Coarse graining method based on generalized degree in complex network
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Degree (music)
The information entropy between coarse granularity and fine granularity is comparatively studied,the influence on decision tree caused by coarse granularity and fine granularity is investigated,and the conclusion is provided that the information entropy under coarse granularity is not less than the one under fine granularity.It is shown that the decision tree generated by selecting the expanded attribute under fine granularity is better than the one under coarse granularity.
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Granular Computing
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This paper discusses a mining problem of approximate periodicity with multi-granularity time in the temporal database. It introduces the concepts and properties of the multi-granularity time interval on the basis of multi-granularity time and multi-granularity time format. It constructs multi-granularity approximate periodic pattern. It proposes an mining algorithm based on self-organizing map to find multi-granularity approximate periodic pattern. Results obtained from experiments on high frequency stock market data of 580000 Bao Steel JBT1 demonstrate that the proposed algorithm is efficient.
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Temporal database
Basis (linear algebra)
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The security of many cryptographic constructions relies on assumptions related to Discrete Logarithms (DL), e.g., the Diffie-Hellman, Square Exponent, Inverse Exponent or Representation Problem assumptions. In the concrete formalizations of these assumptions one has some degrees of freedom offered by parameters such as computational model, the problem type (computational, decisional) or success probability of adversary. However, these parameters and their impact are often not properly considered or are simply overlooked in the existing literature.
In this paper we identify parameters relevant to cryptographic applications and describe a formal framework for defining DL-related assumptions. This enables us to precisely and systematically classify these assumptions.
In particular, we identify a parameter, termed granularity, which describes the underlying probability space in an assumption. Varying granularity we discover the following surprising result: We prove that two DL-related assumptions can be reduced to each other for medium granularity but we also show that they are provably not reducible with generic algorithms for high granularity. Further we show that reductions for medium granularity can achieve much better concrete security than equivalent high-granularity reductions.
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Discrete logarithm
Representation
Concrete security
Exponent
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Granularity
Concrete security
Discrete logarithm
Representation
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A new mathematical formula for colour granularity has recently been proposed by Saunders1. Whereas some previously derived mathematical expressions of colour granularity have proved difficult to apply in practice due to the existence of terms having no real physical correlate, this new formula relates granularity to easily measured film parameters. Using this formula, successful granularity predictions have been made for a series of single-laver colour negative structures in which the coupler silver halide ratio was systematically varied.
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An equation to describe the granularity of an electrophotographic imaging system has been developed to include the density variance attributed to the reflectance of paper and toner surfaces. Granularity measurements from two conventional electrophotographic copiers were used to validate the relationship. The results show good agreement with the overall shape of the granularity-versus-density curve; however, the values are not consistent with estimated toner particle size. Clustering of the toner particles is suggested as the cause of the high granularity values.
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Particle (ecology)
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A mathematical relationship between the degree-rank function and the degree distribution of complex networks is derived firstly.Based on the relationship,a method of constructing complex networks with arbitrary degree distributions is proposed.Taking scale-free network and exponential network as examples,the efficiency of the method is verified.
Degree (music)
Degree distribution
Rank (graph theory)
Scale-free network
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