Local search for stable marriage problems

The stable marriage (SM) problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. In the classical formulation, n men and n women express their preferences (via a strict total order) over the members of the other sex. Solving a SM problem means finding a stable marriage where stability is an envy-free notion: no man and woman who are not married to each other would both prefer each other to their partners or to being single. We consider both the classical stable marriage problem and one of its useful variations (denoted SMTI) where the men and women express their preferences in the form of an incomplete preference list with ties over a subset of the members of the other sex. Matchings are permitted only with people who appear in these lists, an we try to find a stable matching that marries as many people as possible. Whilst the SM problem is polynomial to solve, the SMTI problem is NP-hard. We propose to tackle both problems via a local search approach, which exploits properties of the problems to reduce the size of the neighborhood and to make local moves efficiently. We evaluate empirically our algorithm for SM problems by measuring its runtime behaviour and its ability to sample the lattice of all possible stable marriages. We evaluate our algorithm for SMTI problems in terms of both its runtime behaviour and its ability to find a maximum cardinality stable marriage.For SM problems, the number of steps of our algorithm grows only as O(nlog(n)), and that it samples very well the set of all stable marriages. It is thus a fair and efficient approach to generate stable marriages.Furthermore, our approach for SMTI problems is able to solve large problems, quickly returning stable matchings of large and often optimal size despite the NP-hardness of this problem.Comment: 12 pages, Proc. COMSOC 2010 (Third International Workshop on Computational Social Choice

Effect of sonication on the viscosity of reconstituted skim milk powder and milk protein concentrate as influenced by solids concentration, temperature and sonication

Skim milk powder (SMP) and milk protein concentrates (MPCs) are manufactured by evaporation followed by spray drying and are widely used as functional and nutritional ingredients. This study investigated the effects of temperature (40–60 °C) and total solids content (TS) on the viscosity of reconstituted MPC (rMPC) (≥30% TS) and SMP (rSMP) (≥46% TS) in laboratory conditions. Additionally, the influence of sonication in batch (70% amplitude) and flow through systems (90% amplitude) was studied in a laboratory setting. The viscosity increased for all treatments with an increase in TS and decreased with an increase in temperature. Overall, sonication in both batch (30 s) and flow through systems (10.1, 20.2, and 30.2 s) resulted in significant decreases in viscosity for both rSMP and rMPC. An increase in viscosity was observed after post-sonication circulation; however, the viscosity did not return to the pre-sonication values

Exciton mediated one phonon resonant Raman scattering from one-dimensional systems

We use the Kramers-Heisenberg approach to derive a general expression for the resonant Raman scattering cross section from a one-dimensional (1D) system explicitly accounting for excitonic effects. The result should prove useful for analyzing the Raman resonance excitation profile lineshapes for a variety of 1D systems including carbon nanotubes and semiconductor quantum wires. We apply this formalism to a simple 1D model system to illustrate the similarities and differences between the free electron and correlated electron-hole theories.Comment: 10 pages, 6 figure

Chirality dependence of the radial breathing phonon mode density in single wall carbon nanotubes

A mass and spring model is used to calculate the phonon mode dispersion for single wall carbon nanotubes (SWNTs) of arbitrary chirality. The calculated dispersions are used to determine the chirality dependence of the radial breathing phonon mode (RBM) density. Van Hove singularities, usually discussed in the context of the single particle electronic excitation spectrum, are found in the RBM density of states with distinct qualitative differences for zig zag, armchair and chiral SWNTs. The influence the phonon mode density has on the two phonon resonant Raman scattering cross-section is discussed.Comment: 6 pages, 2 figures, submitted to Phys. Rev.

When to invest in carbon capture and storage technology in the presence of uncertainty: a mathematical model. ESRI WP461, July 2013

We present a model for determining analytically the critical threshold for investment in carbon capture and storage technology in a region where carbon costs are volatile and assuming the cost of investment decreases. We first study a deterministic model with quite general dependence on carbon price and then analyse the effect of carbon price volatility on the optimal investment decision by solving a Bellman equation with an infinite planning horizon. We find that increasing the expected carbon price volatility increases the critical investment threshold and that adoption of this technology is not optimal at current prices, in agreement with other works. However, reducing carbon price volatility by switching from carbon permits to taxes or by introducing a carbon floor as in Great Britain would accelerate the optimal adoption of this technology. Our deterministic model provides a good description of this decision problem

High mass star formation in the infrared dark cloud G11.11-0.12

We report detection of moderate to high-mass star formation in an infrared dark cloud (G11.11-0.12) where we discovered class II methanol and water maser emissions at 6.7 GHz and 22.2 GHz, respectively. We also observed the object in ammonia inversion transitions. Strong emission from the (3,3) line indicates a hot (~60 K) compact component associated with the maser emission. The line width of the hot component (4 km/s), as well as the methanol maser detection, are indicative of high mass star formation. To further constrain the physical parameters of the source, we derived the spectral energy distribution (SED) of the dust continuum by analysing data from the 2MASS survey, HIRAS, MSX, the Spitzer Space Telescope, and interferometric 3mm observations. The SED was modelled in a radiative transfer program: a) the stellar luminosity equals 1200 L_sun corresponding to a ZAMS star of 8 M_sun; b) the bulk of the envelope has a temperature of 19 K; c) the mass of the remnant protostellar cloud in an area 8x10^17 cm or 15 arcsec across amounts to 500M_sun, if assuming standard dust of the diffuse medium, and to about 60 M_sun, should the grains be fluffy and have ice mantles; d) the corresponding visual extinction towards the star is a few hundred magnitudes. The near IR data can be explained by scattering from tenuous material above a hypothetical disk. The class II methanol maser lines are spread out in velocity over 11 km/s. To explain the kinematics of the masing spots, we propose that they are located in a Kepler disk at a distance of about 250 AU. The dust temperatures there are around 150 K, high enough to evaporate methanol--containing ice mantles.Comment: 10 pages, 6 figures, Accepted for publication in Astronomy & Astrophysics Journa