Parametrized Complexity of Weak Odd Domination Problems

Given a graph $G=(V,E)$, a subset $B\subseteq V$ of vertices is a weak odd dominated (WOD) set if there exists $D \subseteq V {\setminus} B$ such that every vertex in $B$ has an odd number of neighbours in $D$. $\kappa(G)$ denotes the size of the largest WOD set, and $\kappa'(G)$ the size of the smallest non-WOD set. The maximum of $\kappa(G)$ and $|V|-\kappa'(G)$, denoted $\kappa_Q(G)$, plays a crucial role in quantum cryptography. In particular deciding, given a graph $G$ and $k>0$, whether $\kappa_Q(G)\le k$ is of practical interest in the design of graph-based quantum secret sharing schemes. The decision problems associated with the quantities $\kappa$, $\kappa'$ and $\kappa_Q$ are known to be NP-Complete. In this paper, we consider the approximation of these quantities and the parameterized complexity of the corresponding problems. We mainly prove the fixed-parameter intractability (W$[1]$-hardness) of these problems. Regarding the approximation, we show that $\kappa_Q$, $\kappa$ and $\kappa'$ admit a constant factor approximation algorithm, and that $\kappa$ and $\kappa'$ have no polynomial approximation scheme unless P=NP.Comment: 16 pages, 5 figure

Optimal accessing and non-accessing structures for graph protocols

An accessing set in a graph is a subset B of vertices such that there exists D subset of B, such that each vertex of V\B has an even number of neighbors in D. In this paper, we introduce new bounds on the minimal size kappa'(G) of an accessing set, and on the maximal size kappa(G) of a non-accessing set of a graph G. We show strong connections with perfect codes and give explicitly kappa(G) and kappa'(G) for several families of graphs. Finally, we show that the corresponding decision problems are NP-Complete

Facilitating agroecosystem resilience : study of local agricultural knowledge Resilience 2014 -Montpellier

International audienceWhat are the farmers representations of soil quality indicators ? Which of them do they know? Which of them do they use? Ten farmers in a French rural department (Cévennes lozériennes) were interviewed between 2012 and 2013. It's an homogeneous field according to geomorphological caracteristics. The farmers comply with the specifications of the "Nature et Progrès" label, which is more binding than the organic label, especially as far as environmental standards are concerned. They practice gGardening on "terrasses". They participate in traditional landscape maintaing through agricultural practices in stressful mountainous environment. Semi-structured enquiries and participant observation on farmers'soil fertility practices. Farmers are set up between 2 years to 40 years and are 25 to nearly 60 years old. An ethnographic study was conducted to identify the farmers' representations of soil quality indicators, allegedly used as decision-making tools in a fragile mountain environment. => Representations are here assumed as at the origin of social practices of nature (Descola, 1986). => Indicators are here chosen as interdisciplinary boundary-object (Trompette et Vinck, 2009) to link agronomy and anthropology, among others. Farmers' agronomy notion oversteps the strictly technical data to go beyond the scope of global ecosociosystem sustainability. This work, by questioning the epistemological bases of the investigated production system, opens the way to think twice about the resilience given by an agriculture which is required to "produce differently.

On Weak Odd Domination and Graph-based Quantum Secret Sharing

A weak odd dominated (WOD) set in a graph is a subset B of vertices for which there exists a distinct set of vertices C such that every vertex in B has an odd number of neighbors in C. We point out the connections of weak odd domination with odd domination, [sigma,rho]-domination, and perfect codes. We introduce bounds on \kappa(G), the maximum size of WOD sets of a graph G, and on \kappa'(G), the minimum size of non WOD sets of G. Moreover, we prove that the corresponding decision problems are NP-complete. The study of weak odd domination is mainly motivated by the design of graph-based quantum secret sharing protocols: a graph G of order n corresponds to a secret sharing protocol which threshold is \kappa_Q(G) = max(\kappa(G), n-\kappa'(G)). These graph-based protocols are very promising in terms of physical implementation, however all such graph-based protocols studied in the literature have quasi-unanimity thresholds (i.e. \kappa_Q(G)=n-o(n) where n is the order of the graph G underlying the protocol). In this paper, we show using probabilistic methods, the existence of graphs with smaller \kappa_Q (i.e. \kappa_Q(G)< 0.811n where n is the order of G). We also prove that deciding for a given graph G whether \kappa_Q(G)< k is NP-complete, which means that one cannot efficiently double check that a graph randomly generated has actually a \kappa_Q smaller than 0.811n.Comment: Subsumes arXiv:1109.6181: Optimal accessing and non-accessing structures for graph protocol

