Convergence Rates for Newton’s Method at Singular Points

If Newton’s method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, the convergence of the Newton iterates to the root is linear rather than quadratic. In this paper we give a detailed analysis of the linear convergence rates for several types of singular problems. For some of these problems we describe modifications of Newton’s method which will restore quadratic convergence

The Mark 3 Haploscope

A computer-operated binocular vision testing device was developed as one part of a system designed for NASA to evaluate the visual function of astronauts during spaceflight. This particular device, called the Mark 3 Haploscope, employs semi-automated psychophysical test procedures to measure visual acuity, stereopsis, phoria, fixation disparity, refractive state and accommodation/convergence relationships. Test procedures are self-administered and can be used repeatedly without subject memorization. The Haploscope was designed as one module of the complete NASA Vision Testing System. However, it is capable of stand-alone operation. Moreover, the compactness and portability of the Haploscope make possible its use in a broad variety of testing environments

Performing joint measurements and transformations on several qubits by operating on a single control qubit

An n-qubit quantum register can in principle be completely controlled by operating on a single qubit that interacts with the register via an appropriate fixed interaction. We consider a hypothetical system consisting of n spin-1/2 nuclei that interact with an electron spin via a magnetic interaction. We describe algorithms that measure non-trivial joint observables on the register by acting on the control spin only. For large n this is not an efficient model for universal quantum computation but it can be modified to an efficient one if one allows n possible positions of the control particle. This toy model of measurements illustrates in which way specific interactions between the register and a probe particle support specific types of joint measurements in the sense that some joint observables can be measured by simple sequences of operations on the probe particle.Comment: 7 pages, revtex, 3 figure

The Optimal Single Copy Measurement for the Hidden Subgroup Problem

The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup problem. Previous work has identified the optimal single copy measurement for the hidden subgroup problem over abelian groups as well as for the non-abelian problem in the setting where the subgroups are restricted to be all conjugate to each other. Here we describe the optimal single copy measurement for the hidden subgroup problem when all of the subgroups of the group are given with equal a priori probability. The optimal measurement is seen to be a hybrid of the two previously discovered single copy optimal measurements for the hidden subgroup problem.Comment: 8 pages. Error in main proof fixe

Elevated atmospheric concentrations of carbon dioxide reduce monarch tolerance and increase parasite virulence by altering the medicinal properties of milkweeds

Hosts combat their parasites using mechanisms of resistance and tolerance, which together determine parasite virulence. Environmental factors, including diet, mediate the impact of parasites on hosts, with diet providing nutritional and medicinal properties. Here, we present the first evidence that ongoing environmental change decreases host tolerance and increases parasite virulence through a loss of dietary medicinal quality. Monarch butterflies use dietary toxins (cardenolides) to reduce the deleterious impacts of a protozoan parasite. We fed monarch larvae foliage from four milkweed species grown under either elevated or ambient CO2, and measured changes in resistance, tolerance, and virulence. The most high‐cardenolide milkweed species lost its medicinal properties under elevated CO2; monarch tolerance to infection decreased, and parasite virulence increased. Declines in medicinal quality were associated with declines in foliar concentrations of lipophilic cardenolides. Our results emphasize that global environmental change may influence parasite–host interactions through changes in the medicinal properties of plants.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/145415/1/ele13101-sup-0003-TableS1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/145415/2/ele13101-sup-0007-TableS5.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/145415/3/ele13101-sup-0006-TableS4.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/145415/4/ele13101.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/145415/5/ele13101_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/145415/6/ele13101-sup-0004-TableS2.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/145415/7/ele13101-sup-0009-AppendixS1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/145415/8/ele13101-sup-0005-TableS3.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/145415/9/ele13101-sup-0002-FigS2.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/145415/10/ele13101-sup-0008-TableS6.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/145415/11/ele13101-sup-0001-FigS1.pd

Approximate Analytic Solution for the Spatiotemporal Evolution of Wave Packets undergoing Arbitrary Dispersion

We apply expansion methods to obtain an approximate expression in terms of elementary functions for the space and time dependence of wave packets in a dispersive medium. The specific application to pulses in a cold plasma is considered in detail, and the explicit analytic formula that results is provided. When certain general initial conditions are satisfied, these expressions describe the packet evolution quite well. We conclude by employing the method to exhibit aspects of dispersive pulse propagation in a cold plasma, and suggest how predicted and experimental effects may be compared to improve the theoretical description of a medium's dispersive properties.Comment: 17 pages, 4 figures, RevTe

Road Traffic Related Injury Severity in Truck Drivers: A Prospective Medical and Technical Analysis of 582 Truck Crashes

Background: While cyclists and pedestrians are known to be at significant risk for severe injuries when exposed to road traffic accidents (RTA) involving trucks, little is known about RTA injury risk for truck drivers. Objectives: The aim of this study was to analyze the injury severity in truck drivers following RTAs. Patients and Methods: Our local accident research unit prospectively documented 43000 RTAs involving 582 trucks between 2000 and 2011. Injury severity, including the abbreviated injury scale (AIS) and the maximum abbreviated injury scale (MAIS) were analyzed. Technical parameters (e.g. delta-v, direction of impact), the location of accident, and its dependency on the road type were also taken into consideration. Results: Thirteen percent (77/582) of truck drivers were injured. Extremities were found to be at highest risk of injury with the lower extremities (36x) being injured most severely (10x: AIS 2 and 3). Death occurred only after collisions with other trucks, and severity of injuries increased with an increased speed limit. The maximum abbreviated injury scale was higher in the crash opponents (56x MAIS ≥ 3) compared to the truck drivers (8x MAIS ≥ 3). Overall, 82% of the crash opponents were injured. Conclusions: The safety of truck drivers is assured by their vehicles, the consequence being that the risk of becoming injured is likely to be low. However, the legs especially are at high risk for severe injuries during RTAs. This probability increases in the instance of a collision with another truck. Nevertheless, in RTAs involving trucks and regular passenger vehicles, the other party is in higher risk of injury

Voyager 2 Observations of Plasma and Pressure Pulses

This paper provides the latest data from Voyager 2 on plasma characteristics in the heliosheath including the observations of pressure waves in the plasma and particle data. Models and observations show that solar transients drive pressure waves through the heliosphere. Pressure pulses that could drive heliosheath waves are observed near the previous solar maximum upstream of the termination shock. We show that the most recent data is consistent with the presence of pressure waves and compare the heliosheath waves with the pressure increases in the heliosheath. The magnetic field is better correlated with density and galactic cosmic ray intensities in the supersonic solar wind than in the heliosheath. The galactic cosmic rays are correlated with the plasma and particles with a ~30-day lag in both the supersonic wind and heliosheath