-body model estimation
Tri-Bimaximal Mixing from Twisted Friedberg-Lee Symmetry
We investigate the Friedberg-Lee (FL) symmetry and its promotion to include
the symmetry, and call that the twisted FL symmetry.Based on the
twisted FL symmetry, two possible schemes are presented toward the realistic
neutrino mass spectrum and the tri-bimaximal mixing.In the first scheme, we
suggest the semi-uniform translation of the FL symmetry.The second one is based
on the permutation family symmetry.The breaking terms, which are twisted
FL symmetric, are introduced.Some viable models in each scheme are also
presented.Comment: 14 pages, no figure. v2: 16 pages, modified some sentences, appendix
added, references added. v3: 14 pages, composition simplified, accepted
version in EPJ
Construction and functional analysis of nattokinase-producing cucumber obtained by the CRISPR-Cas9 system
Nattokinase (NK) is effective in the prevention and treatment of cardiovascular disease. Cucumber is rich in nutrients with low sugar content and is safe for consumption. The aim of this study was to construct a therapeutic cucumber that can express NK, which can prevent and alleviate cardiovascular diseases by consumption. Because the Bitter fruit ( Bt ) gene contributes to bitter taste but has no obvious effect on the growth and development of cucumber, so the NK-producing cucumber was constructed by replacing the Bt gene with NK by using CRISPR/Cas9. The pZHY988-Cas9-sgRNA and pX6-LHA-U6-NK-T-RHA vectors were constructed and transformed into Agrobacterium tumefaciens EHA105, which was transformed into cucumber by floral dip method. The crude extract of NK-producing cucumber had significant thrombolytic activity in vitro . In addition, treatment with the crude extract significantly delayed thrombus tail appearance, and the thrombin time of mice was much longer than that of normal mice. The degrees of coagulation and blood viscosity as well as hemorheological properties improved significantly after crude extract treatment. These findings show that NK-producing cucumber can effectively alleviate thrombosis and improve blood biochemical parameters, providing a new direction for diet therapy against cardiovascular diseases
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