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

An institution-based enquiry into concepts of proficiency, automaticity and second-language learning among dyslexic students

It is, for some, 'common knowledge' that dyslexic students cannot master a foreign language 'because' they cannot master their own. This study enquires into the assumption, and the 'because', above, and seeks other explanatory routes for dyslexic university students' difficulties with foreign language learning. Building on earlier work concerned with notions of 'automaticity' in relation to concepts of 'proficiency' in proficiency and dyslexia literatures, it relates these directly to second language teaching/learning concepts and discusses this in relation to 'phronetic', 'professional' and tacit' views of knowledge. The empirical part of the study comprises cross-comparison of four narrative sources: the narratives of a dozen dyslexic students engaged in a semi-structured, in-depth interview concerning their language difficulty and how they view it; a second narrative relating the voices of the advisors most directly linked to dyslexic language learners in the institution, also including past and future difficulties of some dyslexic students who may face a study year abroad, e.g. on Erasmus and similar schemes; a third interview with the then current head of the unit dealing with both English as a Foreign Language, and Modern Foreign Languages; and the over-arching narrative of the researcher – his story in conducting this study. Within this framework, the research uncovers how, at a practical level as well as theoretically, phronetic, teaching-learning and exceptional language-acquisition 'knowledge' may be open to subversion from several quarters: the pragmatics and economics of 3rd-level EFL and MFL1 language teaching; transposing child language acquisition concepts onto adult language learning ones; the cross- and/or mismatching of these with dyslexia ones; and the possible collision between some areas of professional knowledge – tacit or otherwise. The research shows how for the 'institutional dyslexics' concerned, and sometimes despite their advisors, the unit's academic director and the institution, automaticity is anterior to proficiency and agency is anterior to automaticity. Moreover reversing this, discovering or rediscovering their sense of agency allows certain of the dyslexic participants to attain a qualified measure of automaticity in their language studies and hence, of proficiency. These findings have important implications for those engaged in second language teaching and learning. The organisation of the thesis is as follows: in a first chapter which the researcher introduces with a short autobiography and an account of how the research came about, a broadly descriptive and factual introduction to the piece then summarises previous work in the doctoral degree particularly the critical analytical study, focusing the research questions, and discussing the relationship between methodology and methods, and begins a consideration of what a 'case' is, and what is the case here. Chapter 2 expands the theoretical focus with a discussion of the notion of coherentism and the notion of 'fit', and introduces issues in narrativity and in phronesis. Chapter 3 addresses understandings and terminologies in 'communicative' language teaching, cross-mapping these to both dyslexia and 'proficiency' issues previously discussed. Chapter 4 explores the data, and begins an assessment of the 'fit' between the respondents. Finally, Chapter 5 summarises and discusses the 'findings' of the research – what emerges from the research questions and what from their interpretation; how theoretical understandings now 'fit', or not; what else emerged during the study; what constitutes a finding; and returning to Chapter 1, asks to what extent the study is a foundationalist 'case' which can or should be 'generalisable'. A short discussion of further research avenues is presented

Optimal Space Lower Bound for Deterministic Self-Stabilizing Leader Election Algorithms

Given a boolean predicate ? on labeled networks (e.g., proper coloring, leader election, etc.), a self-stabilizing algorithm for ? is a distributed algorithm that can start from any initial configuration of the network (i.e., every node has an arbitrary value assigned to each of its variables), and eventually converge to a configuration satisfying ?. It is known that leader election does not have a deterministic self-stabilizing algorithm using a constant-size register at each node, i.e., for some networks, some of their nodes must have registers whose sizes grow with the size n of the networks. On the other hand, it is also known that leader election can be solved by a deterministic self-stabilizing algorithm using registers of O(log log n) bits per node in any n-node bounded-degree network. We show that this latter space complexity is optimal. Specifically, we prove that every deterministic self-stabilizing algorithm solving leader election must use ?(log log n)-bit per node registers in some n-node networks. In addition, we show that our lower bounds go beyond leader election, and apply to all problems that cannot be solved by anonymous algorithms

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

Stationary time correlations for fermions after a quench in the presence of an impurity

We consider the quench dynamics of non-interacting fermions in one dimension in the presence of a finite-size impurity at the origin. This impurity is characterized by general momentum-dependent reflection and transmission coefficients which are changed from ${\sf r}_0(k), {\sf t}_0(k)$ to ${\sf r}(k), {\sf t}(k)$ at time $t=0$. The initial state is at equilibrium with ${\sf t}_0(k)=0$ such that the system is cut in two independent halves with ${\sf r}_0^R(k)$, ${\sf r}_0^L(k)$ respectively to the right and to the left of the impurity. We obtain the exact large time limit of the multi-time correlations. These correlations become time translationally invariant, and are non-zero in two different regimes: (i) for $x=O(1)$ where the system reaches a non-equilibrium steady state (NESS) (ii) for $x \sim t$, i.e., the ray-regime. For a repulsive impurity these correlations are independent of ${\sf r}_0^R(k)$, ${\sf r}_0^L(k)$, while in the presence of bound states they oscillate and memory effects persist. We show that these nontrivial relaxational properties can be retrieved in a simple manner from the large time behaviour of the single particle wave functions.Comment: Main text: 7 pages, 3 figures. Supp. Mat.: 31 pages, 4 figure

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