Dynamics of McMullen maps

In this article, we develop the Yoccoz puzzle technique to study a family of rational maps termed McMullen maps. We show that the boundary of the immediate basin of infinity is always a Jordan curve if it is connected. This gives a positive answer to a question of Devaney. Higher regularity of this boundary is obtained in almost all cases. We show that the boundary is a quasi-circle if it contains neither a parabolic point nor a recurrent critical point. For the whole Julia set, we show that the McMullen maps have locally connected Julia sets except in some special cases.Comment: Complex dynamics, 51 pages, 13 figure

Human MicroRNA Oncogenes and Tumor Suppressors Show Significantly Different Biological Patterns: From Functions to Targets

MicroRNAs (miRNAs) are small noncoding RNAs which play essential roles in many important biological processes. Therefore, their dysfunction is associated with a variety of human diseases, including cancer. Increasing evidence shows that miRNAs can act as oncogenes or tumor suppressors, and although there is great interest in research into these cancer-associated miRNAs, little is known about them. In this study, we performed a comprehensive analysis of putative human miRNA oncogenes and tumor suppressors. We found that miRNA oncogenes and tumor suppressors clearly show different patterns in function, evolutionary rate, expression, chromosome distribution, molecule size, free energy, transcription factors, and targets. For example, miRNA oncogenes are located mainly in the amplified regions in human cancers, whereas miRNA tumor suppressors are located mainly in the deleted regions. miRNA oncogenes tend to cleave target mRNAs more frequently than miRNA tumor suppressors. These results indicate that these two types of cancer-associated miRNAs play different roles in cancer formation and development. Moreover, the patterns identified here can discriminate novel miRNA oncogenes and tumor suppressors with a high degree of accuracy. This study represents the first large-scale bioinformatic analysis of human miRNA oncogenes and tumor suppressors. Our findings provide help for not only understanding of miRNAs in cancer but also for the specific identification of novel miRNAs as miRNA oncogenes and tumor suppressors. In addition, the data presented in this study will be valuable for the study of both miRNAs and cancer

Practical Submodule Capacitor Sizing for Modular Multilevel Converter Considering Grid Faults

Submodule (SM) capacitors are key elements in the modular multilevel converter (MMC), the design of which influences the entire system performance. In practical cases, SM capacitor sizing must consider the abnormal system operation (e.g., grid faults). In order to find a clear design boundary for SM capacitors, a practical capacitor sizing method is presented for the first time in this paper, considering the grid-fault-ride-through operation of the MMC, impact of MMC control system, and aging mechanism of capacitors. The SM capacitor rated voltage, capacitance, ESR, thermal resistance, and lifetime can be decided to ensure reliable operations of the MMC during grid faults. The effectiveness of the proposed method has been verified through experimental tests on a down-scale MMC system.Published versio

Distributed attitude and translation consensus for networked rigid bodies based on unit dual quaternion

This paper provides unified solutions for distributed attitude and translation consensus problems for networked fully actuated rigid bodies under the fixed and undirected communication topology with the tool of unit dual quaternion. We investigate two kinds of consensus, that is, leaderless consensus and leader-following consensus with a static leader. Firstly, the dynamics of rigid bodies are presented by unit dual quaternion. The control inputs of rigid bodies are also obtained from unit dual quaternion. Secondly, we propose a distributed consensus law in the form of dual quaternion to guarantee that the attitudes and translations of all rigid bodies reach consensus, respectively, without a leader. Thirdly, the leader-following consensus problem with a static leader is studied. With the proposed leader-following consensus law, the states of all rigid bodies converge to the corresponding states of the static leader, including the attitude and the translation. Finally, numerical examples are provided to validate the effectiveness of the theoretical resultsThe authors were supported in part by Australian Research Council (DP130103610 and DP160104500) and National Natural Science Foundation of China (61375072 and 61503109) and Nature Science Foundation of Zhejiang Province (LQF030005)

Poly[[(2,2′-bipyridine)(μ 3-7-oxabicyclo­[2.2.1]heptane-2,3-dicarboxyl­ato)cadmium] monohydrate]

The title compound, {[Cd(C8H8O5)(C10H8N2)]·H2O}n, was obtained by the reaction of cadmium acetate with 2,2′-bi­pyridine and 7-oxabicyclo­(2.2.1)heptane-2,3-dicarb­oxy­lic anhydride. The CdII atom is seven-coordinated in a distorted penta­gonal–bipyramidal configuration, defined by five O atoms from the carboxyl­ate groups of three 7-oxabicyclo­[2.2.1]heptane-2,3-dicarboxyl­ato ligands and two N atoms from the 2,2′-bipyridine ligand. Two O atoms link two CdII atoms, forming a dinuclear center: the Cd—O—Cd bridging angle is 110.19 (6)°. The polymeric structure extends along [100] and is linked by inter­molecular O—H⋯O hydrogen bonds involving the solvent water molecule. Extensive π–π stacking exists between 2,2-bypiridine ligands along [010] with centroid-centroid distance of 3.650 (2) 

1-(2-Chloro­benzo­yl)-3-[4-(trifluoro­meth­oxy)phen­yl]urea

The title compound, C15H10ClF3N2O3, is considered to belong to a fourth generation of insecticides with properties such as high selectivity, low acute toxicity for mammals and high biological activity. The dihedral angle between the two benzene rings is 59.3 (2)°. Intra­molecular C—H⋯O and N—H⋯O hydrogen bonds are observed. Inter­molecular N—H⋯O hydrogen bonding generates a centrosymmetric dimer. The F atoms are disordered over two positions; the site occupancy factors are 0.52 and 0.48