12,795 research outputs found
Controlled Hopwise Averaging: Bandwidth/Energy-Efficient Asynchronous Distributed Averaging for Wireless Networks
This paper addresses the problem of averaging numbers across a wireless
network from an important, but largely neglected, viewpoint: bandwidth/energy
efficiency. We show that existing distributed averaging schemes have several
drawbacks and are inefficient, producing networked dynamical systems that
evolve with wasteful communications. Motivated by this, we develop Controlled
Hopwise Averaging (CHA), a distributed asynchronous algorithm that attempts to
"make the most" out of each iteration by fully exploiting the broadcast nature
of wireless medium and enabling control of when to initiate an iteration. We
show that CHA admits a common quadratic Lyapunov function for analysis, derive
bounds on its exponential convergence rate, and show that they outperform the
convergence rate of Pairwise Averaging for some common graphs. We also
introduce a new way to apply Lyapunov stability theory, using the Lyapunov
function to perform greedy, decentralized, feedback iteration control. Finally,
through extensive simulation on random geometric graphs, we show that CHA is
substantially more efficient than several existing schemes, requiring far fewer
transmissions to complete an averaging task.Comment: 33 pages, 4 figure
Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problems
In this paper we develop adaptive iterative coupling schemes for the Biot
system modeling coupled poromechanics problems. We particularly consider the
space-time formulation of the fixed-stress iterative scheme, in which we first
solve the problem of flow over the whole space-time interval, then exploiting
the space-time information for solving the mechanics. Two common
discretizations of this algorithm are then introduced based on two coupled
mixed finite element methods in-space and the backward Euler scheme in-time.
Therefrom, adaptive fixed-stress algorithms are build on conforming
reconstructions of the pressure and displacement together with equilibrated
flux and stresses reconstructions. These ingredients are used to derive a
posteriori error estimates for the fixed-stress algorithms, distinguishing the
different error components, namely the spatial discretization, the temporal
discretization, and the fixed-stress iteration components. Precisely, at the
iteration of the adaptive algorithm, we prove that our estimate gives
a guaranteed and fully computable upper bound on the energy-type error
measuring the difference between the exact and approximate pressure and
displacement. These error components are efficiently used to design adaptive
asynchronous time-stepping and adaptive stopping criteria for the fixed-stress
algorithms. Numerical experiments illustrate the efficiency of our estimates
and the performance of the adaptive iterative coupling algorithms
Negative circuits and sustained oscillations in asynchronous automata networks
The biologist Ren\'e Thomas conjectured, twenty years ago, that the presence
of a negative feedback circuit in the interaction graph of a dynamical system
is a necessary condition for this system to produce sustained oscillations. In
this paper, we state and prove this conjecture for asynchronous automata
networks, a class of discrete dynamical systems extensively used to model the
behaviors of gene networks. As a corollary, we obtain the following fixed point
theorem: given a product of finite intervals of integers, and a map
from to itself, if the interaction graph associated with has no
negative circuit, then has at least one fixed point
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