The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces

This paper is concerned with the periodic boundary value problem for a quasilinear evolution equation of the following type: ∂tu+f(u)∂xu+F(u)=0, x∈T=R/2πZ, t∈R+. Under some conditions, we prove that this equation is locally well-posed in Besov space Bp,rs(T). Furthermore, we study the continuity of the solution map for this equation in B2,rs(T). Our work improves some earlier results

The Navigation Engineering in Developed Hydropower Station

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchive

Multimodal estimation of distribution algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima

Revealing divergent evolution, identifying circular permutations and detecting active-sites by protein structure comparison

BACKGROUND: Protein structure comparison is one of the most important problems in computational biology and plays a key role in protein structure prediction, fold family classification, motif finding, phylogenetic tree reconstruction and protein docking. RESULTS: We propose a novel method to compare the protein structures in an accurate and efficient manner. Such a method can be used to not only reveal divergent evolution, but also identify circular permutations and further detect active-sites. Specifically, we define the structure alignment as a multi-objective optimization problem, i.e., maximizing the number of aligned atoms and minimizing their root mean square distance. By controlling a single distance-related parameter, theoretically we can obtain a variety of optimal alignments corresponding to different optimal matching patterns, i.e., from a large matching portion to a small matching portion. The number of variables in our algorithm increases with the number of atoms of protein pairs in almost a linear manner. In addition to solid theoretical background, numerical experiments demonstrated significant improvement of our approach over the existing methods in terms of quality and efficiency. In particular, we show that divergent evolution, circular permutations and active-sites (or structural motifs) can be identified by our method. The software SAMO is available upon request from the authors, or from and . CONCLUSION: A novel formulation is proposed to accurately align protein structures in the framework of multi-objective optimization, based on a sequence order-independent strategy. A fast and accurate algorithm based on the bipartite matching algorithm is developed by exploiting the special features. Convergence of computation is shown in experiments and is also theoretically proven