Since years variational methods belong to the most accurate techniques for computing the optical flow in image sequences. However, if based on the grey value constancy assumption only, such techniques are not robust enough to cope with typical illumination changes in real-world data. In our paper we tackle this problem in two ways: First we discuss different photometric invariants for the desig...

We present numerical solutions to the extended Doering–Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this principle’s spectral constraint, we derive a system of equations that is amenable to numerical treatment in the entire range from low to asymptotically high Reynol...

Latent Dirichlet Allocation (LDA) is a popular topic modeling technique for exploring document collections. Because of the increasing prevalence of large datasets, there is a need to improve the scalability of inference of LDA. In this paper, we propose a technique called MapReduce LDA (Mr. LDA) to accommodate very large corpus collections in the MapReduce framework. In contrast to other techni...

The variation procedure on a teleparallel manifold is studied. The main problem is the non-commutativity of the variation with the Hodge dual map. We establish certain useful formulas for variations and restate the master formula due to Hehl and his collaborates. Our approach is different and sometimes easier for applications. By introducing the technique of the variational matrix we find neces...

in this paper, we present a comparative study between the modified variational iteration method (mvim) and a hybrid of fourier transform and variational iteration method (ftvim). the study outlines the efficiencyand convergence of the two methods. the analysis is illustrated by investigating four singular partial differential equations with variable coefficients. the solution of singular partia...

We explore a recently proposed Variational Dropout technique that provided an elegant Bayesian interpretation to Gaussian Dropout. We extend Variational Dropout to the case when dropout rates are unbounded, propose a way to reduce the variance of the gradient estimator and report first experimental results with individual dropout rates per weight. Interestingly, it leads to extremely sparse sol...

We show that, typically, lower semicontinuous functions on a Banach space densely inherit lower subderivatives of the same degree of smoothness as the norm. In particular every continuous convex function on a space with a Gâteaux (weak Hadamard, Fréchet) smooth renorm is densely Gâteaux (weak Hadamard, Fréchet) differentiable. Our technique relies on a more powerful analogue of Ekeland's variat...

This paper deals with a new system of nonlinear variational inclusion problems involving (A, η)-maximal relaxed monotone and relative (A, η)-maximal monotone mappings in 2-uniformly smooth Banach spaces. Using the generalized resolvent operator technique, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of t...

In this paper, we apply the variational iteration method using He’s polynomials for finding the analytical solution of gas dynamic equation. The proposed method is an elegant combination of He’s variational iteration and the homotopy perturbation methods. The suggested algorithm is quite efficient and is practically well suited for use in such problems. The proposed iterative scheme finds the s...

The variational reconstruction theory from a companion paper finds a solution consistent with some linear constraints and minimizing a quadratic plausibility criterion. It is suitable for treating vector and multidimensional signals. Here, we apply the theory to a generalized sampling system consisting of a multichannel filterbank followed by a nonuniform sampling. We provide ready-made formula...