Fast Consensus under Eventually Stabilizing Message Adversaries

This paper is devoted to deterministic consensus in synchronous dynamic networks with unidirectional links, which are under the control of an omniscient message adversary. Motivated by unpredictable node/system initialization times and long-lasting periods of massive transient faults, we consider message adversaries that guarantee periods of less erratic message loss only eventually: We present a tight bound of $2D+1$ for the termination time of consensus under a message adversary that eventually guarantees a single vertex-stable root component with dynamic network diameter $D$, as well as a simple algorithm that matches this bound. It effectively halves the termination time $4D+1$ achieved by an existing consensus algorithm, which also works under our message adversary. We also introduce a generalized, considerably stronger variant of our message adversary, and show that our new algorithm, unlike the existing one, still works correctly under it.Comment: 13 pages, 5 figures, updated reference

Nonextensive aspects of self-organized scale-free gas-like networks

We explore the possibility to interpret as a 'gas' the dynamical self-organized scale-free network recently introduced by Kim et al (2005). The role of 'momentum' of individual nodes is played by the degree of the node, the 'configuration space' (metric defining distance between nodes) being determined by the dynamically evolving adjacency matrix. In a constant-size network process, 'inelastic' interactions occur between pairs of nodes, which are realized by the merger of a pair of two nodes into one. The resulting node possesses the union of all links of the previously separate nodes. We consider chemostat conditions, i.e., for each merger there will be a newly created node which is then linked to the existing network randomly. We also introduce an interaction 'potential' (node-merging probability) which decays with distance d_ij as 1/d_ij^alpha; alpha >= 0). We numerically exhibit that this system exhibits nonextensive statistics in the degree distribution, and calculate how the entropic index q depends on alpha. The particular cases alpha=0 and alpha to infinity recover the two models introduced by Kim et al.Comment: 7 pages, 5 figure

Selection of noise level in strategy adoption for spatial social dilemmas

We studied spatial Prisoner's Dilemma and Stag Hunt games where both the strategy distribution and the players' individual noise level could evolve to reach higher individual payoff. Players are located on the sites of different two-dimensional lattices and gain their payoff from games with their neighbors by choosing unconditional cooperation or defection. The way of strategy adoption can be characterized by a single $K$ (temperature-like) parameter describing how strongly adoptions depend on the payoff-difference. If we start the system from a random strategy distribution with many different player specific $K$ parameters, the simultaneous evolution of strategies and $K$ parameters drives the system to a final stationary state where only one $K$ value remains. In the coexistence phase of cooperator and defector strategies the surviving $K$ parameter is in good agreement with the noise level that ensures the highest cooperation level if uniform $K$ is supposed for all players. In this paper we give a thorough overview about the properties of this evolutionary process.Comment: 10 two-column pages, 10 figures; accepted for publication in Physical Review

Purification and mechanistic characterisation of two polygalacturonases from Sclerotium rolfsii

Sclerotium rolfsii (strain CBS 350.80) was found to produce extraordinary high amounts of polygalacturonases (PGs). Two of these extracellular enzymes were purified by a recently introduced preparative electrophoretic device (isoelectric focusing mode of free flow electrophoresis). PG 1 (39.5 kDa, pI 6.5) and PG 2 (38 kDa, pI 5.4) exhibited quite similar properties, they were found to be both endo-acting enzymes. Both PGs cleaved penta- and trigalacturonic acid while tetragalacturonic acid was only cleaved when trigalacturonic acid was present. The latter substrate was hydrolysed much faster by PG 2. Both enzymes were active on pectins with different degrees of esterification, they were sensitive towards Ca-cations and not glycosylated. The kinetic properties were measured by viscosimetry with polygalacturonic acid as a substrate. NMR experiments on a model substrate revealed an inverting mechanism of carbohydrate hydrolysis for both enzymes

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

Iterative Approximate Consensus in the presence of Byzantine Link Failures

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each directed link of the underlying communication graph represents a communication channel between a pair of nodes. We adopt the transient Byzantine link failure model [15, 16], where an omniscient adversary controls a subset of the directed communication links, but the nodes are assumed to be fault-free. Recent work has addressed the problem of reaching approximate consen- sus in incomplete graphs with Byzantine nodes using a restricted class of iterative algorithms that maintain only a small amount of memory across iterations [22, 21, 23, 12]. However, to the best of our knowledge, we are the first to consider approximate consensus in the presence of Byzan- tine links. We extend our past work that provided exact characterization of graphs in which the iterative approximate consensus problem in the presence of Byzantine node failures is solvable [22, 21]. In particular, we prove a tight necessary and sufficient condition on the underlying com- munication graph for the existence of iterative approximate consensus algorithms under transient Byzantine link model. The condition answers (part of) the open problem stated in [16].Comment: arXiv admin note: text overlap with arXiv:1202.609

