117,704 research outputs found
Criticality and Heterogeneity in the Solution Space of Random Constraint Satisfaction Problems
Random constraint satisfaction problems are interesting model systems for
spin-glasses and glassy dynamics studies. As the constraint density of such a
system reaches certain threshold value, its solution space may split into
extremely many clusters. In this paper we argue that this ergodicity-breaking
transition is preceded by a homogeneity-breaking transition. For random K-SAT
and K-XORSAT, we show that many solution communities start to form in the
solution space as the constraint density reaches a critical value alpha_cm,
with each community containing a set of solutions that are more similar with
each other than with the outsider solutions. At alpha_cm the solution space is
in a critical state. The connection of these results to the onset of dynamical
heterogeneity in lattice glass models is discussed.Comment: 6 pages, 4 figures, final version as accepted by International
Journal of Modern Physics
Heavy-tailed statistics in short-message communication
Short-message (SM) is one of the most frequently used communication channels
in the modern society. In this Brief Report, based on the SM communication
records provided by some volunteers, we investigate the statistics of SM
communication pattern, including the interevent time distributions between two
consecutive short messages and two conversations, and the distribution of
message number contained by a complete conversation. In the individual level,
the current empirical data raises a strong evidence that the human activity
pattern, exhibiting a heavy-tailed interevent time distribution, is driven by a
non-Poisson nature.Comment: 4 pages, 4 figures and 1 tabl
Spin-one bosons in low dimensional Mott insulating states
We analyze the strong coupling limit of spin-one bosons in low dimensional
Mott insulating states. In 1D lattices, for an odd number of bosons per site
(), the ground state is a dimerized valence bond crystal state with a
two-fold degeneracy; the low lying elementary spin excitations carry spin one.
For an even number of bosons per site, the ground state is a nondegenerate spin
singlet Mott state. We also argue that in a square lattice in a quantum
disordered limit the ground states should be dimerized valence bond crystals
for an odd integer . Finally, we briefly report results for non-integer
numbers of bosons per site in one-dimensional lattices.Comment: 5 pages; discussions on non-integer case have been shortene
Vortex-like surface wave and its role in the transient phenomena of meta-material focusing
We show that a slab of meta-material (with )
possesses a vortex-like surface wave with no ability to transport energy, whose
nature is completely different from a localized mode or a standing wave.
Through computations based on a rigorous time-dependent Green's function
approach, we demonstrate that such a mode inevitably generates characteristic
image oscillations in two dimensional focusing with even a monochromatic
source, which were observed in many numerical simulations, but such
oscillations are weak in three dimensional focusing.Comment: To appear in the March 7th issue of Appl. Phys. Let
Matrix Completion via Max-Norm Constrained Optimization
Matrix completion has been well studied under the uniform sampling model and
the trace-norm regularized methods perform well both theoretically and
numerically in such a setting. However, the uniform sampling model is
unrealistic for a range of applications and the standard trace-norm relaxation
can behave very poorly when the underlying sampling scheme is non-uniform.
In this paper we propose and analyze a max-norm constrained empirical risk
minimization method for noisy matrix completion under a general sampling model.
The optimal rate of convergence is established under the Frobenius norm loss in
the context of approximately low-rank matrix reconstruction. It is shown that
the max-norm constrained method is minimax rate-optimal and yields a unified
and robust approximate recovery guarantee, with respect to the sampling
distributions. The computational effectiveness of this method is also
discussed, based on first-order algorithms for solving convex optimizations
involving max-norm regularization.Comment: 33 page
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