CONVERGENCE RATES IN THE STRONG LAWS OF NONSTATIONARYρ~*-MIXING RANDOM FIELDS

By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.

Complete Convergence Properties of the Sums for -mixing Sequences of Random Variables

This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.

Powder Mixing Simulation Using Random Walk Model in Eco-material Preparation

The eco-material composition is not well-distributed in preparation. The eco-material samples were taken for computer image analysis, and its particle numbers and appearance parameters were measured. Based on the mechanism of connective mixing and diffusion, the particles distribution was simulated by a computer using the random walk with Levy flight. The results show that the eco-material microstructure simulated by a computer has an idealized porous structure. The particles distribution has a cluster characteristic that changes with the different size and number of particles in Levy flight trajectory. Each cluster consists of a collection of clusters and shows a structure of self-similar cluster,hence presents a well-defined fractal property. The results obtained from SEM observation are in good agreement with the numerical simulations, and show that the convective mixing presents in the Levy flight walk.

Some Convergence Results for Sequences of -mixing Random Variables

In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent random variable sequences without any extra conditions.

Moments of the maximum of normed partial sums of ρ^--mixing random variables

Let {Xn,n ≥ 1} be a sequence of identically distributed ρ^--mixing random variables and set Sn =∑i^n=1 Xi,n ≥ 1,the suffcient and necessary conditions for the existence of moments of supn≥1 ｜Sn/n^1/r｜^p（0 〈 r 〈 2,p 〉 0） are given,which are the same as that in the independent case.

Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.

On Moments of the Maximum of Normed Partial Sums of ρ^--mixing Random Variables

In this paper, we obtain the moment conditions for the supermun of normed sums of ρ^--mixing random variables by using the Rosenthal-type inequality for Maximum partial sums of ρ^--mixing random variables. The result obtained generalize the results of Chen(2008) and extend those to negatively associated sequences and ρ^--mixing random variables.

Complete Convergence and Weak Law of Large Numbers for <i><span style="text-decoration:overline;">ρ</span></i>-Mixing Sequences of Random Variables

In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.

PRECISE RATE IN THE LAW OF ITERATED LOGARITHM FOR ρ-MIXING SEQUENCE

Let {X,X n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set S n=n k=1X k,M n=max k≤n｜S k｜,n≥1. Suppose lim n→∞ES2 n/n=∶σ2>0 and ∞n=1ρ 2/d(2n)<∞, where d=2,if -1<b<0 and d>2(b+1),if b≥0. It is proved that,for any b>-1, limε0ε 2(b+1)∞n=1(loglogn)bnlognP{M n≥εσ2nloglogn}= 2(b+1)πГ(b+3/2)∞k=0(-1)k(2k+1) 2b+2,where Г(·) is a Gamma function.

The improved artificial bee colony algorithm for mixed additive and multiplicative random error model and the bootstrap method for its precision estimation

To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.

Ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints

The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

Improved cat swarm optimization for parameter estimation of mixed additive and multiplicative random error model

To estimate the parameters of the mixed additive and multiplicative(MAM)random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array,we introduce a derivative-free cat swarm optimization for parameter estimation.We embed the Powell method,which uses conjugate direction acceleration and does not need to derive the objective function,into the original cat swarm optimization to accelerate its convergence speed and search accuracy.We use the ordinary least squares,weighted least squares,original cat swarm optimization,particle swarm algorithm and improved cat swarm optimization to estimate the parameters of the straight-line fitting MAM model with lower nonlinearity and the DEM MAM model with higher nonlinearity,respectively.The experimental results show that the improved cat swarm optimization has faster convergence speed,higher search accuracy,and better stability than the original cat swarm optimization and the particle swarm algorithm.At the same time,the improved cat swarm optimization can obtain results consistent with the weighted least squares method based on the objective function only while avoiding multiple complex weight array derivations.The method in this paper provides a new idea for theoretical research on parameter estimation of MAM error models.

SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].

The mixed-spins 1/2 and 3/2 Blume-Capel model with a random crystal field

The random crystal field （RCF） effects are investigated on the phase diagrams of the mixed-spins 1/2 and 3/2 Blume-Capel （BC） model on the Bethe lattice. The bimodal random crystal field is assumed and the recursion relations are employed for the solution of the model. The system gives only the second-order phase transitions for all values of the crystal fields in the non-random bimodal distribution for given probability. The randomness does not change the order of the phase transitions for higher crystal field values, i.e., it is always second-order, but it may introduce first-order phase transitions at lower negative crystal field values for the probability in the range about 0.20 and 0.45, which is only the second-order for the non-random case in this range. Thus our work claims that randomness may be used to induce first-order phase transitions at lower negative crystal field values at lower probabilities.

Longitudinal-Random-Field Mixed Ising Model with Arbitrary Spins

The longitudinal-random-fieM mixed Ising model consisting of arbitrary spin values has been studied by the use of an effective field theory with correlations （EFT）. The phase diagrams of systems with mixed spins： σ = 1/2, S = 1; σ = 1/2, S = 3/2 are plotted. Not only the discontinuity at T = 0 K, is found when both longitudinal fields are trimodal distributed, but also the trieritical behavior is observed in these phase diagrams between the bimodal and trimodal distributions of longitudinal fields, which is different from the single-spin one. The appearance of tricritical point is independent of the coordination number and spin values.

