5,356 research outputs found
Stable Feature Selection from Brain sMRI
Neuroimage analysis usually involves learning thousands or even millions of
variables using only a limited number of samples. In this regard, sparse
models, e.g. the lasso, are applied to select the optimal features and achieve
high diagnosis accuracy. The lasso, however, usually results in independent
unstable features. Stability, a manifest of reproducibility of statistical
results subject to reasonable perturbations to data and the model, is an
important focus in statistics, especially in the analysis of high dimensional
data. In this paper, we explore a nonnegative generalized fused lasso model for
stable feature selection in the diagnosis of Alzheimer's disease. In addition
to sparsity, our model incorporates two important pathological priors: the
spatial cohesion of lesion voxels and the positive correlation between the
features and the disease labels. To optimize the model, we propose an efficient
algorithm by proving a novel link between total variation and fast network flow
algorithms via conic duality. Experiments show that the proposed nonnegative
model performs much better in exploring the intrinsic structure of data via
selecting stable features compared with other state-of-the-arts
Background Subtraction via Generalized Fused Lasso Foreground Modeling
Background Subtraction (BS) is one of the key steps in video analysis. Many
background models have been proposed and achieved promising performance on
public data sets. However, due to challenges such as illumination change,
dynamic background etc. the resulted foreground segmentation often consists of
holes as well as background noise. In this regard, we consider generalized
fused lasso regularization to quest for intact structured foregrounds. Together
with certain assumptions about the background, such as the low-rank assumption
or the sparse-composition assumption (depending on whether pure background
frames are provided), we formulate BS as a matrix decomposition problem using
regularization terms for both the foreground and background matrices. Moreover,
under the proposed formulation, the two generally distinctive background
assumptions can be solved in a unified manner. The optimization was carried out
via applying the augmented Lagrange multiplier (ALM) method in such a way that
a fast parametric-flow algorithm is used for updating the foreground matrix.
Experimental results on several popular BS data sets demonstrate the advantage
of the proposed model compared to state-of-the-arts
The progenitors of Type Ia supernovae with long delay times
The nature of the progenitors of Type Ia supernovae (SNe Ia) is still
unclear. In this paper, by considering the effect of the instability of
accretion disk on the evolution of white dwarf (WD) binaries, we performed
binary evolution calculations for about 2400 close WD binaries, in which a
carbon--oxygen WD accretes material from a main-sequence star or a slightly
evolved subgiant star (WD + MS channel), or a red-giant star (WD + RG channel)
to increase its mass to the Chandrasekhar (Ch) mass limit. According to these
calculations, we mapped out the initial parameters for SNe Ia in the orbital
period--secondary mass () plane for various WD
masses for these two channels, respectively. We confirm that WDs in the WD + MS
channel with a mass as low as can accrete efficiently and reach
the Ch limit, while the lowest WD mass for the WD + RG channel is . We have implemented these results in a binary population synthesis
study to obtain the SN Ia birthrates and the evolution of SN Ia birthrates with
time for both a constant star formation rate and a single starburst. We find
that the Galactic SN Ia birthrate from the WD + MS channel is according to our standard model, which is higher than
previous results. However, similar to previous studies, the birthrate from the
WD + RG channel is still low (). We also
find that about one third of SNe Ia from the WD + MS channel and all SNe Ia
from the WD + RG channel can contribute to the old populations (\ga1 Gyr) of
SN Ia progenitors.Comment: 11 pages, 9 figures, 1 table, accepted for publication in MNRA
Interacting heavy fermions in a disordered optical lattice
We have theoretically studied the effect of disorder on ultracold
alkaline-earth atoms governed by the Kondo lattice model in an optical lattice
via simplified double-well model and hybridization mean-field theory.
Disorder-induced narrowing and even complete closure of hybridization gap have
been predicted and the compressibility of the system has also been investigated
for metallic and Kondo insulator phases in the presence of the disordered
potential. To make connection to the experimental situation, we have
numerically solved the disordered Kondo lattice model with an external harmonic
trap and shown both the melting of Kondo insulator plateau and an
compressibility anomaly at low-density
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