The Construction of Statistically Recursive Sets

We have constructed a class of random sets by statistical contraction operators in this paper.When the probability space is some special product space and the statistical contraction operators are affine or similar,these statistically recursive sets are investigated by many authors.It will be very convenient for us to study their distributions and dimensions and measures using our model in this paper.

The Structure and the Sufficent and Necessary Conditions for Generalized Statistically Self-Similar Sets

We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson,Falconer,Graf are the special cases of ours.

HAUSDORFF DIMENSION OF GENERALIZED STATISTICALLY SELF-AFFINE FRACTALS

The authors consider generalized statistically self-affine recursive fractals K with random numbers of subsets on each level. They obtain the Hausdorff dimensions of K without considering whether the subsets on each level are non-overlapping or not. They also give some examples to show that many important sets are the special cases of their models.

FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS

In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.

The Classification of Statistically Recursive Sets

The main aim of this paper is to make a classification of random sets K m(ω) constructed in theorem 2.1 and theorem 2.1' in . We provide five criterions for the classification. Many kinds of random sets such as Hawkes constructed in , Graf constructed in and Mauldin constructed in are the special cases of K m(ω) constructed in ,and then these random sets belong to some model respectively according to our classification.

The Convergence of Statistically Self Similar Sets and the Upper Bound and Lower Bound of Hausdorff Measure

We constructed a class of self-similar sets and proved the convergence in this paper.Besides these,the upper bound and lower bound of Hausdorff measures of them were given too.

Dynamic thermo-mechanical coupled simulation of statistically inhomogeneous materials by statistical second-order two-scale method

In this paper,a statistical second-order twoscale（SSOTS） method is developed to simulate the dynamic thcrmo-mechanical performances of the statistically inhomogeneous materials.For this kind of composite material,the random distribution characteristics of particles,including the shape,size,orientation,spatial location,and volume fractions,are all considered.Firstly,the repre.sentation for the microscopic configuration of the statistically inhomogeneous materials is described.Secondly,the SSOTS formulation for the dynamic thermo-mechanical coupled problem is proposed in a constructive way,including the cell problems,effective thermal and mechanical parameters,homogenized problems,and the SSOTS formulas of the temperatures,displacements,heat flux densities and stresses.And then the algorithm procedure corresponding to the SSOTS method is brought forward.The numerical results obtained by using the SSOTS algorithm are compared with those by classical methods.In addition,the thermo-mechanical coupling effect is studied by comparing the results of coupled case with those of uncoupled case.It demonstrates that the coupling effect on the temperatures,heat flux densities,displacements,and stresses is very distinct.The results show that the SSOTS method is valid to predict the dynamic thermo-mechanical coupled performances of statistically inhomogeneous materials.

Statistically Downscaled Summer Rainfall over the Middle-Lower Reaches of the Yangtze River

The summer rainfall over the middle-lower reaches of the Yangtze River valley (YRSR) has been estimated with a multi-linear regression model using principal atmospheric modes derived from a 500 hPa geopotential height and a 700 hPa zonal vapor flux over the domain of East Asia and the West Pacific.The model was developed using data from 1958 92 and validated with an independent prediction from 1993 2008.The independent prediction was efficient in predicting the YRSR with a correlation coefficient of 0.72 and a relative root mean square error of 18%.The downscaling model was applied to two general circulation models (GCMs) of Flexible Global Ocean-Atmosphere-Land System Model (FGOALS) and Geophysical Fluid Dynamics Laboratory coupled climate model version 2.1 (GFDL-CM2.1) to project rainfall for present and future climate under B1 and A1B emission scenarios.The downscaled results pro-vided a closer representation of the observation compared to the raw models in the present climate.In addition,compared to the inconsistent prediction directly from dif-ferent GCMs,the downscaled results provided a consistent projection for this half-century,which indicated a clear increase in the YRSR.Under the B1 emission scenario,the rainfall could increase by an average of 11.9% until 2011 25 and 17.2% until 2036 50 from the current state;under the A1B emission scenario,rainfall could increase by an average of 15.5% until 2011 25 and 25.3% until 2036 50 from the current state.Moreover,the increased rate was faster in the following decade (2011 25) than the latter of this half-century (2036 50) under both emissions.

