Does ‘better’ discounting lead to ‘worse’ outcomes in long-run decisions? The dilemma of hyperbolic discounting

The shortcomings of conventional discounting, especially in the context of long-run environmental problems, have been extensively discussed in the literature. Recently, hyperbolic discounting, i. e. discounting at declining instead of constant discount rates, has attracted a lot of interest among both scientists and politicians. Although there are compelling arguments for employing hyperbolic discounting, there are also pitfalls, which have to be pointed out. In this paper I show that the problem of time-inconsistency, an inherent characteristics of hyperbolic discounting, leads to a potential clash between economic efficiency and intergenerational equity. As an example, I refer to the weak progress in the controlling of greenhouse gas emissions under the Kyoto protocol. As the problem of time-inconsistency cannot be solved on economic grounds alone, there is a need for an intergenerational moral commitment.

Comparing the performance of hyperbolic and circular rod quadrupole mass spectrometers with applied higher order auxiliary excitation

This work applies higher order auxiliary excitation techniques to two types of quadrupole mass spectrometers (QMSs): commercial systems and spaceborne instruments. The operational settings of a circular rod geometry commercial system and an engineering test-bed for a hyperbolic rod geometry spaceborne instrument were matched, with the relative performance of each sensor characterized with and without applied excitation using isotopic measurements of Kr+. Each instrument was operated at the limit of the test electronics to determine the effect of auxiliary excitation on extending instrument capabilities. For the circular rod sensor, with applied excitation, a doubling of the mass resolution at 1% of peak transmission resulted from the elimination of the low-mass side peak tail typical of such rod geometries. The mass peak stability and ion rejection efficiency were also increased by factors of 2 and 10, respectively, with voltage scan lines passing through the center of stability islands formed from auxiliary excitation. Auxiliary excitation also resulted in factors of 6 and 2 in peak stability and ion rejection efficiency, respectively, for the hyperbolic rod sensor. These results not only have significant implications for the use of circular rod quadrupoles with applied excitation as a suitable replacement for traditional hyperbolic rod sensors, but also for extending the capabilities of existing hyperbolic rod QMSs for the next generation of spaceborne instruments and low-mass commercial systems.

Identification of adequate neurally adjusted ventilatory assist (NAVA) during systematic increases in the NAVA level

Neurally adjusted ventilatory assist (NAVA) delivers airway pressure (P(aw)) in proportion to the electrical activity of the diaphragm (EAdi) using an adjustable proportionality constant (NAVA level, cm·H(2)O/μV). During systematic increases in the NAVA level, feedback-controlled down-regulation of the EAdi results in a characteristic two-phased response in P(aw) and tidal volume (Vt). The transition from the 1st to the 2nd response phase allows identification of adequate unloading of the respiratory muscles with NAVA (NAVA(AL)). We aimed to develop and validate a mathematical algorithm to identify NAVA(AL). P(aw), Vt, and EAdi were recorded while systematically increasing the NAVA level in 19 adult patients. In a multistep approach, inspiratory P(aw) peaks were first identified by dividing the EAdi into inspiratory portions using Gaussian mixture modeling. Two polynomials were then fitted onto the curves of both P(aw) peaks and Vt. The beginning of the P(aw) and Vt plateaus, and thus NAVA(AL), was identified at the minimum of squared polynomial derivative and polynomial fitting errors. A graphical user interface was developed in the Matlab computing environment. Median NAVA(AL) visually estimated by 18 independent physicians was 2.7 (range 0.4 to 5.8) cm·H(2)O/μV and identified by our model was 2.6 (range 0.6 to 5.0) cm·H(2)O/μV. NAVA(AL) identified by our model was below the range of visually estimated NAVA(AL) in two instances and was above in one instance. We conclude that our model identifies NAVA(AL) in most instances with acceptable accuracy for application in clinical routine and research.

