10,319 research outputs found
A Sixth-Order Extension to the MATLAB Package bvp4c of J. Kierzenka and L. Shampine
A new two-point boundary value problem algorithm based upon the MATLAB bvp4c package of Kierzenka and Shampine is described. The algorithm, implemented in a new package bvp6c, uses the residual control framework of bvp4c (suitably modified for a more accurate finite difference approximation) to maintain a user specified accuracy. The new package is demonstrated to be as robust as the existing software, but more efficient for most problems, requiring fewer internal mesh points and evaluations to achieve the required accuracy
Setting the quantum integrand of M-theory
In anomaly-free quantum field theories the integrand in the bosonic
functional integral--the exponential of the effective action after integrating
out fermions--is often defined only up to a phase without an additional choice.
We term this choice ``setting the quantum integrand''. In the low-energy
approximation to M-theory the E(8)-model for the C-field allows us to set the
quantum integrand using geometric index theory. We derive mathematical results
of independent interest about pfaffians of Dirac operators in 8k+3 dimensions,
both on closed manifolds and manifolds with boundary. These theorems are used
to set the quantum integrand of M-theory for closed manifolds and for compact
manifolds with either temporal (global) or spatial (local) boundary conditions.
In particular, we show that M-theory makes sense on arbitrary 11-manifolds with
spatial boundary, generalizing the construction of heterotic M-theory on
cylinders.Comment: 52 pages; revised version for publication in Commun. Math. Phys.
corrects a few typo
Control of Networked Multiagent Systems with Uncertain Graph Topologies
Multiagent systems consist of agents that locally exchange information
through a physical network subject to a graph topology. Current control methods
for networked multiagent systems assume the knowledge of graph topologies in
order to design distributed control laws for achieving desired global system
behaviors. However, this assumption may not be valid for situations where graph
topologies are subject to uncertainties either due to changes in the physical
network or the presence of modeling errors especially for multiagent systems
involving a large number of interacting agents. Motivating from this
standpoint, this paper studies distributed control of networked multiagent
systems with uncertain graph topologies. The proposed framework involves a
controller architecture that has an ability to adapt its feed- back gains in
response to system variations. Specifically, we analytically show that the
proposed controller drives the trajectories of a networked multiagent system
subject to a graph topology with time-varying uncertainties to a close
neighborhood of the trajectories of a given reference model having a desired
graph topology. As a special case, we also show that a networked multi-agent
system subject to a graph topology with constant uncertainties asymptotically
converges to the trajectories of a given reference model. Although the main
result of this paper is presented in the context of average consensus problem,
the proposed framework can be used for many other problems related to networked
multiagent systems with uncertain graph topologies.Comment: 14 pages, 2 figure
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