Buffer operator in grey system prediction model can help to balance the influence of disturbance components and the parameter estimation tracking speed. It can also improve the prediction precision. Some famous buffer operators have been proposed such as Average Strengthening Buffer operator, Arithmetic Average Strengthening Buffer operator and so on. They can be viewed as integer-order buffer operators from the accumulative system opinion. We try to extend them into positive real order and construct the corresponding strengthening buffer operators in this paper. The calculation results show that the proposed buffer operator can improve the prediction accuracy effectively.

This paper presents a new method of predicting propagation path-loss, which idea comes from grey system theory and Verhulst difference equation, which is called Grey Verhuslt Model. In order to validate correction and accuracy of the model, the simulation and prediction values are compared with the experimental data obtained from the laboratory experiment environment and computing results from Method of Moments (MOM). The performance criterion selected for the comparison between the actual and the predicted data are the root mean square error (RMSE), mean relative error (MRE).

In this paper, the parameter λ would be introduced to forecast grey number sequence that was based on the paper with known whitenization weight function published by Bo Zeng. We use variable weight instead of no-preference generation. So the most appropriate parameter to build the DGM (1,1) would be chose by GA. Then an improved grey prediction model for forecasting interval grey number is proposed. An application analysis is presented to illustrate the effectiveness and practicability of the proposed model. Simulation examples show the average relative error of the proposed model has been significantly improved.

To solve the problem that the growth of prediction of discrete grey model is constant, the paper establishes a new grey discrete parameters prediction model by instructing quadratic time-varying parameters, which is called as quadratic time-varying discrete grey model(referred to as QDGM(1,1)). We discuss the affine properties of QDGM model. The paper employed a majorization principle to optimizing the iterative starting value of the new model, and introduced the steps of using QDGM (1, 1) to predict. Finally, there is an instance that demonstrates the new model has the best results in the four discrete grey models. It was proved that the new model greatly improves the simulation and prediction precision.

To solve the problem that the growth of prediction of discrete grey model is constant, the paper establishes a new grey discrete parameters prediction model by instructing quadratic time-varying parameters, which is called as quadratic time-varying discrete grey model(referred to as QDGM (1,1)). We discuss the affine properties of QDGM model. The paper employed a majorization principle to optimizing the iterative starting value of the new model, and introduced the steps of using QDGM (1, 1) to predict. Finally, there is an instance that demonstrates the new model has the best results in the four discrete grey models. It was proved that the new model greatly improves the simulation and prediction precision.

MOTIVATION: RNA-Seq technology based on next-generation sequencing provides the unprecedented ability of studying transcriptomes at high resolution and accuracy, and the potential of measuring expression of multiple isoforms from the same gene at high precision. Solved by maximum likelihood estimation, isoform expression can be inferred in RNA-Seq using statistical models based on the assumption that sequenced reads are distributed uniformly along transcripts. Modification of the model is needed when considering situations where RNA-Seq data do not follow uniform distribution. RESULTS: We proposed two curves, the global bias curve (GBC) and the local bias curves (LBCs), to describe the non-uniformity of read distributions for all genes in a transcriptome and for each gene, respectively. Incorporating the bias curves into the uniform read distribution (URD) model, we introduced non-URD (N-URD) models to infer isoform expression levels. On a series of systematic simulation studies, the proposed models outperform the original model in recovering major isoforms and the expression ratio of alternative isoforms. We also applied the new model to real RNA-Seq datasets and found that its inferences on expression ratios of alternative isoforms are more reasonable. The experiments indicate that incorporating N-URD information can improve the accuracy in modeling and inferring isoform expression in RNA-Seq.

Based on the present theories of buffer operators, We propose in this paper several kinds of buffer operators based on the interpolatory function, which all have the universality and practicability. we prove them to be weakening buffer operators. The problem of some contradictions between qualitative analysis and quantiative forecast in pretreatment for vibration data sequences is resolved effectively.

Grey cluster decision-making is an important part of grey system theory. And 2-tuple linguistic assessment resolves the calculation problems of the result of expert qualitative linguistic assessment. But both of them not mention how to calculate the weight of index. Based on the definitions of entropy, a method of getting weight is proposed, and considers the character of grey cluster decision-making and 2-tuple linguistic assessment, this paper proposed the method of 2-tuple linguistic assessment based on grey cluster. It can combine qualitative analysis and quantitative analysis well.

Based on the present theories of operators, this paper give a new result on the weakening buffer operator. f is a monotonously increasing function, g is its inverse function. If d is a weakening buffer operator, and x(k)d is made of x(k),..., x(n), k = 1, 2, ... n. If we substitute x(k) by f(x(k)), k=1, ..., n. The new result is m = [f(x(k))]d. If g(m) = e, then e is also a weakening buffer operator.