Generation of custom modes in a Nd:YAG laser with a semipassive bimorph adaptive mirror

Custom modes at a wavelength of 1064 nm were generated with a deformable mirror. The required surface deformations of the adaptive mirror were calculated with the Collins integral written in a matrix formalism. The appropriate size and shape of the actuators as well as the needed stroke were determined to ensure that the surface of the controllable mirror matches the phase front of the custom modes. A semipassive bimorph adaptive mirror with five concentric ring-shaped actuators and one defocus actuator was manufactured and characterised. The surface deformation was modelled with the response functions of the adaptive mirror in terms of an expansion with Zernike polynomials. In the experiments the Nd:YAG laser crystal was quasi-CW pumped to avoid thermally induced distortions of the phase front. The adaptive mirror allows to switch between a super-Gaussian mode, a doughnut mode, a Hermite-Gaussian fundamental beam, multi-mode operation or no oscillation in real time during laser operation.

An integral conservative gridding--algorithm using Hermitian curve interpolation

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).

The von Mises-Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.

An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficient.

The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

Higher order parametric excitation modes for spaceborne quadrupole mass spectrometers

This paper describes a technique to significantly improve upon the mass peak shape and mass resolution of spaceborne quadrupolemass spectrometers (QMSs) through higher order auxiliary excitation of the quadrupole field. Using a novel multiresonant tank circuit, additional frequency components can be used to drive modulating voltages on the quadrupole rods in a practical manner, suitable for both improved commercial applications and spaceflight instruments. Auxiliary excitation at frequencies near twice that of the fundamental quadrupole RF frequency provides the advantages of previously studied parametric excitation techniques, but with the added benefit of increased sensed excitation amplitude dynamic range and the ability to operate voltage scan lines through the center of upper stability islands. Using a field programmable gate array, the amplitudes and frequencies of all QMS signals are digitally generated and managed, providing a robust and stable voltage control system. These techniques are experimentally verified through an interface with a commercial Pfeiffer QMG422 quadrupole rod system. When operating through the center of a stability island formed from higher order auxiliary excitation, approximately 50% and 400% improvements in 1% mass resolution and peak stability were measured, respectively, when compared with traditional QMS operation. Although tested with a circular rod system, the presented techniques have the potential to improve the performance of both circular and hyperbolic rod geometry QMS sensors.

Steiner’s formula in the Heisenberg group

Steiner’s tube formula states that the volume of an ϵ-neighborhood of a smooth regular domain in Rn is a polynomial of degree n in the variable ϵ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ϵ-neighborhood with respect to the Heisenberg metric is an analytic function of ϵ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms.

Orbital elements of the material surrounding comet 67P/Churyumov-Gerasimenko

Context. We investigate the dust coma within the Hill sphere of comet 67P/Churyumov-Gerasimenko. Aims. We aim to determine osculating orbital elements for individual distinguishable but unresolved slow-moving grains in the vicinity of the nucleus. In addition, we perform photometry and constrain grain sizes. Methods. We performed astrometry and photometry using images acquired by the OSIRIS Wide Angle Camera on the European Space Agency spacecraft Rosetta. Based on these measurements, we employed standard orbit determination and orbit improvement techniques. Results. Orbital elements and effective diameters of four grains were constrained, but we were unable to uniquely determine them. Two of the grains have light curves that indicate grain rotation. Conclusions. The four grains have diameters nominally in the range 0.14-0.50 m. For three of the grains, we found elliptic orbits, which is consistent with a cloud of bound particles around the nucleus. However, hyperbolic escape trajectories cannot be excluded for any of the grains, and for one grain this is the only known option. One grain may have originated from the surface shortly before observation. These results have possible implications for the understanding of the dispersal of the cloud of bound debris around comet nuclei, as well as for understanding the ejection of large grains far from the Sun.

CPRPLOT2: Stata module to graph component-plus-residual plots for transformed regressors

cprplot2 is a variation of official Stata's cprplot and is used for graphing component-plus-residual plots (a.k.a. partial residual plots). Additional features (compared to cprplot): (1) cprplot2 can handle variables that enter the model repeatedly via different transformations (for example, polynomials). (2) cprplot2 can display component-plus-residual plots using the original units for transformed variables in the model. (3) A wrapper is provided to quickly display several component-plus-residual plots in a single image.