Lodestone: An Efficient Byzantine Fault-Tolerant Protocol in Consortium Blockchains

We present Lodestone, a chain-based Byzantine fault-tolerant (BFT) state machine replication (SMR) protocol under partial synchrony. Lodestone enables replicas to achieve consensus with two phases of voting and enjoys (1) optimistic responsiveness and (2) linear communication complexity on average. Similar to the state-of-the-art chain-based BFT protocols, Lodestone can be optimized with a pipelining idea elegantly. We implement pipelined Lodestone and deploy experiments to evaluate its performance. The evaluation results demonstrate that Lodestone has a lower latency than HotStuff under various workloads.

Entrainment of Chaotic Oscillations in a Colonial Tunicate.

BackgroundTunicates comprise an invertebrate, chordate subphylum which has been shown to be the closest group to vertebrates. Colonial tunicates are clusters of genetic clones generated asexually from a single free swimming larval “tadpole”. Each individual, or zooid, of the colony has a peristaltic heart which circulates blood through that individual. In addition, each zooid is connected to a common, external vascular network. This vascular network has radial extensions that end at the colony periphery in bulbs, or ampullae, which contract and expand to generate reciprocating flow between ampullae and zooids. Surgically detached ampullae continue to beat.ResultsQuantitative scans of videos of individual ampullae in a young Botrylloides viocella colony demonstrate ampullae contractions are often in phase, with occasional abrupt phase shifts out of and back to synchrony. The vessels connecting the ampullae to the zooid also contract, mostly in phase with the ampullae. Total volumes pumped by this colonial system are a significant fraction of the zooid volume, since it contracts 180 degrees out of phase and at the same frequency as the ampullae. Reversals of the peristaltic heart are at least partially synchronized with ampullae contractions. Ampullae that have been surgically detached from the colony contract at a more uniform rate with more symmetrical profiles than when part of the colony. ConclusionContractions of the ampullae and associated vessels pump sufficient blood in and out of the zooid that they should be considered functional hearts, and the partial synchrony of ampullae contractions results in a larger blood flow compared to an alternative asynchronous contraction pattern. The manner in which the ampullae abruptly fall out of and back to synchrony indicates synchrony is due to entrainment while the out of phase contractions of the zooid may be a direct result of pumping. The shape of contraction curves of detached ampullae pairs is almost indistinguishable from a pure sine wave, indicating that the more complex original pattern was due to interactions between out of phase ampullae. Ampullae and associated vessels might be analogous with the system of lymphatic vessels in vertebrates.

Using phase dynamics to study partial synchrony: three examples

Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to analyze coupled oscillatory systems. Typically, the phase dynamics description is obtained in the weak coupling limit, i.e., in the first-order in the coupling strength. The extension beyond the first-order represents an unsolved problem and is an active area of research. In this paper, three partially synchronous states are investigated and presented in order of increasing complexity. First, the usage of the phase response curve for the description of macroscopic oscillators is analyzed. To achieve this, the response of the mean-field oscillations in a model of all-to-all coupled limit-cycle oscillators to pulse stimulation is measured. The next part treats a two-group Kuramoto model, where the interaction of one attractive and one repulsive group results in an interesting solitary state, situated between full synchrony and self-consistent partial synchrony. In the last part, the phase dynamics of a relatively simple system of three Stuart-Landau oscillators are extended beyond the weak coupling limit. The resulting model contains triplet terms in the high-order phase approximation, though the structural connections are only pairwise. Finally, the scaling of the new terms with the coupling is analyzed.

Networks of conforming or nonconforming individuals tend to reach satisfactory decisions

Binary decisions of agents coupled in networks can often be classified into two types: “coordination,” where an agent takes an action if enough neighbors are using that action, as in the spread of social norms, innovations, and viral epidemics, and “anticoordination,” where too many neighbors taking a particular action causes an agent to take the opposite action, as in traffic congestion, crowd dispersion, and division of labor. Both of these cases can be modeled using linear-threshold–based dynamics, and a fundamental question is whether the individuals in such networks are likely to reach decisions with which they are satisfied. We show that, in the coordination case, and perhaps more surprisingly, also in the anticoordination case, the agents will indeed always tend to reach satisfactory decisions, that is, the network will almost surely reach an equilibrium state. This holds for every network topology and every distribution of thresholds, for both asynchronous and partially synchronous decision-making updates. These results reveal that irregular network topology, population heterogeneity, and partial synchrony are not sufficient to cause cycles or nonconvergence in linear-threshold dynamics; rather, other factors such as imitation or the coexistence of coordinating and anticoordinating agents must play a role.