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...

In this paper an estimator for speech enhancement based on Laplacian Mixture Model has been proposed. The proposed method, estimates the complex DFT coefficients of clean speech from noisy speech using the MMSE  estimator, when the clean speech DFT coefficients are supposed mixture of Laplacians and the DFT coefficients of  noise are assumed zero-mean Gaussian distribution. Furthermore, the MMS...

In this thesis we discuss some new results concerning the combinatorial Laplace operator of a simplicial complex. The combinatorial Laplacian of a simplicial complex encodes information about the relationships between adjacent simplices in the complex. This thesis is divided into two relatively disjoint parts. In the first portion of the thesis, we derive a relationship between the Laplacian sp...

In this paper, we prove two new Weyl-type upper estimates for the eigenvalues of the Dirichlet Laplacian. As a consequence, we obtain the following lower bounds for its counting function. For λ ≥ λ1, one has N(λ) > 2 n+ 2 1 Hn (λ− λ1) n/2 λ −n/2 1 , and N(λ) > „ n+ 2 n+ 4 «n/2 1 Hn (λ− (1 + 4/n) λ1) n/2 λ −n/2 1 , where Hn = 2 n j2 n/2−1,1 J2 n/2 (jn/2−1,1) is a constant which depends on n, the...

EXTENDED ABSTRACT. In recent years, networked multi-agent systems have attracted much research attention from various disciplines of engineering and science due to their interdisciplinary nature and broad potential applications. Collective behaviors arise from simple local interaction rules in complex networked systems. Graph Laplacian plays a very important role in analysis of networked multi-...

for a simple connected graph $g$ with $n$-vertices having laplacian eigenvalues‎ ‎$mu_1$‎, ‎$mu_2$‎, ‎$dots$‎, ‎$mu_{n-1}$‎, ‎$mu_n=0$‎, ‎and signless laplacian eigenvalues $q_1‎, ‎q_2,dots‎, ‎q_n$‎, ‎the laplacian-energy-like invariant($lel$) and the incidence energy ($ie$) of a graph $g$ are respectively defined as $lel(g)=sum_{i=1}^{n-1}sqrt{mu_i}$ and $ie(g)=sum_{i=1}^{n}sqrt{q_i}$‎. ‎in th...

In this letter, we propose a new approach to speech enhancement based on a complex Laplacian probability density function (pdf). With a use of a goodness-of-fit (GOF) test, we discover that the complex Laplacian pdf is more desirable to describe noisy speech distribution than the conventional Gaussian pdf for speech enhancement. The likelihood ratio (LR) is computed and then applied to computat...

We study the spectral zeta functions of the Laplacian on self-similar fractals. These functions are known to meromorphically extend to the entire complex plane, and the locations of their poles, sometimes referred to as complex dimensions, are of special interest. We give examples of self-similar sets such that their complex dimensions are not on the imaginary axis, which allows us to interpret...