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This paper proposes a method for the stabilization of vehicle formations in the plane under a fixed, but not necessarily complete, sensing graph. In this method each agent acts to minimize a local alignment error function that measures the difference between the desired relative formation of the agent and its neighbors (as determined by a sensing graph) and their current positions. It is shown that...
The goal of Information Extraction is to automatically generate structured pieces of information from the relevant information contained in text documents. Machine Learning techniques have been applied to reduce the cost of Information Extraction system adaptation. However, elements of human supervision strongly bias the learning process. Unsupervised learning approaches can avoid these biases. In...
Following the procedure used by Kamke, on the basis of the concepts of symmetry and orbital symmetry introduced by S. Lie, aim of this paper is to extend such a reasoning to classify systems for which the semi-invariants can be computed in closed-form, whence possibly used for the computation of Lyapunov functions as well. The concept of semi-invariant extends both the concept of first integral (a...
We consider control systems of the type x?? = Ax+??(t)ub, where u ?? R, (A; b) is a controllable pair and ?? is an unknown time-varying signal with values in [0; 1] satisfying a permanent excitation condition of the kind ??t+Tt ?? ?? ??for 0 < ?? ?? T independent on t. We prove that such a system is stabilizable with a linear feedback depending only on the pair (T; ??) if the real part of the...
A Smith Predictor-like design for compensation of arbitrarily long input delays is available for general, controllable, possibly unstable LTI finite-dimensional systems. Such a design has not been proposed previously for problems where the plant is a PDE. We present a design and stability analysis for a prototype problem, where the plant is a reaction-diffusion (parabolic) PDE, with boundary control...
In this note, the novel representation is proposed for a linear periodic continuous-time system with T-periodic real-valued coefficients. We prove that a T-periodic real-valued factor and two real-valued matrix exponential functions can be extracted from a state transition matrix, while, in the well-known Floquet representation theorem, a 2T-periodic real-valued factor and a real-valued matrix exponential...
We obtain an explicit formula for the absolute difference between two eigenvector components for a weighted graph's Laplacian matrix, in terms of the the Laplacian's eigenvalues as well as the eigenvalues of matrices associated with certain coalesced graphs. We then briefly illustrate two uses of this formula, in analyzing graph modifications.
The so-called PageRank algorithm has been used at Google for properly ranking search results. It quantifies the importance of each page by the structure of links in the web. In our recent work, we have proposed a distributed randomized approach for the PageRank computation, where the pages find their own values by communicating with linked pages. This paper builds upon this approach to improve the...
It is well known that the circulant matrices are very important and special matrix. In recent years, various type of circulant matrices have been applied in such as signal dealing and oil exploration, and so on. In this paper, motivated by [Shen Guangxing (2004)], we give a fast algorithm for evaluating the m-th power of level-k(r1, r2, ??????, rk)-circulant matrices of type (n1, n2, ??????, nk)....
Eigendecomposition has been used to classify three-dimensional objects from two-dimensional images in a variety of computer vision and robotics applications. The biggest on-line computational expense associated with using eigendecomposition is the determination of the closest point on an image manifold embedded in a high-dimensional space. The dimensionality and complexity of the space is a result...
Ensuring the passivity of macromodels obtained from tabulated data has become a critical issue for accurate signal integrity analysis. For delayed rational function based macromodels derived in the admittance domain, the issue of passivity has recently been addressed. In this paper, passivity verification and compensation algorithms for delayed rational function based macromodels derived in the scattering...
Many everyday human skills can be framed in terms of performing some task subject to constraints imposed by the environment. Constraints are usually unobservable and frequently change between contexts. In this paper, we present a novel approach for learning (unconstrained) control policies from movement data, where observations are recorded under different constraint settings. Our approach seamlessly...
We observe that the termination of linear programs relies only on the initial value of program variables and the iteration count. Based on such observation, we present a constructive approach to determine the termination of linear programs. Through our approach, we can also synthesis the termination condition of linear programs if they do not terminate on all inputs, and correct termination defect.
A nonlinear integral equation generalizing that arisen in the antenna synthesis problems is investigated. The semi-analytical solutions are found. They parameters are determined from an equation system consisting of a linearized integral equation and finite-dimensional system of transcendental ones. Branching of the solution is investigated. A particular case related to Fourier transform is numerically...
Unsupervised spectral clustering methods can yield good performance when identifying crisp clusters with low complexity since the learning algorithm does not rely on finding the local minima of an objective function and rather use spectral properties of the graph. Nonetheless, the performance of such approaches are usually affected by their uncertain parameters. Using the underlying structure of a...
Multifractal is employed to analyze standard atlas of the distribution of degree 1~8 eutectic carbides in alloy. We do a research on relationship between partition function & forming element, and multifractal spectrum & singularity. Graph of partition function & forming element presents a favorable linear in the condition of weighting factor q>0 or q<0, which proves that the distribution...
Company usually outsource logistics business to the third party logistics company and it can improve core competition of company. So it is of vital importance to evaluate logistics performance of logistics company. Principal component analysis method is an effective method. In this paper, we take logistics company A as studying object. We construct evaluation index and mathematic model. By quantifying...
This paper considers a new approach to user-item clustering for collaborative filtering problems that achieves personalized recommendation. When user-item relations are given by an alternative process, personalized recommendation is performed by finding user-item neighborhoods (co-clusters) from a rectangular relational data matrix, in which users and items have mutually positive relations. In the...
The problem of fuzzy pattern recognition based on eigenvector is often met with in computer measurement and control system. Both the object to be identified and the standard pattern stored in the database have a certain degree of uncertainty because errors are inevitable in the process of eigenvector extraction. The problem of fuzzy pattern recognition can be turned into the problem of calculating...
The core theory of this article is solving the problem of marking examination papers using Fuzzy similarity selection of Fuzzy mathematical theory. The method considers not only the scores given by every teacher but also every teacher's weigh value. We can give a reasonable and fair method of marking examination papers using this method.
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