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.

Tuning curve of type-0 spontaneous parametric down-conversion

We study the tuning curve of entangled photons generated by type-0 spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate crystal. We demonstrate the X-shaped spatiotemporal structure of the spectrum by means of measurements and numerical simulations. Experiments for different pump waists, crystal temperatures, and crystal lengths are in good agreement with numerical simulations.

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.

Palynological richness and evenness: insights from the taxa accumulation curve

Palynology provides the opportunity to make inferences on changes in diversity of terrestrial vegetation over long time scales. The often coarse taxonomic level achievable in pollen analysis, differences in pollen production and dispersal, and the lack of pollen source boundaries hamper the application of diversity indices to palynology. Palynological richness, the number of pollen types at a constant pollen count, is the most robust and widely used diversity indicator for pollen data. However, this index is also influenced by the abundance distribution of pollen types in sediments. In particular, where the index is calculated by rarefaction analysis, information on taxonomic richness at low abundance may be lost. Here we explore information that can be extracted from the accumulation of taxa over consecutive samples. The log-transformed taxa accumulation curve can be broken up into linear sections with different slope and intersect parameters, describing the accumulation of new taxa within the section. The breaking points may indicate changes in the species pool or in the abundance of high versus low pollen producers. Testing this concept on three pollen diagrams from different landscapes, we find that the break points in the taxa accumulation curves provide convenient zones for identifying changes in richness and evenness. The linear regressions over consecutive samples can be used to inter- and extrapolate to low or extremely high pollen counts, indicating evenness and richness in taxonomic composition within these zones. An evenness indicator, based on the rank-order-abundance is used to assist in the evaluation of the results and the interpretation of the fossil records. Two central European pollen diagrams show major changes in the taxa accumulation curves for the Lateglacial period and the time of human induced land-use changes, while they do not indicate strong changes in the species pool with the onset of the Holocene. In contrast, a central Swedish pollen diagram shows comparatively little change, but high richness during the early Holocene forest establishment. Evenness and palynological richness are related for most periods in the three diagrams, however, sections before forest establishment and after forest clearance show high evenness, which is not necessarily accompanied by high palynological richness, encouraging efforts to separate the two.

Vascular Plants and Biocrusts Modulate How Abiotic Factors Affect Wetting and Drying Events in Drylands

Understanding how organisms control soil water dynamics is a major research goal in dryland ecology. Although previous studies have mostly focused on the role of vascular plants on the hydrological cycle of drylands, recent studies highlight the importance of biological soil crusts formed by lichens, mosses, and cyanobacteria (biocrusts) as a major player in this cycle. We used data from a 6.5-year study to evaluate how multiple abiotic (rainfall characteristics, temperature, and initial soil moisture) and biotic (vascular plants and biocrusts) factors interact to determine wetting and drying processes in a semi-arid grassland from Central Spain. We found that the shrub Retama sphaerocarpa and biocrusts with medium cover (25–75%) enhanced water gain and slowed drying compared with bare ground areas (BSCl). Well-developed biocrusts (>75% cover) gained more water, but lost it faster than BSCl microsites. The grass Stipa tenacissima reduced water gain due to rainfall interception, but increased soil moisture retention compared to BSCl microsites. Biotic modulation of water dynamics was the result of different mechanisms acting in tandem and often in opposite directions. For instance, biocrusts promoted an exponential behavior during the first stage of the drying curve, but reduced the importance of soil characteristics that accentuate drying rates. Biocrust-dominated microsites gained a similar amount of water than vascular plants, although they lost it faster than vascular plants during dry periods. Our results emphasize the importance of biocrusts for water dynamics in drylands, and illustrate the potential mechanisms behind their effects. They will help to further advance theoretical and modeling efforts on the hydrology of drylands and their response to ongoing climate change.