Prestin and the good vibrations

In a recent paper published in the Biochemical Journal (1), Lolli and collaborators presented evidence that the C-terminal STAS domain of the motor protein prestin possesses an anion-binding site. This discovery might bring light to an aspect of the function of this mysterious and fascinating protein that is crucial for the human hearing system

Un modèle débit-durée-fréquence pour caractériser le régime d'étiage d'un bassin versant

La méthodologie débit-durée-fréquence (QdF), appliquée ces dernières années aux étiages, a permis de définir quatre modèles types recouvrant l'ensemble des rivières étudiées. L'identification de la typologie du site étudié et l'estimation de deux descripteurs hydrologiques locaux suffisent au modèle, dit de référence, pour en déduire les courbes QdF (1j ≤ d ≤ 30j) en débit moyen minimum sur l'année (VCNd) ou débit seuil minimum annuel (QCNd) non dépassé sur ces mêmes durées. S'il est relativement aisé de définir les descripteurs hydrologiques, il est plus difficile d'identifier, sans observation de débit, le modèle à prendre en compte. En reconsidérant avec plus de rationalité la démarche d'identification des typologies, et en particulier les distributions multidurées relatives à chaque bassin, il est apparu possible d'évoluer vers un modèle unique pouvant être calé en chaque site observé. Ce nouveau concept de modélisation repose sur la propriété d'affinité des distributions, relatives aux échantillons de valeurs de durées d. Par souci de continuité avec l'approche QdF à référence typologique, la loi statistique log-normale à deux paramètres a été choisie. Le modèle, dont la conceptualisation est indépendante de la loi statistique choisie, aura dans le cas de la loi log-normale trois paramètres à ajuster sur les VCNd échantillonnés. Trente six sous bassins du bassin hydrographique de la Moselle ont été étudiés. Le modèle développé pour les débit moyens VCNd peut être appliqué aux débits seuils QCNd en conservant le même jeu de paramètres, grâce à une relation observée entre débits moyens et débits seuils. Cette nouvelle modélisation rationalise l'approche antérieure basée sur la typologie d'écoulement de basses eaux des bassins versants.The flow-duration-frequency (QdF) concept, as applied in recent years to low flows, has made it possible to establish four reference models (GALEA et al., 1999a), corresponding to four typologies. The hydrological variables concerned are the minimum mean discharge of the year defined for various continuous durations d (1day ≤ d ≤ 30day), called VCNd, and the annual minimum threshold discharge not exceeded over these same durations, called QCNd, according to OBERLIN (1992). These QdF models allow a description of the temporal variability of low flows observed for a river basin, from a statistical point of view. The typology of the basin and two local hydrological descriptors have to be known. For ungauged basins, these two descriptors (GALEA et al., 1999b) are well estimated by various methods, such as multivariate analysis relating to the physiographic characteristics of the basin. Nevertheless, the choice of the reference model still remains contentious.By reconsidering in a more rational manner the step of identification of typologies, and in particular the discharge distributions (for durations d) relating to each basin, it appeared interesting to establish a local model. This new model has a simpler formulation, thanks to a scale invariance assumption. This research (CHAPUT, 1999) was undertaken on 36 sub-basins of the Mosel basin. In order to ensure continuity with the earlier QdF models described above, the two-parameter log-normal law was chosen and adjusted on the distribution of mean discharges. The scale invariance assumption is deduced from the observed parallelism of distributions related to different durations, when discharges are represented in a logarithm scale. This observation means that all of the distributions can be translated to a common point, in order to obtain one "consolidated" distribution, independent on the considered duration. This parallelism has been observed on many basins, and seems to be a realistic assumption. Furthermore, these observations have been made on samples, and do not depend on the choice of statistical law. The methodology described in this paper makes it possible to adjust the local QdF model on sampled discharges. Only three parameters have to be determined: sc, the "consolidated" standard deviation, ∆e the low flow characteristic duration and VCN(2,1), which represents the quantile of the one-day distribution, with the two-year return period (F=0.5).This model is also useful for the determination of threshold discharges (QCNd). An observed property gives a relation between the VCN and QCN quantiles, for a fixed return period, considering different durations d: VCN quantiles can been deduced from QCN quantiles by integrating them, according to d. Consequently, the analytical formulation of the VCN model can be derived according to d, in order to obtain a QCN model. This model has the same three parameters sc, ∆e and VCN(2,1) described above. The comparison between QCN quantiles adjusted on samples and QCN quantiles deduced from the VCN model by derivation shows good results.As a conclusion, this new modelling approach unifies the typological approach for both mean discharges and threshold discharges. It is based on a local adjustment and avoids having to choose between one of the four former reference models. This local model opens up perspectives for a regional model, as it has been done for floods, for example by the Group of Research in Statistical Hydrology (1996). This will make it possible to estimate the low flow regime on an ungauged basin

