Robust designs for models with possible bias and correlated errors

This paper studies the model-robust design problem for general models with an unknown bias or contamination and the correlated errors. The true response function is assumed to be from a reproducing kernel Hilbert space and the errors are fitted by the qth order moving average process MA（q）, especially the MA（1） errors and the MA（2） errors. In both situations, design criteria are derived in terms of the average expected quadratic loss for the least squares estimation by using a minimax method. A case is studied and the orthogonality of the criteria is proved for this special response. The robustness of the design criteria is discussed through several numerical examples.

Almost Sure Convergence and Complete Convergence for the Weighted Sums of Martingale Differences

Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.

An estimation model for the fragmentation properties of brittle rock block due to the impacts against an obstruction

Mountain hazards with large masses of rock blocks in motion – such as rock falls, avalanches and landslides – threaten human lives and structures. Dynamic fragmentation is a common phenomenon during the movement process of rock blocks in rock avalanche, due to the high velocity and impacts against obstructions. In view of the energy consumption theory for brittle rock fragmentation proposed by Bond, which relates energy to size reduction, a theoretical model is proposed to estimate the average fragment size for a moving rock block when it impacts against an obstruction. Then, different forms of motion are studied, with various drop heights and slope angles for the moving rock block. The calculated results reveal that the average fragment size decreases as the drop height increases, whether for free-fall or for a sliding or rolling rock block, and the decline in size is rapid for low heights and slow for increasing heights in the corresponding curves. Moreover, the average fragment size also decreases as the slope angle increases for a slidingrock block. In addition, a rolling rock block has a higher degree of fragmentation than a sliding rock block, even for the same slope angle and block volume. Finally, to compare with others' results, the approximate number of fragments is estimated for each calculated example, and the results show that the proposed model is applicable to a relatively isotropic moving rock block.

Boundary conditions: An effect of average of microscopic Maxwell’s equations

It is well known that the macroscopic Maxwell’s equations can be obtained from the corresponding microscopic or atomic equations by a proper averaging process. The purpose of this paper is to present the macroscopic Maxwell’s equations which are valid in all regions of space, including an interface between two different media; and the boundary conditions can naturally emerge from the macroscopic equations as an effect of average of the microscopic Maxwell’s equations. In addition, the application of the unit step functions and the Dirac delta function to our discussion not only permits great mathematical simplicity but also gives rise to convenient physical concepts for the description and representation of the actual fields in the vicinity of the interface.

The Convergence of a Moving Average Process of AANA Random Variables

Based on the asymptotically almost negatively associated(AANA) random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1 + Y)] < ∞. As an application, Marcinkiewicz-Zygmundtype strong law of large numbers for this moving average process is presented in this paper.

Quality of correlation in quantum information

A strong and stable correlation in quantum information is of high quality for quantum information processing.We define two quantities,selective average correlation and ripple coefficient,to evaluate the quality of correlation in quantum information in a time interval.As a new communication channel,Heisenberg spin chains are widely investigated.We select a two-qubit Heisenberg XXZs pin chain with Dzyaloshinskii-Moriya interaction in an inhomogeneous magnetic field as an example,and use the two quantities to evaluate the qualities of the correlation in quantum information with different measures.The result shows that,if the time evolutions are similar,there needs only evaluating one of them to know when the correlation has high quality for quantum information processing.

Explicit bivariate rate functions for large deviations in AR(1)and MA(1)processes with Gaussian innovations

We investigate the large deviations properties for centered stationary AR(1)and MA(1)processes with independent Gaussian innovations,by giving the explicit bivariate rate functions for the sequence of two-dimensional random vectors.Via the Contraction Principle,we provide the explicit rate functions for the sample mean and the sample second moment.In the AR(1)case,we also give the explicit rate function for the sequence of two-dimensional random vectors(W_(n))n≥2=(n^(-1(∑_(k=1)^(n)X_(k),∑_(k=1)^(n)X_(k)^(2))))_(n∈N)n≥2,but we obtain an analytic rate function that gives different values for the upper and lower bounds,depending on the evaluated set and its intersection with the respective set of exposed points.A careful analysis of the properties of a certain family of Toeplitz matrices is necessary.The large deviations properties of three particular sequences of one-dimensional random variables will follow after we show how to apply a weaker version of the Contraction Principle for our setting,providing new proofs for two already known results on the explicit deviation function for the sample second moment and Yule-Walker estimators.We exhibit the properties of the large deviations of the first-order empirical autocovariance,its explicit deviation function and this is also a new result.

Convergence Rates for Probabilities of Moderate Deviations for Moving Average Processes

The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates （or complete moment convergence） for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.

