A Morse index theorem for elliptic operators on bounded domains

Given a selfadjoint, elliptic operator $L$, one would like to know how the spectrum changes as the spatial domain $\Omega \subset \mathbb{R}^d$ is deformed. For a family of domains $\{\Omega_t\}_{t\in[a,b]}$ we prove that the Morse index of $L$ on $\Omega_a$ differs from the Morse index of $L$ on $\Omega_b$ by the Maslov index of a path of Lagrangian subspaces on the boundary of $\Omega$. This is particularly useful when $\Omega_a$ is a domain for which the Morse index is known, e.g. a region with very small volume. Then the Maslov index computes the difference of Morse indices for the "original" problem (on $\Omega_b$) and the "simplified" problem (on $\Omega_a$). This generalizes previous multi-dimensional Morse index theorems that were only available on star-shaped domains or for Dirichlet boundary conditions. We also discuss how one can compute the Maslov index using crossing forms, and present some applications to the spectral theory of Dirichlet and Neumann boundary value problems.Comment: 21 pages; weaker regularity assumptions than in the first versio

Tactical Opportunities, Risk Attitude and Choice of Farming Strategy: an Application of the Distribution Method

When assessing farming strategies, it is important to account for the opportunities provided for tactically adjusting to outcomes of risk. The hypothesis that accounting for tactical adjustment is more important than accounting for risk attitude was supported in this study with regard to identifying the optimal drainage recirculation strategy for an irrigated dairy farm. Failing to account for tactical adjustment would lead to a sub‐optimal choice, costing the farmer about A$3 100 in present value terms. In contrast, failing to account for risk aversion would not affect the strategy chosen. The distribution method was found to be well suited to modelling tactical adjustment.Research and Development/Tech Change/Emerging Technologies,

Tracking autophagy during proliferation and differentiation of trypanosoma brucei

Autophagy is a lysosome-dependent degradation mechanism that sequesters target cargo into autophagosomal vesicles. The Trypanosoma brucei genome contains apparent orthologues of several autophagy-related proteins including an ATG8 family. These ubiquitin-like proteins are required for autophagosome membrane formation, but our studies show that ATG8.3 is atypical. To investigate the function of other ATG proteins, RNAi compatible T. brucei were modified to function as autophagy reporter lines by expressing only either YFP-ATG8.1 or YFP-ATG8.2. In the insect procyclic lifecycle stage, independent RNAi down-regulation of ATG3 or ATG7 generated autophagy-defective mutants and confirmed a pro-survival role for autophagy in the procyclic form nutrient starvation response. Similarly, RNAi depletion of ATG5 or ATG7 in the bloodstream form disrupted autophagy, but did not impede proliferation. Further characterisation showed bloodstream form autophagy mutants retain the capacity to undergo the complex cellular remodelling that occurs during differentiation to the procyclic form and are equally susceptible to dihydroxyacetone-induced cell death as wild type parasites, not supporting a role for autophagy in this cell death mechanism. The RNAi reporter system developed, which also identified TOR1 as a negative regulator controlling YFP-ATG8.2 but not YFP-ATG8.1 autophagosome formation, will enable further targeted analysis of the mechanisms and function of autophagy in the medically relevant bloodstream form of T. brucei

Magnetoelectric Jones Dichroism in Atoms

The authors suggest that atomic experiments measuring the interference between magnetic-dipole and electric-field-induced electric-dipole transition amplitudes provide a valuable system to study magnetoelectric Jones effects.Comment: 3 pages, 2 figure

On Orbit Manufacture (OOM) and Quantized Inertia

What is On Orbit Manufacture? What Could Humanity Achieve By Having OOM Capability? Top Level OOM Process Example Mission & Product Walkthrough Inertia? A New Model for Quantised Inertia Evidence for QI, Propellant less Thrust for Interstellar Exploratio

FirstLight: Pluggable Optical Interconnect Technologies for Polymeric Electro-Optical Printed Circuit Boards in Data Centers

The protocol data rate governing data storage devices will increase to over 12 Gb/s by 2013 thereby imposing unmanageable cost and performance burdens on future digital data storage systems. The resulting performance bottleneck can be substantially reduced by conveying high-speed data optically instead of electronically. A novel active pluggable 82.5 Gb/s aggregate bit rate optical connector technology, the design and fabrication of a compact electro-optical printed circuit board to meet exacting specifications, and a method for low cost, high precision, passive optical assembly are presented. A demonstration platform was constructed to assess the viability of embedded electro-optical midplane technology in such systems including the first ever demonstration of a pluggable active optical waveguide printed circuit board connector. High-speed optical data transfer at 10.3125 Gb/s was demonstrated through a complex polymer waveguide interconnect layer embedded into a 262 mm × 240 mm × 4.3 mm electro-optical midplane. Bit error rates of less than 10-12 and optical losses as low as 6 dB were demonstrated through nine multimode polymer wave guides with an aggregate data bandwidth of 92.8125 Gb/s

Quantum Vacuum Contribution to the Momentum of the Dielectric Media

Momentum transfer between matter and electromagnetic field is analyzed. The related equations of motion and conservation laws are derived using relativistic formalism. Their correspondence to various, at first sight self-contradicting, experimental data (the so called Abraham-Minkowski controversy) is demonstrated. A new, Casimir like, quantum phenomenon is predicted: contribution of vacuum fluctuations to the motion of dielectric liquids in crossed electric and magnetic fields. Velocities about $50nm/s$ can be expected due to the contribution of high frequency vacuum modes

Antigenic analysis of yeast cell-walls as an aid to classification

Abstract Not Provided