Gathering in Dynamic Rings

The gathering problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced. The extensive existing literature on this problem shares the same fundamental assumption: the topological structure does not change during the rendezvous or the gathering; this is true also for those investigations that consider faulty nodes. In other words, they only consider static graphs. In this paper we start the investigation of gathering in dynamic graphs, that is networks where the topology changes continuously and at unpredictable locations. We study the feasibility of gathering mobile agents, identical and without explicit communication capabilities, in a dynamic ring of anonymous nodes; the class of dynamics we consider is the classic 1-interval-connectivity. We focus on the impact that factors such as chirality (i.e., a common sense of orientation) and cross detection (i.e., the ability to detect, when traversing an edge, whether some agent is traversing it in the other direction), have on the solvability of the problem. We provide a complete characterization of the classes of initial configurations from which the gathering problem is solvable in presence and in absence of cross detection and of chirality. The feasibility results of the characterization are all constructive: we provide distributed algorithms that allow the agents to gather. In particular, the protocols for gathering with cross detection are time optimal. We also show that cross detection is a powerful computational element. We prove that, without chirality, knowledge of the ring size is strictly more powerful than knowledge of the number of agents; on the other hand, with chirality, knowledge of n can be substituted by knowledge of k, yielding the same classes of feasible initial configurations

Yeast diversity in relation to the production of fuels and chemicals

In addition to ethanol, yeasts have the potential to produce many other industrially-relevant chemicals from numerous different carbon sources. However there remains a paucity of information about overall capability across the yeast family tree. Here, 11 diverse species of yeasts with genetic backgrounds representative of different branches of the family tree were investigated. They were compared for their abilities to grow on a range of sugar carbon sources, to produce potential platform chemicals from such substrates and to ferment hydrothermally pretreated rice straw under simultaneous saccharification and fermentation conditions. The yeasts differed considerably in their metabolic capabilities and production of ethanol. A number could produce significant amounts of ethyl acetate, arabinitol, glycerol and acetate in addition to ethanol, including from hitherto unreported carbon sources. They also demonstrated widely differing efficiencies in the fermentation of sugars derived from pre-treated rice straw biomass and differential sensitivities to fermentation inhibitors. A new catabolic property of Rhodotorula mucilaginosa (NCYC 65) was discovered in which sugar substrate is cleaved but the products are not metabolised. We propose that engineering this and some of the other properties discovered in this study and transferring such properties to conventional industrial yeast strains could greatly expand their biotechnological utility

A novel xylan degrading β-D-xylosidase: purification and biochemical characterization

Aspergillus ochraceus, a thermotolerant fungus isolated in Brazil from decomposing materials, produced an extracellular b-xylosidase that was purified using DEAE-cellulose ion exchange chromatography, Sephadex G-100 and Biogel P-60 gel filtration. b-xylosidase is a glycoprotein (39 % carbohydrate content) and has a molecular mass of 137 kDa by SDS-PAGE, with optimal temperature and pH at 70 C and 3.0–5.5, respectively.b-xylosidase was stable in acidic pH (3.0–6.0) and 70 C for 1 h. The enzyme was activated by 5 mM MnCl2 (28 %)and MgCl2 (20 %) salts. The b-xylosidase produced by A. ochraceus preferentially hydrolyzed p-nitrophenyl-b- D-xylopyranoside, exhibiting apparent Km and Vmax values of 0.66 mM and 39 U (mg protein)-1 respectively, and to a lesser extent p-nitrophenyl-b-D-glucopyranoside. The enzyme was able to hydrolyze xylan from different sources,suggesting a novel b-D-xylosidase that degrades xylan. HPLC analysis revealed xylans of different compositions which allowed explaining the differences in specificity observed by b-xylosidase. TLC confirmed the capacity.This work was supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), and the Conselho de Desenvolvimento Científico e Tecnológico (CNPq). J. A. J. and M. L. T. M. P are Research Fellows of CNPq. M. M. was a recipient of a FAPESP fellowship and this work is part of her Doctoral Thesis. It is also part of the project SISBIOTA CNPq: 563260/2010-6 and FAPESP: 2010/52322-3

Anonymous Asynchronous Systems: The Case of Failure Detectors

Due the multiplicity of loci of control, a main issue distributed systems have to cope with lies in the uncertainty on the system state created by the adversaries that are asynchrony, failures, dynamicity, mobility, etc. Considering message-passing systems, this paper considers the uncertainty created by the net effect of three of these adversaries, namely, asynchrony, failures, and anonymity. This means that, in addition to be asynchronous and crash-prone, the processes have no identity. Trivially, agreement problems (e.g., consensus) that cannot be solved in presence of asynchrony and failures cannot be solved either when adding anonymity. The paper consequently proposes anonymous failure detectors to circumvent these impossibilities. It has several contributions. First it presents three classes of failure detectors (denoted AP, A∩ and A∑) and show that they are the anonymous counterparts of the classes of perfect failure detectors, eventual leader failure detectors and quorum failure detectors, respectively. The class A∑ is new and showing it is the anonymous counterpart of the class ∑ is not trivial. Then, the paper presents and proves correct a genuinely anonymous consensus algorithm based on the pair of anonymous failure detector classes (A∩, A∑) (“genuinely” means that, not only processes have no identity, but no process is aware of the total number of processes). This new algorithm is not a “straightforward extension” of an algorithm designed for non-anonymous systems. To benefit from A∑, it uses a novel message exchange pattern where each phase of every round is made up of sub-rounds in which appropriate control information is exchanged. Finally, the paper discusses the notions of failure detector class hierarchy and weakest failure detector class for a given problem in the context of anonymous systems