Modélisation régionale des débits de crue du bassin hydrographique du Cris : approche régionale classique et par modèles de référence

Une régionalisation débit-durée-fréquence des débits de crue est réalisée sur les sous bassins du Cris qui draine une superficie d'environ 14 300 km2 à l'ouest de la Roumanie. Cette régionalisation concerne 78 sous bassins dont les chroniques de débit quotidien et de pointe observées sont de trente ans en moyenne et pour lesquels nous disposons des pluies maximales de bassin de 1 jour à 10 jours calculées à partir de 92 postes pluviométriques. La régionalisation est menée selon deux approches : une approche régionale classique et une approche à partir de trois modèles adimensionnels de référence établis sur trois sites observés de France. La différence fondamentale entre les deux approches réside en ce que l'une prend en compte l'information spatiale pluie-débit inventoriée du Cris et que l'autre considère essentiellement l'information pluie-débit de chaque site de référence français. L'approche modèles de référence a pour base conceptuelle une typologie des crues qui pour un site cible est prédéfinie par un critère de choix, tandis que l'approche classique nécessite que soient définis des régions hydrologiques homogènes. Cette démarche est menée sur les trois sous bassins hydrographiques du Cris et permet d'étendre la région hydrologique homogène à l'ensemble du bassin du Cris. L'approche régionale comme l'approche modèles de référence privilégie la loi exponentielle adaptée aux valeurs supérieures à un seuil pour ce qui concerne les quantiles de crue de faible période de retour et pour des durées de 1j à 10j selon la dynamique de crue des sous bassins. Pour les quantiles de crue de grande période de retour les deux approches sous tendent le modèle du GRADEX, forme d'extrapolation des distributions observées par le gradex des pluies maximales. Quelle que soit l'approche de régionalisation, en tout site cible doivent être disponibles deux descripteurs de régime : le débit de pointe décennal Q10 et une durée caractéristique de crue D. Afin de comparer essentiellement l'incertitude des modélisations sur les quantiles de crue, D et Q10 sont connus et déduits des observations. Les résultats présentés montrent une bonne validité du modèle régional ajusté sur l'ensemble du Cris. Ceci indique que la zone étudiée est relativement bien homogène. Concernant les modèles de référence, leur critère de choix n'apparaît pas pertinent lorsqu'on s'intéresse aux faibles périodes de retour, mais se révèle significatif pour les fortes périodes de retour. Ce résultat est en grande partie dû à la méthode d'extrapolation appliquée. Celle ci est liée à la méthode du GRADEX et utilise l'information locale sur les gradex de pluie, comme cela est souvent le cas en France. Il est à noter que ces modèles de référence établis sur des chroniques de débit et pluie d'avant 1992 n'ont pas été réactualisés. L'exemple du bassin du Cris montre qu'ils n'en gardent pas moins un caractère opérationnel pour l'estimation des quantiles de crue de durée d (0 < d(j) < 10) et de période moyenne de retour T (5 < T(an) < 1000).When local information on streamflows is insufficient for estimating flood quantiles, a Regional Flood Frequency Analysis (RFFA) is usually carried out. Once homogeneous hydrological regions are defined, methods such as the "Index-Flood" method can be applied. In most cases, the variable understudy is the maximum peak flood (instantaneous or mean daily value, depending available data). However, the severity of a flood is not only defined by its peak, but also by its volume and duration.For this reason, Cemagref has developed for several years an approach which, in addition to the classic flood/frequency relationship, takes into account the notion of duration: the flood-duration-frequency approach (QdF). In a similar manner to the rainfall intensity-duration-frequency analysis, averaged discharges are computed over different fixed durations d. For each duration, a frequency distribution of maximum averaged discharges is studied. Finally, a continuous formulation is fitted, as a function of the return period (T) and the duration (d) over which discharges have been averaged. Rare quantiles are determined using rainfall frequency