Statistically Downscaled Temperature Scenarios over China

Monthly mean temperatures at 562 stations in China are estimated using a statistical downscaling technique. The technique used is multiple linear regressions （MLRs） of principal components （PCs）. A stepwise screening procedure is used for selecting the skilful PCs as predictors used in the regression equation. The predictors include temperature at 850 hPa （7）, the combination of sea-level pressure and temperature at 850 hPa （P＋T） and the combination of geo-potential height and temperature at 850 hPa （H＋T）. The downscaling procedure is tested with the three predictors over three predictor domains. The optimum statistical model is obtained for each station and month by finding the predictor and predictor domain corresponding to the highest correlation. Finally, the optimum statistical downscaling models are applied to the Hadley Centre Coupled Model, version 3 （HadCM3） outputs under the Special Report on Emission Scenarios （SRES） A2 and B2 scenarios to construct local future temperature change scenarios for each station and month, The results show that （1） statistical downscaling produces less warming than the HadCM3 output itself; （2） the downscaled annual cycles of temperature differ from the HadCM3 output, but are similar to the observation; （3） the downscaled temperature scenarios show more warming in the north than in the south; （4） the downscaled temperature scenarios vary with emission scenarios, and the A2 scenario produces more warming than the B2, especially in the north of China.

STATISTICALLY FRACTAL STRENGTH THEORY FOR BRITTLE MATERIALS

Based on the hypothesis of the fractal distribution of crack sizes in brittle materials and the weakest link principle, the relationship between the fractal dimension of the size-frequency distribution of cracks and the Weibull Modulus is derived, which reveals the geometrical nature of the Weibull Modulus. The influences of the size distribution and the orientation distribution of cracks as well as the irregularity of the crack propagation on the strength are all taken into account. Finally, a general expression for the statistical strength of brittle materials in complex tensile stress state is obtained.

Finding Statistically Significant Communities in Networks with Weighted Label Propagation

Various networks exist in the world today including biological, social, information, and communication networks with the Internet as the largest network of all. One salient structural feature of these networks is the formation of groups or communities of vertices that tend to be more connected to each other within the same group than to those outside. Therefore, the detection of these communities is a topic of great interest and importance in many applications and different algorithms including label propagation have been developed for such purpose. Speaker-listener label propagation algorithm (SLPA) enjoys almost linear time complexity, so desirable in dealing with large networks. As an extension of SLPA, this study presented a novel weighted label propagation algorithm (WLPA), which was tested on four real world social networks with known community structures including the famous Zachary's karate club network. Wilcoxon tests on the communities found in the karate club network by WLPA demonstrated an improved statistical significance over SLPA. Withthehelp of Wilcoxon tests again, we were able to determine the best possible formation of two communities in this network relative to the ground truth partition, which could be used as a new benchmark for assessing community detection algorithms. Finally WLPA predicted better communities than SLPA in two of the three additional real social networks, when compared to the ground truth.

Ideal Statistically Pre-Cauchy Triple Sequences of Fuzzy Number and Orlicz Functions

In this paper, we extend the notions of ideal statistically convergence for sequence of fuzzy number. We introduce the notions ideal statistically pre-Cauchy triple sequences of fuzzy number about Orlicz function, and give some correlation theorem. It is shown that x = {xijk} is ideal statistically pre-Cauchy if and only if D (xijk, xpqr) ≥ ε, i ≤ m, j ≤ n, t ≤ k}| ≥ δ} ∈I. At the same time, we have proved x = {xijk} is ideal statistically convergent to x0 if and only if . Also, some properties of these new sequence spaces are investigated.

