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In this thesis, the emission of protons as well as the production of Λ hyperons, Κ0S mesons and 3ΛH hypernuclei are analyzed multi-differentially as a function of transverse momentum, rapidity and centrality. Therefore, the 3.03 billion 30 % most central Ag(1.58A GeV)+Ag events recorded by HADES are used. Furthermore, the lifetimes of Λ hyperons, Κ0S mesons and 3ΛH hypernuclei are measured. The obtained 3ΛH lifetime of (253 ± 24 ± 42) ps is compatible with the lifetime of free Λ hyperons, as predicted by theoretic calculations due to its low binding energy. Finally, also the double strange Ξ– hyperons are reconstructed. Unfortunately, the fully optimized signals lie below the confidence threshold of 5σ, which is why both an production rate and an upper production limit are estimated using averaged acceptance and efficiency corrections. Never before, 3ΛH or Ξ– were successfully reconstructed and analyzed in heavy-ion collisions at such low energies. The obtained results are compared to previous measurements and put in context with world data form different energies and collision systems. In dieser Arbeit werden die Emission von Protonen sowie die Produktion von Λ Hyperonen, Κ0S Mesonen und 3ΛH Hyperkernen multi-differentiell in Abhängigkeit von Transversalimpuls, Rapidität und Zentralität analysiert. Hierzu werden die 3,03 Milliarden 30 % zentralsten Ag(1.58A GeV)+Ag Kollisionen, die von HADES aufgezeichnet wurden, verwendet. Zusätzlich werden die Lebensdauern von Λ Hyperonen, Κ0S Mesonen und 3ΛH Hyperkernen gemessen. Die gemessene 3ΛH Lebensdauer von (253 ± 24 ± 42) ps ist kompatibel mit der Lebensdauer freier Λ Hyperonen wie es von theoretischen Berechnungen aufgrund der niedrigen Bindungsenergie erwartet wird. Darüber hinaus werden auch die doppelt „seltsamen“ Ξ– Hyperonen rekonstruiert. Leider liegt das vollständig optimierte Signal immernoch unterhalb der Schwelle von 5σ weshalb sowohl die Produktionsrate als auch ein oberes Produktionslimit mithilfe gemittelter Akzeptanz- und Effizienzkorrekturen bestimmt werden. Dies ist das erste Mal dass 3ΛH und Ξ– erfolgreich in Schwerionenkollisionen bei derart niedrigen Energien rekonstruiert und analysiert werden. Alle Ergebnisse werden letztendlich mit vorherigen Messungen sowie dem weltweiten Datensatz, bestehend aus unterschiedlichsten Energien und Kollisionssystemen, verglichen.

Step-indexed logical relations are an extremely useful technique for building operational-semantics-based models and program logics for realistic, richly-typed programming languages. They have proven to be indispensable for modeling features like higher-order state , which many languages support but which were difficult to accommodate using traditional denotational models. However, the conventional wisdom is that, because they only support reasoning about finite traces of computation, (unary) step-indexed models are only good for proving safety properties like “well-typed programs don’t go wrong”. There has consequently been very little work on using step-indexing to establish liveness properties, in particular termination. In this paper, we show that step-indexing can in fact be used to prove termination of well-typed programs—even in the presence of dynamically-allocated, shared, mutable, higher-order state—so long as one’s type system enforces disciplined use of such state. Specifically, we consider a language with asynchronous channels, inspired by promises in JavaScript, in which higher-order state is used to implement communication, and linearity is used to ensure termination. The key to our approach is to generalize from natural number step-indexing to transfinite step-indexing , which enables us to compute termination bounds for program expressions in a compositional way. Although transfinite step-indexing has been proposed previously, we are the first to apply this technique to reasoning about termination in the presence of higher-order state.

In March 2019 the HADES experiment recorded 14 billion Ag+Ag collisions at √SNN = 2.55 GeV as a part of the FAIR phase-0 physics program. With the capabilities to measure and analyze particles forming the bulk matter, namely pions, protons and light nuclei, as well as rare probes like dilepton decays of vectormesons and strange hadrons, the HADES experiment allows to study the properties of matter at high densities in great detail. In this contribution a special focus is put on the reconstruction of weakly decaying strange hadrons.

In March 2019 the HADES experiment recorded 14 billion Ag+Ag collisions at √sNN = 2.55 GeV as a part of the FAIR phase-0 physics program. In this contribution, we present and investigate our capabilities to reconstruct and analyze weakly decaying strange hadrons and hypernuclei emerging from these collisions. The focus is put on measuring the mean lifetimes of these particles.

We formalise undecidability results concerning higher-order unification in the simply-typed λ-calculus with β-conversion in Coq. We prove the undecidability of general higher-order unification by reduction from Hilbert’s tenth problem, the solvability of Diophantine equations, following a proof by Dowek. We sharpen the result by establishing the undecidability of second-order and third-order unification following proofs by Goldfarb and Huet, respectively. Goldfarb’s proof for second-order unification is by reduction from Hilbert’s tenth problem. Huet’s original proof uses the Post correspondence problem (PCP) to show the undecidability of third-order unification. We simplify and formalise his proof as a reduction from modified PCP. We also verify a decision procedure for first-order unification. All proofs are carried out in the setting of synthetic undecidability and rely on Coq’s built-in notion of computation.