information, according the so-called "GRADEX" method ("aesthetic" version). The regionalization of the QdF approach leaded to define three sets of dimensionless QdF curves. The originality of the method is that each set was fitted to one unique basin, located in France, and corresponding to a distinct hydrological regime. A choice criterion, involving maximal rainfall distributions, determines which reference basin has to be considered. In this way, the QdF regionalization differs from the classic concepts mentioned in the first paragraph. The classic approach takes into account the whole streamflow-rainfall information available on a homogeneous hydrological region, while the QdF regionalization developed at Cemagref considers the streamflow-rainfall information available on the three French reference basins. The aim of this research is to apply classical regional concepts (homogeneous regions) to the QdF approach and to compare results with thus obtained using the three French reference basins. One interest of the study is that it has been conducted in Romania, ie, outside the area where the three reference basins are located.The case study is carried out on the Cris river sub-catchments which cover an area of about 14 300 km2, in the west of Romania. This regionalization concerns 78 sub-catchments having about thirty years of streamflow measurements (daily flow and instantaneous flood peaks). For validation purpose, two basin sets are constituted: a calibration set (54 basins) and a validation set (24 basins). Furthermore, maximal rainfalls over 1 day to 10 days are available for these basins, from 92 rain-gauge stations. First, regional QdF curves are deduced according the definition of homogeneous regions. Three regions are defined, corresponding to the three main sub-catchments of the Cris basins. After different tests, it is shown that the whole Cris basin can be considered as a unique homogeneous region. Then, the regionalization involving the three French reference basins is carried out. In both cases, methods are applied with the exponential law adjusted on peak over threshold values, for small return periods. Durations are ranging from 1 day to 10 days, according to the flood dynamic of the studied basins. For long return periods, both approaches use the GRADEX method, which extrapolates discharge distributions according to the rainfall distributions. Whatever the regional approach used, two descriptors have to be estimated for each target site, in order to unscale the dimensionless regional QdF curves. Theses two descriptors are the 10-year-return-period peak flood Q10 and a flood characteristic duration D. In order to compare the uncertainty of the two approaches, D and Q10 are local values, deduced from observations.The results presented shows a good validity of the regional model fitted to the whole Cris basin. This indicates that this region is quite homogeneous. Concerning the reference models, their choice criterion does not appear to be pertinent for small return periods, but becomes relevant for high return periods. In this case, estimations are comparable to thus provided using the whole regional information available on the Cris basin. This result is mainly due to the extrapolation method used. It is related to the GRADEX method and takes into account the local information about rainfall gradex, as it is often done in France. One point to be noticed is that these reference models have not been updated since they have been established in 1992. Despite that, the Cris basin example shows their operational ability for estimating flood quantiles of duration d (0 < d(day) < 10) and return period T (5 < T(year) < 1000). From an operational point of view, the three reference basins can be a valuable option. Indeed, a regional analysis is sometime difficult to carry out: data not available or too costly, time available for the study to short, etc. On the other hand, the three reference basins method is easier to apply and requires less data. However, uncertainties and hypothesis of the method should be kept in mind. In particular, we should be aware that high return period quantiles are given according the GRADEX method, ie using the frequency rainfall information. Consequently, the hypothesis of this method should be respected

