Relational semantics of linear logic and higher-order model-checking

In this article, we develop a new and somewhat unexpected connection between higher-order model-checking and linear logic. Our starting point is the observation that once embedded in the relational semantics of linear logic, the Church encoding of any higher-order recursion scheme (HORS) comes together with a dual Church encoding of an alternating tree automata (ATA) of the same signature. Moreover, the interaction between the relational interpretations of the HORS and of the ATA identifies the set of accepting states of the tree automaton against the infinite tree generated by the recursion scheme. We show how to extend this result to alternating parity automata (APT) by introducing a parametric version of the exponential modality of linear logic, capturing the formal properties of colors (or priorities) in higher-order model-checking. We show in particular how to reunderstand in this way the type-theoretic approach to higher-order model-checking developed by Kobayashi and Ong. We briefly explain in the end of the paper how his analysis driven by linear logic results in a new and purely semantic proof of decidability of the formulas of the monadic second-order logic for higher-order recursion schemes.Comment: 24 pages. Submitte

Bayesian inverse problems with Gaussian priors

The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the minimax rate. The frequentist coverage of credible sets is shown to depend on the combination of prior and true parameter, with smoother priors leading to zero coverage and rougher priors to conservative coverage. In the latter case credible sets are of the correct order of magnitude. The results are numerically illustrated by the problem of recovering a function from observation of a noisy version of its primitive.Comment: Published in at http://dx.doi.org/10.1214/11-AOS920 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multi-wavelength Calibration Procedure for the Pierre Auger Observatory Fluorescence Detectors

We present a method to measure the relative spectral response of the Pierre Auger Observatory Fluorescence Detector. The calibration was done at wavelengths of 320, 337, 355, 380 and 405 nm using an end-to-end technique in which the response of all detector components are combined in a single measurement. A xenon flasher and notch-filters were used as the light source for the calibration device. The overall uncertainty is 5%.Comment: Submitted to Astroparticle Physics. V2: section 5.2 extended; author list change

Injury rates and injury risk factors among federal bureau of investigation new agent trainees

<p>Abstract</p> <p>Background</p> <p>A one-year prospective examination of injury rates and injury risk factors was conducted in Federal Bureau of Investigation (FBI) new agent training.</p> <p>Methods</p> <p>Injury incidents were obtained from medical records and injury compensation forms. Potential injury risk factors were acquired from a lifestyle questionnaire and existing data at the FBI Academy.</p> <p>Results</p> <p>A total of 426 men and 105 women participated in the project. Thirty-five percent of men and 42% of women experienced one or more injuries during training. The injury incidence rate was 2.5 and 3.2 injuries/1,000 person-days for men and women, respectively (risk ratio (women/men) = 1.3, 95% confidence interval = 0.9-1.7). The activities most commonly associated with injuries (% of total) were defensive tactics training (58%), physical fitness training (20%), physical fitness testing (5%), and firearms training (3%). Among the men, higher injury risk was associated with older age, slower 300-meter sprint time, slower 1.5-mile run time, lower total points on the physical fitness test (PFT), lower self-rated physical activity, lower frequency of aerobic exercise, a prior upper or lower limb injury, and prior foot or knee pain that limited activity. Among the women higher injury risk was associated with slower 300-meter sprint time, slower 1.5-mile run time, lower total points on the PFT, and prior back pain that limited activity.</p> <p>Conclusion</p> <p>The results of this investigation supported those of a previous retrospective investigation emphasizing that lower fitness and self-reported pain limiting activity were associated with higher injury risk among FBI new agents.</p

Physical Stability and Viscoelastic Properties of Co-Amorphous Ezetimibe/Simvastatin System

The purpose of this paper is to examine the physical stability as well as viscoelastic properties of the binary amorphous ezetimibe–simvastatin system. According to our knowledge, this is the first time that such an amorphous composition is prepared and investigated. The tendency toward re-crystallization of the amorphous ezetimibe–simvastatin system, at both standard storage and elevated temperature conditions, have been studied by means of X-ray diffraction (XRD). Our investigations have revealed that simvastatin remarkably improves the physical stability of ezetimibe, despite the fact that it works as a plasticizer. Pure amorphous ezetimibe, when stored at room temperature, begins to re-crystallize after 14 days after amorphization. On the other hand, the ezetimibe-simvastatin binary mixture (at the same storage conditions) is physically stable for at least 1 year. However, the devitrification of the binary amorphous composition was observed at elevated temperature conditions (T = 373 K). Therefore, we used a third compound to hinder the re-crystallization. Finally, both the physical stability as well as viscoelastic properties of the ternary systems containing different concentrations of the latter component have been thoroughly investigated

Базовый алгоритм действия системы поддержки принятия решений

We consider two-player parity games played on transition graphs of higher order pushdown automata. They are ``game-equivalent'' to a kind of model-checking game played on graphs of the infinite hierarchy introduced recently by Caucal. Then in this hierarchy we show how to reduce a game to a graph of lower level. This leads to an effective solution and a construction of the winning strategies

Bayesian recovery of the initial condition for the heat equation

We study a Bayesian approach to recovering the initial condition for the heat equation from noisy observations of the solution at a later time. We consider a class of prior distributions indexed by a parameter quantifying "smoothness" and show that the corresponding posterior distributions contract around the true parameter at a rate that depends on the smoothness of the true initial condition and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the optimal minimax rate. One type of priors leads to a rate-adaptive Bayesian procedure. The frequentist coverage of credible sets is shown to depend on the combination of the prior and true parameter as well, with smoother priors leading to zero coverage and rougher priors to (extremely) conservative results. In the latter case credible sets are much larger than frequentist confidence sets, in that the ratio of diameters diverges to infinity. The results are numerically illustrated by a simulated data example.Comment: 17 pages, 4 figures. Published in Comm. Statist. Theory Methods. This version differs from the original in pagination and typographic detail. arXiv admin note: text overlap with arXiv:1103.269