Physical meaning of the radial index of Laguerre-Gauss beams

The Laguerre-Gauss modes are a class of fundamental and well-studied optical fields. These stable, shape-invariant photons - exhibiting circular-cylindrical symmetry - are familiar from laser optics, micro-mechanical manipulation, quantum optics, communication, and foundational studies in both classical optics and quantum physics. They are characterized, chiefly, by two modes numbers: the azimuthal index indicating the orbital angular momentum of the beam - which itself has spawned a burgeoning and vibrant sub-field - and the radial index, which up until recently, has largely been ignored. In this manuscript we develop a differential operator formalism for dealing with the radial modes in both the position and momentum representations, and - more importantly - give for the first time the meaning of this quantum number in terms of a well-defined physical parameter: the "intrinsic hyperbolic momentum charge".Comment: 12 pages, 4 figures, comments encourage

Bayesian Synthesis: Combining subjective analyses, with an application to ozone data

Bayesian model averaging enables one to combine the disparate predictions of a number of models in a coherent fashion, leading to superior predictive performance. The improvement in performance arises from averaging models that make different predictions. In this work, we tap into perhaps the biggest driver of different predictions---different analysts---in order to gain the full benefits of model averaging. In a standard implementation of our method, several data analysts work independently on portions of a data set, eliciting separate models which are eventually updated and combined through a specific weighting method. We call this modeling procedure Bayesian Synthesis. The methodology helps to alleviate concerns about the sizable gap between the foundational underpinnings of the Bayesian paradigm and the practice of Bayesian statistics. In experimental work we show that human modeling has predictive performance superior to that of many automatic modeling techniques, including AIC, BIC, Smoothing Splines, CART, Bagged CART, Bayes CART, BMA and LARS, and only slightly inferior to that of BART. We also show that Bayesian Synthesis further improves predictive performance. Additionally, we examine the predictive performance of a simple average across analysts, which we dub Convex Synthesis, and find that it also produces an improvement.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS444 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Acute management of poor condition subarachnoid hemorrhage patients

Poor condition subarachnoid hemorrhage (SAH) patients present a high mortality and morbidity. In this study, we reviewed the acute interventional (surgical and endovascular) management of 109 SAH-poor condition patients, who were treated as early as logistically possible after confirming stable circulation parameters. Patients over the age of 70 years, without clinical response to painful stimulation were excluded. We recognized at least 3 different postinterventional therapeutic approaches: (1) Norm- or hypovolemic, normotensive hemodilution in 30 patients with space-occupying intracranial hematomas as well as in 31 cases with acute cerebro-spinal-fluid obstruction. (2) Normovolemic, hypertensive hemodilution after unilateral decompressive craniotomy in 23 surgical- and 2 endovascular-treated patients with focalized space occupying lesions and reduced cerebral perfusion. (3) Hypovolemic, normo-, or hypertensive hemodilution after bilateral decompressive craniotomy in 23 cases with massive brain-swelling. We observed a reduced mortality (21%). The overall late outcome was favorable in 56% and unfavorable in 23%. Selective aggressive treatment adapted to increase the cerebral perfusion, seems to be an effective therapy to improve the survival and outcome of several poor condition SAH-patients

Rediscovering a little known fact about the t-test and the F-test: Algebraic, Geometric, Distributional and Graphical Considerations

We discuss the role that the null hypothesis should play in the construction of a test statistic used to make a decision about that hypothesis. To construct the test statistic for a point null hypothesis about a binomial proportion, a common recommendation is to act as if the null hypothesis is true. We argue that, on the surface, the one-sample t-test of a point null hypothesis about a Gaussian population mean does not appear to follow the recommendation. We show how simple algebraic manipulations of the usual t-statistic lead to an equivalent test procedure consistent with the recommendation. We provide geometric intuition regarding this equivalence and we consider extensions to testing nested hypotheses in Gaussian linear models. We discuss an application to graphical residual diagnostics where the form of the test statistic makes a practical difference. By examining the formulation of the test statistic from multiple perspectives in this familiar example, we provide simple, concrete illustrations of some important issues that can guide the formulation of effective solutions to more complex statistical problems.Comment: 22 pages, 5 figure

Robustness analysis of evolutionary controller tuning using real systems

A genetic algorithm (GA) presents an excellent method for controller parameter tuning. In our work, we evolved the heading as well as the altitude controller for a small lightweight helicopter. We use the real flying robot to evaluate the GA's individuals rather than an artificially consistent simulator. By doing so we avoid the ldquoreality gaprdquo, taking the controller from the simulator to the real world. In this paper we analyze the evolutionary aspects of this technique and discuss the issues that need to be considered for it to perform well and result in robust controllers

On the Difficulty of Comparing the Spatial Distribution of Service Industries Across Nations: Contrasting Spain and Canada.

The spatial distribution of employment in service industries is compared for Spain and Canada for nine (9) industry classes. The empirical and theoretical literature on modern services stresses the importance of agglomeration economies for high-order services. The relationship between city-size and location is examined with emphasis on cases that deviate from predicted patterns. The results for Spain and Canada reconfirm the weight of city-size as a determinant of location for high-order services. However, once one goes beyond this fairly predictable result, national differences in geography, institutions, and development come to the fore, making generalizations more difficult. Unlike most manufacturing industries, the definition and the spatial behavior of many service sectors is highly sensitive to institutional factors, creating unique patterns largely fashioned by national context.

Nonlinear surface impurity in a semi-infinite 2D square lattice

We examine the formation of localized states on a generalized nonlinear impurity located at, or near the surface of a semi-infinite 2D square lattice. Using the formalism of lattice Green functions, we obtain in closed form the number of bound states as well as their energies and probability profiles, for different nonlinearity parameter values and nonlinearity exponents, at different distances from the surface. We specialize to two cases: impurity close to an "edge" and impurity close to a "corner". We find that, unlike the case of a 1D semi-infinite lattice, in 2D, the presence of the surface helps the formation of a localized state.Comment: 6 pages, 7 figures, submitted to PR