12,342 research outputs found
Graph Laplacians and Stabilization of Vehicle Formations
Control of vehicle formations has emerged as a topic of significant interest to the controls community. In this paper, we merge tools from graph theory and control theory to derive stability criteria for formation stabilization. The interconnection between vehicles (i.e., which vehicles are sensed by other vehicles) is modeled as a graph, and the eigenvalues of the Laplacian matrix of the graph are used in stating a Nyquist-like stability criterion for vehicle formations. The location of the Laplacian eigenvalues can be correlated to the graph structure, and therefore used to identify desirable and undesirable formation interconnection topologies
Double quiver gauge theory and nearly Kahler flux compactifications
We consider G-equivariant dimensional reduction of Yang-Mills theory with
torsion on manifolds of the form MxG/H where M is a smooth manifold, and G/H is
a compact six-dimensional homogeneous space provided with a never integrable
almost complex structure and a family of SU(3)-structures which includes a
nearly Kahler structure. We establish an equivalence between G-equivariant
pseudo-holomorphic vector bundles on MxG/H and new quiver bundles on M
associated to the double of a quiver Q, determined by the SU(3)-structure, with
relations ensuring the absence of oriented cycles in Q. When M=R^2, we describe
an equivalence between G-invariant solutions of Spin(7)-instanton equations on
MxG/H and solutions of new quiver vortex equations on M. It is shown that
generic invariant Spin(7)-instanton configurations correspond to quivers Q that
contain non-trivial oriented cycles.Comment: 42 pages; v2: minor corrections; Final version to be published in
JHE
Information flow and cooperative control of vehicle formations
We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability
Generalized Kruithof approach for traffic matrix estimation
[Abstract]: In this paper, the traffic matrix estimation problem is formulated as an nonlinear optimization problem based on the generalized Kruithof approach which uses the Kullback distance to measure the probabilistic distance between two traffic matrices. In addition, an algorithm using the affine scaling method is provided to solve the constraint optimization problem
Quiver Gauge Theory of Nonabelian Vortices and Noncommutative Instantons in Higher Dimensions
We construct explicit BPS and non-BPS solutions of the Yang-Mills equations
on the noncommutative space R^{2n}_\theta x S^2 which have manifest spherical
symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show
that the solutions imply an equivalence between instantons on R^{2n}_\theta x
S^2 and nonabelian vortices on R^{2n}_\theta, which can be interpreted as a
blowing-up of a chain of D0-branes on R^{2n}_\theta into a chain of spherical
D2-branes on R^{2n} x S^2. The low-energy dynamics of these configurations is
described by a quiver gauge theory which can be formulated in terms of new
geometrical objects generalizing superconnections. This formalism enables the
explicit assignment of D0-brane charges in equivariant K-theory to the
instanton solutions.Comment: 45 pages, 4 figures; v2: minor correction
Quiver Gauge Theory and Noncommutative Vortices
We construct explicit BPS and non-BPS solutions of the Yang-Mills equations
on noncommutative spaces R^{2n}_theta x G/H which are manifestly G-symmetric.
Given a G-representation, by twisting with a particular bundle over G/H, we
obtain a G-equivariant U(k) bundle with a G-equivariant connection over
R^{2n}_theta x G/H. The U(k) Donaldson-Uhlenbeck-Yau equations on these spaces
reduce to vortex-type equations in a particular quiver gauge theory on
R^{2n}_theta. Seiberg-Witten monopole equations are particular examples. The
noncommutative BPS configurations are formulated with partial isometries, which
are obtained from an equivariant Atiyah-Bott-Shapiro construction. They can be
interpreted as D0-branes inside a space-filling brane-antibrane system.Comment: talk by O.L. at the 21st Nishinomiya-Yukawa Memorial Symposium,
Kyoto, 15 Nov. 200
SU(3)-Equivariant Quiver Gauge Theories and Nonabelian Vortices
We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on
Kaehler manifolds of the form M x SU(3)/H, with H = SU(2) x U(1) or H = U(1) x
U(1). The induced rank two quiver gauge theories on M are worked out in detail
for representations of H which descend from a generic irreducible
SU(3)-representation. The reduction of the Donaldson-Uhlenbeck-Yau equations on
these spaces induces nonabelian quiver vortex equations on M, which we write
down explicitly. When M is a noncommutative deformation of the space C^d, we
construct explicit BPS and non-BPS solutions of finite energy for all cases. We
compute their topological charges in three different ways and propose a novel
interpretation of the configurations as states of D-branes. Our methods and
results generalize from SU(3) to any compact Lie group.Comment: 1+56 pages, 9 figures; v2: clarifying comments added, final version
to appear in JHE
Working with Nonassociative Geometry and Field Theory
We review aspects of our formalism for differential geometry on
noncommutative and nonassociative spaces which arise from cochain twist
deformation quantization of manifolds. We work in the simplest setting of
trivial vector bundles and flush out the details of our approach providing
explicit expressions for all bimodule operations, and for connections and
curvature. As applications, we describe the constructions of physically viable
action functionals for Yang-Mills theory and Einstein-Cartan gravity on
noncommutative and nonassociative spaces, as first steps towards more elaborate
models relevant to non-geometric flux deformations of geometry in closed string
theory.Comment: 20 pages; v2: Reference added; Contribution to the proceedings of the
Corfu Summer Institute on Elementary Particle Physics and Gravity, September
1-26, 2015, Corfu, Greece; Final version published in Proceedings of Scienc
Testing gravitational parity violation with coincident gravitational waves and short gamma-ray bursts
Gravitational parity violation is a possibility motivated by particle
physics, string theory and loop quantum gravity. One effect of it is amplitude
birefringence of gravitational waves, whereby left and right
circularly-polarized waves propagate at the same speed but with different
amplitude evolution. Here we propose a test of this effect through coincident
observations of gravitational waves and short gamma-ray bursts from binary
mergers involving neutron stars. Such gravitational waves are highly left or
right circularly-polarized due to the geometry of the merger. Using
localization information from the gamma-ray burst, ground-based gravitational
wave detectors can measure the distance to the source with reasonable accuracy.
An electromagnetic determination of the redshift from an afterglow or host
galaxy yields an independent measure of this distance. Gravitational parity
violation would manifest itself as a discrepancy between these two distance
measurements. We exemplify such a test by considering one specific effective
theory that leads to such gravitational parity-violation, Chern-Simons gravity.
We show that the advanced LIGO-Virgo network and all-sky gamma-ray telescopes
can be sensitive to the propagating sector of Chern-Simons gravitational parity
violation to a level roughly two orders of magnitude better than current
stationary constraints from the LAGEOS satellites.Comment: 21 pages, 2 figures, submitted to Phys. Rev.
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