131,367 research outputs found
Consensus problems in networks of agents with switching topology and time-delays
In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results
Ultrafast Consensus in Small-World Networks
In this paper, we demonstrate a phase transition phenomenon in algebraic connectivity of small-world networks. Algebraic connectivity of a graph is the second smallest eigenvalue of its Laplacian matrix and a measure of speed of solving consensus problems in networks. We demonstrate that it is possible to dramatically increase the algebraic connectivity of a regular complex network by 1000 times or more without adding new links or nodes to the network. This implies that a consensus problem can be solved incredibly fast on certain small-world networks giving rise to a network design algorithm for ultra fast information networks. Our study relies on a procedure called "random rewiring" due to Watts & Strogatz (Nature, 1998). Extensive numerical results are provided to support our claims and conjectures. We prove that the mean of the bulk Laplacian spectrum of a complex network remains invariant under random rewiring. The same property only asymptotically holds for scale-free networks. A relationship between increasing the algebraic connectivity of complex networks and robustness to link and node failures is also shown. This is an alternative approach to the use of percolation theory for analysis of network robustness. We also show some connections between our conjectures and certain open problems in the theory of random matrices
Agent-Based Simulations of Blockchain protocols illustrated via Kadena's Chainweb
While many distributed consensus protocols provide robust liveness and
consistency guarantees under the presence of malicious actors, quantitative
estimates of how economic incentives affect security are few and far between.
In this paper, we describe a system for simulating how adversarial agents, both
economically rational and Byzantine, interact with a blockchain protocol. This
system provides statistical estimates for the economic difficulty of an attack
and how the presence of certain actors influences protocol-level statistics,
such as the expected time to regain liveness. This simulation system is
influenced by the design of algorithmic trading and reinforcement learning
systems that use explicit modeling of an agent's reward mechanism to evaluate
and optimize a fully autonomous agent. We implement and apply this simulation
framework to Kadena's Chainweb, a parallelized Proof-of-Work system, that
contains complexity in how miner incentive compliance affects security and
censorship resistance. We provide the first formal description of Chainweb that
is in the literature and use this formal description to motivate our simulation
design. Our simulation results include a phase transition in block height
growth rate as a function of shard connectivity and empirical evidence that
censorship in Chainweb is too costly for rational miners to engage in. We
conclude with an outlook on how simulation can guide and optimize protocol
development in a variety of contexts, including Proof-of-Stake parameter
optimization and peer-to-peer networking design.Comment: 10 pages, 7 figures, accepted to the IEEE S&B 2019 conferenc
Economic Games as Estimators
Discrete event games are discrete time dynamical systems whose state transitions are discrete events caused by actions taken by agents within the game. The agents’ objectives and associated decision rules need not be known to the game designer in order to impose struc- ture on a game’s reachable states. Mechanism design for discrete event games is accomplished by declaring desirable invariant properties and restricting the state transition functions to conserve these properties at every point in time for all admissible actions and for all agents, using techniques familiar from state-feedback control theory. Building upon these connections to control theory, a framework is developed to equip these games with estimation properties of signals which are private to the agents playing the game. Token bonding curves are presented as discrete event games and numerical experiments are used to investigate their signal processing properties with a focus on input-output response dynamics.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc
Asynchronous Gossip for Averaging and Spectral Ranking
We consider two variants of the classical gossip algorithm. The first variant
is a version of asynchronous stochastic approximation. We highlight a
fundamental difficulty associated with the classical asynchronous gossip
scheme, viz., that it may not converge to a desired average, and suggest an
alternative scheme based on reinforcement learning that has guaranteed
convergence to the desired average. We then discuss a potential application to
a wireless network setting with simultaneous link activation constraints. The
second variant is a gossip algorithm for distributed computation of the
Perron-Frobenius eigenvector of a nonnegative matrix. While the first variant
draws upon a reinforcement learning algorithm for an average cost controlled
Markov decision problem, the second variant draws upon a reinforcement learning
algorithm for risk-sensitive control. We then discuss potential applications of
the second variant to ranking schemes, reputation networks, and principal
component analysis.Comment: 14 pages, 7 figures. Minor revisio
Physical Origin of the Boson Peak Deduced from a Two-Order-Parameter Model of Liquid
We propose that the boson peak originates from the (quasi-) localized
vibrational modes associated with long-lived locally favored structures, which
are intrinsic to a liquid state and are randomly distributed in a sea of
normal-liquid structures. This tells us that the number density of locally
favored structures is an important physical factor determining the intensity of
the boson peak. In our two-order-parameter model of the liquid-glass
transition, the locally favored structures act as impurities disturbing
crystallization and thus lead to vitrification. This naturally explains the
dependence of the intensity of the boson peak on temperature, pressure, and
fragility, and also the close correlation between the boson peak and the first
sharp diffraction peak (or prepeak).Comment: 5 pages, 1 figure, An error in the reference (Ref. 7) was correcte
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