L'approche débit-durée-fréquence : historique et avancées

La prévention du risque d'inondation nécessite une connaissance détaillée du régime hydrologique en crue du bassin étudié. Dans ce but, l'approche débit-durée-fréquence (QdF), développée depuis déjà plusieurs années, a permis de définir un modèle statistique décrivant les crues observées en fonction de leur débit, de leur durée et de leur fréquence. Un récent travail a revisité cette approche. Grâce à son nombre réduit de paramètres, le modèle proposé, appelé modèle local convergent, peut être facilement ajusté pour chaque bassin. Dans l'ancienne approche, que nous appelons approche " bassin de référence ", l'ajustement local avait été effectué sur seulement trois bassins, dits de référence, et réputés être chacun représentatif d'une typologie d'écoulement différente. Ces trois paramétrisations types ont ensuite donné lieu à trois modèles adimensionnels, capables de caractériser la majorité des régimes observés. Le modèle adimensionnel correspondant au régime du bassin étudié devait être dénormé par deux caractéristiques locales du bassin : le débit instantané maximal de crue décennale et une durée caractéristique de crue. Une comparaison du nouveau modèle, appelé modèle local convergent, et de l'approche type " bassin de référence " a été effectuée sur une cinquantaine de bassins jaugés. Elle met en évidence la robustesse du modèle convergent et permet de discuter du choix du modèle relatif à l'approche " bassin de référence ". Le modèle local convergent autorise d'envisager le développement d'un modèle QdF régional, s'inspirant de différentes méthodes de régionalisation. Ceci permettra alors une application à des bassins peu ou non observés.Flood risk mitigation requires a good knowledge of hydrological flood regime, which can be described by a flow-duration-frequency (QdF) approach. New developments of this approach are presented and compared to the former method.Usually, flood frequency analysis deals only with the maximum flood peak distribution or the maximum daily discharge distribution. The QdF approach analyses maximum average flows over different durations d (d =1, 3, …, N days). Similar to intensity-duration-frequency curves, each of the QdF curves represents the flood frequency distribution, for the duration d. QdF modelling aims to express QdF curves by a Q(d,T) function (d : the duration; T : the return period).Before this present work, QdF modelling was associated with the "reference basin" approach. In this approach, QdF curves (plotted as a function of d, for fixed T) of many studied basins are converted into a dimensionless form. The two characteristics used are the 10-year peak flood, Q(d=0, T=10 years), and a characteristic flood duration (D) of the studied catchment, calculated from different flood hydrographs. Then, three different families are determined, grouping basins with similar dimensionless QdF curves. For each of these families, one reference basin is chosen. Their dimensionless curves are parameterised, in order to obtain a continuous formulation, as a function on T and d. By denormalising one of these dimensionless QdF models with the local parameters Q(0,10) and D, it is possible to obtain the continuous Q(d,T) formulation for the studied basin. The choice of the correct dimensionless model is made via a choice criterion. It involves Q(0,10), D and shape parameters of local maximal rainfall distributions (a Gumbel law is assumed), for different durations, d. These distributions are obtained according to the intensity-duration-frequency approach. If the studied basin is ungauged, local parameters Q(0,10) and D are estimated by regional formulas, involving significant variables such as catchment area and rainfall.Recent work has improved this "reference basin" approach. A new QdF model, called convergent local, has been developed. For fixed T, the model assumes that the Q(d,T) is described by a hyperbolic form, as a function of d. This choice of the hyperbolic form is based on the observation of many catchments (about one hundred). It has also been observed that QdF curves, plotted for fixed d as a function of T, converge toward the same point, when T decreases. Using these observations as assumptions, the model is then able to calculate Q(d,T) for any return period T and any duration d.If a two-parameter statistical law (such as the exponential law) is adopted, the model contains only 4 parameters. The first parameter is the limit of Q(d,T), when d tends to infinity. It is estimated by calculating the average value over the entire observed period of the Q(t) discharge time series. The second one gives the hyperbolas curvatures and is ∆. The ∆ parameter has a time dimension and is consequently a characteristic duration of the studied basin. The final two parameters are the location and shape parameters, x0 (0) and aq (0), of the exponential maximal flood distribution for d=0. x0 (0), aq (0) and ∆ parameters are directly adjusted on observed QdF curves of the studied basin.The comparison between the convergent local model and the "reference basin" approach has been carried out on about 50 basins, drawn from different regions of France. For each basin, the two approaches have been tested. First, the two characteristic durations D and∆, defined respectively by the "reference basins" approach and the convergent local model, are compared. As mentioned earlier, ∆ characteristic duration is an adjusted parameter and its calculation does not depend on D. In spite of their different definitions, a strong correlation between these two parameters is observed. This shows a good coherence between the two tested approaches. Second, in order to compare results, a relative mean error between calculated and observed values is determined for each basin and each model. Only the observed domain (T ≤ 20 years) has been considered, because the extrapolations cannot been validated with observed data.Concerning the "reference basin" approach, the three reference basin models are studied, and the choice criterion is applied. Results show that this choice criterion is not relevant. Concerning the convergent local model, the observed mean relative error is lower than in the "reference basin" approach. These good results are confirmed by a very small error dispersion. Consequently, the convergent local model is robust.As a conclusion, this paper presents new developments of the QdF approach: the convergent local continuous model. This model, locally adjusted, yields very satisfactory results. The next step is to apply it on ungauged basins, as is possible in the "reference basins" approach. This could be done by adapting regional methods, such as the index flood method

