26,878 research outputs found
Congruences for sequences analogous to Euler numbers
For a given real number we define the sequence by
and , where is the greatest integer not
exceeding . Since is the n-th Euler number, can be
viewed as a natural generalization of Euler numbers. In this paper we deduce
some identities and an inversion formula involving , and establish
congruences for , and provided that is a
nonzero integer, where is the least nonnegative integer
such that p^{\a}\mid n but p^{\a+1}\nmid n.Comment: 16 page
Collaborative similarity analysis of multilayer developer-project bipartite network
To understand the multiple relations between developers and projects on
GitHub as a whole, we model them as a multilayer bipartite network and analyze
the degree distributions, the nearest neighbors' degree distributions and their
correlations with degree, and the collaborative similarity distributions and
their correlations with degree. Our results show that all degree distributions
have a power-law form, especially, the degree distribution of projects in
watching layer has double power-law form. Negative correlations between nearest
neighbors' degree and degree for both developers and projects are observed in
both layers, exhibiting a disassortative mixing pattern. The collaborative
similarity of both developers and projects negatively correlates with degree in
watching layer, while a positive correlations is observed for developers in
forking layer and no obvious correlation is observed for projects in forking
layer
Emergence of cooperation induced by preferential learning
The evolutionary Prisoner's Dilemma Game (PDG) and the Snowdrift Game (SG)
with preferential learning mechanism are studied in the Barab\'asi-Albert
network. Simulation results demonstrate that the preferential learning of
individuals remarkably promotes the cooperative behavior for both two games
over a wide range of payoffs. To understand the effect of preferential learning
on the evolution of the systems, we investigate the time series of the
cooperator density for different preferential strength and payoffs. It is found
that in some specific cases two games both show the -scaling behaviors,
which indicate the existence of long range correlation. We also figure out that
when the large degree nodes have high probability to be selected, the PDG
displays a punctuated equilibrium-type behavior. On the contrary, the SG
exhibits a sudden increase feature. These temporary instable behaviors are
ascribed to the strategy shift of the large degree nodes.Comment: 10 pages, 5 figure
Secure quantum key distribution network with Bell states and local unitary operations
We propose a theoretical scheme for secure quantum key distribution network
following the ideas in quantum dense coding. In this scheme, the server of the
network provides the service for preparing and measuring the Bell states, and
the users encodes the states with local unitary operations. For preventing the
server from eavesdropping, we design a decoy when the particle is transmitted
between the users. It has high capacity as one particle carries two bits of
information and its efficiency for qubits approaches 100%. Moreover, it is not
necessary for the users to store the quantum states, which makes this scheme
more convenient for application than others.Comment: 5 pages, 2 figures. The decoy-photon technique is presented in a
clear way for preventing a potentially dishonest server on a network from
eavesdropping quantum communication freely. This technique may be useful in
quantum secret sharing (of classical information or quantum information),
controlled teleportation, and so o
The effect of social welfare system based on the complex network
With the passage of time, the development of communication technology and
transportation broke the isolation among people. Relationship tends to be
complicated, pluralism, dynamism. In the network where interpersonal
relationship and evolved complex net based on game theory work serve
respectively as foundation architecture and theoretical model, with the
combination of game theory and regard public welfare as influencing factor, we
artificially initialize that closed network system. Through continual loop
operation of the program, we summarize the changing rule of the cooperative
behavior in the interpersonal relationship, so that we can analyze the policies
about welfare system about whole network and the relationship of frequency of
betrayal in cooperative behavior. Most analytical data come from some simple
investigations and some estimates based on internet and environment and the
study put emphasis on simulating social network and analyze influence of social
welfare system on Cooperative Behavio
Dynamical Coarse Graining of Large Scale-Free Boolean networks
We present a renormalization-grouplike method performed in the state space
for detecting the dynamical behaviors of large scale-free Boolean networks,
especially for the chaotic regime as well as the edge of chaos. Numerical
simulations with different coarse-graining level show that the state space
networks of scale-free Boolean networks follow universal power-law
distributions of in and out strength, in and out degree, as well as weight.
