In this paper, we specify the performance of our pioneering billiard robot in pulling game training. We discuss the important role of practical demonstration in sports education, and introduce the robot technology to teaching demonstration of sports item. And put forward our algorithm for the fast image calculation of the ball obstructed by other balls, the problem that must be resolved while t...

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish a lower bound on the minimax risk of estimators under the l2 loss, in the joint limit as dimension and sample size increase to infinity, under various models of sparsity for the population eigenvectors. The lower bound on the ris...

We state below two results that we use frequently in our proofs. The first is well-known consequence of the CS decomposition. It relates the canonical angles between subspaces to the singular values of products and differences of their corresponding projection matrices.

The assessment of a cluster’s significance given the null (configuration) model relies on the estimation of the probability described in Eq. 1 of the main text. This function has to be evaluated many times along the execution of OSLOM in order to clean up each cluster and to evaluate the clusters at the different hierarchical levels. We explain here how the values of the distribution function c...

this paper presents a deterministic approach for performance assessment of different province’s road safety level at iran. a data envelopment analysis (dea) model considering undesirable input and output indices and a multivariate statistical method, principle component analysis (pca) are used in this paper, while previous studies do not use composite pca-dea method and undesirable input and ou...

Erratum: Equation (22) contains an error. It should read 100 ɛ(t, 0 °C) = 8.79 × 10 −4 t + 0.805 × 10 −7 t 2. (22) Also, the data presented in Table 12 under the column Day and Sosman Eq. (22) should be evaluated by using the corrected Eq. (22) above.

00 00 u(t-T/2) u (t + T/2) exp(-jwt) dt was introduced by Ville (1), and its significance with respect to the quality of radar measurements was suggested by Woodward (2), and enlarged upon by Siebert (3). For some time we have been studying the mathematical properties of this function-with the hope of ultimately devising the necessary and sufficient conditions that a function of two variables b...

In this paper we initiate the study of whether or not sparse estimation tasks can be performed efficiently in high dimensions, in the robust setting where an ε-fraction of samples are corrupted adversarially. We study the natural robust version of two classical sparse estimation problems, namely, sparse mean estimation and sparse PCA in the spiked covariance model. For both of these problems, w...