Distributed Graph Automata and Verification of Distributed Algorithms

Combining ideas from distributed algorithms and alternating automata, we introduce a new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic. By restricting transitions to be nondeterministic or deterministic, we also obtain two strictly weaker variants of our automata for which the emptiness problem is decidable. As an application, we suggest how suitable graph automata might be useful in formal verification of distributed algorithms, using Floyd-Hoare logic.Comment: 26 pages, 6 figures, includes a condensed version of the author's Master's thesis arXiv:1404.6503. (This version of the article (v2) is identical to the previous one (v1), except for minor changes in phrasing.

Asynchronous Distributed Automata: A Characterization of the Modal Mu-Fragment

We establish the equivalence between a class of asynchronous distributed automata and a small fragment of least fixpoint logic, when restricted to finite directed graphs. More specifically, the logic we consider is (a variant of) the fragment of the modal mu-calculus that allows least fixpoints but forbids greatest fixpoints. The corresponding automaton model uses a network of identical finite-state machines that communicate in an asynchronous manner and whose state diagram must be acyclic except for self-loops. Exploiting the connection with logic, we also prove that the expressive power of those machines is independent of whether or not messages can be lost

A Classification of Weak Asynchronous Models of Distributed Computing

We conduct a systematic study of asynchronous models of distributed computing consisting of identical finite-state devices that cooperate in a network to decide if the network satisfies a given graph-theoretical property. Models discussed in the literature differ in the detection capabilities of the agents residing at the nodes of the network (detecting the set of states of their neighbors, or counting the number of neighbors in each state), the notion of acceptance (acceptance by halting in a particular configuration, or by stable consensus), the notion of step (synchronous move, interleaving, or arbitrary timing), and the fairness assumptions (non-starving, or stochastic-like). We study the expressive power of the combinations of these features, and show that the initially twenty possible combinations fit into seven equivalence classes. The classification is the consequence of several equi-expressivity results with a clear interpretation. In particular, we show that acceptance by halting configuration only has non-trivial expressive power if it is combined with counting, and that synchronous and interleaving models have the same power as those in which an arbitrary set of nodes can move at the same time. We also identify simple graph properties that distinguish the expressive power of the seven classes

Was verbirgt sich hinter dem Ninos-Roman? Ein Blick auf die Rückseiten der Berliner Fragmente

P.Berol. 6926 A and B, two large fragments of a papyrus roll, contain parts of the famous Ninus-Romance on the recto. They were published in 1893 by Wilcken and have since then been most extensively studied and several times republished. The verso instead has not come under any scrutiny since the times of Wilcken. The contribution presents first results of an attempt to decipher the pretty cursively written accounts contained on the verso sides and especially to find hints regarding chronology and provenance as well as other pieces of information which might contribute to potentially contextualizing the papyrus

Eine Neuedition von P.Berl. Cohen 8

A new edition of the sale of an ass from Kerkesoucha P.Berl. Cohen 8, offering new readings especially of the prescript, gives new weight to the text in regard to the discussion of the process of centralization of the activities of the state notaries in the Arsinoite nome at the end of the II cent. C.E

Spin- and momentum-correlated atom pairs mediated by photon exchange and seeded by vacuum fluctuations

Engineering pairs of massive particles that are simultaneously correlated in their external and internal degrees of freedom is a major challenge, yet essential for advancing fundamental tests of physics and quantum technologies. In this work, we experimentally demonstrate a mechanism for generating pairs of atoms in well-defined spin and momentum modes. This mechanism couples atoms from a degenerate Bose gas via a superradiant photon-exchange process in an optical cavity, producing pairs via a single or two discernible channels. The scheme is independent of collisional interactions, fast and tunable. We observe a collectively enhanced production of pairs and probe inter-spin correlations in momentum space. We characterize the emergent pair statistics, and find that the observed dynamics is consistent with being primarily seeded by vacuum fluctuations in the corresponding atomic modes. Together with our observations of coherent many-body oscillations involving well-defined momentum modes, our results offer promising prospects for quantum-enhanced interferometry and quantum simulation experiments using entangled matter waves.Comment: 15 pages, 6 figure

Multifrequency magnetic resonance elastography-based tomoelastography of the parotid glands–feasibility and reference values

Objectives: Accurate radiological differentiation of parotid tumors remains challenging despite recent technical advances in quantitative medical imaging. Multifrequency magnetic resonance elastography (MRE) could provide additional information on viscoelastic properties of normal and abnormal biological tissues. This study investigates the feasibility of MRE of the parotid glands in healthy participants and provides first reference values. Methods: 20 healthy participants underwent multifrequency MRE of both parotid glands at 3 Tesla. Shear waves at frequencies of 25, 30, 40, and 50 Hz were introduced into the participants' heads through the occiput using pressurized-air actuators. Shear wave speed (SWS) and loss angle of the shear modulus (φ) were reconstructed by tomoelastography post-processing as surrogate parameters for tissue stiffness and viscosity or fluidity. 10 participants underwent repeated MRE to determine test-retest reliability based on intraclass correlation coefficients. Results: All MRE datasets acquired could be included in the analysis. Mean SWS was 0.97 ± 0.13 m/s, and mean φ was 0.59 ± 0.05 rad, each for both sides combined and without notable lateral difference (p = 0.88/0.87). Test-retest reliability was good for SWS (ICC = 0.84 for both sides/ICC = 0.77 for the right side/ICC = 0.79 for the left side) and good to excellent for φ(ICC = 0.94/0.86/0.90). Conclusions: Multifrequency MRE of the parotid glands is feasible and reliable. This technique, therefore, is a promising method for investigating the viscoelastic properties of salivary gland tumors in future studies

Which city is the greenest? A multi-dimensional deconstruction of city rankings

The question “which city is the greenest” sounds trivial, but in reality, this question contains statistical ambiguities. In this study, we approach this issue by ranking cities by green space shares. However, we do not base our ranking only on one green parameter and the commonly used administrative boundaries. Instead, we broaden access to rankings through several approaches: First, we calculate two parameters, i.e. green space shares and green space per capita. Second, we apply these parameters for two cases: for all green areas as well as for green areas with a minimum size of one hectare. The latter are considered to have an impact on near-home recreation and the local climate. Third, we relate these parameters on the one hand to administrative spatial units constituting the entity ‘city’, but juxtapose these on the other hand with two alternative spatial reference units: a morphological spatial unit that closely encompasses the built-up pattern of the city, and a standardized buffer unit around the city centers. The variability of these manifold rankings obtained by this study makes clear: the rank of one city in a relational system to other cities depends strongly on these parameters and spatial units applied. In our experiments we rank and compare the 80 major cities in Germany. The diversity of results allows to discuss the susceptibility of spatial statistics to ambiguities that may arise from the use of different concepts. By integrating these multidimensional concepts into one final ranking, we propose a strategy for a more holistic and robust approach while revealing uncertainties