Smale's mean value conjecture for finite Blaschke products

Motivated by a dictionary between polynomials and finite Blaschke products, we study both Smale's mean value conjecture and its dual conjecture for finite Blaschke products in this paper. Our result on the dual conjecture for finite Blaschke products allows us to improve a bound obtained by V. Dubinin and T. Sugawa for the dual mean value conjecture for polynomials.Comment: To appear in an issue of Journal of Analysis denoted to the Proceedings of the Conference on Modern Aspects of Complex Geometry (MindaFest)

Geodesic planes in a geometrically finite end and the halo of a measured lamination

Recent works [MMO1, arXiv:1802.03853, arXiv:1802.04423, arXiv:2101.08956] have shed light on the topological behavior of geodesic planes in the convex core of a geometrically finite hyperbolic 3-manifolds $M$ of infinite volume. In this paper, we focus on the remaining case of geodesic planes outside the convex core of $M$, giving a complete classification of their closures in $M$. In particular, we show that the behavior is different depending on whether exotic roofs exist or not. Here an exotic roof is a geodesic plane contained in an end $E$ of $M$, which limits on the convex core boundary $\partial E$, but cannot be separated from the core by a support plane of $\partial E$. A necessary condition for the existence of exotic roofs is the existence of exotic rays for the bending lamination. Here an exotic ray is a geodesic ray that has finite intersection number with a measured lamination $\mathcal{L}$ but is not asymptotic to any leaf nor eventually disjoint from $\mathcal{L}$. We establish that exotic rays exist if and only if $\mathcal{L}$ is not a multicurve. The proof is constructive, and the ideas involved are important in the construction of exotic roofs. We also show that the existence of geodesic rays satisfying a stronger condition than being exotic, phrased in terms of only the hyperbolic surface $\partial E$ and the bending lamination, is sufficient for the existence of exotic roofs. As a result, we show that geometrically finite ends with exotic roofs exist in every genus. Moreover, in genus $1$, when the end is homotopic to a punctured torus, a generic one (in the sense of Baire category) contains uncountably many exotic roofs.Comment: 42 pages, 14 figures, 39 pages without appendix and references. Supersedes arXiv:2105.0037

On quasiconformal non-equivalence of gasket Julia sets and limit sets

This paper studies quasiconformal non-equivalence of Julia sets and limit sets. We proved that any Julia set is quasiconformally different from the Apollonian gasket. We also proved that any Julia set of a quadratic rational map is quasiconformally different from the gasket limit set of a geometrically finite Kleinian group.Comment: 25 pages without references, 7 figure

Gelechiidae Moths Are Capable of Chemically Dissolving the Pollen of Their Host Plants

Background: Many insects feed on pollen surface lipids and contents accessible through the germination pores. Pollen walls, however, are not broken down because they consist of sporopollenin and are highly resistant to physical and enzymatic damage. Here we report that certain Microlepidoptera chemically dissolve pollen grains with exudates from their mouthparts. Methodology/Principal Findings: Field observations and experiments in tropical China revealed that two species of Deltophora (Gelechioidea) are the exclusive pollinators of two species of Phyllanthus (Phyllanthaceae) on which their larvae develop and from which the adults take pollen and nectar. DNA sequences placed the moths and plants phylogenetically and confirmed that larvae were those of the pollinating moths; molecular clock dating suggests that the moth clade is younger than the plant clade. Captive moths with pollen on their mouthparts after 2-3 days of starvation no longer carried intact grains, and SEM photographs showed exine fragments on their proboscises. GC-MS revealed cis-b-ocimene as the dominant volatile in leaves and flowers, but GC-MS analyses of proboscis extracts failed to reveal an obvious sporopollenindissolving compound. A candidate is ethanolamine, which occurs in insect hemolymphs and is used to dissolve sporopollenin by palynologists. Conclusions/Significance: This is the first report of any insect and indeed any animal chemically dissolving pollen

Analysis and Improvement of a Threshold Signature Scheme Based on the General Access Structure

