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In this paper, we consider the reconstruction of matrices whose graph is a star with root at the central vertex from given partial eigen data. Three inverse spectral problems are discussed. The necessary and sufficient conditions for the solvability of the problems are studied. Furthermore, the corresponding numerical algorithms are presented. Some numerical examples are also provided to demonstrate the applicability of the results obtained here.

In spectral graph theory, the Laplacian energy of undirected graphs has been studied extensively. However, there has been little work yet for digraphs. Recently, Perera and Mizoguchi (2010) introduced the directed Laplacian matrix$L=D-A$ and directed Laplacian energy$LE\left(G\right)=\sum _{i=1}^n{\lambda }_i^2$ using the second spectral moment of $L$ for a digraph $G$ with $n$ vertices, where $D$ is the diagonal out-degree matrix, and $A=\left(a_{ij}\right)$ with $a_{ij}=1$ whenever there is an arc $(i,j)$ from the vertex $i$ to the vertex $j$ and 0 otherwise. They studied the directed Laplacian energies of two special families of digraphs (simple digraphs and symmetric digraphs). In this paper, we extend the study of Laplacian energy for digraphs which allow both simple and symmetric arcs. We present lower and upper bounds for the Laplacian energy for such digraphs and also characterize the extremal graphs that attain the lower and upper bounds. We also present a polynomial algorithm to find an optimal orientation of a simple undirected graph such that the resulting oriented graph has the minimum Laplacian energy among all orientations. This solves an open problem proposed by Perera and Mizoguchi at 2010.

To enhance the efficiency of malicious intrusion detection of network communication, a malicious intrusion detection model for the network communication in cloud data center is designed. Firstly, the data preprocessing includes three parts: normal sample data modeling, standard data membership calculation and standard data membership calculation. Then, the characteristic value collection stage is completed. Finally, the intrusion detection classification and trust value calculation are completed to conclude the malicious intrusion detection of the network communication in cloud data center. Exploratory findings show that the malicious intrusion detection model for the network communication in cloud data center improves the intrusion detection rate, and reduces the detection time and false alarm rate.

Our objective is to describe the speech production system from a non-linear physiological system perspective and reconstruct the attractor from the experimental speech data. Mutual information method is utilized to find out the time delay for embedding. The False Nearest Neighbour (FNN) method and Principal Component Analysis (PCA) method are used for optimizing the embedding dimension of time series. The time series obtained from the typical non-linear systems, Lorenz system and Rössler system, is used to standardize the methods and the Malayalam speech vowel time series of both genders of different age groups, sampled at three sampling frequencies (16kHz, 32kHz, 44.1kHz), are taken for analysis. It was observed that time delay varies from sample to sample and, it ought to be better to figure out the time delay with the embedding dimension analysis. The embedding dimension is shown to be independent of gender, age and sampling frequency and can be projected as five. Hence a five-dimensional hyperspace will probably be adequate for reconstructing attractor of speech time series.