47,186 research outputs found
Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition
A geometric graph is angle-monotone if every pair of vertices has a path
between them that---after some rotation---is - and -monotone.
Angle-monotone graphs are -spanners and they are increasing-chord
graphs. Dehkordi, Frati, and Gudmundsson introduced angle-monotone graphs in
2014 and proved that Gabriel triangulations are angle-monotone graphs. We give
a polynomial time algorithm to recognize angle-monotone geometric graphs. We
prove that every point set has a plane geometric graph that is generalized
angle-monotone---specifically, we prove that the half--graph is
generalized angle-monotone. We give a local routing algorithm for Gabriel
triangulations that finds a path from any vertex to any vertex whose
length is within times the Euclidean distance from to .
Finally, we prove some lower bounds and limits on local routing algorithms on
Gabriel triangulations.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Generalized Huberman-Rudnick scaling law and robustness of -Gaussian probability distributions
We generalize Huberman-Rudnick universal scaling law for all periodic windows
of the logistic map and show the robustness of -Gaussian probability
distributions in the vicinity of chaos threshold. Our scaling relation is
universal for the self-similar windows of the map which exhibit period-doubling
subharmonic bifurcations. Using this generalized scaling argument, for all
periodic windows, as chaos threshold is approached, a developing convergence to
-Gaussian is numerically obtained both in the central regions and tails of
the probability distributions of sums of iterates.Comment: 13 pages, 3 figure
``Critical'' phonons of the supercritical Frenkel-Kontorova model: renormalization bifurcation diagrams
The phonon modes of the Frenkel-Kontorova model are studied both at the
pinning transition as well as in the pinned (cantorus) phase. We focus on the
minimal frequency of the phonon spectrum and the corresponding generalized
eigenfunction. Using an exact decimation scheme, the eigenfunctions are shown
to have nontrivial scaling properties not only at the pinning transition point
but also in the cantorus regime. Therefore the phonons defy localization and
remain critical even where the associated area-preserving map has a positive
Lyapunov exponent. In this region, the critical scaling properties vary
continuously and are described by a line of renormalization limit cycles.
Interesting renormalization bifurcation diagrams are obtained by monitoring the
cycles as the parameters of the system are varied from an integrable case to
the anti-integrable limit. Both of these limits are described by a trivial
decimation fixed point. Very surprisingly we find additional special parameter
values in the cantorus regime where the renormalization limit cycle degenerates
into the above trivial fixed point. At these ``degeneracy points'' the phonon
hull is represented by an infinite series of step functions. This novel
behavior persists in the extended version of the model containing two
harmonics. Additional richnesses of this extended model are the one to two-hole
transition line, characterized by a divergence in the renormalization cycles,
nonexponentially localized phonons, and the preservation of critical behavior
all the way upto the anti-integrable limit.Comment: 10 pages, RevTeX, 9 Postscript figure
Gravitating Monopole--Antimonopole Chains and Vortex Rings
We construct monopole-antimonopole chain and vortex solutions in
Yang-Mills-Higgs theory coupled to Einstein gravity. The solutions are static,
axially symmetric and asymptotically flat. They are characterized by two
integers (m,n) where m is related to the polar angle and n to the azimuthal
angle. Solutions with n=1 and n=2 correspond to chains of m monopoles and
antimonopoles. Here the Higgs field vanishes at m isolated points along the
symmetry axis. Larger values of n give rise to vortex solutions, where the
Higgs field vanishes on one or more rings, centered around the symmetry axis.