The Precise Asymptotics of the Complete Convergence for Moving Average Processes of m-Dependent B-Valued Elements

Let {εt;t ∈ Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {a3;j ∈ Z} is a sequence of real numbers satisfying ∑j=-∞^∞｜aj｜ 〈 ∞. Define a moving average process Xt = ∑j=-∞^∞aj＋tEj,t ≥ 1, and Sn = ∑t=1^n Xt,n ≥ 1. In this article, by using the weak convergence theorem of { Sn/√ n _〉 1}, we study the precise asymptotics of the complete convergence for the sequence {Xt; t ∈ N}.

STRONG N-DISCOUNT AND FINITE-HORIZON OPTIMALITY FOR CONTINUOUS-TIME MARKOV DECISION PROCESSES

This paper studies the strong n(n =—1,0)-discount and finite horizon criteria for continuoustime Markov decision processes in Polish spaces.The corresponding transition rates are allowed to be unbounded,and the reward rates may have neither upper nor lower bounds.Under mild conditions,the authors prove the existence of strong n(n =—1,0)-discount optimal stationary policies by developing two equivalence relations:One is between the standard expected average reward and strong—1-discount optimality,and the other is between the bias and strong 0-discount optimality.The authors also prove the existence of an optimal policy for a finite horizon control problem by developing an interesting characterization of a canonical triplet.

Complete qth-Moment Convergence of Moving Average Process for m-WOD Random Variable

In this paper,we obtained complete qth-moment convergence of the moving average processes,which is generated by m-WOD moving random variables.The results in this article improve and extend the results of the moving average process.mWOD random variables include WOD,m-NA,m-NOD and mEND random variables,so the results in the paper also promote the corresponding ones in WOD,m-NA,m-NOD,m-END random variables.

Integration of fault-tolerant feature to OMIEEPB routing protocol in wireless sensor network

Purpose-Whereas a human operator is hard to observe the networking infrastructure and its functions on a continuous basis,wireless sensor network(WSN)nodes must overcome faults and route the perceived data to the sink/base stations(BS).The main target of this research article is to ensure the fault-tolerance(FT)capability,especially for transmission of sensed data to its destinationwithout failure.Thus,through this paper,a fuzzy-based subordinate support(FSS)system is introduced as an additional feature to the existing optimized mobile sink improved energy efficient Power-Efficient Gathering in Sensor Information Systems(PEGASIS)-based(OMIEEPB)routing protocol,which lacks focus on ensuring the FT capabilities to the selected leaders of the corresponding chain.The central focus of FSS is to prevent the incident of fault,especially to the cluster heads.Design/methodology/approach-WSNs encounter several issues owing to random events or different causes such as energy exhaustion,negative influences of the deployed region,signal interference,unbalanced supply routes,instability of motes due to misalignments and collision,which ultimately intends the failure of the network.Throughout the past investigation periods,researchers gain an understanding of fault-tolerant strategies that may improve the data integrity or reliability,precision,energy efficiency,the life expectancy of the system and reduce/prevent the failure of deployed components.If that is the case,the maximum chances of data packets(sensed)needed to be transferred reliably and accurately to the sink node or BS are degraded.Findings-The FSS system utilizes the fuzzy logic concepts that have been proved to be beneficial since it permits several parameters to be combined effectively and evaluated.Here,near-point,residual energy,total operation time and past average processing time are considered as vital parameters.Moreover,the FSS system ensures the key performance activities of the network,such as optimization of response time,enhancing the data transmission reliability and accuracy.Simulation-based experiments are carried out through the Mannasim framework.After several experimental executions,the outcome of the proposed system is analyzed through elaborated comparison with the advanced existing systems.Originality/value-Finally,it has been observed that the FSS system not only enhanced the FT features to OMIEEPB but also assures the improved accuracy level(>95%)with optimized response time(<0.09 s)during data communication between leaders and the normal nodes.

Convergence of Recursive Identification for ARMAX Process with Increasing Variances

The autoregressive moving average exogenous （ARMAX） model is commonly adopted for describing linear stochastic systems driven by colored noise. The model is a finite mixture with the ARMA component and external inputs. In this paper we focus on a parameter estimate of the ARMAX model. Classical modeling methods are usually based on the assumption that the driven noise in the moving average （MA） part has bounded variances, while in the model considered here the variances of noise may increase by a power of log n. The plant parameters are identified by the recursive stochastic gradient algorithm. The diminishing excitation technique and some results of martingale difference theory are adopted in order to prove the convergence of the identification. Finally, some simulations are given to show the reliability of the theoretical results.