The VL control measure for symmetric networks

In this paper we measure “control” of nodes in a network by solving an associated optimisation problem. We motivate this so-called VL control measure by giving an interpretation in terms of allocating resources optimally to the nodes in order to maximise some search probability. We determine the VL control measure for various classes of networks. Furthermore, we provide two game theoretic interpretations of this measure. First it turns out that the VL control measure is a particular proper Shapley value of the associated cooperative network game. Secondly, we relate the measure to optimal strategies in an associated matrix search game.     

一类两端奇异带有转移条件的S-L问题的Weyl矩阵与谱矩阵

研究了一类带有转移条件二阶S-L问题两端奇异的情形,在定义的新的内积空间下进行,首先在有限区间I上进行讨论,然后将有限区间I的结论进一步推广到无限区间,最终给出了Weyl矩阵与谱矩阵的关系.     

Maximum likelihood estimation using the empirical fisher information matrix

In this paper the use of the empirical Fisher information matrix as an estimator of the information matrix is considered in the context of response models and incomplete data problems. The introduction of an additional stochastic component into such models is shown to greatly increase the range of situations in which the estimator can be employed. In particular the conditions for its use in incomplete data problems are shown to be the same as those needed to justify the use of the EM algorithm.     

An alternative approach to reliability analysis of cold standby systems

ABSTRACT

An alternative approach is applied for reliability analysis of standby systems on the basis of matrix renewal function. In this regard, a single-server, two identical unit cold standby systems with an imperfect switch is considered as a three-state semi-Markov process. Several important reliability measures such as availability, mean time to failure, expected number of failures, etc., are obtained for general lifetime distributions. Also, the main results have been treated to the case of exponential lifetimes and explicit formulas obtained for this case in addition of some numerical illustrations. This approach can easily be extended to more general standby systems with different configurations.     

Some remarks on a ridge-type-estimator and good prior means

Pliskin (1987) compared modified ridge regression estimators based on prior information with respect to their mean square error matrices. A further characterization of good prior mean is given here, and the case of different ridge parameters is also considered.     

Characterizing Relationships Between Estimations Under a General Linear Model with Explicit and Implicit Restrictions by Rank of Matrix

In the investigation of the restricted linear model ? _r  = {y, X β | A β = b, σ² Σ}, the parameter constraints A β = b are often handled by transforming the model into certain implicitly restricted model. Any estimation derived from the explicitly and implicitly restricted models on the vector β and its functions should be equivalent, although the expressions of the estimation under the two models may be different. However, people more likely want to directly compare different expressions of estimations and yield a conclusion on their equivalence by using some algebraic operations on expressions of estimations. In this article, we give some results on equivalence of the well-known OLSEs and BLUEs under the explicitly and implicitly restricted linear models by using some expansion formulas for ranks of matrices.     

Fluid Flow Models and Queues—A Connection by Stochastic Coupling

We establish in a direct manner that the steady state distribution of Markovian fluid flow models can be obtained from a quasi birth and death queue. This is accomplished through the construction of the processes on a common probability space and the demonstration of a distributional coupling relation between them. The results here provide an interpretation for the quasi-birth-and-death processes in the matrix-geometric approach of Ramaswami and subsequent results based on them obtained by Soares and Latouche.     

Order-preserving Estimators and an Inequality on the Integration of Zonal Polynomial

ABSTRACT

Suppose X , p × p p.d. random matrix, has the distribution which depends on a p × p p.d. parameter matrix Σ and this distribution is orthogonally invariant. The orthogonally invariant estimator of Σ which has the eigenvalues of the same order as the eigenvalues of X is called order-preserving. We conjecture that a non-order-preserving estimator is dominated by modified order-preserving estimators with respect to the entropy (Stein's) loss function. We show that an inequality on the integration of zonal polynomial is sufficient for this conjecture. We also prove this inequality for the case p = 2.     

Dispersion-diminishing transformations

Let D(σ) consist of matrices congruent to and dominated by a given matrix σ , and let T(σ) be the corresponding congruent transformations. These classes are characterized and their properties studied when σ is positive definite. Dispersion orderings are considered, including dispersion-diminishing linear transformations, concentration properties of which are shown. Arbitrary linear transformations are decomposed into contractions, isometries and dilations on subspaces relative to Mahalanobis norms. Applications are noted in statistical process control and linear inference     

Recombinative Generalization of Tacts Through Matrix Training with Individuals with Autism Spectrum Disorder

Foss (Journal of Experimental Psychology, 76, 450–459, 1968a; Journal of Experimental Psychology, 77, 341–344, 1968b) compared overlap and non-overlap instruction to promote recombinative response generalization using a matrix training procedure. In the present study, we used a similar set of procedures to teach tacting of kitchen items and prepositions (i.e., relational autoclitics) to three females ages 13–20, diagnosed with autism spectrum disorder. We taught some kitchen items/prepositions as tacts (e.g., “the strainer is to the right of the box”) according to a non-overlap instructional sequence. Subsequently, we taught more combinations in an overlap instructional sequence. Each training procedure was followed by probes of untrained relations. Two participants demonstrated recombinative generalization of untrained combinations following the first non-overlap phase, while the third participant demonstrated some response generalization of untrained relations after a few additional training sequences. All three participants demonstrated generalized tacting of object components while two participants showed generalized tacting of preposition components.