22,141 research outputs found
Statistical Methods in Topological Data Analysis for Complex, High-Dimensional Data
The utilization of statistical methods an their applications within the new
field of study known as Topological Data Analysis has has tremendous potential
for broadening our exploration and understanding of complex, high-dimensional
data spaces. This paper provides an introductory overview of the mathematical
underpinnings of Topological Data Analysis, the workflow to convert samples of
data to topological summary statistics, and some of the statistical methods
developed for performing inference on these topological summary statistics. The
intention of this non-technical overview is to motivate statisticians who are
interested in learning more about the subject.Comment: 15 pages, 7 Figures, 27th Annual Conference on Applied Statistics in
Agricultur
On the relevance of numerical simulations to booming sand
We have performed a simulation study of 3D cohesionless granular flows down
an inclined chute. We find that the oscillations observed in [L.E. Silbert,
Phys. Rev. Lett., 94, 098002 (2005)] near the angle of repose are harmonic
vibrations of the lowest normal mode. Their frequencies depend on the contact
stiffness as well as on the depth of the flow. Could these oscillations account
for the phenomena of "booming sand"? We estimate an effective contact stiffness
from the Hertz law, but this leads to frequencies several times higher than
observed. However, the Hertz law also predicts interpenetrations of a few
nanometers, indicating that the oscillations frequencies are governed by the
surface stiffness, which can be much lower than the bulk one. This is in
agreement with previous studies ascribing the ability to sing to the presence
of a soft coating on the grain surface.Comment: accepted for publication in Physical Review E http://pre.aps.org;
Physical Review E (2012) to be publishe
U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
We formulate a U(1) gauge theory of the Hubbard model in the slave-rotor
representation. From this formalism it is argued that spin liquid phases may
exist near the Mott transition in the Hubbard model on triangular and honeycomb
lattices at half filling. The organic compound k-(BEDT-TTF)_2 Cu_2 (CN)_3 is a
good candidate for the spin liquid state on a triangular lattice. We predict a
highly unusual temperature dependence for the thermal conductivity of this
material.Comment: 5 pages, 2 figures; paper shortened and the phase diagram of
anisotropic triangular lattice correcte
Random quantum codes from Gaussian ensembles and an uncertainty relation
Using random Gaussian vectors and an information-uncertainty relation, we
give a proof that the coherent information is an achievable rate for
entanglement transmission through a noisy quantum channel. The codes are random
subspaces selected according to the Haar measure, but distorted as a function
of the sender's input density operator. Using large deviations techniques, we
show that classical data transmitted in either of two Fourier-conjugate bases
for the coding subspace can be decoded with low probability of error. A
recently discovered information-uncertainty relation then implies that the
quantum mutual information for entanglement encoded into the subspace and
transmitted through the channel will be high. The monogamy of quantum
correlations finally implies that the environment of the channel cannot be
significantly coupled to the entanglement, and concluding, which ensures the
existence of a decoding by the receiver.Comment: 9 pages, two-column style. This paper is a companion to
quant-ph/0702005 and quant-ph/070200
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