AbstractHua-wang Qin et al. proposed a novel threshold signature scheme based on the general access structure in order to break the applied limitation of the conventional threshold signature schemes. The security of the scheme was analyzed in this paper, and it is pointed out that the scheme is insecure because it cannot withstand conspiracy attacks and what's more, the identity of signer cannot be investigated. To overcome these security vulnerabilities, this paper proposed an improved threshold signature scheme, and the security analysis results show that the improved scheme can not only resist the conspiracy attack, but also have the properties of anonymity and traceability simultaneously

Regulatory elements controlling the expression of OR37 genes

The genes of the OR37 family are clustered in two loci (cluster I and cluster II) on mouse chromosome 4. These genes encode distinct olfactory receptors (ORs) which are characterised by an insertion of six amino acids in the third extracellular loop and moreover, these receptor types are only expressed in cells which are segregated in a small patch on the central nasal turbinate. As first steps to unravel the molecular basis of this unique topographic expression pattern previous studies have led to the identification of highly conserved sequence motifs including an olf-1 site in the putative promoter region of these genes and subsequently several transcription factors were identified which did bind to these sites. However, it remained elusive if an interaction between the transcription factors and the putative promoter sites may have functional implications. Therefore, a heterologous system was employed to assess the consequence of an interaction between the putative promoters and the transcription factors. HEK 293 cells were cotransfected with a reporter gene under the control of putative mOR37 promoter regions and an expression vector based gene encoding the transcription factor. The expression rate of the reporter gene was monitored by measuring luciferase activity. It was found that the three O/E transcription factors (O/E-1, O/E-2 and O/E-4) induced significant activation of the mOR37 promoters; in addition, it was observed that the putative promoters of other OR genes were also activated, suggesting that the O/E proteins may play a general role in the regulation of OR gene expression. Mutagenesis experiments revealed that the effects of O/E proteins were dependent on the presence of an olf-1 site within the promoter region. For the transcription factor Lhx-2 it was found that not all but only promoters of distinct OR-genes were affected. For the mOR37 promoters a simultaneous action of O/E protein and Lhx-2 elicited an increase of reporter gene expression. The data indicate that the putative mOR37 promoters could drive gene expression in the presence of the crucial transcription factors in this heterologous system. In order to explore to what extent the promoter may contribute to the characteristic topographic expression pattern of the mOR37 genes in vivo, a mOR37C transgene which included the coding exon and the putative promoter, was randomly inserted into the mouse genome. Seven lines were obtained; in all lines the transgene was specifically expressed in olfactory sensory neurons (OSN). In six lines the transgene expression was restricted to the central patch of the olfactory turbinates, typical for the OR37 genes. In one line (line 7) the transgene was also expressed in OSNs ectopically positioned outside the patch within the medial zone. It was found that the transgene was expressed in a mutually exclusive manner and from only one allele. The axons of OSNs expressing the transgene co-converged in the same glomerulus with the axons from neurons expressing the endogenous gene. In line #7 the formation of ectopic glomeruli was observed. The number of OSNs expressing the transgene varied considerably among lines; these differences were independent from the copy number of the transgene. The data indicate that the short putative promoters, most likely the conserved motifs, were sufficient to drive the OR37 gene expression in a tissue specific way and most aspects of the OR37 gene expression were mimicked by the transgene; however, considerable differences between certain lines suggested additional regulatory elements, such as a locus control region (LCR). Since regulatory elements for gene transcription, such as promoters, enhancers and LCRs, appear to be conserved across species, a comparative approach was utilized to search for the LCR-like element for the OR37 locus by sequence alignment across distantly related mammals. A segment of 270 base pairs located 137 Kb upstream of OR37 cluster I was found to be highly conserved between mouse, human, dog and opossum. It was not associated with an exon of any known gene and was highly correlated with OR37 cluster I rather than with the neighboring genes, since the flanking genes did not show syntenic conservation in the opossum genome. A homologous counterpart for this segment was found downstream of the OR37 cluster II locus; an alignment of the cluster II sequence across species identified the conservation of this counterpart. Examination for relevant motifs in this segment and comparison with the conserved H element revealed two common transcription factor binding sites, at least one of