Signatures of Classical Periodic Orbits on a Smooth Quantum System

Gutzwiller's trace formula and Bogomolny's formula are applied to a non--specific, non--scalable Hamiltonian system, a two--dimensional anharmonic oscillator. These semiclassical theories reproduce well the exact quantal results over a large spatial and energy range.Comment: 12 pages, uuencoded postscript file (1526 kb

Learning When Training Data are Costly: The Effect of Class Distribution on Tree Induction

For large, real-world inductive learning problems, the number of training examples often must be limited due to the costs associated with procuring, preparing, and storing the training examples and/or the computational costs associated with learning from them. In such circumstances, one question of practical importance is: if only n training examples can be selected, in what proportion should the classes be represented? In this article we help to answer this question by analyzing, for a fixed training-set size, the relationship between the class distribution of the training data and the performance of classification trees induced from these data. We study twenty-six data sets and, for each, determine the best class distribution for learning. The naturally occurring class distribution is shown to generally perform well when classifier performance is evaluated using undifferentiated error rate (0/1 loss). However, when the area under the ROC curve is used to evaluate classifier performance, a balanced distribution is shown to perform well. Since neither of these choices for class distribution always generates the best-performing classifier, we introduce a budget-sensitive progressive sampling algorithm for selecting training examples based on the class associated with each example. An empirical analysis of this algorithm shows that the class distribution of the resulting training set yields classifiers with good (nearly-optimal) classification performance

A simple derivation of Kepler's laws without solving differential equations

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to en explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by beginners at university (or even before) can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest

Collective action problems in the contracting of public services: Evidence from the UK’s Ministry of Justice

In this paper, we examine collective action problems in the UK government in the process of contracting public services to the private sector. In particular, we examine the Ministry of Justice (MoJ) and its evolution in contract monitoring as part of a larger effort of the government to join up departments in contract management. By analyzing MoJ’s management of the electronic tagging contract with G4S and Serco, we show that a lack of coordination within the department and with other departments was a major reason for the overbilling by the two companies. Recent efforts to join up contract management efforts throughout government show promise in rectifying these contracting issues

A Model for Prediction of the Tidal Currents in the English Channel

A model for prediction of tidal currents in the English Channel is presented. It is based on the classical harmonic description of tides deduced from the spectral development of the luni-solar tidal potential. The spatial distribution of the characteristic parameters (intensity, phase, and direction of the maximum velocity vector, ellipticity of the hodograph) for the 26 harmonic constituents introduced in the prediction procedure are deduced from a numerical simulation of 1 month’s duration for the entire English Channel. Two kinds of documents can be produced from this model : instantaneous velocity fields over a given area, and time series of the intensity and the direction of the velocity vector at a given location, over a given period. Four examples of prediction are presented, corresponding to specific areas and over periods where tidal currents have actually been observed. The comparison between predictions and observations is very satisfactory

Axial instability of rotating relativistic stars

Perturbations of rotating relativistic stars can be classified by their behavior under parity. For axial perturbations (r-modes), initial data with negative canonical energy is found with angular dependence $e^{im\phi}$ for all values of $m\geq 2$ and for arbitrarily slow rotation. This implies instability (or marginal stability) of such perturbations for rotating perfect fluids. This low $m$-instability is strikingly different from the instability to polar perturbations, which sets in first for large values of $m$. The timescale for the axial instability appears, for small angular velocity $\Omega$, to be proportional to a high power of $\Omega$. As in the case of polar modes, viscosity will again presumably enforce stability except for hot, rapidly rotating neutron stars. This work complements Andersson's numerical investigation of axial modes in slowly rotating stars.Comment: Latex, 18 pages. Equations 84 and 85 are corrected. Discussion of timescales is corrected and update