Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions

We study oscillations in the eigenfunctions for a fractional Schrödinger operator on the real line. An argument in the spirit of Courant's nodal domain theorem applies to an associated local problem in the upper half plane and provides a bound on the number of nodal domains for the extensions of the eigenfunctions. Using the combinatorial properties of noncrossing partitions, we turn the nodal domain bound into an estimate for the number of sign changes in the eigenfunctions. We discuss applications in the periodic setting and the Steklov problem on planar domains

A Framework to Manage the Complex Organisation of Collaborating: Its Application to Autonomous Systems

In this paper we present an analysis of the complexities of large group collaboration and its application to develop detailed requirements for collaboration schema for Autonomous Systems (AS). These requirements flow from our development of a framework for collaboration that provides a basis for designing, supporting and managing complex collaborative systems that can be applied and tested in various real world settings. We present the concepts of "collaborative flow" and "working as one" as descriptive expressions of what good collaborative teamwork can be in such scenarios. The paper considers the application of the framework within different scenarios and discuses the utility of the framework in modelling and supporting collaboration in complex organisational structures

Recognition of some perfectly orderable graph classes

AbstractThis paper presents new algorithms for recognizing several classes of perfectly orderable graphs. Bipolarizable and P4-simplicial graphs are recognized in O(n3.376) time, improving the previous bounds of O(n4) and O(n5), respectively. Brittle and semi-simplicial graphs are recognized in O(n3) time using a randomized algorithm, and O(n3log2n) time if a deterministic algorithm is required. The best previous time bound for recognizing these classes of graphs is O(m2). Welsh–Powell opposition graphs are recognized in O(n3) time, improving the previous bound of O(n4). HHP-free graphs and maxibrittle graphs are recognized in O(mn) and O(n3.376) time, respectively

Electric Motor & Power Source Selection for Small Aircraft Propulsion

The research conducted in this project is on electrical propulsion in aviation. A Cessna 172K aircraft with a Lycoming O-320-E2D piston engine serves as a baseline measurement. Investigation of the components required for electrical flight is performed, and components are selected based on market availability and operational performance criteria. This research focuses on electrical propulsion in the aviation industry, and is tailored to aircraft within the General Aviation sector leading to the following research question: Can current electric motor and battery technologies conceptually support flight operations for a Cessna 172K in terms of aircraft performance criteria? The results explore the potential for a fully-electric aircraft powered by means of batteries. A demonstrated flight is examined and the center of gravity is calculated

Antiviral protection and the importance of Wolbachia density and: tissue tropism in Drosophila simulans

Wolbachia, a maternally transmitted endosymbiont of insects, is increasingly being seen as an effective biological control agent that can interfere with transmission of pathogens, including dengue virus. However, the mechanism of antiviral protection is not well understood. The density and distribution of Wolbachia in host tissues have been implicated as contributing factors by previous studies with both mosquitoes and flies. Drosophila flies infected with five diverse strains of Wolbachia were screened for the ability to mediate antiviral protection. The three protective Wolbachia strains were more closely related and occurred at a higher density within whole flies than the two nonprotective Wolbachia strains. In this study, to further investigate the relationship between whole-fly Wolbachia density and the ability to mediate antiviral protection, tetracycline was used to decrease the abundance of the high-density, protective Wolbachia strain wAu prior to viral challenge. Antiviral protection was lost when the density of the protective Wolbachia strain was decreased to an abundance similar to that of nonprotective Wolbachia strains. We determined the Wolbachia density and distribution in tissues of the same five fly-Wolbachia combinations as used previously. The Wolbachia density within the head, gut, and Malpighian tubules correlated with the ability to mediate antiviral protection. These findings may facilitate the development of Wolbachia biological control strategies and help to predict host-Wolbachia pairings that may interfere with virus-induced pathology

Anatomic Femoral and Tibial Tunnel Placement During Anterior Cruciate Ligament Reconstruction: Anteromedial Portal All-Inside and Outside-In Techniques

Tunnel malposition is one of the most common technical reasons for anterior cruciate ligament reconstruction failure. Small changes in tunnel placement can result in significant differences in outcome. More anatomic placement of the tunnels can lead to greater knee stability and a more accurate reproduction of native knee kinematics. This Technical Note describes 2 tibial tunnel–independent methods to obtain anatomic femoral tunnel placement. The all-inside anteromedial portal technique requires only minimal surgical incisions but allows precise femoral tunnel placement. However, hyperflexion of the knee is required, adequate surgical assistance is necessary, and this technique may be susceptible to graft-tunnel mismatch. The outside-in technique may be more beneficial in obese patients, skeletally immature patients, or revision cases. On the downside, it does require an additional 2-cm surgical incision. This article also provides surgical pearls to fine-tune tibial tunnel placement