Probably Safe or Live

This paper presents a formal characterisation of safety and liveness properties \`a la Alpern and Schneider for fully probabilistic systems. As for the classical setting, it is established that any (probabilistic tree) property is equivalent to a conjunction of a safety and liveness property. A simple algorithm is provided to obtain such property decomposition for flat probabilistic CTL (PCTL). A safe fragment of PCTL is identified that provides a sound and complete characterisation of safety properties. For liveness properties, we provide two PCTL fragments, a sound and a complete one. We show that safety properties only have finite counterexamples, whereas liveness properties have none. We compare our characterisation for qualitative properties with the one for branching time properties by Manolios and Trefler, and present sound and complete PCTL fragments for characterising the notions of strong safety and absolute liveness coined by Sistla

Property (RD) for Hecke pairs

As the first step towards developing noncommutative geometry over Hecke C*-algebras, we study property (RD) (Rapid Decay) for Hecke pairs. When the subgroup H in a Hecke pair (G,H) is finite, we show that the Hecke pair (G,H) has (RD) if and only if G has (RD). This provides us with a family of examples of Hecke pairs with property (RD). We also adapt Paul Jolissant's works in 1989 to the setting of Hecke C*-algebras and show that when a Hecke pair (G,H) has property (RD), the algebra of rapidly decreasing functions on the set of double cosets is closed under holomorphic functional calculus of the associated (reduced) Hecke C*-algebra. Hence they have the same K_0-groups.Comment: A short note added explaining other methods to prove that the subalgebra of rapidly decreasing functions is smooth. This is the final version as published. The published version is available at: springer.co

Analytic curves in algebraic varieties over number fields

We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'olya-Bertrandias valid over the projective line to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and rigid analytic geometry (notably, potential theory over complex and $p$-adic curves). We also discuss geometric analogues, pertaining to the algebraic geometry of projective surfaces, of these arithmetic criteria.Comment: 55 pages. To appear in "Algebra, Arithmetic, and Geometry: In Honor of Y.i. Manin", Y. Tschinkel & Yu. Manin editors, Birkh\"auser, 200

Optimization Of Detergent-Mediated Reconstitution Of Influenza A M2 Protein Into Proteoliposomes

We report the optimization of detergent-mediated reconstitution of an integral membrane-bound protein, full-length influenza M2 protein, by direct insertion into detergent-saturated liposomes. Detergent-mediated reconstitution is an important method for preparing proteoliposomes for studying membrane proteins, and must be optimized for each combination of protein and membrane constituents used. The purpose of the reconstitution was to prepare samples for site-directed spin-labeling electron paramagnetic resonance (SDSL-EPR) studies. Our goals in optimizing the protocol were to minimize the amount of detergent used, reduce overall proteoliposome preparation time, and confirm the removal of all detergent. The liposomes were comprised of (1-palmitoyl-2-oleyl-sn-glycero-phosphocholine (POPC) and 1-palmitoyl-2-oleyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (POPG), and the detergent octylglucoside (OG) was used for reconstitution. Rigorous physical characterization was applied to optimize each step of the reconstitution process. We used dynamic light scattering (DLS) to determine the amount of OG needed to saturate the preformed liposomes. During detergent removal by absorption with Bio-Beads, we quantified the detergent concentration by means of a colorimetric assay, thereby determining the number of Bio-Bead additions needed to remove all detergent from the final proteoliposomes. We found that the overnight Bio-Bead incubation used in previously published protocols can be omitted, reducing the time needed for reconstitution. We also monitored the size distribution of the proteoliposomes with DLS, confirming that the size distribution remains essentially constant throughout the reconstitution process

Single Strand Annealing Plays a Major Role in RecA-Independent Recombination between Repeated Sequences in the Radioresistant Deinococcus radiodurans Bacterium

© 2015 Ithurbide et al. The bacterium Deinococcus radiodurans is one of the most radioresistant organisms known. It is able to reconstruct a functional genome from hundreds of radiation-induced chromosomal fragments. Our work aims to highlight the genes involved in recombination between 438 bp direct repeats separated by intervening sequences of various lengths ranging from 1,479 bp to 10,500 bp to restore a functional tetA gene in the presence or absence of radiation-induced DNA double strand breaks. The frequency of spontaneous deletion events between the chromosomal direct repeats were the same in recA+ and in ΔrecA, ΔrecF, and ΔrecO bacteria, whereas recombination between chromosomal and plasmid DNA was shown to be strictly dependent on the RecA and RecF proteins. The presence of mutations in one of the repeated sequence reduced, in a MutS-dependent manner, the frequency of the deletion events. The distance between the repeats did not influence the frequencies of deletion events in recA+as well in ΔrecA bacteria. The absence of the UvrD protein stimulated the recombination between the direct repeats whereas the absence of the DdrB protein, previously shown to be involved in DNA double strand break repair through a single strand annealing (SSA) pathway, strongly reduces the frequency of RecA- (and RecO-) independent deletions events. The absence of the DdrB protein also increased the lethal sectoring of cells devoid of RecA or RecO protein. γ-irradiation of recA+cells increased about 10-fold the frequencies of the deletion events, but at a lesser extend in cells devoid of the DdrB protein. Altogether, our results suggest a major role of single strand annealing in DNA repeat deletion events in bacteria devoid of the RecA protein, and also in recA+bacteria exposed to ionizing radiation

A Short Counterexample Property for Safety and Liveness Verification of Fault-tolerant Distributed Algorithms

Distributed algorithms have many mission-critical applications ranging from embedded systems and replicated databases to cloud computing. Due to asynchronous communication, process faults, or network failures, these algorithms are difficult to design and verify. Many algorithms achieve fault tolerance by using threshold guards that, for instance, ensure that a process waits until it has received an acknowledgment from a majority of its peers. Consequently, domain-specific languages for fault-tolerant distributed systems offer language support for threshold guards. We introduce an automated method for model checking of safety and liveness of threshold-guarded distributed algorithms in systems where the number of processes and the fraction of faulty processes are parameters. Our method is based on a short counterexample property: if a distributed algorithm violates a temporal specification (in a fragment of LTL), then there is a counterexample whose length is bounded and independent of the parameters. We prove this property by (i) characterizing executions depending on the structure of the temporal formula, and (ii) using commutativity of transitions to accelerate and shorten executions. We extended the ByMC toolset (Byzantine Model Checker) with our technique, and verified liveness and safety of 10 prominent fault-tolerant distributed algorithms, most of which were out of reach for existing techniques.Comment: 16 pages, 11 pages appendi