On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

The Bad Truth about Laplace\u27s Transform

Inverting the Laplace transform is a paradigm for exponentially ill-posed problems. For a class of operators, including the Laplace transform, we give forward and inverse formulae that have fast implementations using the fast Fourier transform. These formulae lead easily to regularized inverses whose effects on noise and filtered data can be precisely described. Our results give cogent reasons for the general sense of dread most mathematicians feel about inverting the Laplace transform

Energy Density-Flux Correlations in an Unusual Quantum State and in the Vacuum

In this paper we consider the question of the degree to which negative and positive energy are intertwined. We examine in more detail a previously studied quantum state of the massless minimally coupled scalar field, which we call a ``Helfer state''. This is a state in which the energy density can be made arbitrarily negative over an arbitrarily large region of space, but only at one instant in time. In the Helfer state, the negative energy density is accompanied by rapidly time-varying energy fluxes. It is the latter feature which allows the quantum inequalities, bounds which restrict the magnitude and duration of negative energy, to hold for this class of states. An observer who initially passes through the negative energy region will quickly encounter fluxes of positive energy which subsequently enter the region. We examine in detail the correlation between the energy density and flux in the Helfer state in terms of their expectation values. We then study the correlation function between energy density and flux in the Minkowski vacuum state, for a massless minimally coupled scalar field in both two and four dimensions. In this latter analysis we examine correlation functions rather than expectation values. Remarkably, we see qualitatively similar behavior to that in the Helfer state. More specifically, an initial negative energy vacuum fluctuation in some region of space is correlated with a subsequent flux fluctuation of positive energy into the region. We speculate that the mechanism which ensures that the quantum inequalities hold in the Helfer state, as well as in other quantum states associated with negative energy, is, at least in some sense, already ``encoded'' in the fluctuations of the vacuum.Comment: 21 pages, 7 figures; published version with typos corrected and one added referenc

Clinical and economic evaluation of laparoscopic surgery compared with medical management for gastro-oesophageal reflux disease : 5-year follow-up of multicentre randomised trial (the REFLUX trial)

Peer reviewedPublisher PD

Galactic Cosmic Rays from Supernova Remnants: II Shock Acceleration of Gas and Dust

This is the second paper (the first was astro-ph/9704267) of a series analysing the Galactic Cosmic Ray (GCR) composition and origin. In this we present a quantitative model of GCR origin and acceleration based on the acceleration of a mixture of interstellar and/or circumstellar gas and dust by supernova remnant blast waves. We present results from a nonlinear shock model which includes (i) the direct acceleration of interstellar gas-phase ions, (ii) a simplified model for the direct acceleration of weakly charged dust grains to energies of order 100keV/amu simultaneously with the gas ions, (iii) frictional energy losses of the grains colliding with the gas, (iv) sputtering of ions of refractory elements from the accelerated grains and (v) the further shock acceleration of the sputtered ions to cosmic ray energies. The calculated GCR composition and spectra are in good agreement with observations.Comment: to appear in ApJ, 51 pages, LaTeX with AAS macros, 9 postscript figures, also available from ftp://wonka.physics.ncsu.edu/pub/elliso

Transepithelial Corneal Cross-Linking With Vitamin E-Enhanced Riboflavin Solution and Abbreviated, Low-Dose UV-A: 24-Month Clinical Outcomes

Purpose: To report the clinical outcomes with 24-month follow-up of transepithelial cross-linking using a combination of a D-alpha-tocopheryl polyethylene-glycol 1000 succinate (vitamin E-TPGS)-enhanced riboflavin solution and abbreviated low fluence UV-A treatment. Methods: In a nonrandomized clinical trial, 25 corneas of 19 patients with topographically proven, progressive, mild to moderate keratoconus over the previous 6 months were cross-linked, and all patients were examined at 1, 3, 6, 12, and 24 months. The treatments were performed using a patented solution of riboflavin and vitamin E-TPGS, topically applied for 15 minutes, followed by two 5-minute UV-A treatments with separate doses both at fluence below 3 mW/cm2 that were based on preoperative central pachymetry. Results: During the 6-month pretreatment observation, the average Kmax increased by +1.99 +/- 0.29 D (diopter). Postoperatively, the average Kmax decreased, changing by -0.55 +/- 0.94 D, by -0.88 +/- 1.02 D and by -1.01 +/- 1.22 D at 6, 12, and 24 months. Postoperatively, Kmax decreased in 19, 20, and 20 of the 25 eyes at 6 months, 12 months, and 24 months, respectively. Refractive cylinder was decreased by 3 months postoperatively and afterward, changing by -1.35 +/- 0.69 D at 24 months. Best spectacle-corrected visual acuity (BSCVA) improved at 6, 12, and 24 months, including an improvement of -0.19 +/- 0.13 logarithm of the minimum angle of resolution units at 24 months. There was no reduction in endothelial cell count. No corneal abrasions occurred, and no bandage contact lenses or prescription analgesics were used during postoperative recovery. Conclusions: Transepithelial cross-linking using the riboflavin-vitamin E solution and brief, low-dose, pachymetry-dependent UV-A treatment safely stopped keratoconus progression

Scheduling over Scenarios on Two Machines

We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all possible scenarios. Each scenario is a subset of jobs that must be executed in that scenario and all scenarios are given explicitly. The two objectives that we consider are minimizing the maximum makespan over all scenarios and minimizing the sum of the makespans of all scenarios. For both versions, we give several approximation algorithms and lower bounds on their approximability. With this research into optimization problems over scenarios, we have opened a new and rich field of interesting problems.Comment: To appear in COCOON 2014. The final publication is available at link.springer.co

Measuring public perceptions of sex offenders: reimagining the Community Attitudes Toward Sex Offenders (CATSO) scale

The Community Attitudes Toward Sex Offenders (CATSO) scale is an 18-item self-report questionnaire designed to measure respondents’ attitudes toward sex offenders. Its original factor structure has been questioned by a number of previous studies, and so this paper sought to reimagine the scale as an outcome measure, as opposed to a scale of attitudes. A face validity analysis produced a provisional three-factor structure underlying the CATSO: ‘punitiveness,’ ‘stereotype endorsement,’ and ‘risk perception.’ A sample of 400 British members of the public completed a modified version of the CATSO, the Attitudes Toward Sex Offenders scale, the General Punitiveness Scale, and the Rational-Experiential Inventory. A three-factor structure of a 22-item modified CATSO was supported using half of the sample, with factors being labeled ‘sentencing and management,’ ‘stereotype endorsement,’ and ‘risk perception.’ Confirmatory factor analysis on data from the other half of the sample endorsed the three-factor structure; however, two items were removed in order to improve ratings of model fit. This new 20-item ‘Perceptions of Sex Offenders scale’ has practical utility beyond the measurement of attitudes, and suggestions for its future use are provided

Expert advice and political choice in constructing European banking union

International actors promoted the transfer of regulatory authority and financial resources from national governments to the European Union (EU) in the context of establishing the prerequisites for financial stability in Europe through banking union. It was supplied, however, by a political process that kept significant resources in resolution and deposit insurance largely in national hands. This article examines the politics behind those decisions, and how the hybrid of European and national competences affects bank regulation and financial stability in the EU. It concludes that the tension between strong EU supervisory powers and weak capacity to deal with insolvent institutions will persist