them is known to be essential for generating DNase I hypersensitive sites in the LCR of the beta globin gene locus. Further studies are required to evaluate a possible role of this conserved segment in the regulation of the OR37 gene expression.Die olfaktorischen Rezeptoren (OR) der OR37-Familie sind durch eine verlängerte dritte extrazelluläre Domäne und ihre spezifische Expression in olfaktorischen Sinneszellen (OSZ) eines kleinen Areals der zentralen Nasenturbinale charakterisiert. Die kodierenden Gene dieser distinkten OR-Familie sind an 2 Loci (Cluster I und II) auf dem Chromosom 4 der Maus lokalisiert. Im Hinblick auf ein Verständnis der molekularen Grundlagen für das einzigartige topographische Expressionsmuster dieser Gene wurden in früheren Untersuchungen hochkonservierte Sequenzmotive, inklusive eine olf-1 Bindungsstelle, in ihren putativen Promotorregionen ermittelt; darüber hinaus wurden mehrere Transkriptionsfaktoren identifiziert, die von diesen Promotor-Regionen gebunden werden. Ob Interaktionen dieser Transkriptionsfaktoren und der Promotorregion funktionelle Auswirkungen auf eine Expression der Gene haben, ist noch ungeklärt. Diese Frage wurde mit Hilfe eines heterologen Systems untersucht; dazu wurde in HEK 293-Zellen ein Reportergen unter der Kontrolle von Promotorregionen der mOR37-Gene eingeschleust und Transkriptionsfaktoren mittels spezifischer Expressionsvektoren generiert. Die Expressionsrate des Reportergens wurde durch die Ermittlung der jeweiligen Luciferaseaktivität bestimmt. Dabei zeigte sich, dass drei Transkriptionsfaktoren der O/E-Familie (O/E-1, O/E-2 und O/E-4) eine signifikante Aktivierung der mOR37 Promotoren induzierten; allerdings wurden auch putative Promotoren anderer OR-Gene aktiviert. Mutagenese-Experimente haben gezeigt, dass der Einfluss der O/E-Proteine die Anwesenheit einer intakten olf-1 Bindungsstelle der Promotorregion benötigt. Diese Befunde sprechen dafür, dass O/E-Proteinen eine generelle Bedeutung für die Regulation der OR-Expression zukommen könnte. Für den Transkriptionsfaktor Lhx-2 wurde festgestellt, dass nur Promotoren von distinkten OR-Genen beeinflusst wurden. Eine gleichzeitige Aktion von O/E- und von Lhx-2-Proteinen bewirkte eine erhöhte Expressionsrate des Reportergens. Diese Ergebnisse sprechen für eine Beteiligung der putativen Promotoren und der identifizierten Transkriptionsfaktoren an der Expressions-Kontrolle von OR37-Genen. Um herauszufinden, in welchem Maße die identifizierte putative Promotor-Region das charakteristische topographische Expressionsmuster der mOR37-Gene in vivo bestimmt, wurde ein Transgen von mOR37C, bestehend aus dem kodierenden Exon sowie dem putativen Promotor generiert und anschließend zufällig in das Mausgenom integriert, um zu prüfen, ob die putative Promotor-Region der OR37-Gene alle Informationen für die zellspezifische und topographische Expression beinhaltet oder ob die Integrationsstelle im Genom entsprechenden Einfluß ausübt. In den sieben generierten Mauslinien wurde das Transgen exklusiv in OSZ exprimiert. In 6 Linien beschränkte sich die Expression des Transgens auf die typische zentrale OR37-Region des olfaktorischen Epithels. In einer Linie (Linie 7) wurde das Transgen auch ektopisch, d.h. außerhalb der zentralen Region exprimiert. In den entsprechenden OSZ wurde ausschließlich das Transgen und nur ein Allel exprimiert (monoallelisch). Die Anzahl der transgen- exprimierenden OSZ variierte zwischen den Linien beträchtlich, wobei allerdings keine Korrelation mit der Anzahl der Transgen-Kopien bestand. Die Axone der transgen-exprimierenden OSZ projizierten in denselben Glomerulus wie die Axone von Neuronen, die das endogene Gen exprimierten. In Linie 7 wurde die Bildung von ektopischen Glomeruli beobachtet. Die Ergebnisse zeigen, dass eine relativ kurze Promoter-Region offenbar ausreicht, um die gewebespezifische und regionsspezifische Expression der OR37-Gene sicherzustellen; die beträchtlichen Unterschiede in der Zellzahl deutet jedoch auf zusätzliche Regulationselemente hin. Da Regulationselemente für die Transkription von Genen, wie Promotoren, Enhancer und Locuskontrollregionen (LCR) oft speziesübergreifend konserviert sind, wurde durch Sequenzvergleiche von weitläufig verwandten Säugetierspezies versucht, solche konservierten Sequenz-Abschnitte für die OR37-Loci zu ermitteln. Dabei wurde ein Segment von 270 Basenpaaren entdeckt, das sich 137 Kb oberhalb des OR37-Clusters I befindet und zwischen Maus, Mensch, Hund und Opossum hochkonserviert ist. Das 270 bp Segment korrelierte sehr viel stärker mit dem OR37 Cluster I als mit benachbarten Genen, da die begleitenden Gene keine syntenische Konservierung im Opossumgenom aufwiesen. In der Nähe von Cluster-II des OR37-Locus wurde ein entsprechendes Element entdeckt; ein Spezies- Vergleich des Segments für Cluster II zeigte die Konservierung dieses Elementes. Untersuchungen hinsichtlich potentiell relevanter Motive in diesem Segment und Vergleiche mit dem konservierten H element haben zu Identifizierung von zwei Bindungsstellen für Transkriptionsfaktoren geführt; eine davon entspricht der essentiellen hypersensitiven DNase-I Stelle in der LCR des Betaglobin-Genlocus. Zukünftige molekulargenetische Studien sollten zur Klärung der funktionellen Bedeutung dieses konservierten DNA-Segmentes für die Regulation der Expression von OR37-Genen beitragen

