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

Response of male \u3ci\u3eCentruroides vittatus\u3c/i\u3e (Scorpiones: Buthidae) to aerial and substrate-borne chemical signals

Chemical signaling promotes mate location throughout numerous animal taxa. In this study we investigated the possibility that striped scorpions, Centruroides vittatus, use chemical signaling in the form of odor plumes or substrate-borne deposits as communication channels. A Y-shaped arena was constructed to test scorpions’ use of air-borne chemical cues in the detection of potential mates. A second, circular behavioral choice chamber was used to test male scorpions’ responses to female deposits by direct substrate contact. Male scorpions showed no tendency to move toward the female in tests of air-borne chemical transmission but they did demonstrate behavior associated with chemical detection when exposed to substrate-borne feminine deposits. Our experiments do not provide evidence that male C. vittatus use aerial pheromones to locate female scorpions but that they are highly sensitive to direct contact of substrate-borne chemical deposits

The recruitment of knowledge regarding plurality and compound formation during language comprehension

Compound formation has been a major focus of research and debate in mental lexicon research. In particular, it has been widely observed that compounds with a regular plural non-head are dispreferred, and a long line of research has examined the nature of this constraint, including which morphological, semantic or phonological properties of the non-head underlie this dispreference. While it is typically assumed that this constraint in fact leads to the barring of a compound analysis to a noun-noun string which would otherwise violate the constraint, its implementation during sentence comprehension has not been thoroughly examined. Using self-paced reading, we demonstrate that knowledge of pluralization and compound formation is immediately utilized in the assignment of structure to noun-noun strings, and that the dispreference for regular plural non-heads in fact leads the parser away from the compound analysis in favor of a more complex grammatical alternative. These results provide new evidence for the online deployment of knowledge regarding pluralization and its interaction with compound formation, and inform our understanding of how morphological information is deployed during, and impacts real-time sentence comprehension

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

The European Space Analogue Rock Collection (ESAR) at the OSUC-Orleans for in situ planetary missions

International audienceThe ESAR is a collection of well-characterised planetary analogue rocks and minerals that can be used for testing in situ instrumentation for planetary exploration. An online database of all relevant structural, compositional and geotechnics information is also available to the instrument teams and to aid data interpretation during missions

Approximate Consensus in Highly Dynamic Networks: The Role of Averaging Algorithms

In this paper, we investigate the approximate consensus problem in highly dynamic networks in which topology may change continually and unpredictably. We prove that in both synchronous and partially synchronous systems, approximate consensus is solvable if and only if the communication graph in each round has a rooted spanning tree, i.e., there is a coordinator at each time. The striking point in this result is that the coordinator is not required to be unique and can change arbitrarily from round to round. Interestingly, the class of averaging algorithms, which are memoryless and require no process identifiers, entirely captures the solvability issue of approximate consensus in that the problem is solvable if and only if it can be solved using any averaging algorithm. Concerning the time complexity of averaging algorithms, we show that approximate consensus can be achieved with precision of $\varepsilon$ in a coordinated network model in $O(n^{n+1} \log\frac{1}{\varepsilon})$ synchronous rounds, and in $O(\Delta n^{n\Delta+1} \log\frac{1}{\varepsilon})$ rounds when the maximum round delay for a message to be delivered is $\Delta$. While in general, an upper bound on the time complexity of averaging algorithms has to be exponential, we investigate various network models in which this exponential bound in the number of nodes reduces to a polynomial bound. We apply our results to networked systems with a fixed topology and classical benign fault models, and deduce both known and new results for approximate consensus in these systems. In particular, we show that for solving approximate consensus, a complete network can tolerate up to 2n-3 arbitrarily located link faults at every round, in contrast with the impossibility result established by Santoro and Widmayer (STACS '89) showing that exact consensus is not solvable with n-1 link faults per round originating from the same node

Monitoring Partially Synchronous Distributed Systems using SMT Solvers

In this paper, we discuss the feasibility of monitoring partially synchronous distributed systems to detect latent bugs, i.e., errors caused by concurrency and race conditions among concurrent processes. We present a monitoring framework where we model both system constraints and latent bugs as Satisfiability Modulo Theories (SMT) formulas, and we detect the presence of latent bugs using an SMT solver. We demonstrate the feasibility of our framework using both synthetic applications where latent bugs occur at any time with random probability and an application involving exclusive access to a shared resource with a subtle timing bug. We illustrate how the time required for verification is affected by parameters such as communication frequency, latency, and clock skew. Our results show that our framework can be used for real-life applications, and because our framework uses SMT solvers, the range of appropriate applications will increase as these solvers become more efficient over time.Comment: Technical Report corresponding to the paper accepted at Runtime Verification (RV) 201

Habitability on Mars from a Microbial Point of View

International audienceExtraterrestrial habitability is a complex notion. We briefly review what is known about the origin of life on Earth, that is, life based on carbon chemistry and water. We then discuss habitable conditions (past and present) for established life and for the survival of microorganisms. Based on these elements, we propose to use the term habitable only for conditions necessary for the origin of life, the proliferation of life, and the survival of life. Not covered by this term would be conditions necessary for prebiotic chemistry and conditions that would allow the recognition of extinct or hibernating life. Finally, we apply this concept to the potential emergence of life on Mars where suitable conditions for life to start, proliferate, and survive have been heterogeneous throughout its history. These considerations have a profound impact on the nature and distribution of eventual traces of martian life, or any precursor, and must therefore inform our search-for-life strategies. Key Words: Mars-- Microbial life--Punctuated habitabilit

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