4,800 research outputs found
Estimation of high-dimensional low-rank matrices
Suppose that we observe entries or, more generally, linear combinations of
entries of an unknown -matrix corrupted by noise. We are
particularly interested in the high-dimensional setting where the number
of unknown entries can be much larger than the sample size . Motivated by
several applications, we consider estimation of matrix under the assumption
that it has small rank. This can be viewed as dimension reduction or sparsity
assumption. In order to shrink toward a low-rank representation, we investigate
penalized least squares estimators with a Schatten- quasi-norm penalty term,
. We study these estimators under two possible assumptions---a modified
version of the restricted isometry condition and a uniform bound on the ratio
"empirical norm induced by the sampling operator/Frobenius norm." The main
results are stated as nonasymptotic upper bounds on the prediction risk and on
the Schatten- risk of the estimators, where . The rates that we
obtain for the prediction risk are of the form (for ), up to
logarithmic factors, where is the rank of . The particular examples of
multi-task learning and matrix completion are worked out in detail. The proofs
are based on tools from the theory of empirical processes. As a by-product, we
derive bounds for the th entropy numbers of the quasi-convex Schatten class
embeddings , , which are of independent
interest.Comment: Published in at http://dx.doi.org/10.1214/10-AOS860 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Økologisk hvidkløver - hvordan kan det lade sig gøre?
Økologisk hvidkløver - hvordan kan det lade sig gøre
Symmetry Protected Topological phases and Generalized Cohomology
We discuss the classification of SPT phases in condensed matter systems. We
review Kitaev's argument that SPT phases are classified by a generalized
cohomology theory, valued in the spectrum of gapped physical systems. We
propose a concrete description of that spectrum and of the corresponding
cohomology theory. We compare our proposal to pre-existing constructions in the
literature.Comment: 27 pages, 10 figures. v2: citation updat
Probabilistic state preparation of a single molecular ion by projection measurement
We show how to prepare a single molecular ion in a specific internal quantum
state in a situation where the molecule is trapped and sympathetically cooled
by an atomic ion and where its internal degrees of freedom are initially in
thermal equilibrium with the surroundings. The scheme is based on conditional
creation of correlation between the internal state of the molecule and the
translational state of the collective motion of the two ions, followed by a
projection measurement of this collective mode by atomic ion shelving
techniques. State preparation in a large number of internal states is possible.Comment: 4 pages, 2 figures, 2 table
Fluxes of microbes, organic aerosols, dust, sea-salt Na ions, non-sea-salt Ca ions, and methanesulfonate onto Greenland and Antarctic ice
Using a spectrofluorimeter with 224-nm laser excitation and six emission bands from 300 to 420 nm to measure fluorescence intensities at 0.3-mm depth intervals in ice cores, we report results of the first comparative study of concentrations of microbial cells (using the spectrum of protein-bound tryptophan (Trp) as a proxy) and of aerosols with autofluorescence spectra different from Trp (denoted "non-Trp") as a function of depth in ice cores from West Antarctica (WAIS Divide and Siple Dome) and Greenland (GISP2). The ratio of fluxes of microbial cells onto West Antarctic (WAIS Divide) versus Greenland sites is 0.13&plusmn;0.06; the ratio of non-Trp aerosols onto WAIS Divide versus Greenland sites is 0.16&plusmn;0.08; and the ratio of non-sea-salt Ca<sup>2+</sup> ions (a proxy for dust grains) onto WAIS Divide versus Greenland sites is 0.06&plusmn;0.03. All of these are roughly comparable to the ratio of fluxes of dust onto Antarctic versus Greenland sites (0.08&plusmn;0.05). By contrast to those values, which are considerably lower than unity, the ratio of fluxes of methanesulfonate (MSA) onto Antarctic versus Greenland sites is 1.9&plusmn;0.4 and the ratio of sea-salt Na<sup>2+</sup> ions onto WAIS Divide versus Greenland sites is 3.0&plusmn;2. These ratios are more than an order of magnitude higher than those in the first grouping. We infer that the correlation of microbes and non-Trp aerosols with non-sea-salt Ca and dust suggests a largely terrestrial rather than marine origin. The lower fluxes of microbes, non-Trp aerosols, non-sea-salt Ca and dust onto WAIS Divide ice than onto Greenland ice may be due to the smaller areas of their source regions and less favorable wind patterns for transport onto Antarctic ice than onto Greenland ice. The correlated higher relative fluxes of MSA and marine Na onto Antarctic versus Greenland ice is consistent with the view that both originate largely on or around sea ice, with the Antarctic sea ice being far more extensive than that around Greenland
Experiments towards quantum information with trapped Calcium ions
Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap
is the prerequisite for quantum information experiments with trapped ions. With
resolved sideband cooling on the optical S1/2 - D5/2 quadrupole transition we
have cooled one and two 40Ca+ ions to the ground state of vibration with up to
99.9% probability. With a novel cooling scheme utilizing electromagnetically
induced transparency on the S1/2 - P1/2 manifold we have achieved simultaneous
ground state cooling of two motional sidebands 1.7 MHz apart. Starting from the
motional ground state we have demonstrated coherent quantum state manipulation
on the S1/2 - D5/2 quadrupole transition at 729 nm. Up to 30 Rabi oscillations
within 1.4 ms have been observed in the motional ground state and in the n=1
Fock state. In the linear quadrupole rf-trap with 700 kHz trap frequency along
the symmetry axis (2 MHz in radial direction) the minimum ion spacing is more
than 5 micron for up to 4 ions. We are able to cool two ions to the ground
state in the trap and individually address the ions with laser pulses through a
special optical addressing channel.Comment: Proceedings of the ICAP 2000, Firenz
Exploiting the capacity of 1mm PMMA step-index polymer optical fibers
Three different techniques are discussed that are currently under investigation at Siemens Corporate Technology – Information and Communications in order to exploit the bandwidth capacity of 1 mm PMMA Step-Index Polymer Optical Fiber (SI-POF). By using Adaptive Multitone Modulation (AMTM) a record result of 540 Mb/s transmission over 100 m of SI-POF is achieved
Simultaneous Matrix Diagonalization for Structural Brain Networks Classification
This paper considers the problem of brain disease classification based on
connectome data. A connectome is a network representation of a human brain. The
typical connectome classification problem is very challenging because of the
small sample size and high dimensionality of the data. We propose to use
simultaneous approximate diagonalization of adjacency matrices in order to
compute their eigenstructures in more stable way. The obtained approximate
eigenvalues are further used as features for classification. The proposed
approach is demonstrated to be efficient for detection of Alzheimer's disease,
outperforming simple baselines and competing with state-of-the-art approaches
to brain disease classification
- …