Star-shaped order for distributions characterized by several parameters and some applications

The star-shaped ordering between probability distributions is a common way to express aging properties. A well-known criterion was proposed by Saunders and Moran [(1978). On the quantiles of the gamma and F distributions. Journal of Applied Probability 15(2): 426–432], to order families of distributions depending on one real parameter. However, the lifetime of complex systems usually depends on several parameters, especially when considering heterogeneous components. We extend the Saunders and Moran criterion characterizing the star-shaped order when the multidimensional parameter moves along a given direction. A few applications to the lifetime of complex models, namely parallel and series models assuming different individual components behavior, are discussed.

Improved ensemble of differential evolution variants

In the field of Differential Evolution (DE), a number of measures have been used to enhance algorithm. However, most of the measures need revision for fitting ensemble of different combinations of DE operators—ensemble DE algorithm. Meanwhile, although ensemble DE algorithm may show better performance than each of its constituent algorithms, there still exists the possibility of further improvement on performance with the help of revised measures. In this paper, we manage to implement measures into Ensemble of Differential Evolution Variants (EDEV). Firstly, we extend the collecting range of optional external archive of JADE—one of the constituent algorithm in EDEV. Then, we revise and implement the Event-Triggered Impulsive (ETI) control. Finally, Linear Population Size Reduction (LPSR) is used by us. Then, we obtain Improved Ensemble of Differential Evolution Variants (IEDEV). In our experiments, good performers in the CEC competitions on real parameter single objective optimization among population-based metaheuristics, state-of-the-art DE algorithms, or up-to-date DE algorithms are involved. Experiments show that our IEDEV is very competitive.

BSO20: efficient brain storm optimization for real-parameter numerical optimization

Brain storm optimization (BSO) is an emerging global optimization algorithm. The primary idea is to divide the population into different clusters, and offspring are generated within a cluster or between two clusters. However, the problems of inefficient clustering strategy and insufficient exploration exist in BSO. In this paper, a novel and efficient BSO is proposed, called BSO20 (proposed in 2020). BSO20 pays attention to both the clustering strategy and the mutation strategy. First, we propose a hybrid clustering strategy, which combines two clustering strategies, i.e., nearest-better clustering and random grouping strategy. The size of the subpopulation clustered by two strategies is dynamically adjusted as the population evolves. Second, a modified mutation strategy is used in BSO20 to share information within a cluster or among multiple clusters to enhance the ability of exploration. BSO20 is tested on the problems of the 2017 IEEE Congress on Evolutionary Computation competition on real parameter numerical optimization. BSO20 is compared with several variants of BSO and two variants of particle swarm optimization, and the experimental results show that BSO20 is competitive.

Numerical twist-even SU(1,1)-singlet solutions in open string field theory around the identity-based solution

Using the level truncation method, we construct numerical solutions, which are twist even and SU(1) singlet, in the theory around the Takahashi-Tanimoto identity-based solution (TT solution) with a real parameter a in the framework of bosonic open string field theory. We find solutions corresponding to “double brane” and “ghost brane” solutions which were constructed by Kudrna and Schnabl in the conventional theory around the perturbative vacuum. Our solutions show somewhat similar a-dependence to tachyon vacuum and single brane solutions, which we found in the earlier works. In this sense, we might be able to expect that they are consistent with the conventional interpretation of a-dependence of the TT solution. We observe that numerical complex solutions at low levels become real ones at higher levels for some region of the parameter a. However, these real solutions do not so improve interpretation for double brane.

Combined effects of singular and exponential nonlinearities in fractional Kirchhoff problems

<p style='text-indent:20px;'>In this paper we establish the existence of at least two (weak) solutions for the following fractional Kirchhoff problem involving singular and exponential nonlinearities</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{cases} M\left(\|u\|^{{n}/{s}}\right)(-\Delta)^s_{n/s}u = \mu u^{-q}+ u^{r-1}\exp( u^{\beta})\quad\text{in } \Omega,\\ u&gt;0\qquad\text{in } \Omega,\\ u = 0\qquad\text{in } \mathbb R^n \setminus{ \Omega}, \end{cases} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula> is a smooth bounded domain of <inline-formula><tex-math id="M2">\begin{document}$ \mathbb R^n $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$ n\geq 1 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M4">\begin{document}$ s\in (0,1) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ \mu&gt;0 $\end{document}</tex-math></inline-formula> is a real parameter, <inline-formula><tex-math id="M6">\begin{document}$ \beta &lt;{n/(n-s)} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M7">\begin{document}$ q\in (0,1) $\end{document}</tex-math></inline-formula>.The paper covers the so called degenerate Kirchhoff case andthe existence proofs rely on the Nehari manifold techniques.</p>

Polynomial bivariate copulas of degree five: characterization and some particular inequalities

Bivariate polynomial copulas of degree 5 (containing the family of Eyraud-Farlie-Gumbel-Morgenstern copulas) are in a one-to-one correspondence to certain real parameter triplets (a, b, c), i.e., to some set of polynomials in two variables of degree 1: p(x, y) = ax + by + c. The set of the parameters yielding a copula is characterized and visualized in detail. Polynomial copulas of degree 5 satisfying particular (in)equalities (symmetry, Schur concavity, positive and negative quadrant dependence, ultramodularity) are discussed and characterized. Then it is shown that for polynomial copulas of degree 5 the values of several dependence parameters (including Spearman’s rho, Kendall’s tau, Blomqvist’s beta, and Gini’s gamma) lie in exactly the same intervals as for the Eyraud-Farlie-Gumbel-Morgenstern copulas. Finally we prove that these dependence parameters attain all possible values in ]−1, 1[ if polynomial copulas of arbitrary degree are considered.