Geometry of logarithmic forms and deformations of complex structures

We present a new method to solve certain $\bar{\partial}$-equations for logarithmic differential forms by using harmonic integral theory for currents on Kahler manifolds. The result can be considered as a $\bar{\partial}$-lemma for logarithmic forms. As applications, we generalize the result of Deligne about closedness of logarithmic forms, give geometric and simpler proofs of Deligne's degeneracy theorem for the logarithmic Hodge to de Rham spectral sequences at $E_1$-level, as well as certain injectivity theorem on compact Kahler manifolds. Furthermore, for a family of logarithmic deformations of complex structures on Kahler manifolds, we construct the extension for any logarithmic $(n,q)$-form on the central fiber and thus deduce the local stability of log Calabi-Yau structure by extending an iteration method to the logarithmic forms. Finally we prove the unobstructedness of the deformations of a log Calabi-Yau pair and a pair on a Calabi-Yau manifold by differential geometric method.Comment: Several typos have been fixed. Final version to appear in Journal of Algebraic Geometr

The molecular evolution of PL10 homologs

<p>Abstract</p> <p>Background</p> <p><it>PL10 </it>homologs exist in a wide range of eukaryotes from yeast, plants to animals. They share a DEAD motif and belong to the DEAD-box polypeptide 3 (<it>DDX3</it>) subfamily with a major role in RNA metabolism. The lineage-specific expression patterns and various genomic structures and locations of <it>PL10 </it>homologs indicate these homologs have an interesting evolutionary history.</p> <p>Results</p> <p>Phylogenetic analyses revealed that, in addition to the sex chromosome-linked <it>PL10 </it>homologs, <it>DDX3X </it>and <it>DDX3Y</it>, a single autosomal <it>PL10 </it>putative homologous sequence is present in each genome of the studied non-rodent eutheria. These autosomal homologous sequences originated from the retroposition of <it>DDX3X </it>but were pseudogenized during the evolution. In rodents, besides <it>Ddx3x </it>and <it>Ddx3y</it>, we found not only <it>Pl10 </it>but another autosomal homologous region, both of which also originated from the <it>Ddx3x </it>retroposition. These retropositions occurred after the divergence of eutheria and opossum. In contrast, an additional X putative homologous sequence was detected in primates and originated from the transposition of <it>DDX3Y</it>. The evolution of <it>PL10 </it>homologs was under positive selection and the elevated Ka/Ks ratios were observed in the eutherian lineages for <it>DDX3Y </it>but not <it>PL10 </it>and <it>DDX3X</it>, suggesting relaxed selective constraints on <it>DDX3Y</it>. Contrary to the highly conserved domains, several sites with relaxed selective constraints flanking the domains in the mammalian <it>PL10 </it>homologs may play roles in enhancing the gene function in a lineage-specific manner.</p> <p>Conclusion</p> <p>The eutherian <it>DDX3X/DDX3Y </it>in the X/Y-added region originated from the translocation of the ancient <it>PL10 </it>ortholog on the ancestral autosome, whereas the eutherian <it>PL10 </it>was retroposed from <it>DDX3X</it>. In addition to the functional <it>PL10</it>/<it>DDX3X</it>/<it>DDX3Y</it>, conserved homologous regions on the autosomes and X chromosome are present. The autosomal homologs were also derived from <it>DDX3X</it>, whereas the additional X-homologs were derived from <it>DDX3Y</it>. These homologs were apparently pseudogenized but may still be active transcriptionally. The evolution of <it>PL10 </it>homologs was positively selected.</p

Investigation of a Side-polished Fiber MZI and Its Sensing Performance

A novel all-fiber Mach–Zehnder interferometer (MZI), which consists of lateral core fusion splicing of a short section of side-polished single mode fiber (SMF) between two SMFs was proposed and demonstrated. A simple fiber side-polished platform was built to control the side polished depth through a microscope. The sensitivity of the fiber MZI structure to the surrounding refractive index (RI) can be greatly improved with the increase of the side-polished depth, but has no effect on the temperature sensitivity. The sensor with a polished depth of 44.2 μm measured RI sensitivity up to -118.0 nm/RIU (RI unit) in the RI range from 1.333 to 1.387, which agrees well with simulation results by using the beam propagation method (BPM). In addition, the fiber MZI structure also can achieve simultaneous measurement of both RI and temperature. These results show its potential for use in-line fiber type sensing application

Scalable Tactile Sensing for an Omni-adaptive Soft Robot Finger

Robotic fingers made of soft material and compliant structures usually lead to superior adaptation when interacting with the unstructured physical environment. In this paper, we present an embedded sensing solution using optical fibers for an omni-adaptive soft robotic finger with exceptional adaptation in all directions. In particular, we managed to insert a pair of optical fibers inside the finger's structural cavity without interfering with its adaptive performance. The resultant integration is scalable as a versatile, low-cost, and moisture-proof solution for physically safe human-robot interaction. In addition, we experimented with our finger design for an object sorting task and identified sectional diameters of 94\% objects within the $\pm$6mm error and measured 80\% of the structural strains within $\pm$0.1mm/mm error. The proposed sensor design opens many doors in future applications of soft robotics for scalable and adaptive physical interactions in the unstructured environment.Comment: 8 pages, 6 figures, full-length version of a submission to IEEE RoboSoft 202