We introduce and investigate a one parameter family of quantum spaces invariant under the left (right) coactions of the group-like element T (j=1) h of the Jordanian function algebra Funh(SL(2)). These spaces may be regarded as Jordanian quantization of the two-dimensional spheres.

Steady-state analysis of dynamical systems for biological networks gives rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here, the variety is described by a polynomial system in 19 unknowns and 36 parameters. It has degree 9 over the parameter space. This case study expl...

Summary Biological models contain many parameters whose values are difficult to measure directly via experimentation and therefore require calibration against experimental data. Markov chain Monte Carlo (MCMC) methods are suitable to estimate multivariate posterior model parameter distributions, but these methods may exhibit slow or premature convergence in high-dimensional search spaces. Here,...

We study a third-order partial differential equation in the form τuttt +αutt −cuxx −buxxt = 0, (1) that corresponds to the one-dimensional version of the Moore-Gibson-Thompson equation arising in high-intensity ultrasound and linear vibrations of elastic structures. In contrast with the current literature on the subject, we show that when the critical parameter γ := α − τc2 b is negative, the e...

in this paper, we deal with the subdierential concept onhadamard spaces. flat hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in hadamard spaces is nonempty. proximal subdierentialin hadamard spaces is addressed and some basic properties are high-lighted. finally, a density theorem for subdierential set is establi...

The problem of operating or designing a system with robust stability with respect to many parameters can be viewed as a geometric problem in multidimensional parameter space of finding the position of nominal parameters λ0 relative to hypersurfaces at which stability is lost in a bifurcation. The position of λ0 relative to these hypersurfaces may be quantified by numerically computing the bifur...

A new software tool making use of a genetic algorithm for multi-objective experimental optimization (GAME.opt) was developed based on a strength Pareto evolutionary algorithm. The software deals with high dimensional variable spaces and unknown interactions of design variables. This approach was evaluated by means of multi-objective test problems replacing the experimental results. A default pa...

Indexing high-dimensional data spaces is an emerging research domain. It gains increasing importance by the need to support modern applications by powerful search tools. In the so-called non-standard applications of database systems such as multimedia, CAD, molecular biology, medical imaging, time series processing and many others, similarity search in large data sets is required as a basic fun...

We show that, under certain assumptions, the fitness of almost all quasi-species becomes independent of mutational probabilities and the initial frequency distributions of the sequences in high dimensional sequence spaces. This result is the consequence of the concentration of measure on a high dimensional hypersphere and its extension to Lipschitz functions knows as the Levy’s Lemma. Therefore...