Multivariate spline space over cross-cut partition

AbstractIn this paper, we mainly study the generator bases of the prime module determined by the global conformality condition of multivariate spline over star cross-cut partition. The results can help us to get the dimension and construct the spline bases for multivariate spline space over cross-cut partition, quasi-cross-cut partition, and super-cross-cut partition

Symmetry-Defying Iron Pyrite (FeS2) Nanocrystals through Oriented Attachment

A grant from the One-University Open Access Fund at the University of Kansas was used to defray the author’s publication fees in this Open Access journal. The Open Access Fund, administered by librarians from the KU, KU Law, and KUMC libraries, is made possible by contributions from the offices of KU Provost, KU Vice Chancellor for Research & Graduate Studies, and KUMC Vice Chancellor for Research. For more information about the Open Access Fund, please see http://library.kumc.edu/authors-fund.xml.Iron pyrite (fool's gold, FeS2) is a promising earth abundant and environmentally benign semiconductor material that shows promise as a strong and broad absorber for photovoltaics and high energy density cathode material for batteries. However, controlling FeS2 nanocrystal formation (composition, size, shape, stoichiometry, etc.) and defect mitigation still remains a challenge. These problems represent significant limitations in the ability to control electrical, optical and electrochemical properties to exploit pyrite's full potential for sustainable energy applications. Here, we report a symmetry-defying oriented attachment FeS2 nanocrystal growth by examining the nanostructure evolution and recrystallization to uncover how the shape, size and defects of FeS2 nanocrystals changes during growth. It is demonstrated that a well-controlled reaction temperature and annealing time results in polycrystal-to-monocrystal formation and defect annihilation, which correlates with the performance of photoresponse devices. This knowledge opens up a new tactic to address pyrite's known defect problems

DNA-Packing Portal and Capsid-Associated Tegument Complexes in the Tumor Herpesvirus KSHV.

Assembly of Kaposi's sarcoma-associated herpesvirus (KSHV) begins at a bacteriophage-like portal complex that nucleates formation of an icosahedral capsid with capsid-associated tegument complexes (CATCs) and facilitates translocation of an ∼150-kb dsDNA genome, followed by acquisition of a pleomorphic tegument and envelope. Because of deviation from icosahedral symmetry, KSHV portal and tegument structures have largely been obscured in previous studies. Using symmetry-relaxed cryo-EM, we determined the in situ structure of the KSHV portal and its interactions with surrounding capsid proteins, CATCs, and the terminal end of KSHV's dsDNA genome. Our atomic models of the portal and capsid/CATC, together with visualization of CATCs' variable occupancy and alternate orientation of CATC-interacting vertex triplexes, suggest a mechanism whereby the portal orchestrates procapsid formation and asymmetric long-range determination of CATC attachment during DNA packaging prior to pleomorphic tegumentation/envelopment. Structure-based mutageneses confirm that a triplex deep binding groove for CATCs is a hotspot that holds promise for antiviral development

Single-photon transport and mechanical NOON state generation in microcavity optomechanics

We investigate the single-photon transport in a single-mode optical fiber coupled to an optomechanical system in the single-photon strong-coupling regime. The single-photon transmission amplitude is analytically obtained with a real-space approach and the effects of thermal noises are studied via master-equation simulations. The results provide an explicit understanding of optomechanical interaction and offer a useful guide for manipulating single photons in optomechanical systems. Based on the theoretical framework, we further propose a scheme to generate the mechanical NOON states with arbitrary phonon numbers by measuring the sideband photons. The probability for generating the NOON state with five phonons is over 0.15.Comment: 13 pages, 6 figure

Annotating Protein Functional Residues by Coupling High-Throughput Fitness Profile and Homologous-Structure Analysis.

Identification and annotation of functional residues are fundamental questions in protein sequence analysis. Sequence and structure conservation provides valuable information to tackle these questions. It is, however, limited by the incomplete sampling of sequence space in natural evolution. Moreover, proteins often have multiple functions, with overlapping sequences that present challenges to accurate annotation of the exact functions of individual residues by conservation-based methods. Using the influenza A virus PB1 protein as an example, we developed a method to systematically identify and annotate functional residues. We used saturation mutagenesis and high-throughput sequencing to measure the replication capacity of single nucleotide mutations across the entire PB1 protein. After predicting protein stability upon mutations, we identified functional PB1 residues that are essential for viral replication. To further annotate the functional residues important to the canonical or noncanonical functions of viral RNA-dependent RNA polymerase (vRdRp), we performed a homologous-structure analysis with 16 different vRdRp structures. We achieved high sensitivity in annotating the known canonical polymerase functional residues. Moreover, we identified a cluster of noncanonical functional residues located in the loop region of the PB1 β-ribbon. We further demonstrated that these residues were important for PB1 protein nuclear import through the interaction with Ran-binding protein 5. In summary, we developed a systematic and sensitive method to identify and annotate functional residues that are not restrained by sequence conservation. Importantly, this method is generally applicable to other proteins about which homologous-structure information is available.ImportanceTo fully comprehend the diverse functions of a protein, it is essential to understand the functionality of individual residues. Current methods are highly dependent on evolutionary sequence conservation, which is usually limited by sampling size. Sequence conservation-based methods are further confounded by structural constraints and multifunctionality of proteins. Here we present a method that can systematically identify and annotate functional residues of a given protein. We used a high-throughput functional profiling platform to identify essential residues. Coupling it with homologous-structure comparison, we were able to annotate multiple functions of proteins. We demonstrated the method with the PB1 protein of influenza A virus and identified novel functional residues in addition to its canonical function as an RNA-dependent RNA polymerase. Not limited to virology, this method is generally applicable to other proteins that can be functionally selected and about which homologous-structure information is available