Analysis of dynamic characteristic for misalignment-spline gear shaft based on whole transfer matrix method

Spline-gear-shaft (SGF), which is mainly composed of gear and spline shaft, is an important transmission system of RAT (driving the generator to output power with ram air). And its dynamic characteristics affect performance of RAT greatly. In this situation, gear coupling and spline coupling, must be taken into account when analyzing dynamics characteristics of SGF. The misalignment of axis for internal and external spline is inevitable owing to mass eccentricity and unconstrained in axial direction in a high-speed operation. Consequently, the dynamic model of SGF is established considering gear coupling and spline coupling based on whole transfer matrix method (WTMM) in this paper. In addition, numerical calculation method of meshing force for spline teeth under the condition of misalignment is presented considering the distribution force on contact surface of spline teeth in this paper, based on this, the coupled transfer matrix of misaligned spline coupling is established and the dynamic characteristics of SGF is analyzed using whole transfer matrix method with Riccati (WTMMR). The test experiments of dynamic characteristics for SGF are carried out by using portable vibration monitoring analyzer in this paper, furthermore, the time-frequency characteristics of SGF are analyzed through the analysis and processing of acceleration signal. The orders of magnitude for the first four natural frequencies with WTMMR are respectively consistent with experiment results, and the relative error is in the accepted range. Therefore, the correctness of solving meshing force and WTMMR for SGF are all verified. Moreover, it also shows that WTMMR is suitable for the analysis of complex coupled systems SGF and provides a new thought for dynamic analysis of complex shafting and promotes dynamic analysis to efficient and streamlined development

HIP Network: Historical Information Passing Network for Extrapolation Reasoning on Temporal Knowledge Graph

In recent years, temporal knowledge graph (TKG) reasoning has received significant attention. Most existing methods assume that all timestamps and corresponding graphs are available during training, which makes it difficult to predict future events. To address this issue, recent works learn to infer future events based on historical information. However, these methods do not comprehensively consider the latent patterns behind temporal changes, to pass historical information selectively, update representations appropriately and predict events accurately. In this paper, we propose the Historical Information Passing (HIP) network to predict future events. HIP network passes information from temporal, structural and repetitive perspectives, which are used to model the temporal evolution of events, the interactions of events at the same time step, and the known events respectively. In particular, our method considers the updating of relation representations and adopts three scoring functions corresponding to the above dimensions. Experimental results on five benchmark datasets show the superiority of HIP network, and the significant improvements on Hits@1 prove that our method can more accurately predict what is going to happen.Comment: 7 pages, 3 figure