Call-by-push-value (CBPV) is an idealised calculus for functional and imperative programming, introduced as a subsuming paradigm for both call-by-value (CBV) and call-by-name (CBN). We formalise weak and strong operational semantics for (effect-free) CBPV, define its equational theory, and verify adequacy for the standard set/algebra denotational semantics. Furthermore, we prove normalisation of the standard reduction, confluence of strong reduction, strong normalisation using Kripke logical relations, and soundness of the equational theory using logical equivalence. We adapt and verify the known translations from CBV and CBN into CBPV for strong reduction. This yields, for instance, proofs of strong normalisation and confluence for the full λ-calculus with sums and products. Thanks to the automation provided by Coq and the Autosubst 2 framework, there is little formalisation overhead compared to detailed paper proofs.

Step-indexed separation logic has proven to be a powerful tool for modular reasoning about higher-order stateful programs. However, it has only been used to reason about safety properties, never liveness properties. In this paper, we observe that the inability of step-indexed separation logic to support liveness properties stems fundamentally from its failure to validate the existential property, connecting the meaning of existential quantification inside and outside the logic. We show how to validate the existential property-and thus enable liveness reasoning-by moving from finite step-indices (natural numbers) to transfinite step-indices (ordinals). Concretely, we transform the Coq-based step-indexed logic Iris to Transfinite Iris, and demonstrate its effectiveness in proving termination and termination-preserving refinement for higher-order stateful programs.

Background and objective : The composition of the salivary microbiota, as determined using various molecular methods, has been reported to differentiate oral health from diseases. Thus, the purpose of this study was to utilize the newly developed molecular technique HOMI NGS (Human Oral Microbe Identification using Next Generation Sequencing) for comparison of the salivary microbiota in patients with periodontitis, patients with dental caries, and orally healthy individuals. The hypothesis was that this method could add on to the existing knowledge on salivary bacterial profiles in oral health and disease. Design : Stimulated saliva samples ( n =30) were collected from 10 patients with untreated periodontitis, 10 patients with untreated dental caries, and 10 orally healthy individuals. Salivary microbiota was analyzed using HOMI NGS and statistical analysis was performed using Kruskal–Wallis test with Benjamini–Hochberg’s correction. Results : From a total of 30 saliva samples, a mean number of probe targets of 205 (range 120–353) were identified, and a statistically significant higher mean number of targets was registered in samples from patients with periodontitis (mean 220, range 143–306) and dental caries (mean 221, range 165–353) as compared to orally healthy individuals (mean 174, range 120–260) ( p =0.04 and p =0.04). Nine probe targets were identified with a different relative abundance between groups ( p

Background and objective : The bacterial profile of saliva is composed of bacteria from different oral surfaces. The objective of this study was to determine whether different diet intake, lifestyle, or socioeconomic status is associated with characteristic bacterial saliva profiles. Design : Stimulated saliva samples from 292 participants with low levels of dental caries and periodontitis, enrolled in the Danish Health Examination Survey (DANHES), were analyzed for the presence of approximately 300 bacterial species by means of the Human Oral Microbe Identification Microarray (HOMIM). Using presence and levels (mean HOMIM-value) of bacterial probes as endpoints, the influence of diet intake, lifestyle, and socioeconomic status on the bacterial saliva profile was analyzed by Mann–Whitney tests with Benjamini–Hochberg’s correction for multiple comparisons and principal component analysis. Results : Targets for 131 different probes were identified in 292 samples, with Streptococcus and Veillonella being the most predominant genera identified. Two bacterial taxa ( Streptococcus sobrinus and Eubacterium [11][G-3] brachy ) were more associated with smokers than non-smokers (adjusted p- value

Background and objective : The microbial profiles of stimulated saliva samples have been shown to differentiate between patients with periodontitis, patients with dental caries, and orally healthy individuals. Saliva was stimulated to allow for easy and rapid collection; however, microbial composition may not reflect the more natural, unstimulated state. The purpose of this study was to validate whether stimulated saliva is an adequate surrogate for unstimulated saliva in determining salivary microbiomes. Design : Unstimulated ( n =20) and stimulated ( n =20) saliva samples were collected from 20 orally and systemically healthy, non-smoking participants. Salivary bacterial profiles were analyzed by means of the Human Oral Microbe Identification using Next Generation Sequencing (HOMI NGS ), and statistical analysis was performed using Mann–Whitney test with Benjamini–Hochberg’s correction for multiple comparison, cluster analysis, principal component analysis, and correspondence analysis. Results : From a total of 40 saliva samples, 496 probe targets were identified with a mean number of targets per sample of 203 (range: 146–303), and a mean number of probe targets of 206 and 200 in unstimulated and stimulated saliva samples, respectively ( p =0.62). Based on all statistical methods used for this study, the microbial profiles of unstimulated and stimulated saliva samples collected from the same person were not statistically significantly different. Conclusions : Analysis of bacterial salivary profiles in unstimulated and stimulated saliva samples collected from the same individual showed comparable results. Thus, the results verify that stimulated saliva is an adequate surrogate of unstimulated saliva for microbiome-related studies. Keywords: saliva; HOMI NGS; bacteria (Published: 16 March 2016) Citation: Journal of Oral Microbiology 2016, 8: 30112 - http://dx.doi.org/10.3402/jom.v8.30112