firstly, in this paper, we apply the fuzzy restricted variation method to achieve an analytical and approximate unsymmetrical fuzzy solution for fully fuzzy quadratic equation. in this application, after finding the real root of 1-cut of $tilde{a}tilde{x}^{2}+tilde{b}tilde{x}+tilde{c}=tilde{d}$, initial guess is always chosen with possible unknown parameters that leads to highly accurate soluti...

We deliver a novel approach towards the variational description of Lagrangian mechanical systems subject to fractional damping by establishing restricted Hamilton’s principle. Fractional is particular instance non-local (in time) damping, which ubiquitous in engineering applications. The principle relies on including derivatives state space, doubling curves (which implies an extra mirror system...

We propose a number of new algorithms for learning deep energy models from data motivated by a recent Stein variational gradient descent (SVGD) algorithm, including a Stein contrastive divergence (SteinCD) that integrates CD with SVGD based on their theoretical connections, and a SteinGAN that trains an auxiliary generator to generate the negative samples in maximum likelihood estimation (MLE)....

We study online versions ofMinimum Dominating Set Min imum Connected Dominating Set andMinimum Independent Dom inating Set where we restrict the input graphs to belong to a certain graph class after each insertion step We show that straight forward and easy to implement online strategies achieve optimum or nearly optimum competitive ratios for trees unit disk graphs and bounded degree graphs fo...

A pretraining algorithm, which is a layer-bylayer greedy learning algorithm, for a deep Boltzmann machine (DBM) is presented in this paper. By considering the deep belief net type of pretraining for the DBM, which is a simplified version of the original pretraining of the DBM, two interesting theoretical facts about pretraining can be obtained. (1) By applying two different types of approximati...

We propose a novel adaptive importance sampling algorithm which incorporates Stein variational gradient decent algorithm (SVGD) with importance sampling (IS). Our algorithm leverages the nonparametric transforms in SVGD to iteratively decrease the KL divergence between importance proposals and target distributions. The advantages of our algorithm are twofold: 1) it turns SVGD into a standard IS...