Brief Announcement: Memory Lower Bounds for Self-Stabilization

In the context of self-stabilization, a silent algorithm guarantees that the communication registers (a.k.a register) of every node do not change once the algorithm has stabilized. At the end of the 90\u27s, Dolev et al. [Acta Inf. \u2799] showed that, for finding the centers of a graph, for electing a leader, or for constructing a spanning tree, every silent deterministic algorithm must use a memory of Omega(log n) bits per register in n-node networks. Similarly, Korman et al. [Dist. Comp. \u2707] proved, using the notion of proof-labeling-scheme, that, for constructing a minimum-weight spanning tree (MST), every silent algorithm must use a memory of Omega(log^2n) bits per register. It follows that requiring the algorithm to be silent has a cost in terms of memory space, while, in the context of self-stabilization, where every node constantly checks the states of its neighbors, the silence property can be of limited practical interest. In fact, it is known that relaxing this requirement results in algorithms with smaller space-complexity. In this paper, we are aiming at measuring how much gain in terms of memory can be expected by using arbitrary deterministic self-stabilizing algorithms, not necessarily silent. To our knowledge, the only known lower bound on the memory requirement for deterministic general algorithms, also established at the end of the 90\u27s, is due to Beauquier et al. [PODC \u2799] who proved that registers of constant size are not sufficient for leader election algorithms. We improve this result by establishing the lower bound Omega(log log n) bits per register for deterministic self-stabilizing algorithms solving (Delta+1)-coloring, leader election or constructing a spanning tree in networks of maximum degree Delta

Memory lower bounds for deterministic self-stabilization

In the context of self-stabilization, a \emph{silent} algorithm guarantees that the register of every node does not change once the algorithm has stabilized. At the end of the 90's, Dolev et al. [Acta Inf. '99] showed that, for finding the centers of a graph, for electing a leader, or for constructing a spanning tree, every silent algorithm must use a memory of $\Omega(\log n)$ bits per register in $n$-node networks. Similarly, Korman et al. [Dist. Comp. '07] proved, using the notion of proof-labeling-scheme, that, for constructing a minimum-weight spanning trees (MST), every silent algorithm must use a memory of $\Omega(\log^2n)$ bits per register. It follows that requiring the algorithm to be silent has a cost in terms of memory space, while, in the context of self-stabilization, where every node constantly checks the states of its neighbors, the silence property can be of limited practical interest. In fact, it is known that relaxing this requirement results in algorithms with smaller space-complexity. In this paper, we are aiming at measuring how much gain in terms of memory can be expected by using arbitrary self-stabilizing algorithms, not necessarily silent. To our knowledge, the only known lower bound on the memory requirement for general algorithms, also established at the end of the 90's, is due to Beauquier et al.~[PODC '99] who proved that registers of constant size are not sufficient for leader election algorithms. We improve this result by establishing a tight lower bound of $\Theta(\log \Delta+\log \log n)$ bits per register for self-stabilizing algorithms solving $(\Delta+1)$-coloring or constructing a spanning tree in networks of maximum degree~$\Delta$. The lower bound $\Omega(\log \log n)$ bits per register also holds for leader election

Correction of upstream flow and hydraulic state with data assimilation in the context of flood forecasting

The present study describes the assimilation of river water level observations and the resulting improvement in flood forecasting. The Kalman Filter algorithm was built on top of a one-dimensional hydraulic model which describes the Saint-Venant equations. The assimilation algorithm folds in two steps: the first one was based on the assumption that the upstream flow can be adjusted using a three-parameter correction; the second one consisted of directly correcting the hydraulic state. This procedure was applied using a four- day sliding window over the flood event. The background error covariances for water level and discharge were repre- sented with anisotropic correlation functions where the cor- relation length upstream of the observation points is larger than the correlation length downstream of the observation points. This approach was motivated by the implementation of a Kalman Filter algorithm on top of a diffusive flood wave propagation model. The study was carried out on the Adour and the Marne Vallage (France) catchments. The correction of the upstream flow as well as the control of the hydraulic state during the flood event leads to a significant improve- ment in the water level and discharge in both analysis and forecast modes

Fostering knowledge sharing about agroforestry systems through gaming and simulation in Irituia (Northeast Para, Brasil)

In the Eastern Amazon, many small-scale farmers have been spontaneously initiating expe-riences in forest restoration, mainly through agroforestry systems. To guide more inclusiverestoration policies, it is important to assess the socio-economic viability and ecological benefits of the different systems. Following a companion modelling approach, simulation and gaming tools were developed to enable exploring how and why smallholders would engage in farming systems oriented toward agroforestry systems. A stylized model of 4 similar 25-hafamily farms was first designed by researchers. This virtual landscape represents a game board. During gaming sessions, participants are requested to select the activities they would like to perform, to locate them in the game board and to indicate the practices related to these activities. These human-made decisions are inputted into a computer simulation model that allows simulating the growth of the plants and calculating a set of indicators to assess the balance between environmental and socioeconomic benefits. This tool has been co-designed with a small group of farmers from the Municipe of Irituia (North-eastern Para, Brazil) who were selected because of the experience in agroforestry systems. The game was then tested by students from Itabocal, a rural school of Irituia Municipe. We present how it enabled fostering knowledge sharing among students, farmers and researchers

