We study the spectral properties of the Laplacian matrices and the normalized Laplacian matrices of the Erdös-Rényi random graph G(n, pn) for large n. Although the graph is simple, we discover some interesting behaviors of the two Laplacian matrices. In fact, under the dilute case, that is, pn ∈ (0, 1) and npn → ∞, we prove that the empirical distribution of the eigenvalues of the Laplacian mat...

This paper proposes a voice activity detector (VAD) based on the complex Laplacian model. With the use of a goodness-of-fit (GOF) test, it is discovered that the Laplacian model is more suitable to describe noisy speech distribution than the conventional Gaussian model. The likelihood ratio (LR) based on the Laplacian model is computed and then applied to the VAD operation. According to the exp...

Let −→ G be a digraph and A( −→ G) be the adjacency matrix of −→ G . Let D( −→ G) be the diagonal matrix with outdegrees of vertices of −→ G and Q( −→ G) = D( −→ G) + A( −→ G) be the signless Laplacian matrix of −→ G . The spectral radius of Q( −→ G) is called the signless Laplacian spectral radius of −→ G . In this paper, we determine the unique digraph which attains the maximum (or minimum) s...

In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that (i) the law of large numbers for the spectral norms and the largest eigenvalues of the adjacency and the Laplacian matrices; (ii) under some further independent conditions, the normalized largest eigenvalues of the Laplacian matrices are dense in a compact interval a...

This paper studies a generalization of the standard continuous-time consensus protocol, obtained by replacing the Laplacian matrix of the communication graph with the so-called deformed Laplacian. The deformed Laplacian is a second-degree matrix polynomial in the real variable s which reduces to the standard Laplacian for s equal to unity. The stability properties of the ensuing deformed consen...

Reaction of [PtMe(C^N)(SMe2)] (C^N = 2-phenylpyridinate (ppy); 1a, C^N = benzo[h]quinolate, (bhq); 1b) with hydrogen peroxide gives the platinum(IV) complexes trans-[PtMe(OH)2(C^N)(H2O)] (C^N = ppy; 3a, C^N = bhq, 3b) bearing platinum-oxygen bonds. The Pt(II) complexes 1a and 1b have 5dπ(Pt)→π*(C^N) MLCT band in the visible region which is used to easily follow the kinetic of its reaction with ...

Background. Mechanical relation between the foot and pelvic alignment had been studied in healthy subjects and individuals with other musculoskeletal disorders; however, in chronic ankle instability (CAI), it has not yet been determined. Objectives. To investigate the difference in pelvic torsion (PT) among individuals with CAI and uninjured subjects and correlate PT with perceived ankle insta...

A noncommutative extension of the Lévy Laplacian, called the quantum Lévy Laplacian, is introduced and its relevant properties are studied, in particular, a relation between the classical and quantum Lévy Laplacians is studied. We construct a semigroup and a quantum stochastic process generated by the quantum Lévy Laplacian.

Abstract. A signed graph Γ = (G, σ) consists of an unsigned graph G = (V, E) and a mapping σ : E → {+,−}. Let Γ be a connected signed graph and L(Γ),L(Γ) be its Laplacian matrix and normalized Laplacian matrix, respectively. Suppose μ1 ≥ · · · ≥ μn−1 ≥ μn ≥ 0 and λ1 ≥ · · · ≥ λn−1 ≥ λn ≥ 0 are the Laplacian eigenvalues and the normalized Laplacian eigenvalues of Γ, respectively. In this paper, ...

This paper proposes a voice activity detector (VAD) based on the complex Laplacian model. With the use of a goodness-of-fit (GOF) test, it is discovered that the Laplacian model is more suitable to describe noisy speech distribution than the conventional Gaussian model. The likelihood ratio (LR) based on the Laplacian model is computed and then applied to the VAD operation. According to the exp...