Cutting A Pie Is Not A Piece Of Cake

Is there a division among n players of a cake using n-1 parallel vertical cuts, or of a pie using n radial cuts, that is envy-free (each player thinks he or she receives a largest piece and so does not envy another player) and undominated (there is no other allocation as good for all players and better for at least one)? David Gale first asked this question for pies. We provide complete answers for both cakes and pies. The answers depend on the number of players (two versus three or more players) and whether the players' preferences satisfy certain continuity assumptions. We also give some simple algorithms for cutting a pie when there are two or more players, but these algorithms do not guarantee all the properties one might desire in a division, which makes pie-cutting harder than cake-cutting. We suggest possible applications and conclude with two open questions

Fast switching current detection at low critical currents

A pulse-and-hold technique is used to measure the switching of small critical current Josephson junctions. This technique allows one to achieve a good binary detection and therefore measure switching probabilities. The technique overcomes limitations on simple square pulses and allows for the measurement of junctions with critical currents of the order of 10nA with bias pulses of the order of 100ns. A correlation analysis of the switching events is performed to show how the switching probability depends on the wait time between repeated bias pulses.Comment: Changed abstract Added reference 1

Influence of Tire Tread Pattern and Runway Surface Condition on Braking Friction and Rolling Resistance of a Modern Aircraft Tire

A series of taxiing tests was conducted at the Langley landing loads track with both braked and unbraked (freely rolling) single and tandem wheels equipped with 32x8.8 type VII aircraft tires of different tread designs to obtain data on tire and braking characteristics during operation on dry and on contaminated concrete and asphalt run ways. Contaminants used were water, slush, JP-4 jet fuel, and organic and detergent fire-extinguishing foams. Forward velocities for the tests ranged from approximately 13 to 104 knots. Vertical loads of approximately 9,000 to 22,000 pounds and tire inflation pressures of 85 to 350 pounds per square inch were used. Results indicated that the unbraked tire rolling resistance increased with increasing forward velocity on dry and on contaminated runway surfaces. Peak tire-ground friction coefficients developed during wheel braking decreased rapidly with increasing velocity on contaminated runways but remained relatively unchanged on dry runways as the forward velocity was increased. Dry-runway friction coefficients were found to be relatively insensitive to tire tread pattern. However, the magnitude of the friction coefficients developed by tires on contaminated runways was extremely sensitive to the tire tread pat tern used, with circumferential-groove treads developing the highest values of friction coefficient, and smooth and dimple treads the lowest values for the tread patterns and runway conditions investigated

The Extinction Distribution in the Galaxy UGC 5041

We probe the dust extinction through the foreground disk of the overlapping galaxy pair UGC 5041 by analyzing B,I, and H band images. The inclined foreground disk of this infrared-selected pair is almost opaque in B at a projected distance of ~8kpc. From the images, we estimate directly the area-weighted distribution of differential near-IR extinction: it is nearly Gaussian with =0.6 and sigma=0.27. For a homogenous dust distribution and a Milky Way extinction curve, this corresponds to a face-on distribution p(tau) with a mean of =0.34 and sigma_V=0.15. For a clumpy dust model the optical depth estimate increases to =0.41 and sigma_V=0.19. Even though the galaxy pair is subject to different selection biases and our analysis is subject to different systematics, the result is consistent with existing case studies, indicating that ~0.3 is generic for late-type spirals near their half-light radii. We outline how to estimate from p(tau) by how much background quasars are underreresented, where projected within ~10kpc of nearby spirals, such as damped Ly-alpha absorbers or gravitational lenses; from our data we derive a factor of two deficit for flux-limited, optical surveys.Comment: 18 pages, 3 figures; To appear in the Astronomical Journa

Decline in condition of northern bluefin tuna (Thunnus thynnus) in the Gulf of Maine

The northern bluefin tuna (Thunnus thynnus) is a highly mobile apex predator in the Gulf of Maine. Despite current stock assessments that indicate historically high abundance of its main prey, Atlantic herring (Clupea harengus), commercial fishermen have observed declines in the somatic condition of northern bluefin tuna during the last decade. We examined this claim by reviewing detailed logbooks of northern bluefin tuna condition from a local fishermen’s cooperative and applying multinomial regression, a robust tool for exploring how a categorical variable may be related to other variables of interest. The data set contained >3082 observations of condition (fat and oil content and fish shape) from fish landed between 1991 and 2004. Energy from stored lipids is used for migration and reproduction; therefore a reduction in energy acquisition on bluefin tuna feeding grounds could diminish allocations to growth and gamete production and have detrimental consequences for rebuilding the western Atlantic population. A decline in northern bluefin tuna somatic condition could indicate substantial changes in the bottom-up transfer of energy in the Gulf of Maine, shifts in their reproductive or migratory patterns, impacts of fishing pressure, or synergistic effects from multiple causes

Cutting a pie is not a piece of cake

Is there a division among n players of a cake using n-1 parallel vertical cuts, or of a pie using n radial cuts, that is envy-free (each player thinks he or she receives a largest piece and so does not envy another player) and undominated (there is no other allocation as good for all players and better for at least one)? David Gale first asked this question for pies. We provide complete answers for both cakes and pies. The answers depend on the number of players (two versus three or more players) and whether the players' preferences satisfy certain continuity assumptions. We also give some simple algorithms for cutting a pie when there are two or more players, but these algorithms do not guarantee all the properties one might desire in a division, which makes pie-cutting harder than cake-cutting. We suggest possible applications and conclude with two open questions.Fair division; cake-cutting; pie-cutting; divisible good; envy-freeness; allocative efficiency

Absolute Calibration of the Radio Astronomy Flux Density Scale at 22 to 43 GHz Using Planck

The Planck mission detected thousands of extragalactic radio sources at frequencies from 28 to 857 GHz. Planck's calibration is absolute (in the sense that it is based on the satellite's annual motion around the Sun and the temperature of the cosmic microwave background), and its beams are well characterized at sub-percent levels. Thus Planck's flux density measurements of compact sources are absolute in the same sense. We have made coordinated VLA and ATCA observations of 65 strong, unresolved Planck sources in order to transfer Planck's calibration to ground-based instruments at 22, 28, and 43 GHz. The results are compared to microwave flux density scales currently based on planetary observations. Despite the scatter introduced by the variability of many of the sources, the flux density scales are determined to 1-2% accuracy. At 28 GHz, the flux density scale used by the VLA runs 3.6% +- 1.0% below Planck values; at 43 GHz, the discrepancy increases to 6.2% +- 1.4% for both ATCA and the VLA.Comment: 16 pages, 4 figures and 4 table

Reflectance of Polytetrafluoroethylene (PTFE) for Xenon Scintillation Light

Gaseous and liquid xenon particle detectors are being used in a number of applications including dark matter search and neutrino-less double beta decay experiments. Polytetrafluoroethylene (PTFE) is often used in these detectors both as electrical insulator and as a light reflector to improve the efficiency of detection of scintillation photons. However, xenon emits in the vacuum ultraviolet wavelength region (175 nm) where the reflecting properties of PTFE are not sufficiently known. In this work we report on measurements of PTFE reflectance, including its angular distribution, for the xenon scintillation light. Various samples of PTFE, manufactured by different processes (extruded, expanded, skived and pressed) have been studied. The data were interpreted with a physical model comprising both specular and diffuse reflections. The reflectance obtained for these samples ranges from about 47% to 66% for VUV light. Fluoropolymers, namely ETFE, FEP and PFA were also measured