21,271 research outputs found
Measure preserving homomorphisms and independent sets in tensor graph powers
In this note, we study the behavior of independent sets of maximum
probability measure in tensor graph powers. To do this, we introduce an upper
bound using measure preserving homomorphisms. This work extends some previous
results about independence ratios of tensor graph powers.Comment: 5 page
Dynamic Packet Scheduling in Wireless Networks
We consider protocols that serve communication requests arising over time in
a wireless network that is subject to interference. Unlike previous approaches,
we take the geometry of the network and power control into account, both
allowing to increase the network's performance significantly. We introduce a
stochastic and an adversarial model to bound the packet injection. Although
taken as the primary motivation, this approach is not only suitable for models
based on the signal-to-interference-plus-noise ratio (SINR). It also covers
virtually all other common interference models, for example the multiple-access
channel, the radio-network model, the protocol model, and distance-2 matching.
Packet-routing networks allowing each edge or each node to transmit or receive
one packet at a time can be modeled as well.
Starting from algorithms for the respective scheduling problem with static
transmission requests, we build distributed stable protocols. This is more
involved than in previous, similar approaches because the algorithms we
consider do not necessarily scale linearly when scaling the input instance. We
can guarantee a throughput that is as large as the one of the original static
algorithm. In particular, for SINR models the competitive ratios of the
protocol in comparison to optimal ones in the respective model are between
constant and O(log^2 m) for a network of size m.Comment: 23 page
Dynamical effects of QCD in systems
We study the coupling of a tetraquark system to an exchanged meson-meson
channel, using a pure gluonic theory based four-quark potential {\em matrix}
model which is known to fit well a large number of data points for lattice
simulations of different geometries of a four-quark system. We find that if
this minimal-area-based potential matrix replaces the earlier used simple
Gaussian form for the gluon field overlap factor in its off-diagonal terms,
the resulting -matrix and phase shifts develop an angle dependence whose
partial wave analysis reveals wave and higher angular momentum components
in it. In addition to the obvious implications of this result for the
meson-meson scattering, this new feature indicates the possibility of orbital
excitations influencing properties of meson-meson molecules through a
polarization potential. We have used a formalism of the resonating group
method, treated kinetic energy and overlap matrices on model of the potential
matrix, but decoupled the resulting complicated integral equations through the
Born approximation. In this exploratory study we have used a quadratic
confinement and not included the spin-dependence; we also used the
approximation of equal constituent quark masses.Comment: 18 pages, 9 figure
Weakly Submodular Functions
Submodular functions are well-studied in combinatorial optimization, game
theory and economics. The natural diminishing returns property makes them
suitable for many applications. We study an extension of monotone submodular
functions, which we call {\em weakly submodular functions}. Our extension
includes some (mildly) supermodular functions. We show that several natural
functions belong to this class and relate our class to some other recent
submodular function extensions.
We consider the optimization problem of maximizing a weakly submodular
function subject to uniform and general matroid constraints. For a uniform
matroid constraint, the "standard greedy algorithm" achieves a constant
approximation ratio where the constant (experimentally) converges to 5.95 as
the cardinality constraint increases. For a general matroid constraint, a
simple local search algorithm achieves a constant approximation ratio where the
constant (analytically) converges to 10.22 as the rank of the matroid
increases
The heavy quark decomposition of the S-matrix and its relation to the pinch technique
We propose a decomposition of the S-matrix into individually gauge invariant
sub-amplitudes, which are kinematically akin to propagators, vertices, boxes,
etc. This decompsition is obtained by considering limits of the S-matrix when
some or all of the external particles have masses larger than any other
physical scale. We show at the one-loop level that the effective gluon
self-energy so defined is physically equivalent to the corresponding gauge
independent self-energy obtained in the framework of the pinch technique. The
generalization of this procedure to arbitrary gluonic -point functions is
briefly discussed.Comment: 11 uuencoded pages, NYU-TH-94/10/0
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