22,112 research outputs found
On large bipartite graphs of diameter 3
We consider the bipartite version of the {\it degree/diameter problem},
namely, given natural numbers and , find the maximum number
of vertices in a bipartite graph of maximum degree and diameter
. In this context, the bipartite Moore bound \M^b(d,D) represents a
general upper bound for . Bipartite graphs of order \M^b(d,D) are
very rare, and determining still remains an open problem for most
pairs.
This paper is a follow-up to our earlier paper \cite{FPV12}, where a study on
bipartite -graphs (that is, bipartite graphs of order \M^b(d,D)-4)
was carried out. Here we first present some structural properties of bipartite
-graphs, and later prove there are no bipartite -graphs.
This result implies that the known bipartite -graph is optimal, and
therefore . Our approach also bears a proof of the uniqueness of
the known bipartite -graph, and the non-existence of bipartite
-graphs.
In addition, we discover three new largest known bipartite (and also
vertex-transitive) graphs of degree 11, diameter 3 and order 190, result which
improves by 4 vertices the previous lower bound for
Capacity Theorems for the AWGN Multi-Way Relay Channel
The L-user additive white Gaussian noise multi-way relay channel is
considered, where multiple users exchange information through a single relay at
a common rate. Existing coding strategies, i.e., complete-decode-forward and
compress-forward are shown to be bounded away from the cut-set upper bound at
high signal-to-noise ratios (SNR). It is known that the gap between the
compress-forward rate and the capacity upper bound is a constant at high SNR,
and that between the complete-decode-forward rate and the upper bound increases
with SNR at high SNR. In this paper, a functional-decode-forward coding
strategy is proposed. It is shown that for L >= 3, complete-decode-forward
achieves the capacity when SNR <= 0 dB, and functional-decode-forward achieves
the capacity when SNR >= 0 dB. For L=$, functional-decode-forward achieves the
capacity asymptotically as SNR increases.Comment: accepted and to be presented at ISIT 201
The distribution of geodesic excursions into the neighborhood of a cone singularity on a hyperbolic 2-orbifold
A generic geodesic on a finite area, hyperbolic 2-orbifold exhibits an
infinite sequence of penetrations into a neighborhood of a cone singularity, so
that the sequence of depths of maximal penetration has a limiting distribution.
The distribution function is the same for all such surfaces and is described by
a fairly simple formula.Comment: 20 page
CAT(0) is an algorithmic property
In this article we give an explicit algorithm which will determine, in a
discrete and computable way, whether a finite piecewise Euclidean complex is
non-positively curved. In particular, given such a complex we show how to
define a boolean combination of polynomial equations and inequalities in real
variables, i.e. a real semi-algebraic set, which is empty if and only if the
complex is non-positively curved. Once this equivalence has been shown, the
main result follows from a standard theorem in real algebraic geometry.Comment: (23 pages) To appear in Geometriae Dedicat
Cusps of lattices in rank 1 Lie groups over local fields
Let G be the group of rational points of a semisimple algebraic group of rank
1 over a nonarchimedean local field. We improve upon Lubotzky's analysis of
graphs of groups describing the action of lattices in G on its Bruhat-Tits tree
assuming a condition on unipotents in G. The condition holds for all but a few
types of rank 1 groups. A fairly straightforward simplification of Lubotzky's
definition of a cusp of a lattice is the key step to our results. We take the
opportunity to reprove Lubotzky's part in the analysis from this foundation.Comment: to appear in Geometriae Dedicat
The Nub of an Automorphism of a Totally Disconnected, Locally Compact Group
To any automorphism, , of a totally disconnected, locally compact
group, , there is associated a compact, -stable subgroup of ,
here called the \emph{nub} of , on which the action of is
topologically transitive. Topologically transitive actions of automorphisms of
compact groups have been studied extensively in topological dynamics and
results obtained transfer, via the nub, to the study of automorphisms of
general locally compact groups.
A new proof that the contraction group of is dense in the nub is
given, but it is seen that the two-sided contraction group need not be dense.
It is also shown that each pair , with compact and
topologically transitive, is an inverse limit of pairs that have `finite depth'
and that analogues of the Schreier Refinement and Jordan-H\"older Theorems hold
for pairs with finite depth
The -algebras of finitely aligned higher-rank graphs
We generalise the theory of Cuntz-Krieger families and graph algebras to the
class of finitely aligned -graphs. This class contains in particular all
row-finite -graphs. The Cuntz-Krieger relations for non-row-finite
-graphs look significantly different from the usual ones, and this
substantially complicates the analysis of the graph algebra. We prove a
gauge-invariant uniqueness theorem and a Cuntz-Krieger uniqueness theorem for
the -algebras of finitely aligned -graphs.Comment: 27 page
Multiple Loop Self-Triggered Model Predictive Control for Network Scheduling and Control
We present an algorithm for controlling and scheduling multiple linear
time-invariant processes on a shared bandwidth limited communication network
using adaptive sampling intervals. The controller is centralized and computes
at every sampling instant not only the new control command for a process, but
also decides the time interval to wait until taking the next sample. The
approach relies on model predictive control ideas, where the cost function
penalizes the state and control effort as well as the time interval until the
next sample is taken. The latter is introduced in order to generate an adaptive
sampling scheme for the overall system such that the sampling time increases as
the norm of the system state goes to zero. The paper presents a method for
synthesizing such a predictive controller and gives explicit sufficient
conditions for when it is stabilizing. Further explicit conditions are given
which guarantee conflict free transmissions on the network. It is shown that
the optimization problem may be solved off-line and that the controller can be
implemented as a lookup table of state feedback gains. Simulation studies which
compare the proposed algorithm to periodic sampling illustrate potential
performance gains.Comment: Accepted for publication in IEEE Transactions on Control Systems
Technolog
Facilitating goal-oriented behaviour in the Stroop task: when executive control is influenced by automatic processing.
A portion of Stroop interference is thought to arise from a failure to maintain goal-oriented behaviour (or goal neglect). The aim of the present study was to investigate whether goal- relevant primes could enhance goal maintenance and reduce the Stroop interference effect. Here it is shown that primes related to the goal of responding quickly in the Stroop task (e.g. fast, quick, hurry) substantially reduced Stroop interference by reducing reaction times to incongruent trials but increasing reaction times to congruent and neutral trials. No effects of the primes were observed on errors. The effects on incongruent, congruent and neutral trials are explained in terms of the influence of the primes on goal maintenance. The results show that goal priming can facilitate goal-oriented behaviour and indicate that automatic processing can modulate executive control
Theoretical analysis of control properties for the brushless doubly fed reluctance machine
Presents the fundamental theory, modelling aspects and operating/control principles of the BDFRM. This emerging machine technology is being regarded by academic and industrial communities as a prospective brushless candidate for wind turbine generators (especially off-shore installations) and large pump drives where it can offer reliable, maintenance-free, operation and competitive performance at low cost due to the use of a smaller inverter. The results in the paper are the outcomes of a joint research project (Australian Research Council - ARC funded) of the author
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