40,186 research outputs found
Deep Chronnectome Learning via Full Bidirectional Long Short-Term Memory Networks for MCI Diagnosis
Brain functional connectivity (FC) extracted from resting-state fMRI
(RS-fMRI) has become a popular approach for disease diagnosis, where
discriminating subjects with mild cognitive impairment (MCI) from normal
controls (NC) is still one of the most challenging problems. Dynamic functional
connectivity (dFC), consisting of time-varying spatiotemporal dynamics, may
characterize "chronnectome" diagnostic information for improving MCI
classification. However, most of the current dFC studies are based on detecting
discrete major brain status via spatial clustering, which ignores rich
spatiotemporal dynamics contained in such chronnectome. We propose Deep
Chronnectome Learning for exhaustively mining the comprehensive information,
especially the hidden higher-level features, i.e., the dFC time series that may
add critical diagnostic power for MCI classification. To this end, we devise a
new Fully-connected Bidirectional Long Short-Term Memory Network (Full-BiLSTM)
to effectively learn the periodic brain status changes using both past and
future information for each brief time segment and then fuse them to form the
final output. We have applied our method to a rigorously built large-scale
multi-site database (i.e., with 164 data from NCs and 330 from MCIs, which can
be further augmented by 25 folds). Our method outperforms other
state-of-the-art approaches with an accuracy of 73.6% under solid
cross-validations. We also made extensive comparisons among multiple variants
of LSTM models. The results suggest high feasibility of our method with
promising value also for other brain disorder diagnoses.Comment: The paper has been accepted by MICCAI201
Four conjectures in Nonlinear Analysis
In this chapter, I formulate four challenging conjectures in Nonlinear
Analysis. More precisely: a conjecture on the Monge-Amp\`ere equation; a
conjecture on an eigenvalue problem; a conjecture on a non-local problem; a
conjecture on disconnectedness versus infinitely many solutions.Comment: arXiv admin note: text overlap with arXiv:1504.01010,
arXiv:1409.5919, arXiv:1612.0819
Relativistic Photon Mediated Shocks
A system of equations governing the structure of a steady, relativistic
radiation dominated shock is derived, starting from the general form of the
transfer equation obeyed by the photon distribution function. Closure is
obtained by truncating the system of moment equations at some order. The
anisotropy of the photon distribution function inside the shock is shown to
increase with increasing shock velocity, approaching nearly perfect beaming at
upstream Lorentz factors . Solutions of the shock equations are
presented for some range of upstream conditions. These solutions are shown to
converge as the truncation order is increased.Comment: 5 pages, a shorter version will appear in PR
{CoSSL}: {C}o-Learning of Representation and Classifier for Imbalanced Semi-Supervised Learning
In this paper, we propose a novel co-learning framework (CoSSL) with decoupled representation learning and classifier learning for imbalanced SSL. To handle the data imbalance, we devise Tail-class Feature Enhancement (TFE) for classifier learning. Furthermore, the current evaluation protocol for imbalanced SSL focuses only on balanced test sets, which has limited practicality in real-world scenarios. Therefore, we further conduct a comprehensive evaluation under various shifted test distributions. In experiments, we show that our approach outperforms other methods over a large range of shifted distributions, achieving state-of-the-art performance on benchmark datasets ranging from CIFAR-10, CIFAR-100, ImageNet, to Food-101. Our code will be made publicly available
Modeling GRB 050904: Autopsy of a Massive Stellar Explosion at z=6.29
GRB 050904 at redshift z=6.29, discovered and observed by Swift and with
spectroscopic redshift from the Subaru telescope, is the first gamma-ray burst
to be identified from beyond the epoch of reionization. Since the progenitors
of long gamma-ray bursts have been identified as massive stars, this event
offers a unique opportunity to investigate star formation environments at this
epoch. Apart from its record redshift, the burst is remarkable in two respects:
first, it exhibits fast-evolving X-ray and optical flares that peak
simultaneously at t~470 s in the observer frame, and may thus originate in the
same emission region; and second, its afterglow exhibits an accelerated decay
in the near-infrared (NIR) from t~10^4 s to t~3 10^4 s after the burst,
coincident with repeated and energetic X-ray flaring activity. We make a
complete analysis of available X-ray, NIR, and radio observations, utilizing
afterglow models that incorporate a range of physical effects not previously
considered for this or any other GRB afterglow, and quantifying our model
uncertainties in detail via Markov Chain Monte Carlo analysis. In the process,
we explore the possibility that the early optical and X-ray flare is due to
synchrotron and inverse Compton emission from the reverse shock regions of the
outflow. We suggest that the period of accelerated decay in the NIR may be due
to suppression of synchrotron radiation by inverse Compton interaction of X-ray
flare photons with electrons in the forward shock; a subsequent interval of
slow decay would then be due to a progressive decline in this suppression. The
range of acceptable models demonstrates that the kinetic energy and circumburst
density of GRB 050904 are well above the typical values found for low-redshift
GRBs.Comment: 45 pages, 7 figures, and ApJ accepted. Revised version, minor
modifications and 1 extra figur
Initial Hypersurface Formulation: Hamilton-Jacobi Theory for Strongly Coupled Gravitational Systems
Strongly coupled gravitational systems describe Einstein gravity and matter
in the limit that Newton's constant G is assumed to be very large. The
nonlinear evolution of these systems may be solved analytically in the
classical and semiclassical limits by employing a Green function analysis.
Using functional methods in a Hamilton-Jacobi setting, one may compute the
generating functional (`the phase of the wavefunctional') which satisfies both
the energy constraint and the momentum constraint. Previous results are
extended to encompass the imposition of an arbitrary initial hypersurface. A
Lagrange multiplier in the generating functional restricts the initial fields,
and also allows one to formulate the energy constraint on the initial
hypersurface. Classical evolution follows as a result of minimizing the
generating functional with respect to the initial fields. Examples are given
describing Einstein gravity interacting with either a dust field and/or a
scalar field. Green functions are explicitly determined for (1) gravity, dust,
a scalar field and a cosmological constant and (2) gravity and a scalar field
interacting with an exponential potential. This formalism is useful in solving
problems of cosmology and of gravitational collapse.Comment: 30 pages Latex (IOP) file with 2 IOP style files, to be published in
Classical and Quantum Gravity (1998
The Nullity of Bicyclic Signed Graphs
Let \Gamma be a signed graph and let A(\Gamma) be the adjacency matrix of
\Gamma. The nullity of \Gamma is the multiplicity of eigenvalue zero in the
spectrum of A(\Gamma). In this paper we characterize the signed graphs of order
n with nullity n-2 or n-3, and introduce a graph transformation which preserves
the nullity. As an application we determine the unbalanced bicyclic signed
graphs of order n with nullity n-3 or n-4, and signed bicyclic signed graphs
(including simple bicyclic graphs) of order n with nullity n-5
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