Matching with Couples: a Multidisciplinary Survey

This survey deals with two-sided matching markets where one set of agents (workers/residents) has to be matched with another set of agents (firms/hospitals). We first give a short overview of a selection of classical results. Then, we review recent contributions to a complex and representative case of matching with complementarities, namely matching markets with couples. We discuss contributions from computer scientists, economists, and game theorists.matching; couples; stability; computational complexity; incentive compatibility; restricted domains; large markets

Statistical Power Law due to Reservoir Fluctuations and the Universal Thermostat Independence Principle

Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed automatically by an equipartition relation, while the q-parameter is related to the scaled variance and to the expectation value of the particle number. For the binomial distribution q is smaller, for the negative binomial q is larger than one. These results also represent an approximation for general particle number distributions in the reservoir up to second order in the canonical expansion. For general systems the average phase-space volume ratio expanded to second order delivers a q parameter related to the heat capacity and to the variance of the temperature. However, q differing from one leads to non-additivity of the Boltzmann-Gibbs entropy. We demonstrate that a deformed entropy, K(S), can be constructed and used for demanding additivity. This requirement leads to a second order differential equation for K(S). Finally, the generalized q-entropy formula contains the Tsallis, Renyi and Boltzmann-Gibbs-Shannon expressions as particular cases. For diverging temperature variance we obtain a novel entropy formula.Comment: Talk given by T.S.Biro at Sigma Phi 2014, Rhodos, Greec

Robust hand-eye calibration of 2D laser sensors using a single-plane calibration artefact

When a vision sensor is used in conjunction with a robot, hand-eye calibration is necessary to determine the accurate position of the sensor relative to the robot. This is necessary to allow data from the vision sensor to be defined in the robot's global coordinate system. For 2D laser line sensors hand-eye calibration is a challenging process because they only collect data in two dimensions. This leads to the use of complex calibration artefacts and requires multiple measurements be collected, using a range of robot positions. This paper presents a simple and robust hand-eye calibration strategy that requires minimal user interaction and makes use of a single planar calibration artefact. A significant benefit of the strategy is that it uses a low-cost, simple and easily manufactured artefact; however, the lower complexity can lead to lower variation in calibration data. In order to achieve a robust hand-eye calibration using this artefact, the impact of robot positioning strategies is considered to maintain variation. A theoretical basis for the necessary sources of input variation is defined by a mathematical analysis of the system of equations for the calibration process. From this, a novel strategy is specified to maximize data variation by using a circular array of target scan lines to define a full set of required robot positions. A simulation approach is used to further investigate and optimise the impact of robot position on the calibration process, and the resulting optimal robot positions are then experimentally validated for a real robot mounted laser line sensor. Using the proposed optimum method, a semi-automatic calibration process, which requires only four manually scanned lines, is defined and experimentally demonstrated