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With the scale expansion and structural upgrading of pipeline network, the detection methods based on both ends of the pipeline pressure have appeared the limitations of judging pipeline status in the multi-mode and complex network system. To overcome the limitation of early methods, a pipeline network status detection method based on data transformation convolutional neural network (DT-CNN) is proposed in this paper. Firstly, the difference among the eigenvalue distribution of data covariance matrices is calculated to detect the pipeline status by Kullback-Leibler divergence (KLD). If the eigenvalue distribution deviates from the normal status, the KLD will exceed the given threshold. Furthermore, an improved CNN model is proposed to judge pipeline status by converting the largest eigenvectors of data covariance matrices to extract features. The effectiveness of the proposed detection method is demonstrated through the simulation results of a practical pipeline network. [ABSTRACT FROM AUTHOR]

The V-law under generalized Lindeberg condition for the independent blocks of random matrices having double stochastic matrix of covariances and different expectations of their array is proven. [ABSTRACT FROM AUTHOR]

The lower bounds for the minimal singular eigenvalue of the matrix whose entries have zero means and bounded variances are obtained. The new method is based on the G-method of perpendiculars and the RESPECT method. [ABSTRACT FROM AUTHOR]

V-density under Lindeberg condition for the independent blocks of random matrices having different variances and expectations is found. [ABSTRACT FROM AUTHOR]

Let Γn be an n × n Haar-invariant orthogonal matrix. Let Zn be the p × q upper-left submatrix of Γn, where p = pn and q = qn are two positive integers. Let Gn be a p × q matrix whose pq entries are independent standard normals. In this paper we consider the distance between √ nZn and Gn in terms of the total variation distance, the Kullback-Leibler distance, the Hellinger distance, and the Euclidean distance. We prove that each of the first three distances goes to zero as long as pq/n goes to zero, and not so if (p, q) sits on the curve pq = σn, where σ is a constant. However, it is different for the Euclidean distance, which goes to zero provided pq²/n goes to zero, and not so if (p, q) sits on the curve pq² = σn. A previous work by Jiang (2006) shows that the total variation distance goes to zero if both p/ √ n and q/ √ n go to zero, and it is not true provided p = c √ n and q = d √ n with c and d being constants. One of the above results confirms a conjecture that the total variation distance goes to zero as long as pq/n → 0 and the distance does not go to zero if pq = σn for some constant σ. [ABSTRACT FROM AUTHOR]

In this paper, we propose a scheme to implement hybrid encryption of images using generalized Arnold transformation and matrix nonlinear operations. This scheme consists of two stages. In the first stage, the pixels scrambling encryption is achieved by using generalized Arnold transformation. In the second stage, the pixels sequence encryption is carried out by a nonlinear matrix operation based on the key stream generated by a random matrix. Accordingly, the decryption process is completed by two steps inverse transformations. The hybrid encryption algorithm is one-time pad, and therefore has good anti-attack performance. The algorithm is featured by good confidentiality, low computational complexity, and easy-to-program processing. Moreover, the effectiveness, security and robustness of the algorithm are demonstrated by an image encryption simulation and the encryption performance analysis. Compared with the traditional Arnold scrambling encryption scheme and the chaotic encryption method based on the generalized standard mapping, the superiority of the proposed algorithm is demonstrated. [ABSTRACT FROM AUTHOR]

We study the asymptotic behavior of the smallest eigenvalue, λN, of the Hankel (or moments) matrix denoted by HN=μm+n0≤m,n≤N, with respect to the weight w(x)=xαe−xβ,x∈[0,∞),α>−1,β>12. An asymptotic expression of the polynomials orthogonal with w(x) is established. Using this, we obtain the specific asymptotic formulas of λN in this paper. Applying a parallel numerical algorithm, we get a variety of numerical results of λN corresponding to our theoretical calculations. [ABSTRACT FROM AUTHOR]

We discuss the limiting spectral density of real symmetric random matrices. In contrast to standard random matrix theory, the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic process. Under assumptions on this process which are satisfied, e.g., by stationary Markov chains on finite sets, by stationary Gibbs measures on finite state spaces, or by Gaussian Markov processes, we show that the limiting spectral distribution depends on the way the matrix is filled with the stochastic process. If the filling is in a certain way compatible with the symmetry condition on the matrix, the limiting law of the empirical eigenvalue distribution is the well-known semi-circle law. For other fillings we show that the semi-circle law cannot be the limiting spectral density. [ABSTRACT FROM AUTHOR]

We prove a central limit theorem for the mesoscopic linear statistics of N × N Wigner matrices H satisfying E | H ij | 2 = 1 / N and E H ij 2 = σ / N , where σ ∈ [ - 1 , 1 ] . We show that on all mesoscopic scales η ( 1 / N ≪ η ≪ 1 ), the linear statistics of H have a sharp transition at 1 - σ ∼ η . As an application, we identify the mesoscopic linear statistics of Dyson's Brownian motion H t started from a real symmetric Wigner matrix H 0 at any nonnegative time t ∈ [ 0 , ∞ ] . In particular, we obtain the transition from the central limit theorem for GOE to the one for GUE at time t ∼ η . [ABSTRACT FROM AUTHOR]