Conservation des semences de cocotier en emballage étanche

Une expérimentation réalisée sur la Station Marc-Delorme (Côte d'Ivoire) en collaboration avec la Société Bernhardt (France) montre qu'il est possible de conserver les semences de cocotier en les conditionnant dans des emballages hermétiques. Cette technique permet de retarder la germination de la noix qui naturellement ne présente pas de dormance. Le conditionnement en simple sac étanche sans mise sous vide, ni enrichissement de l'atmosphère par l'azote ou le gaz carbonique apparaît, pour l'heure, comme la solution la plus satisfaisante et la plus simple à mettre en oeuvre. En prenant soin de récolter des noix mûres à épiderme encore coloré, on peut conserver les semences pendant 4 mois sans affecter leur pouvoir germinatif. Il est par ailleurs indispensable de traiter les noix par poudrage pour limiter le développement de moisissures communes favorisé par le confinement de l'atmosphère du sac et la richesse en eau du frui

Symbolic Supervisory Control of Distributed Systems with Communications

We consider the control of distributed systems composed of subsystems communicating asynchronously; the aim is to build local controllers that restrict the behavior of a distributed system in order to satisfy a global state avoidance property. We model distributed systems as \emph{communicating finite state machines} with reliable unbounded FIFO queues between subsystems. Local controllers can only observe the behavior of their proper subsystem and do not see the queue contents. To refine their control policy, controllers can use the FIFO queues to communicate by piggy-backing extra information (some timestamps and their state estimates) to the messages sent by the subsystems. We provide an algorithm that computes, for each local subsystem (and thus for each controller), during the execution of the system, an estimate of the current global state of the distributed system. We then define a synthesis algorithm to compute local controllers. Our method relies on the computation of (co-)reachable states. Since the reachability problem is undecidable in our model, we use abstract interpretation techniques to obtain overapproximations of (co-)reachable states. An implementation of our algorithms provides an empirical evaluation of our method

Synthesis of Communicating Controllers for Distributed Systems

International audienceWe consider the control of distributed systems composed of subsystems communicating asynchronously; the aim is to build local controllers that restrict the behavior of a distributed system in order to satisfy a global state avoidance property. We model our distributed systems as communicating finite state machines with reliable unbounded FIFO queues between subsystems. Local controllers can only observe their proper local subsystems and do not observe the queues. To refine their control policy, they can use the FIFO queues to communicate by piggybacking extra information to the messages sent by the subsystems. We define synthesis algorithms allowing to compute the local controllers. We explain how we can ensure the termination of this control algorithm by using abstract interpretation techniques, to overapproximate queue contents by regular languages. An implementation of our algorithms provides an empirical evaluation of our method

Rev\^etements du demi-plan de Drinfeld et correspondance de Langlands p-adique

We describe the de Rham complex of the \'etale coverings of Drinfeld's p-adic upper half-plane for GL_2(Q_p). Conjectured by Breuil and Strauch, this description gives a geometric realization of the p-adic local Langlands correspondence for certain two-dimensional de Rham representations of the absolute Galois group of Q_p.Comment: Final version, to appear in the Annals of Mat

The universal cover of an algebra without double bypass

Let A be a basic finite dimensional and connected algebra over an algebraically closed field k with zero characteristic. If the ordinary quiver of A has no double bypasses, we show that A admits a Galois covering which satisfies a universal property with respect to the Galois coverings of A. This universal property is similar to the one of the universal cover of a connected topological space.Comment: This text (21 pages) gives detailed proofs of the results announced in a previous note of the author (The fundamental group of a triangular algebra without double bypasses) and extends the study of this previous note to the Galois coverings of an algebr

How mineralogy and geochemistry can improve the significance of Pb isotopes in metal provenance studies

Lead isotopes combined with trace element data represent a powerful tool for non-ferrous metal provenance studies. Nevertheless, unconsidered geological factors and archaeological data, as well as ignored analytical procedures, may substantially modify the interpretation of the isotopic and trace element signature obtained as a potential ore candidate. Three archaeological examples, accompanied by high-resolution lead isotopic measurements (MC–ICP–MS), are presented here to discuss the above-mentioned criticisms and to propose some solutions. The first example deals with prehistoric/historical gold/silver-mining activity from Romania (the Baia Borşa and Roşia Montană ore deposits). The second one regards the lead/silver metallurgical activity from the Mont-Lozère massif (France) during medieval times. The third example focuses on the comparison between two batches of lead isotope data gathered on Roman lead ingots from Saintes-Maries-de-la-Mer, using different SRM 981 Pb values