This paper studies the problem of fault detection and isolation (FDI) for multi-agent systems (MAS) via complex Laplacian subject to actuator faults. A planar formation of point agents in the plane using simple and linear interaction rules related to complex Laplacian is achieved. The communication network is a directed, and yet connected graph with a fixed topology. The loss of symmetry in the...

We show that the Gaussian random fields and harmonic energy minimizing function framework for semi-supervised learning can be viewed in terms of Gaussian processes, with covariance matrices derived from the graph Laplacian. We derive hyperparameter learning with evidence maximization, and give an empirical study of various ways to parameterize the graph weights.

Semi-supervised regression based on the graph Laplacian suffers from the fact that the solution is biased towards a constant and the lack of extrapolating power. Based on these observations, we propose to use the second-order Hessian energy for semi-supervised regression which overcomes both these problems. If the data lies on or close to a low-dimensional submanifold in feature space, the Hess...

Decision-making (DM) is a process in which several persons concurrently engage, examine the problems, evaluate potential alternatives, and select an appropriate option to problem. Technique for determining order preference by similarity ideal solution (TOPSIS) established DM process. The objective of this report happens broaden approach TOPSIS solve issues designed with Hesitancy fuzzy data, ev...

the k-th semi total point graph of a graph g, , ‎is a graph‎ obtained from g by adding k vertices corresponding to each edge and‎ connecting them to the endpoints of edge considered‎. ‎in this paper‎, a formula for laplacian polynomial of in terms of‎ characteristic and laplacian polynomials of g is computed‎, ‎where is a connected regular graph‎.the kirchhoff index of is also computed‎.

The Laplacian spread of a graph is defined as the difference between the largest and second smallest eigenvalues of the Laplacian matrix of the graph. In this paper, bounds are obtained for the Laplacian spread of graphs. By the Laplacian spread, several upper bounds of the Nordhaus-Gaddum type of Laplacian eigenvalues are improved. Some operations on Laplacian spread are presented. Connected c...