7,043 research outputs found
Modeling Covariate Effects in Group Independent Component Analysis with Applications to Functional Magnetic Resonance Imaging
Independent component analysis (ICA) is a powerful computational tool for
separating independent source signals from their linear mixtures. ICA has been
widely applied in neuroimaging studies to identify and characterize underlying
brain functional networks. An important goal in such studies is to assess the
effects of subjects' clinical and demographic covariates on the spatial
distributions of the functional networks. Currently, covariate effects are not
incorporated in existing group ICA decomposition methods. Hence, they can only
be evaluated through ad-hoc approaches which may not be accurate in many cases.
In this paper, we propose a hierarchical covariate ICA model that provides a
formal statistical framework for estimating and testing covariate effects in
ICA decomposition. A maximum likelihood method is proposed for estimating the
covariate ICA model. We develop two expectation-maximization (EM) algorithms to
obtain maximum likelihood estimates. The first is an exact EM algorithm, which
has analytically tractable E-step and M-step. Additionally, we propose a
subspace-based approximate EM, which can significantly reduce computational
time while still retain high model-fitting accuracy. Furthermore, to test
covariate effects on the functional networks, we develop a voxel-wise
approximate inference procedure which eliminates the needs of computationally
expensive covariance estimation. The performance of the proposed methods is
evaluated via simulation studies. The application is illustrated through an
fMRI study of Zen meditation.Comment: 36 pages, 5 figure
Fermion Pairing across a Dipolar Interaction Induced Resonance
It is known from the solution of the two-body problem that an anisotropic
dipolar interaction can give rise to s-wave scattering resonances, which are
named as dipolar interaction induced resonaces (DIIR). In this letter, we study
zero-temperature many-body physics of a two-component Fermi gas across a DIIR.
In the low-density regime, it is very striking that the resulting pairing order
parameter is a nearly isotropic singlet pairing and the physics can be well
described by an s-wave resonant interaction potential with finite range
corrections, despite of the anisotropic nature of dipolar interaction. The
pairing energy is as strong as a unitary Fermi gas nearby a magnetic Feshbach
resonance. In the high density regime, the anisotropic effect plays an
important role. We find phase transitions from singlet pairing to a state with
mixed singlet and triplet pairing, and then from mixed pairing to pure triplet
pairing. The state with mixed pairing spontaneously breaks the time-reversal
symmetry.Comment: 4.5 pages, 4 figures, figures updated, minor changes in tex
s-Wave Scattering Resonances Induced by Dipolar Interactions of Polar Molecules
We show that s-wave scattering resonances induced by dipolar interactions in
a polar molecular gas have a universal large and positive effective range,
which is very different from Feshbach resonances realized in cold atoms before,
where the effective range is either negligible or negative. Such a difference
has important consequence in many-body physics. At high temperature regime, a
positive effective range gives rise to stronger repulsive interaction energy
for positive scattering length, and weaker attractive interaction energy for
negative scattering length. While at low-temperatures, we study polaron problem
formed by single impurity molecule, and we find that the polaron binding energy
increases at the BEC side and decreases at the BCS side. All these effects are
in opposite to narrow Feshbach resonances where the effective range is
negative.Comment: 5 pages, 3 figures, published versio
RKKY interaction in three-dimensional electron gases with linear spin-orbit coupling
We theoretically study the impacts of linear spin-orbit coupling (SOC) on the
Ruderman-Kittel-Kasuya-Yosida interaction between magnetic impurities in two
kinds of three-dimensional noncentrosymmetric systems. It has been found that
linear SOCs lead to the Dzyaloshinskii-Moriya interaction and the Ising
interaction, in addition to the conventional Heisenberg interaction. These
interactions possess distinct range functions from three dimensional electron
gases and Dirac/Weyl semimetals. In the weak SOC limit, the Heisenberg
interaction dominates over the other two interactions in a moderately large
region of parameters. Sufficiently strong Rashba SOC makes the
Dzyaloshinskii-Moriya interaction or the Ising interaction dominate over the
Heisenberg interaction in some regions. The change in topology of the Fermi
surface leads to some quantitative changes in periods of oscillations of range
functions. The anisotropy of Ruderman-Kittel-Kasuya-Yosida interaction in
bismuth tellurohalides family BiTe ( = Br, Cl, and I) originates from
both the specific form of Rashba SOC and the anisotropic effective mass. Our
work provides some insights into understanding observed spin textures and the
application of these materials in spintronics.Comment: 11 pages, 4 figures, Final Version in PR
- …