STUDY ON STATISTICALLY-FAIR SERVICE IN STATISTICALLY-MULTIPLEXED NETWORKS

A new type of fair service, referred to as Statistically-Fair Service (SFS), is proposed in this paper. The SFS discipline is given based on the SFS criterion. Compared to "strict" fair service available, SFS is mainly characterized by its flexible suitability for the nature of statistically-multiplexed networks. By its statistically-fair service to users, therefore, SFS can ensure well end-to-end QoS requirements on a statistical basis with a benefit of enhancement in network utilization. Two useful properties of SFS is presented. One of them, the property of retaining Exponentially Bounded Burstiness(EBB), can facilitate end-to-end delay estimation of EBB-type traffic. Finally, some numerical results obtained from a simulation study on SFS shows that an SFS-equipped node in steady states will in deed retain the EBB attribute of any input flow.

Statistically Convergent Double Sequence Spaces in 2-Normed Spaces Defined by Orlicz Function

The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-normed spaces to be statistically Cauchy sequence in 2-normed spaces.

I.I.D.STATISTICAL CONTRACTION OPERATORS AND STATISTICALLY SELF-SIMILAR SETS

I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.

Multifractal Decomposition of Statistically Self-Similar Sets

Let K be a statistically self-similar set defined by Graf.In this paper,we construct a random measure ρ which is supported by K and study the multifractal decomposition for K with p. Under such a decomposition,we obtain the expression of the spectrum function f(α).

A novel statistically tracked particle swarm optimization method for automatic generation control

Particle swarm optimization(PSO)is one of the popular stochastic optimization based on swarm intelligence algorithm.This simple and promising algorithm has applications in many research fields.In PSO,each particle can adjust its‘flying’according to its own flying experience and its companions’flying experience.This paper proposes a new PSO variant,called the statistically tracked PSO,which uses group statistical characteristics to update the velocity of the particle after certain iterations,thus avoiding localminima and helping particles to explore global optimum with an improved convergence.The performance of the proposed algorithm is tested on a deregulated automatic generation control problem in power systems and encouraging results are obtained.

A novel method for clustering cellular data to improve classification

Many fields,such as neuroscience,are experiencing the vast prolife ration of cellular data,underscoring the need fo r organizing and interpreting large datasets.A popular approach partitions data into manageable subsets via hierarchical clustering,but objective methods to determine the appropriate classification granularity are missing.We recently introduced a technique to systematically identify when to stop subdividing clusters based on the fundamental principle that cells must differ more between than within clusters.Here we present the corresponding protocol to classify cellular datasets by combining datadriven unsupervised hierarchical clustering with statistical testing.These general-purpose functions are applicable to any cellular dataset that can be organized as two-dimensional matrices of numerical values,including molecula r,physiological,and anatomical datasets.We demonstrate the protocol using cellular data from the Janelia MouseLight project to chara cterize morphological aspects of neurons.

Statistically Convergent Difference Double Sequence Spaces

In this article we define the notion of statistically convergent difference double sequence spaces. We examine the spaces 2l∞（△, q）, 2c（△, q）, 2cB（△, q）, 2cR（△, q）, 2cBR（△,q） etc. being symmetric, solid, monotone, etc. We prove some inclusion results too.

Statistically designed enzymatic hydrolysis of an icariin/b-cyclodextrin inclusion complex optimized for production of icaritin

This study focuses on the preparation and enzymic hydrolysis of an icariin/bcyclodextrin inclusion complex to efficiently generate icaritin.The physical characteristics of the inclusion complex were evaluated by differential scanning calorimetry(DSC).Enzymatic hydrolysis was optimized for the conversion of icariin/b-cyclodextrin complex to icaritin by Box–Behnken statistical design.The inclusion complex formulation increased the solubility of icariin approximately 17-fold,from 29.2 to 513.5 mg/mL at 60℃.The optimum conditions were predicted by Box–Behnken statistical design as follows:60℃,pH 7.0,the ratio of enzyme/substrate(1:1.1)and reaction time 7 h.Under the optimal conditions the conversion of icariin was 97.91%and the reaction time was decreased by 68%compared with that without b-CD inclusion.Product analysis by melting point,ESI-MS,UV,IR,1H NMR and 13C NMR confirmed the authenticity of icaritin with a purity of 99.3%and a yield of 473 mg of icaritin from 1.1 g icariin.