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

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

Collision of High Frequency Plane Gravitational and Electromagnetic Waves

We study the head-on collision of linearly polarized, high frequency plane gravitational waves and their electromagnetic counterparts in the Einstein-Maxwell theory. The post-collision space-times are obtained by solving the vacuum Einstein-Maxwell field equations in the geometrical optics approximation. The head-on collisions of all possible pairs of these systems of waves is described and the results are then generalised to non-linearly polarized waves which exhibit the maximum two degrees of freedom of polarization.Comment: Latex file, 17 pages, accepted for publication in International Journal of Modern Physics

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.

Evaluation of Stress Corrosion Cracking Susceptibility Using Fracture Mechanics Techniques, Part 1

Stress corrosion cracking (SSC) tests were performed on 13 aluminum alloys, 13 precipitation hardening stainless steels, and two titanium 6Al-4V alloy forgings to compare fracture mechanics techniques with the conventional smooth specimen procedures. Commercially fabricated plate and rolled or forged bars 2 to 2.5-in. thick were tested. Exposures were conducted outdoors in a seacoast atmosphere and in an inland industrial atmosphere to relate the accelerated tests with service type environments. With the fracture mechanics technique tests were made chiefly on bolt loaded fatigue precracked compact tension specimens of the type used for plane-strain fracture toughness tests. Additional tests of the aluminum alloy were performed on ring loaded compact tension specimens and on bolt loaded double cantilever beams. For the smooth specimen procedure 0.125-in. dia. tensile specimens were loaded axially in constant deformation type frames. For both aluminum and steel alloys comparative SCC growth rates obtained from tests of precracked specimens provide an additional useful characterization of the SCC behavior of an alloy

The Phase Diagram of 1-in-3 Satisfiability Problem

We study the typical case properties of the 1-in-3 satisfiability problem, the boolean satisfaction problem where a clause is satisfied by exactly one literal, in an enlarged random ensemble parametrized by average connectivity and probability of negation of a variable in a clause. Random 1-in-3 Satisfiability and Exact 3-Cover are special cases of this ensemble. We interpolate between these cases from a region where satisfiability can be typically decided for all connectivities in polynomial time to a region where deciding satisfiability is hard, in some interval of connectivities. We derive several rigorous results in the first region, and develop the one-step--replica-symmetry-breaking cavity analysis in the second one. We discuss the prediction for the transition between the almost surely satisfiable and the almost surely unsatisfiable phase, and other structural properties of the phase diagram, in light of cavity method results.Comment: 30 pages, 12 figure

The physiological effects of Transcranial Electrical Stimulation do not apply to parameters commonly used in studies of Cognitive Neuromodulation

Transcranial direct current stimulation (tDCS) and transcranial random noise stimulation (tRNS) have been claimed to produce many remarkable enhancements in perception, cognition, learning and numerous clinical conditions. The physiological basis of the claims for tDCS rests on the finding that 1 mA of unilateral anodal stimulation increases cortical excitation and 1 mA of cathodal produces inhibition. Here we show that these classic excitatory and inhibitory effects do not hold for the bilateral stimulation or 2 mA intensity conditions favoured in cognitive enhancement experiments. This is important because many, including some of the most salient claims are based on experiments using 2 mA bilateral stimulation. The claims for tRNS are also based on unilateral stimulation. Here we show that, again the classic excitatory effects of unilateral tRNS do not extend to the bilateral stimulation preferred in enhancement experiments. Further, we show that the effects of unilateral tRNS do not hold when one merely doubles the stimulation duration. We are forced to two conclusions: (i) that even if all the data on TES enhancements are true, the physiological explanations on which the claims are based are at best not established but at worst false, and (ii) that we cannot explain, scientifically at least, how so many experiments can have obtained data consistent with physiological effects that may not exist

The importance of socio-economic variables in cancer screening participation: A comparison between population-based and opportunistic screening in the EU-15

Objectives To investigate differences in participation with breast and cervical cancer screening related to individual socio-economic characteristics, across population-based versus opportunistic screening programmes. Methods Data from Eurobarometer 66.2 “Health in the European Union” 2006 on self-reported breast and cervical cancer screening participation in the preceding 12 months within the EU 15 was obtained The sample was restricted to those eligible for screening based on the screening age within each country. Observations for 2214 and 5025 individuals respectively for breast and cervical cancer screening were available. Data on marital status, self-reported health, socio-economic group and years of education were also available. Screening programmes were categorised as population-based or opportunistic and logistic regression analysis used to examine the relationship between participation, individual characteristics and programme type. Results Differences in participation related to socio-economic status were observed in opportunistic screening programmes for breast cancer (OR = 0.63* and OR = 0.51**) and cervical cancer (OR = 0.75** and OR = 0.64**). Differences related to socio-economic characteristics were not found with respect to participation in population-based programmes. Conclusions In opportunistic programmes, differences in participation across socio-economic groups are evident in respect of both breast and cervical cancer screening. These differences may have implications for treatment and outcomes across socio-economic groups. Such differences were not evident in population-based programmes

Exact and Fast Numerical Algorithms for the Stochastic Wave Equation

On the basis of integral representations we propose fast numerical methods to solve the Cauchy problem for the stochastic wave equation without boundaries and with the Dirichlet boundary conditions. The algorithms are exact in a probabilistic sense