Recursions for distribution functions and stop-loss transforms.

For any functions on the non-negative integers, we can evaluate the cumulative function given by (s) = sx=o(x) from the values of by the recursion (s) = (s - 1) + (s). Analogously we can use this procedure t times to evaluate the t-th order cumulative function t when itself satisfies a certain sort of recursion. We shall also derive recursions for the tth order tails t where (s) = x=s+1(x). The recursions can be applied for exact and approximate evaluation of distribution functions and stop-loss transforms of probability distributions. The class of recursions for includes the classes discussed by Sundt (1992), incorporating the class studied by Panjer (1981). We discuss in particular convolutions and compound functions.Distribution; Functions;

Minimum Wage and Compliance in a Model of Search On-the-Job

minimum wages, compliance, job search, wage growth

Critical slowing down and hyperuniformity on approach to jamming

Hyperuniformity characterizes a state of matter that is poised at a critical point at which density or volume-fraction fluctuations are anomalously suppressed at infinite wavelengths. Recently, much attention has been given to the link between strict jamming and hyperuniformity in frictionless hard-particle packings. Doing so requires one to study very large packings, which can be difficult to jam properly. We modify the rigorous linear programming method of Donev et al. [J. Comp. Phys. 197, 139 (2004)] in order to test for jamming in putatively jammed packings of hard-disks in two dimensions. We find that various standard packing protocols struggle to reliably create packings that are jammed for even modest system sizes; importantly, these packings appear to be jammed by conventional tests. We present evidence that suggests that deviations from hyperuniformity in putative maximally random jammed (MRJ) packings can in part be explained by a shortcoming in generating exactly-jammed configurations due to a type of "critical slowing down" as the necessary rearrangements become difficult to realize by numerical protocols. Additionally, various protocols are able to produce packings exhibiting hyperuniformity to different extents, but this is because certain protocols are better able to approach exactly-jammed configurations. Nonetheless, while one should not generally expect exact hyperuniformity for disordered packings with rattlers, we find that when jamming is ensured, our packings are very nearly hyperuniform, and deviations from hyperuniformity correlate with an inability to ensure jamming, suggesting that strict jamming and hyperuniformity are indeed linked. This raises the possibility that the ideal MRJ packings have no rattlers. Our work provides the impetus for the development of packing algorithms that produce large disordered strictly jammed packings that are rattler-free.Comment: 15 pages, 11 figures. Accepted for publication in Phys. Rev.

Forecast Rationality and Monetary Policy Frameworks: Evidence from UK Interest Rate Forecasts

This paper explores the heterogeneity and rationality of professional forecasts at both short and long forecast horizons. We employ disaggregated survey data for forecasts of three-month inter-bank rates and ten-year gilt yields for the period 1989-2006. We find evidence of heterogeneity among forecasters. Moreover, forecasts violate both the unbiasedness and orthogonality conditions of the rational expectations hypothesis. The majority of biased forecasts underestimate the future spot rate. The rationality of forecasts varies across maturities and forecast horizons with short horizon and short maturity forecasts exhibiting more rationality. It also varies across sub-periods corresponding to different monetary policy frameworks. We produce evidence indicating that both monetary policy actions and elements of communication policy have information content regarding the rationality of forecasts. Changes in official bank rates and disagreement, as recorded in the minutes of the Monetary Policy Committee, influence the rationality of forecasts. The publication of inflation reports has no effect

Do methanethiol adsorbates on the Au(111) surface dissociate?

The interaction of methanethiol molecules CH$_{3}$SH with the Au(111) surface is investigated, and it is found for the first time that the S-H bond remains intact when the methanethiol molecules are adsorbed on the regular Au(111) surface. However, it breaks if defects are present in the Au(111) surface. At low coverage, the fcc region is favored for S atom adsorption, but at saturated coverage the adsorption energies at various sites are almost iso-energetic. The presented calculations show that a methanethiol layer on the regular Au(111) surface does not dimerize.Comment: 4 pages, 2 figures, 4 tables, submitted to Phys. Rev. Let

Neutrino mixing with broken S3S_3 symmetry

We explore the consequences of assuming that the neutrino mass matrix is a linear combination of the matrices of a three dimensional representation of the group $S_3$ and that it has one zero mass eigenvalue. When implemented, these two assumptions allow us to express the transformation matrix relating the mass eigenstates to the flavor eigenstates in terms of a single parameter which we fit to the available data.Comment: Final version. Published in Phys. Rev. D 82, 033005 (2010

T1ρ-based fibril-reinforced poroviscoelastic constitutive relation of human articular cartilage using inverse finite element technology

BackgroundMapping of T1ρ relaxation time is a quantitative magnetic resonance (MR) method and is frequently used for analyzing microstructural and compositional changes in cartilage tissues. However, there is still a lack of study investigating the link between T1ρ relaxation time and a feasible constitutive relation of cartilage which can be used to model complicated mechanical behaviors of cartilage accurately and properly.MethodsThree-dimensional finite element (FE) models of ten in vitro human tibial cartilage samples were reconstructed such that each element was assigned by material-level parameters, which were determined by a corresponding T1ρ value from MR maps. A T1ρ-based fibril-reinforced poroviscoelastic (FRPE) constitutive relation for human cartilage was developed through an inverse FE optimization technique between the experimental and simulated indentations.ResultsA two-parameter exponential relationship was obtained between the T1ρ and the volume fraction of the hydrated solid matrix in the T1ρ-based FRPE constitutive relation. Compared with the common FRPE constitutive relation (i.e., without T1ρ), the T1ρ-based FRPE constitutive relation indicated similar indentation depth results but revealed some different local changes of the stress distribution in cartilages.ConclusionsOur results suggested that the T1ρ-based FRPE constitutive relation may improve the detection of changes in the heterogeneous, anisotropic, and nonlinear mechanical properties of human cartilage tissues associated with joint pathologies such as osteoarthritis (OA). Incorporating T1ρ relaxation time will provide a more precise assessment of human cartilage based on the individual in vivo MR quantification

[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]

We study the Hopf algebra structure and the highest weight representation of a multiparameter version of $U_{q}gl(2)$. The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter universal ${\cal R}$ matrix can be constructed directly as a quantum double intertwiner, without using Reshetikhin's transformation. An interesting feature automatically appears in the representation theory: it can be divided into two types, one for generic $q$, the other for $q$ being a root of unity. When applying the representation theory to the multiparameter universal ${\cal R}$ matrix, the so called standard and nonstandard colored solutions $R(\mu,\nu; {\mu}', {\nu}')$ of the Yang-Baxter equation is obtained.Comment: [14]pages, latex, no figure

DC-Prophet: Predicting Catastrophic Machine Failures in DataCenters

When will a server fail catastrophically in an industrial datacenter? Is it possible to forecast these failures so preventive actions can be taken to increase the reliability of a datacenter? To answer these questions, we have studied what are probably the largest, publicly available datacenter traces, containing more than 104 million events from 12,500 machines. Among these samples, we observe and categorize three types of machine failures, all of which are catastrophic and may lead to information loss, or even worse, reliability degradation of a datacenter. We further propose a two-stage framework-DC-Prophet-based on One-Class Support Vector Machine and Random Forest. DC-Prophet extracts surprising patterns and accurately predicts the next failure of a machine. Experimental results show that DC-Prophet achieves an AUC of 0.93 in predicting the next machine failure, and a F3-score of 0.88 (out of 1). On average, DC-Prophet outperforms other classical machine learning methods by 39.45% in F3-score.Comment: 13 pages, 5 figures, accepted by 2017 ECML PKD