Firstly, the initiation and propagation of fatigue crack is modeled efficiently by means of cohesive zone elements [24 26].
Since uncertainties can be modeled and recorded very efficiently by probabilistic terms, in contrast to other approaches in optimal regulator design, the occurring errors are modeled here by realizations of random variables having a given or at least partly known probability distribution.
For this purpose, we have proposed a method to efficiently infer CAL networks, i.e. small logic networks in which allele-specific interactions are modeled by Boolean functions.
The orientations of vessels can be efficiently modeled by the energy distribution of Fourier transformation.
Based on this, the HRTF can be efficiently modeled by using poles that are independent of source directions, with zeros that are dependent on source directions.
On the other hand various irradiation conditions can be efficiently modeled by ion irradiation method without leading to the radioactivity of the sample.
Although among site-rate heterogeneity can be efficiently modelled by fitting a gamma-distribution [ 24] or by assuming a proportion of invariable sites [ 25], these standard models make several assumptions, such as the independent evolution of nucleotide sites, and the spatial homogeneity of the substitution process across sites.
Fractures and barriers are efficiently modeled by lower-dimensional interfaces which yield comparable results to those of the equi-dimensional model.
The problem is formulated as a mixed-integer nonlinear programming model that cannot be solved efficiently by the existing solution algorithms.
In this paper, we show that by extending EGR to Bregman projection, this faster rate of convergence can be retained, and more importantly, the updates can be performed efficiently by exploiting graphical model factorization.
