A Note on the Use of Sum in the Logic of Proofs

The Logic of Proofs~LP, introduced by Artemov, encodes the same reasoning as the modal logic~S4 using proofs explicitly present in the language. In particular, Artemov showed that three operations on proofs (application~$\cdot$, positive introspection~!, and sum~+) are sufficient to mimic provability concealed in S4~modality. While the first two operations go back to G{\"o}del, the exact role of~+ remained somewhat unclear. In particular, it was not known whether the other two operations are sufficient by themselves. We provide a positive answer to this question under a very weak restriction on the axiomatization of LP.

Integration of Truncated Distributions in Exponential Family with Simulation Models of Logistics and Supply Chain Management

Truncated distributions of the exponential family have great influence in the simulation models. This paper discusses the truncated Weibull distribution specifically. The truncation of the distribution is achieved by the Maximum Likelihood Estimation method or combined with the expectation and variance expressions. After the fitting of distribution, the goodness-of-fit tests (the Chi-Square test and the Kolmogorov-Smirnov test) are executed to rule out the rejected hypotheses. Finally the distributions are integrated in various simulation models, e. g. shipment consolidation model, to compare the influence of truncated and original versions of Weibull distribution on the model.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

Item Sum: A New Technique for Asking Quantitative Sensitive Questions

This article contributes to an ongoing debate about how to measure sensitive topics in population surveys. We propose a novel technique that can be applied to the measurement of quantitative sensitive variables: the item sum technique (IST). This method is closely related to the item count technique, which was developed for the measurement of dichotomous sensitive items. First, we provide a description of our new technique and discuss how data collected by the IST can be analyzed. Second, we present the results of a CATI survey on undeclared work in Germany, in which the IST has been applied. Using an experimental design, we compare the IST to direct questioning. Our empirical results indicate that the IST is a promising data-collection technique for sensitive questions. We conclude by discussing the limitations of the new technique and outlining possible improvements for future studies.

Non-exponential return time distributions for vorticity extremes explained by fractional Poisson processes

Serial correlation of extreme midlatitude cyclones observed at the storm track exits is explained by deviations from a Poisson process. To model these deviations, we apply fractional Poisson processes (FPPs) to extreme midlatitude cyclones, which are defined by the 850 hPa relative vorticity of the ERA interim reanalysis during boreal winter (DJF) and summer (JJA) seasons. Extremes are defined by a 99% quantile threshold in the grid-point time series. In general, FPPs are based on long-term memory and lead to non-exponential return time distributions. The return times are described by a Weibull distribution to approximate the Mittag–Leffler function in the FPPs. The Weibull shape parameter yields a dispersion parameter that agrees with results found for midlatitude cyclones. The memory of the FPP, which is determined by detrended fluctuation analysis, provides an independent estimate for the shape parameter. Thus, the analysis exhibits a concise framework of the deviation from Poisson statistics (by a dispersion parameter), non-exponential return times and memory (correlation) on the basis of a single parameter. The results have potential implications for the predictability of extreme cyclones.

Quasi-Self-Dual Exponential Lévy Processes

The important application of semistatic hedging in financial markets naturally leads to the notion of quasi--self-dual processes. The focus of our study is to give new characterizations of quasi--self-duality. We analyze quasi--self-dual Lévy driven markets which do not admit arbitrage opportunities and derive a set of equivalent conditions for the stochastic logarithm of quasi--self-dual martingale models. Since for nonvanishing order parameter two martingale properties have to be satisfied simultaneously, there is a nontrivial relation between the order and shift parameter representing carrying costs in financial applications. This leads to an equation containing an integral term which has to be inverted in applications. We first discuss several important properties of this equation and, for some well-known Lévy-driven models, we derive a family of closed-form inversion formulae.

Systematic analysis of the intravoxel incoherent motion threshold separating perfusion and diffusion effects: Proposal of a standardized algorithm

PURPOSE To systematically evaluate the dependence of intravoxel-incoherent-motion (IVIM) parameters on the b-value threshold separating the perfusion and diffusion compartment, and to implement and test an algorithm for the standardized computation of this threshold. METHODS Diffusion weighted images of the upper abdomen were acquired at 3 Tesla in eleven healthy male volunteers with 10 different b-values and in two healthy male volunteers with 16 different b-values. Region-of-interest IVIM analysis was applied to the abdominal organs and skeletal muscle with a systematic increase of the b-value threshold for computing pseudodiffusion D*, perfusion fraction Fp , diffusion coefficient D, and the sum of squared residuals to the bi-exponential IVIM-fit. RESULTS IVIM parameters strongly depended on the choice of the b-value threshold. The proposed algorithm successfully provided optimal b-value thresholds with the smallest residuals for all evaluated organs [s/mm2]: e.g., right liver lobe 20, spleen 20, right renal cortex 150, skeletal muscle 150. Mean D* [10(-3) mm(2) /s], Fp [%], and D [10(-3) mm(2) /s] values (±standard deviation) were: right liver lobe, 88.7 ± 42.5, 22.6 ± 7.4, 0.73 ± 0.12; right renal cortex: 11.5 ± 1.8, 18.3 ± 2.9, 1.68 ± 0.05; spleen: 41.9 ± 57.9, 8.2 ± 3.4, 0.69 ± 0.07; skeletal muscle: 21.7 ± 19.0; 7.4 ± 3.0; 1.36 ± 0.04. CONCLUSION IVIM parameters strongly depend upon the choice of the b-value threshold used for computation. The proposed algorithm may be used as a robust approach for IVIM analysis without organ-specific adaptation. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.

Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon’s implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike’s preceding ISI. As we show, the EIF’s exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron’s ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation.

The bottom-quark mass from non-relativistic sum rules at NNNLO

We determine the mass of the bottom quark from high moments of the bbproduction cross section in e+e−annihilation, which are dominated by the threshold region. On the theory side next-to-next-to-next-to-leading order (NNNLO) calculations both for the resonances and the continuum cross section are used for the first time. We find mPSb(2GeV) =4.532+0.013−0.039GeVfor the potential-subtracted mass and mMSb(mMSb) =4.193+0.022−0.035GeVfor the MSbottom-quark mass.