78,245 research outputs found
Evolutionary of Online Social Networks Driven by Pareto Wealth Distribution and Bidirectional Preferential Attachment
Understanding of evolutionary mechanism of online social networks is greatly
significant for the development of network science. However, present researches
on evolutionary mechanism of online social networks are neither deep nor clear
enough. In this study, we empirically showed the essential evolution
characteristics of Renren online social network. From the perspective of Pareto
wealth distribution and bidirectional preferential attachment, the origin of
online social network evolution is analyzed and the evolution mechanism of
online social networks is explained. Then a novel model is proposed to
reproduce the essential evolution characteristics which are consistent with the
ones of Renren online social network, and the evolutionary analytical solution
to the model is presented. The model can also well predict the ordinary
power-law degree distribution. In addition, the universal bowing phenomenon of
the degree distribution in many online social networks is explained and
predicted by the model. The results suggest that Pareto wealth distribution and
bidirectional preferential attachment can play an important role in the
evolution process of online social networks and can help us to understand the
evolutionary origin of online social networks. The model has significant
implications for dynamic simulation researches of social networks, especially
in information diffusion through online communities and infection spreading in
real societies.Comment: 19 pages, 8 figures,31 reference
Early thermalization of quark-gluon matter by elastic 3-to-3 scattering
The early thermalization is crucial to the quark-gluon plasma as a perfect
liquid and results from many-body scattering. We calculate squared amplitudes
for elastic parton-parton-parton scattering in perturbative QCD. Transport
equations with the squared amplitudes are established and solved to obtain the
thermalization time of initially produced quark-gluon matter and the initial
temperature of quark-gluon plasma. We find that the thermalization times of
quark matter and gluon matter are different.Comment: 5 pages, 1 figure, proceedings for Extreme QCD 201
Early Thermalization at RHIC
Triple-gluon elastic scatterings are briefly reviewed since the scatterings
explain the early thermalization puzzle in Au-Au collisions at RHIC energies. A
numerical solution of the transport equation with the triple-gluon elastic
scatterings demonstrates gluon momentum isotropy achieved at a time of the
order of 0.65 fm/c. Triple-gluon scatterings lead to a short thermalization
time of gluon matter.Comment: LaTex, 8 pages and 4 figures, talk presented in the Weihai workshop
on relativistic heavy ion collision
Early thermalization of quark-gluon matter initially created in high-energy nucleus-nucleus collisions
Elastic parton-parton-parton scattering is briefly reviewed and is included
in transport equations of quark-gluon matter. We solve the transport equations
and get thermal states from initially produced quark-gluon matter. Both gluon
matter and quark matter take early thermalization, but gloun matter has a
shorter thermalization time than quark matter.Comment: 7 pages, 4 figures, proceedings for the 29th Winter Workshop on
Nuclear Dynamic
Origin of Temperature of Quark-Gluon Plasma in Heavy Ion Collisions
Initially produced quark-gluon matter at RHIC and LHC does not have a
temperature. A quark-gluon plasma has a high temperature. From this quark-gluon
matter to the quark-gluon plasma is the early thermalization or the rapid
creation of temperature. Elastic three-parton scattering plays a key role in
the process. The temperature originates from the two-parton scattering, the
three-parton scattering, the four-parton scattering and so forth in quark-gluon
matter.Comment: 6 pages, proceedings for the XXX-th International Workshop on High
Energy Physic
Hall algebras associated to triangulated categories
By counting with triangles and the octohedral axiom, we find a direct way to
prove the formula of To\"en in \cite{Toen2005} for a triangulated category with
(left) homological-finite condition.Comment: 12 pages. Final version, to appear in Duk
The Impact of Alternation
Alternating automata have been widely used to model and verify systems that
handle data from finite domains, such as communication protocols or hardware.
The main advantage of the alternating model of computation is that
complementation is possible in linear time, thus allowing to concisely encode
trace inclusion problems that occur often in verification. In this paper we
consider alternating automata over infinite alphabets, whose transition rules
are formulae in a combined theory of booleans and some infinite data domain,
that relate past and current values of the data variables. The data theory is
not fixed, but rather it is a parameter of the class. We show that union,
intersection and complementation are possible in linear time in this model and,
though the emptiness problem is undecidable, we provide two efficient
semi-algorithms, inspired by two state-of-the-art abstraction refinement model
checking methods: lazy predicate abstraction \cite{HJMS02} and the \impact~
semi-algorithm \cite{mcmillan06}. We have implemented both methods and report
the results of an experimental comparison
Energy Optimal Interpolation in Quantum Evolution
We introduce the concept of interpolation in quantum evolution and present a
general framework to find the energy optimal Hamiltonian for a quantum system
evolving among a given set of middle states using variational and geometric
methods. A few special cases are carefully studied. The quantum brachistochrone
problem is proved as a special case.Comment: 8 pages, 0 figure
Understanding Weight Normalized Deep Neural Networks with Rectified Linear Units
This paper presents a general framework for norm-based capacity control for
weight normalized deep neural networks. We establish the upper bound
on the Rademacher complexities of this family. With an normalization
where , and , we discuss properties of a
width-independent capacity control, which only depends on depth by a square
root term. We further analyze the approximation properties of weight
normalized deep neural networks. In particular, for an weight
normalized network, the approximation error can be controlled by the norm
of the output layer, and the corresponding generalization error only depends on
the architecture by the square root of the depth
Green's formula with \bbc^{*}-action and Caldero-Keller's formula for cluster algebras
It is known that Green's formula over finite fields gives rise to the
comultiplications of Ringel-Hall algebras and quantum groups (see\cite{Green},
also see \cite{Lusztig}). In this paper, we deduce the projective version of
Green's formula in a geometric way. Then following the method of Hubery in
\cite{Hubery2005}, we apply this formula to proving Caldero-Keller's
multiplication formula for acyclic cluster algebras of arbitrary type.Comment: 26 page
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