An integer programming Model for the Hospitals/Residents Problem with Couples

The Hospitals/Residents problem with Couples (hrc) is a generalisation of the classical Hospitals/Residents problem (hr) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of hrc. Further, we present an Integer Programming (IP) model for hrc and extend it the case where preference lists can include ties. Further, we describe an empirical study of an IP model for HRC and its extension to the case where preference lists can include ties. This model was applied to randomly generated instances and also real-world instances arising from previous matching runs of the Scottish Foundation Allocation Scheme, used to allocate junior doctors to hospitals in Scotland

Abrasion of flat rotating shapes

We report on the erosion of flat linoleum "pebbles" under steady rotation in a slurry of abrasive grit. To quantify shape as a function of time, we develop a general method in which the pebble is photographed from multiple angles with respect to the grid of pixels in a digital camera. This reduces digitization noise, and allows the local curvature of the contour to be computed with a controllable degree of uncertainty. Several shape descriptors are then employed to follow the evolution of different initial shapes toward a circle, where abrasion halts. The results are in good quantitative agreement with a simple model, where we propose that points along the contour move radially inward in proportion to the product of the radius and the derivative of radius with respect to angle

Where is the fuzz? Undetected Lyman alpha nebulae around QSOs at z~2.3

We observed a small sample of 5 radio-quiet QSOs with integral field spectroscopy to search for possible extended emission in the Ly$\alpha$ line. We subtracted the QSO point sources using a simple PSF self-calibration technique that takes advantage of the simultaneous availability of spatial and spectral information. In 4 of the 5 objects we find no significant traces of extended Ly$\alpha$ emission beyond the contribution of the QSO nuclei itself, while in UM 247 there is evidence for a weak and spatially quite compact excess in the Ly$\alpha$ line at several kpc outside the nucleus. For all objects in our sample we estimated detection limits for extended, smoothly distributed Ly$\alpha$ emission by adding fake nebulosities into the datacubes and trying to recover them after PSF subtraction. Our observations are consistent with other studies showing that giant Ly$\alpha$ nebulae such as those found recently around some quasars are very rare. Ly$\alpha$ fuzz around typical radio-quiet QSOs is fainter, less extended and is therefore much harder to detect. The faintness of these structures is consistent with the idea that radio-quiet QSOs typically reside in dark matter haloes of modest masses.Comment: 12 Pages, Accepted for publication in A&

The collapse of a medical clearinghouse (and why such failures are rare)

The collapse of the clearinghouse for the entry-level gastroenterology labor market offers a unique opportunity to study how stable clearinghouses succeed and fail. To explore the reasons for the failure of the clearinghouse (and why failures of this kind of clearinghouse have been so rare), we conduct an experimental investigation of demand shocks of the kind that occurred in the gastroenterology market. We find that a reduction in demand for positions leads to the collapse of the match only when it is detectable by firms before being detected by workers (as in the unexpected shock that took place in 1996, which could be seen by firms in their reduced applicant pools). Simple demand and supply imbalances do not seem to interfere with the operation of the centralized match. Our results suggest an affirmative answer to the question posed by market participants about whether the clearinghouse could be successfully restarted, and that this would relieve some of the distress now reported in that market, by allowing it to operate later, at a more uniform time, and with more national scope.

Microscopic two-nucleon overlaps and knockout reactions from 12^{12}C

The nuclear structure dependence of direct reactions that remove a pair of like or unlike nucleons from a fast $^{12}$C projectile beam are considered. Specifically, we study the differences in the two-nucleon correlations present and the predicted removal cross sections when using $p$-shell shell-model and multi-$\hbar\omega$ no-core shell-model (NCSM) descriptions of the two-nucleon overlaps for the transitions to the mass $A$=10 projectile residues. The NCSM calculations use modern chiral two-nucleon and three-nucleon (NN+3N) interactions. The $np$-removal cross sections to low-lying $T$=0, $^{10}$B final states are enhanced when using the NCSM two-nucleon amplitudes. The calculated absolute and relative partial cross sections to the low energy $^{10}$B final states show a significant sensitivity to the interactions used, suggesting that assessments of the overlap functions for these transitions and confirmations of their structure could be made using final-state-exclusive measurements of the $np$-removal cross sections and the associated momentum distributions of the forward travelling projectile-like residues.Comment: 9 pages, 7 figure

Forebody and vertical stabilizer effects on directional stability of a reusable LOX/RP (061) booster AR 12161-2

Results are presented of a wind tunnel test on the directional stability of space shuttle booster configurations. The test was conducted at the 14-inch trisonic tunnel starting 6 December 1971 and continued through 11 December 1971 for a total of 66 occupancy hours. Configurations tested included a cylindrical body with two axisymmetrical noses, one with and without canopy, one delta wing, located in two positions, five vertical tails (including a V tail), two having split rudders, ventral fins, two sets of chines, three airbreathing engine pods, and rocket engine shrouds. The model scale was 0.003366

Evaporation of high speed sporadic meteors

International audienceRecent measurements conducted at the Arecibo Observatory report high-speed sporadic meteors having velocities near 50 km/s. The results seem to indicate a bimodal velocity distribution in the sporadic meteors (maxima at ~20 km/s and ~50 km/s). The particles have a maximum mass of ~1 ?g. This paper will present an analysis of the ablation of 1 ?g meteoroids having velocities of 20, 30, 50, and 70 km/s. The calculations show that there is fractionation even for the fast meteoroids, the effect being particularly noticeable for the 1 ?g sporadic particles, and less so for the heavier particles. The relevance of the calculations to the radar observations of the sporadic meteors will be discussed

The Hospitals/Residents Problem with Couples: complexity and integer programming models

The Hospitals / Residents problem with Couples (hrc) is a generalisation of the classical Hospitals / Residents problem (hr) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of hrc, and also an inapproximability bound for finding a matching with the minimum number of blocking pairs in equally restricted instances of hrc. Further, we present a full description of the first Integer Programming model for finding a maximum cardinality stable matching in an instance of hrc and we describe empirical results when this model applied to randomly generated instances of hrc

Bubble statistics and coarsening dynamics for quasi-two dimensional foams with increasing liquid content

We report on the statistics of bubble size, topology, and shape and on their role in the coarsening dynamics for foams consisting of bubbles compressed between two parallel plates. The design of the sample cell permits control of the liquid content, through a constant pressure condition set by the height of the foam above a liquid reservoir. We find that in the scaling state, all bubble distributions are independent not only of time but also of liquid content. For coarsening, the average rate decreases with liquid content due to the blocking of gas diffusion by Plateau borders inflated with liquid. By observing the growth rate of individual bubbles, we find that von Neumann's law becomes progressively violated with increasing wetness and with decreasing bubble size. We successfully model this behavior by explicitly incorporating the border blocking effect into the von Neumann argument. Two dimensionless bubble shape parameters naturally arise, one of which is primarily responsible for the violation of von Neumann's law for foams that are not perfectly dry