When gravity is coupled to the flat space solutions, a branch of gravitating
monopole-antimonopole chain or vortex solutions arises, and merges at a maximal
value of the coupling constant with a second branch of solutions. This upper
branch has no flat space limit. Instead in the limit of vanishing coupling
constant it either connects to a Bartnik-McKinnon or generalized
Bartnik-McKinnon solution, or, for m>4, n>4, it connects to a new
Einstein-Yang-Mills solution. In this latter case further branches of solutions
appear. For small values of the coupling constant on the upper branches, the
solutions correspond to composite systems, consisting of a scaled inner
Einstein-Yang-Mills solution and an outer Yang-Mills-Higgs solution.Comment: 18 pages, 12 figures, uses revte
Nonlinear rheological properties of dense colloidal dispersions close to a glass transition under steady shear
The nonlinear rheological properties of dense colloidal suspensions under
steady shear are discussed within a first principles approach. It starts from
the Smoluchowski equation of interacting Brownian particles in a given shear
flow, derives generalized Green-Kubo relations, which contain the transients
dynamics formally exactly, and closes the equations using mode coupling
approximations. Shear thinning of colloidal fluids and dynamical yielding of
colloidal glasses arise from a competition between a slowing down of structural
relaxation, because of particle interactions, and enhanced decorrelation of
fluctuations, caused by the shear advection of density fluctuations. The
integration through transients approach takes account of the dynamic
competition, translational invariance enters the concept of wavevector
advection, and the mode coupling approximation enables to quantitatively
explore the shear-induced suppression of particle caging and the resulting
speed-up of the structural relaxation. Extended comparisons with shear stress
data in the linear response and in the nonlinear regime measured in model
thermo-sensitive core-shell latices are discussed. Additionally, the single
particle motion under shear observed by confocal microscopy and in computer
simulations is reviewed and analysed theoretically.Comment: Review submited to special volume 'High Solid Dispersions' ed. M.
Cloitre, Vol. xx of 'Advances and Polymer Science' (Springer, Berlin, 2009);
some figures slightly cu
The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing
and protecting fragile qubits against the undesirable effects of quantum
decoherence. Similar to classical codes, hashing bound approaching QECCs may be
designed by exploiting a concatenated code structure, which invokes iterative
decoding. Therefore, in this paper we provide an extensive step-by-step
tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided
concatenated quantum codes based on the underlying quantum-to-classical
isomorphism. These design lessons are then exemplified in the context of our
proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the
outer component of a concatenated quantum code. The proposed QIRCC can be
dynamically adapted to match any given inner code using EXIT charts, hence
achieving a performance close to the hashing bound. It is demonstrated that our
QIRCC-based optimized design is capable of operating within 0.4 dB of the noise
limit
Threadable Curves
We define a plane curve to be threadable if it can rigidly pass through a
point-hole in a line L without otherwise touching L. Threadable curves are in a
sense generalizations of monotone curves. We have two main results. The first
is a linear-time algorithm for deciding whether a polygonal curve is
threadable---O(n) for a curve of n vertices---and if threadable, finding a
sequence of rigid motions to thread it through a hole. We also sketch an
argument that shows that the threadability of algebraic curves can be decided
in time polynomial in the degree of the curve. The second main result is an O(n
polylog n)-time algorithm for deciding whether a 3D polygonal curve can thread
through hole in a plane in R^3, and if so, providing a description of the rigid
motions that achieve the threading.Comment: 16 pages, 12 figures, 12 references. v2: Revised with brief addendum
after Mikkel Abrahamsen pointed us to a relevant reference on "sweepable
polygons." v3: Major revisio
Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring
We study an evolutionary algorithm that locally adapts thresholds and wiring
in Random Threshold Networks, based on measurements of a dynamical order
parameter. A control parameter determines the probability of threshold
adaptations vs. link rewiring. For any , we find spontaneous symmetry
breaking into a new class of self-organized networks, characterized by a much
higher average connectivity than networks without threshold
adaptation (). While and evolved out-degree distributions
are independent from for , in-degree distributions become broader
when , approaching a power-law. In this limit, time scale separation
between threshold adaptions and rewiring also leads to strong correlations
between thresholds and in-degree. Finally, evidence is presented that networks
converge to self-organized criticality for large .Comment: 4 pages revtex, 6 figure
- …