In uncertainty quantification, critical parameters of mathematical models are substituted by random variables. We consider dynamical systems composed of ordinary differential equations. The unknown solution is expanded into an orthogonal basis of the random space, e.g., the polynomial chaos expansions. A Galerkin method yields a numerical solution of the stochastic model. In the linear case, th...

In the present paper, we propose a new theory named “Theory of indeterminate natural transformation (TINT)” to investigate the dynamical creation of meanings as association relationships between images, focusing on the metaphor comprehension as an example. TINT models the meaning creation as a kind of stochastic processes based on the mathematical structure defined by association relationships ...

A new method of summation of slowly convergent series is proposed. It may be successfully applied to the summation of generalized and basic hypergeometric series, as well as some classical orthogonal polynomial series expansions. In some special cases, our algorithm is equivalent to Wynn’s epsilon algorithm, Weniger transformation (Computer Physics Reports 10 (1989) 189371) or the technique rec...

In the construction process of smart grid, an assessment on primary equipments intelligent transformation is an urgent content in the first batch of intelligent substation pilot project. Wide investigation of intelligent substation pilot projects was conducted seriously in several regional power grids in China. An mathematical model was established to assess the substation primary equipments in...

Recently Lunin and Maldacena used an SL(3, R) transformation of theAdS5×S background to generate a supergravity solution dual to a so-called β-deformation of N = 4 super Yang-Mills theory. We use a T-duality-shift-T-duality (TsT) transformation to obtain the β-deformed background for real β ≡ γ, and show that solutions of string theory equations of motion in this background are in one-to-one co...

Recently in Burer et al. (Mathematical Programming A, submitted), the authors of this paper introduced a nonlinear transformation to convert the positive definiteness constraint on an n × n matrix-valued function of a certain form into the positivity constraint on n scalar variables while keeping the number of variables unchanged. Based on this transformation, they proposed a first-order interi...

Gliomas are the most frequent type of primary brain tumours. Low grade gliomas (LGGs, WHO grade II gliomas) may grow very slowly for the long periods of time, however they inevitably cause death due to the phenomenon known as the malignant transformation. This refers to the transition of LGGs to more aggressive forms of high grade gliomas (HGGs, WHO grade III and IV gliomas). In this paper we p...

Cardiologists assume that analysis of the motion of the heart (especially the left ventricle) can give some information about the health of the myocardium. A 4D polar transformation is defined to describe the left ventricle (LV) motion and a method is presented to estimate it from sequences of 3D images. The transformation is defined in 3Dplanispheric coordinates (3PC) by a small number of para...

This article extends results described in a recent article detailing a structural scale invariance property of the simulated annealing (SA) algorithm. These extensions are based on generalizations of the SA algorithm based on Tsallis statistics and a non-extensive form of entropy. These scale invariance properties show how arbitrary aggregations of energy levels retain certain mathematical char...

This paper discusses a generalization of the function transformation scheme for global energy minimization applied to the molecular conformation problem. A mathematical theory for the method as a special continuation approach to global o p timization is established. We show that the method can transform a nonlinear objective function into a class of &dua l ly deformed, but “smoother” or “easier...