Minimum Weight Flat Antichains of Subsets

Building on classical theorems of Sperner and Kruskal-Katona, we investigate antichains $\mathcal F$ in the Boolean lattice $B_n$ of all subsets of $[n]:=\{1,2,\dots,n\}$, where $\mathcal F$ is flat, meaning that it contains sets of at most two consecutive sizes, say $\mathcal F=\mathcal{A}\cup\mathcal{B}$, where $\mathcal{A}$ contains only $k$-subsets, while $\mathcal{B}$ contains only $(k-1)$-subsets. Moreover, we assume $\mathcal{A}$ consists of the first $m$ $k$-subsets in squashed (colexicographic) order, while $\mathcal{B}$ consists of all $(k-1)$-subsets not contained in the subsets in $\mathcal{A}$. Given reals $\alpha,\beta>0$, we say the weight of $\mathcal F$ is $\alpha\cdot|\mathcal{A}|+\beta\cdot|\mathcal{B}|$. We characterize the minimum weight antichains $\mathcal F$ for any given $n,k,\alpha,\beta$, and we do the same when in addition $\mathcal F$ is a maximal antichain. We can then derive asymptotic results on both the minimum size and the minimum Lubell function

Functional dependencies over XML documents with DTDs

In this article an axiomatisation for functional dependencies over XML documents is presented. The approach is based on a representation of XML document type definitions (or XML schemata) by nested attributes using constructors for records, disjoint unions and lists, and a particular null value, which covers optionality. Infinite structures that may result from referencing attributes in XML are captured by rational trees. Using a partial order on nested attributes we obtain non-distributive Brouwer algebras. The operations of the Brouwer algebra are exploited in the soundness and completeness proofs for derivation rules for functional dependencies

Regimes of atomic diffraction: Raman versus Bragg diffraction in retroreflective geometries

We provide a comprehensive study of atomic Raman and Bragg diffraction when coupling to a pair of counterpropagating light gratings (double diffraction) or to a single one (single diffraction) and discuss the transition from one case to the other in a retroreflective geometry as the Doppler detuning changes. In contrast to single diffraction, double Raman loses its advantage of high diffraction efficiency for short pulses and has to be performed in a Bragg-type regime. Moreover, the structure of double diffraction leads to further limitations for broad momentum distributions on the efficiency of mirror pulses, making the use of (ultra) cold ensembles essential for high diffraction efficiency.Comment: 16 pages, 14 figure

Erratum to: Effects of drought and N-fertilization on N cycling in two grassland soils

Changes in frequency and intensity of drought events are anticipated in many areas of the world. In pasture, drought effects on soil nitrogen (N) cycling are spatially and temporally heterogeneous due to N redistribution by grazers. We studied soil N cycling responses to simulated summer drought and N deposition by grazers in a 3-year field experiment replicated in two grasslands differing in climate and management. Cattle urine and NH4NO3 application increased soil NH4 + and NO3 − concentrations, and more so under drought due to reduced plant uptake and reduced nitrification and denitrification. Drought effects were, however, reflected to a minor extent only in potential nitrification, denitrifying enzyme activity (DEA), and the abundance of functional genes characteristic of nitrifying (bacterial and archaeal amoA) and denitrifying (narG, nirS, nirK, nosZ) micro-organisms. N2O emissions, however, were much reduced under drought, suggesting that this effect was driven by environmental limitations rather than by changes in the activity potential or the size of the respective microbial communities. Cattle urine stimulated nitrification and, to a lesser extent, also DEA, but more so in the absence of drought. In contrast, NH4NO3 reduced the activity of nitrifiers and denitrifiers due to top-soil acidification. In summary, our data demonstrate that complex interactions between drought, mineral N availability, soil acidification, and plant nutrient uptake control soil N cycling and associated N2O emissions. These interactive effects differed between processes of the soil N cycle, suggesting that the spatial heterogeneity in pastures needs to be taken into account when predicting changes in N cycling and associated N2O emissions in a changing climat

Atomic Raman scattering: Third-order diffraction in a double geometry

In a retroreflective scheme atomic Raman diffraction adopts some of the properties of Bragg diffraction due to additional couplings to off-resonant momenta. As a consequence, double Raman diffraction has to be performed in a Bragg-type regime. Taking advantage of this regime, double Raman allows for resonant higher-order diffraction. We study theoretically the case of third-order diffraction and compare it to first order as well as a sequence of first-order pulses giving rise to the same momentum transfer as the third-order pulse. In fact, third-order diffraction constitutes a competitive tool for the diffraction of ultracold atoms and interferometry based on large momentum transfer since it allows to reduce the complexity of the experiment as well as the total duration of the diffraction process compared to a sequence.Comment: 10 pages, 13 figure

Robustness estimation and optimisation for semantic web service composition with stochastic service failures

Service-oriented architecture (SOA) is a widely adopted software engineering paradigm that encourages modular and reusable applications. One popular application of SOA is web service composition, which aims to loosely couple web services to accommodate complex goals not achievable through any individual web service. Many approaches have been proposed to construct composite services with optimized Quality of Service (QoS), assuming that QoS of web services never changes. However, the constructed composite services may not perform well and may not be executable later due to its component services' failure. Therefore, it is important to build composite services that are robust to stochastic service failures. Two challenges of building robust composite services are to efficiently generate service composition with near-optimal quality in a large search space of available services and to accurately measure the robustness of composite services considering all possible failure scenarios. This article proposes a novel two-stage GA-based approach to robust web service composition with an adaptive evolutionary control and an efficient robustness measurement. This approach can generate robust composite service at the design phase, which can cope with stochastic service failures and maintain high quality at the time of execution. We have conducted experiments with benchmark datasets to evaluate the performance of our proposed approach. Our experiments show that our method can produce highly robust composite services, achieving outstanding performance consistently in the event of stochastic service failures, on service repositories with varying sizes

An inconspicuous, conspicuous new species of Asian pipesnake, genus Cylindrophis (Reptilia: Squamata: Cylindrophiidae), from the south coast of Jawa Tengah, Java, Indonesia, and an overview of the tangled taxonomic history of C. ruffus (Laurenti, 1768)

We describe a new species of Cylindrophis currently known only from Grabag, Purworejo Regency, Jawa Tengah Province (Central Java), Java, Indonesia. Cylindrophis subocularis sp. nov. can be distinguished from all congeners by the presence of a single, eponymous subocular scale between the 3rd and 4th or 4th and 5th supralabial, preventing contact between the 4th or 5th supralabial and the orbit, and by having the prefrontal in narrow contact with or separated from the orbit. We preface our description with a detailed account of the tangled taxonomic history of the similar and putatively wide-ranging species C. ruffus, which leads us to (1) remove the name Scytale scheuchzeri from the synonymy of C. ruffus, (2) list the taxon C. rufa var. javanica as species inquirenda, and (3) synonymize C. mirzae with C. ruffus. We provide additional evidence to confirm that the type locality of C. ruffus is Java. Cylindrophis subocularis sp. nov. is the second species of Asian pipesnake from Java