Blind separation of signals through the info-max algorithm may be viewed as maximum likelihood learning in a latent variable model. In this paper we present an alternative approach to maximum likelihood learning in these models, namely Bayesian inference. It has already been shown how Bayesian inference can be applied to determine latent dimensionality in principal component analysis models (Bi...

Snakelike robots have been employed in applications ranging from search-and-rescue to minimally invasive surgical procedures, and may yet find new applications in maintaining civil infrastructure and the repair of satellites. This paper reviews how variational methods have been used previously to analyze three classes of snakelike robots: (1) hyper-redundant manipulators guided by backbone curv...

We propose simple transformation of the hidden states in variational Bayesian factor analysis models to speed up the learning procedure. The speed-up is achieved by using proper parameterization of the posterior approximation which allows joint optimization of its individual factors, thus the transformation is theoretically justified. We derive the transformation formulae for variational Bayesi...

Recent advances in variational and optimization methods applied to increasingly complex numerical weather prediction models with larger numbers of degrees of freedom mandate to take a perspective view of past and recent developments in this field, and present a view of the state of art in the field. Variational methods attempt to achieve a best fit between data and model subject to some ‘a prio...

This paper develops some mathematical models arising in psychology and some other areas of behavioral sciences that are formalized via general preferences with variable ordering structures. Our considerations are based on the recent “variational rationality approach” that unifies numerous theories in different branches of behavioral sciences by using, in particular, worthwhile change and stay d...

The concept of a shape space is linked both to concepts from geometry and from physics. On one hand, a path-based viscous flow approach leads to Riemannian distances between shapes, where shapes are boundaries of objects that mainly behave like fluids. On the other hand, a state-based elasticity approach induces a (by construction) non-Riemanniandissimilaritymeasure between shapes, which is giv...

in this article, an analytical approximate solution of nonlinear fractional convection-diffusion with modifiedriemann-liouville derivative was obtained with the help of fractional variational iteration method (fvim). a newapplication of fractional variational iteration method (fvim) was extended to derive analytical solutions in theform of a series for this equation. it is indicated that the so...

In this paper we study mathematical programs with equilibrium constraints (MPECs) described by generalized equations in the extended form 0 ∈ G(x, y) +Q(x, y), where both mappings G and Q are set-valued. Such models arise, in particular, from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We esta...

In this paper we first develop two new results of variational analysis. One is a fixed point theorem for parametric dynamic systems in quasimetric spaces, which can also be interpreted as an existence theorem of minimal points with respect to reflexive and transitive preferences for sets in products spaces. The other one is a variational principle for set-valued mappings acting from quasimetric...

In this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. These problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive Banach space. To make the nonlinear methods work, some careful analysis of t...