Geometric monotone properties of the first nonzero eigenvalue of Laplacian form operator under the action of the Ricci flow in a compact nmanifold ( ) 2 ≥ n are studied. We introduce certain energy functional which proves to be monotonically non-decreasing, as an application, we show that all steady breathers are gradient steady solitons, which are Ricci flat metric. The results are also extend...

Large, sparse, Hermitian eigenvalue problems are still some of the most computationally challenging tasks. Despite the need for a robust, nearly optimal preconditioned iterative method that can operate under severe memory limitations, no such method has surfaced as a clear winner. In this research we approach the eigenproblem from the nonlinear perspective that helps us develop two nearly optim...

In this paper we develop a novel randomized block-coordinate descent method for minimizing multi-agent convex optimization problems with singly linear coupled constraints over networks and prove that it obtains in expectation an ε accurate solution in at most O( 1 λ2(Q)ε ) iterations, where λ2(Q) is the second smallest eigenvalue of a matrix Q that is defined in terms of the probabilities and t...

The `1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing `1-regularized covariance matrix estimation is presented. Although numerous algorithms have be...

The `1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing `1-regularized covariance matrix estimation is presented. Although numerous algorithms have be...

Large, sparse, Hermitian eigenvalue problems are still some of the most computationally challenging tasks. Despite the need for a robust, nearly optimal preconditioned iterative method that can operate under severe memory limitations, no such method has surfaced as a clear winner. In this research we approach the eigenproblem from the nonlinear perspective that helps us develop two nearly optim...

Minimum mode following algorithms are widely used for saddle point searching in chemical and material systems. Common to these algorithms is a component to find the minimum curvature mode of the second derivative, or Hessian matrix. Several methods, including Lanczos, dimer, Rayleigh-Ritz minimization, shifted power iteration, and locally optimal block preconditioned conjugate gradient, have be...

Recently, it has been found that the synchronizability of a scale-free network can be enhanced by introducing some proper gradient in the coupling. This result has been obtained by using eigenvalue-spectrum analysis under the assumption of identical node dynamics. Here we obtain an analytic formula for the onset of synchronization by incorporating the Kuramoto model on gradient scale-free netwo...

This paper demonstrates the potential of a two-dimensional (2D) gradient mapping technique that utilized the eigenvalue manipulating transformation (EMT) of the spectral data set. The EMT technique, by lowering the power of a set of eigenvalues associated with the original data, enhances the contributions of minor principle components (PCs). The operation converts the original spectral data set...

the study describes the synthesis and characterization of zinc(ii) minoxidil nanocomposite (1). the reaction between zinc(ii) acetate, minoxidil, {c9h15n5o=minoxidil=(2,4-diamino-6-piperidine-1-yl) pyrimidine n-oxide)} as a ligand and ki as bridging agent, in methanol at 60°c leads to the formation of nano-sized zn(ii) minoxidil nanocomposite, 1. characterization of (1) was carried out by eleme...