Identification of Mixtures of Two Types of Body Fluids Using the Multiplex Methylation System and Random Forest Models

Objective Body fluid mixtures are complex biological samples that frequently occur in crime scenes,and can provide important clues for criminal case analysis.DNA methylation assay has been applied in the identification of human body fluids,and has exhibited excellent performance in predicting single-source body fluids.The present study aims to develop a methylation SNaPshot multiplex system for body fluid identification,and accurately predict the mixture samples.In addition,the value of DNA methylation in the prediction of body fluid mixtures was further explored.Methods In the present study,420 samples of body fluid mixtures and 250 samples of single body fluids were tested using an optimized multiplex methylation system.Each kind of body fluid sample presented the specific methylation profiles of the 10 markers.Results Significant differences in methylation levels were observed between the mixtures and single body fluids.For all kinds of mixtures,the Spearman’s correlation analysis revealed a significantly strong correlation between the methylation levels and component proportions(1:20,1:10,1:5,1:1,5:1,10:1 and 20:1).Two random forest classification models were trained for the prediction of mixture types and the prediction of the mixture proportion of 2 components,based on the methylation levels of 10 markers.For the mixture prediction,Model-1 presented outstanding prediction accuracy,which reached up to 99.3%in 427 training samples,and had a remarkable accuracy of 100%in 243 independent test samples.For the mixture proportion prediction,Model-2 demonstrated an excellent accuracy of 98.8%in 252 training samples,and 98.2%in 168 independent test samples.The total prediction accuracy reached 99.3%for body fluid mixtures and 98.6%for the mixture proportions.Conclusion These results indicate the excellent capability and powerful value of the multiplex methylation system in the identification of forensic body fluid mixtures.

Ferrimagnetic Properties of Bond Dilution Mixed Blume-Capel Model with Random Single-Ion Anisotropy

We study the ferrimagnetic properties of spin 1/2 and spin-1 systems by means of the effective field theory. The system is considered in the framework of bond dilution mixed Blume-Capel mode/ （BCM） with random single-ion anisotropy. The investigation of phase diagrams and magnetization curves indicates the existence of induced magnetic ordering and single or multi-compensation points. Special emphasis is placed on the influence of bond dilution and random single-ion anisotropy on normal or induced magnetic ordering states and single or multi-compensation points. Normal magnetic ordering states take on new phase diagrams with increasing randomness （bond and anisotropy）, while anisotropy induced magnetic ordering states are always occurrence no matter whether concentration of anisotropy is large or small. Existence and disappearance of compensation points rely strongly on bond dilution and random singleion anisotropy. Some results have not been revealed in previous papers and predicted by Néel theory of ferrimagnetism.

Set Programming Method and Performance Improvement of Phase Change Random Access Memory Arrays

A novel slow-down set waveform is proposed to improve the set performance and a 1 kb phase change random access memory chip fabricated with a 13nm CMOS technology is implemented to investigate the set performance by different set programming strategies based on this new set pulse. The amplitude difference （I1 - I2） of the set pulse is proved to be a crucial parameter for set programming. We observe and analyze the cell characteristics with different I1 - I2 by means of thermal simulations and high-resolution transmission electron microscopy, which reveal that an incomplete set programming will occur when the proposed slow-down pulse is set with an improperly high I1 - I2. This will lead to an amorphous residue in the active region. We also discuss the programming method to avoid the set performance degradations.

Developing Three-Dimensional Beamshaping Techniques on Volumetric Random Arrays to Suppress Array Sidelobes

This paper proposes a three-dimensional (3-D) amplitude tapering technique on volumetric random arrays to minimize array sidelobes and emulate phased array operations on mobile platforms. Our ultimate goal is to realize wireless phased array applications carried out by mobile platforms;in this paper, we focus on the development of collaborative beamforming algorithms. This beamshaping technique mitigates the discontinuity of the current distribution along the array aperture and lower array sidelobe level (SLL) by specially paying attention to the array element’s depth deviation. In this work, step by step amplitude tapering procedures are clearly illustrated. Further, a reconfigurable phased array with sixteen patch antennas is tested to verify the fidelity of the 3-D beamshaping algorithm. Measured and simulated radiation patterns are benchmarked to evaluate the sidelobe suppression results, and the best sidelobe suppressed region is around the array’s main beam.

HIERACHICAL STRUCTURES FOR GENERATING PSEUDO-RANDOM SEQUENCES AND ARRAYS

This paper proposes new hierarchical structures for generating pseudorandom sequences and arrays. The principle of the structures is based on a new concept-multi-interleaving. It is the generalization of normal sequence decimation(sampling). The kernal of the structures is a lower speed linear feedback shift register together with several high speed time-division multiplexers arranged hierarchically. These new structures have much higher speed compared with that of other schemes proposed before.