We introduce the concept of matrix liberation process, a random matrix counterpart of the liberation process in free probability, and prove a large deviation upper bound for its empirical distribution and several properties on its rate function. As a simple consequence, we obtain the almost sure convergence of the empirical distribution of the matrix liberation process to that of the corresponding liberation process as continuous processes in the large N limit. [ABSTRACT FROM AUTHOR]

Estimating eigenvectors and low-dimensional subspaces is of central importance for numerous problems in statistics, computer science and applied mathematics. In this paper we characterize the behaviour of perturbed eigenvectors for a range of signal-plus-noise matrix models encountered in statistical and random-matrix-theoretic settings. We establish both first-order approximation results, i.e. sharp deviations, and second-order distributional limit theory, i.e. fluctuations. The concise methodology presented in this paper synthesizes tools rooted in two core concepts, namely deterministic decompositions of matrix perturbations and probabilistic matrix concentration phenomena. We illustrate our theoretical results with simulation examples involving stochastic block model random graphs. [ABSTRACT FROM AUTHOR]

We study the question of extracting a sequence of functions |$\{\boldsymbol{f}_{\!i}, \boldsymbol{g}_{i}\}_{i=1}^{s}$| from observing only the sum of their convolutions, i.e. from |$\boldsymbol{y} = \sum _{i=1}^{s} \boldsymbol{f}_{\!i}\ast \boldsymbol{g}_{i}$|⁠. While convex optimization techniques are able to solve this joint blind deconvolution–demixing problem provably and robustly under certain conditions, for medium-size or large-size problems we need computationally faster methods without sacrificing the benefits of mathematical rigor that come with convex methods. In this paper we present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. Our two-step algorithm converges to the global minimum linearly and is also robust in the presence of additive noise. While the derived performance bounds are suboptimal in terms of the information-theoretic limit, numerical simulations show remarkable performance even if the number of measurements is close to the number of degrees of freedom. We discuss an application of the proposed framework in wireless communications in connection with the Internet-of-Things. [ABSTRACT FROM AUTHOR]

The limit G-Law for the solutions of the systems of linear algebraic equations with independent random coefficients is proven under the G-Lindeberg condition. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to establish a noncommutative analogue of the Efron-Stein inequality, which bounds the variance of a general function of some independent random variables. Moreover, we state an operator version including random matrices, which extends a result of D. Paulin et al., [Ann. Probab.44(5) (2016), 3431–3473]. Further, we state a Steele type inequality in the framework of noncommutative probability spaces. [ABSTRACT FROM AUTHOR]

In this paper we consider N×N real generalized Wigner matrices whose entries are only assumed to have finite (2+ε)th moment for some fixed, but arbitrarily small, ε>0. We show that the Stieltjes transforms mN(z) of these matrices satisfy a weak local semicircle law on the nearly smallest possible scale, when η=I(z) is almost of order N-1. As a consequence, we establish bulk universality for local spectral statistics of these matrices at fixed energy levels, both in terms of eigenvalue gap distributions and correlation functions, meaning that these statistics converge to those of the Gaussian orthogonal ensemble in the large N limit. [ABSTRACT FROM AUTHOR]

We study an "inner-product kernel" random matrix model, whose empirical spectral distribution was shown by Xiuyuan Cheng and Amit Singer to converge to a deterministic measure in the large n and p limit. We provide an interpretation of this limit measure as the additive free convolution of a semicircle law and a Marchenko-Pastur law. By comparing the tracial moments of this matrix to an additive deformation of a Wigner matrix, we establish that for odd kernel functions, the spectral norm of this matrix converges almost surely to the edge of the limiting spectrum. Our study is motivated by the analysis of a covariance thresholding procedure for the statistical detection and estimation of sparse principal components, and our results characterize the limit of the largest eigenvalue of the thresholded sample covariance matrix in the null setting. [ABSTRACT FROM AUTHOR]

We derive new expressions for the densities of extreme eigenvalues of a Beta–MANOVA matrix, which generalize the classical result of Khatri for the real case. We also present new expressions for the distributions of those eigenvalues which are valid for any values of the parameters. [ABSTRACT FROM AUTHOR]

• Conventional relay protection schemes cannot be applied to HWL line directly. • Random matrix theory could be construct a robust directional element for the HWL line. • Real time digital simulation has verified the correctness of the scheme. The fault characteristics of ultra-high voltage (UHV) half-wavelength (HWL) transmission lines exhibit significant differences from those of conventional transmission lines, which renders the conventional relay protection method unsuitable for ensuring the protection of HWL. To solve this problem, a pilot protection method of HWTL based on random matrix theory was proposed. Voltage and current fault components obtained at the protection installation on both sides of the line were used as the input of the random matrix to form the singular value equivalent matrix, and the eigenvalues of the random matrix at both ends were calculated. The faults inside and outside the area were determined according to the distribution of the eigenvalues in the circular plane area. The protection scheme avoids the data synchronization problem at both ends of the line. Real time digital simulation system (RTDS) simulation revealed that the proposed protection method can protect the full length of the line, is suitable for various fault types and fault conditions, and exhibits excellent resistance to transition resistance. [ABSTRACT FROM AUTHOR]