Quantum Secret Sharing with Graph States

Revised Selected Papers - http://www.memics.cz/2012/International audienceWe study the graph-state-based quantum secret sharing protocols [24,17] which are not only very promising in terms of physical implementation, but also resource efficient since every player's share is composed of a single qubit. The threshold of a graph-state-based protocol admits a lower bound: for any graph of order n, the threshold of the corresponding n-player protocol is at least 0.506n. Regarding the upper bound, lexicographic product of the C 5 graph (cycle of size 5) are known to provide n-player protocols which threshold is n − n 0.68. Using Paley graphs we improve this bound to n − n 0.71. Moreover, using probabilistic methods, we prove the existence of graphs which associated threshold is at most 0.811n. Albeit non-constructive, probabilistic methods permit to prove that a random graph G of order n has a threshold at most 0.811n with high probability. However, verifying that the threshold of a given graph is acually smaller than 0.811n is hard since we prove that the corresponding decision problem is NP-Complete. These results are mainly based on the graphical characterization of the graph-state-based secret sharing properties, in particular we point out strong connections with domination with parity constraints

How crucial is it to account for the antecedent moisture conditions in flood forecasting? Comparison of event-based and continuous approaches on 178 catchments

This paper compares event-based and continuous hydrological modelling approaches for real-time forecasting of river flows. Both approaches are compared using a lumped hydrologic model (whose structure includes a soil moisture accounting (SMA) store and a routing store) on a data set of 178 French catchments. The main focus of this study was to investigate the actual impact of soil moisture initial conditions on the performance of flood forecasting models and the possible compensations with updating techniques. The rainfall-runoff model assimilation technique we used does not impact the SMA component of the model but only its routing part. Tests were made by running the SMA store continuously or on event basis, everything else being equal. The results show that the continuous approach remains the reference to ensure good forecasting performances. We show, however, that the possibility to assimilate the last observed flow considerably reduces the differences in performance. Last, we present a robust alternative to initialize the SMA store where continuous approaches are impossible because of data availability problems