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The exact controllability research framework of complex networks points out that the controllability of the network has a great relationship with the minimum number of driver nodes. It is generally believed that the smaller the minimum number of driver nodes and the lower the cost of external control of the whole network to achieve the ideal state, the better the controllability of networks. In this paper, the minimum driver node problem of a hypernetwork is transformed into the maximum multiplicative problem of the eigenvalue of its 2-section graph. The minimum driver node numbers of two types of typical k -uniform hypertree networks are described, and their bounds are also given. By designing an algorithm, the method of characterizing the driver node set is obtained, and it is found that the selection of the minimum driver nodes of the network tends to the nodes with low hyperdegree. In addition, the paper verifies the minimum driver node set and the theoretical analysis results of controllability by simulation analysis. • Transforming the problem of a hypernetwork to the problem of its 2-section graph. • Giving the minimum driver node number of k-uniform hypertree networks and its bounds. • The driver nodes of the k-uniform linear hypertree networks tend to be the nodes with low hyperdegree. [ABSTRACT FROM AUTHOR]

• Triangular high-dimensional discrete systems. • Behavior of solutions. • Algorithms determining the initial values. • MATLAB program. Investigation of the asymptotic properties of solutions to systems of discrete equations is a topic of permanent interest. Numerous papers analyze the so-called prescribed behaviour of solutions giving sufficient conditions for the existence of at least one solution having a given asymptotic behaviour. To a smaller extent the problem is considered of determining the initial data generating such solutions. The present paper finds its niche being concerned with the case of a triangular system of linear discrete equations. The existence of solutions with a prescribed asymptotic behaviour is proved and algorithms suggested for computing stepwise the initial data defining such solutions and eventually suggesting these. Illustrative examples (supported with a MATLAB program) are considered and some open problems are formulated as well. [ABSTRACT FROM AUTHOR]

• We propose efficient algorithms for two geometric problems that arise in music information retrieval; linear scaling and data compression. • Linear scaling is used for tempo variation and melody matching, while an important application of data compression is clustering and classification. • We use geometric matching techniques to measure the similarity between two melodies. • Our algorithms take advantage of the properties of an optimal solution and are based on line sweeping and dynamic programming techniques. Melodic similarity measurement is of key importance in music information retrieval. In this paper, we use geometric matching techniques to measure the similarity between two melodies. We represent music as sets of points or sets of horizontal line segments in the Euclidean plane and propose efficient algorithms for optimization problems inspired in two operations on melodies; linear scaling and audio compression. In the scaling problem, an incoming query melody is scaled forward until the similarity measure between the query and a reference melody is minimized. The compression problem asks for a subset of notes of a given melody such that the matching cost between the selected notes and the reference melody is minimized. [ABSTRACT FROM AUTHOR]