These interesting results indicate scale-free Boolean networks still possess
self-organized mechanism near the edge of chaos in the chaotic regime. The
number of state nodes as a function of biased parameter for distinct
coarse-graining level also demonstrates that the power-law behaviors are not
the artifact of coarse-graining procedure. Our work may also shed some light on
the investigation of brain dynamics.Comment: 5 pages, 6 figure
A New Type of Two-photon Forward Radiation in Pure Liquids
Unexpected spectral features are observed in the two photon spectrum of the
pure water in the forward direction when an 80 femtosecond laser pulse is
focused at 10^10Wcm-2 or less. Such intensity is much lower than the breakdown
or stimulated threshold of the liquid water. The two broad features are about
2700cm-1 and 5000cm-1 red shifted from the hyper-Rayleigh wavelength,
respectively, and they are quadratic with the laser intensity. They do not
match the known Raman or hyper-Raman frequencies of water, and they are both
centered at a narrow angle in the forward direction. Several other liquids also
exhibited similar but molecular specific spectral features.Comment: 4 pages, 4 figure
Diffusion-limited-aggregation on a directed small world network
For real world systems, nonuniform medium is ubiquitous. Therefore, we
investigate the diffusion-limited-aggregation process on a two dimensional
directed small-world network instead of regular lattice. The network structure
is established by rewiring connections on the two dimensional directed lattice.
Those rewired edges are controlled by two parameters and , which
characterize the spatial length and the density of the long-range connections,
respectively. Simulations show that there exists a maximum value of the fractal
dimension when equals zero. Interestingly, we find that the symmetry
of the aggregation pattern is broken when rewired connections are long enough,
which may be an explanation for the formation of asymmetrical fractal in
nature. Then, we perform multifractal analysis on the patterns further.Comment: 5 pages, 5 figure
Eigenvectors of Z-tensors associated with least H-eigenvalue with application to hypergraphs
Unlike an irreducible -matrices, a weakly irreducible -tensor
can have more than one eigenvector associated with the least
H-eigenvalue. We show that there are finitely many eigenvectors of
associated with the least H-eigenvalue. If is
further combinatorial symmetric, the number of such eigenvectors can be
obtained explicitly by the Smith normal form of the incidence matrix of
. When applying to a connected uniform hypergraph , we prove
that the number of Laplacian eigenvectors of associated with the zero
eigenvalue is equal to the the number of adjacency eigenvectors of
associated with the spectral radius, which is also equal to the number of
signless Laplacian eigenvectors of associated with the zero eigenvalue if
zero is an signless Laplacian eigenvalue
A New Target-specific Object Proposal Generation Method for Visual Tracking
Object proposal generation methods have been widely applied to many computer
vision tasks. However, existing object proposal generation methods often suffer
from the problems of motion blur, low contrast, deformation, etc., when they
are applied to video related tasks. In this paper, we propose an effective and
highly accurate target-specific object proposal generation (TOPG) method, which
takes full advantage of the context information of a video to alleviate these
problems. Specifically, we propose to generate target-specific object proposals
by integrating the information of two important objectness cues: colors and
edges, which are complementary to each other for different challenging
environments in the process of generating object proposals. As a result, the
recall of the proposed TOPG method is significantly increased. Furthermore, we
propose an object proposal ranking strategy to increase the rank accuracy of
the generated object proposals. The proposed TOPG method has yielded
significant recall gain (about 20%-60% higher) compared with several
state-of-the-art object proposal methods on several challenging visual tracking
datasets. Then, we apply the proposed TOPG method to the task of visual
tracking and propose a TOPG-based tracker (called as TOPGT), where TOPG is used
as a sample selection strategy to select a small number of high-quality target
candidates from the generated object proposals. Since the object proposals
generated by the proposed TOPG cover many hard negative samples and positive
samples, these object proposals can not only be used for training an effective
classifier, but also be used as target candidates for visual tracking.
Experimental results show the superior performance of TOPGT for visual tracking
compared with several other state-of-the-art visual trackers (about 3%-11%
higher than the winner of the VOT2015 challenge in term of distance precision).Comment: 14pages,11figures, Submited to IEEE Transactions on Cybernetis
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