4,495 research outputs found
D-brane categories
This is an exposition of recent progress in the categorical approach to
D-brane physics. I discuss the physical underpinnings of the appearance of
homotopy categories and triangulated categories of D-branes from a string field
theoretic perspective, and with a focus on applications to homological mirror
symmetry.Comment: 37 pages, IJMPA styl
Video Compressive Sensing for Dynamic MRI
We present a video compressive sensing framework, termed kt-CSLDS, to
accelerate the image acquisition process of dynamic magnetic resonance imaging
(MRI). We are inspired by a state-of-the-art model for video compressive
sensing that utilizes a linear dynamical system (LDS) to model the motion
manifold. Given compressive measurements, the state sequence of an LDS can be
first estimated using system identification techniques. We then reconstruct the
observation matrix using a joint structured sparsity assumption. In particular,
we minimize an objective function with a mixture of wavelet sparsity and joint
sparsity within the observation matrix. We derive an efficient convex
optimization algorithm through alternating direction method of multipliers
(ADMM), and provide a theoretical guarantee for global convergence. We
demonstrate the performance of our approach for video compressive sensing, in
terms of reconstruction accuracy. We also investigate the impact of various
sampling strategies. We apply this framework to accelerate the acquisition
process of dynamic MRI and show it achieves the best reconstruction accuracy
with the least computational time compared with existing algorithms in the
literature.Comment: 30 pages, 9 figure
Atlas construction and image analysis using statistical cardiac models
International audienceThis paper presents a brief overview of current trends in the construction of population and multi-modal heart atlases in our group and their application to atlas-based cardiac image analysis. The technical challenges around the construction of these atlases are organized around two main axes: groupwise image registration of anatomical, motion and fiber images and construction of statistical shape models. Application-wise, this paper focuses on the extraction of atlas-based biomarkers for the detection of local shape or motion abnormalities, addressing several cardiac applications where the extracted information is used to study and grade different pathologies. The paper is concluded with a discussion about the role of statistical atlases in the integration of multiple information sources and the potential this can bring to in-silico simulations
FlowNet: Learning Optical Flow with Convolutional Networks
Convolutional neural networks (CNNs) have recently been very successful in a
variety of computer vision tasks, especially on those linked to recognition.
Optical flow estimation has not been among the tasks where CNNs were
successful. In this paper we construct appropriate CNNs which are capable of
solving the optical flow estimation problem as a supervised learning task. We
propose and compare two architectures: a generic architecture and another one
including a layer that correlates feature vectors at different image locations.
Since existing ground truth data sets are not sufficiently large to train a
CNN, we generate a synthetic Flying Chairs dataset. We show that networks
trained on this unrealistic data still generalize very well to existing
datasets such as Sintel and KITTI, achieving competitive accuracy at frame
rates of 5 to 10 fps.Comment: Added supplementary materia
Corrector theory for MsFEM and HMM in random media
We analyze the random fluctuations of several multi-scale algorithms such as
the multi-scale finite element method (MsFEM) and the finite element
heterogeneous multiscale method (HMM), that have been developed to solve
partial differential equations with highly heterogeneous coefficients. Such
multi-scale algorithms are often shown to correctly capture the homogenization
limit when the highly oscillatory random medium is stationary and ergodic. This
paper is concerned with the random fluctuations of the solution about the
deterministic homogenization limit. We consider the simplified setting of the
one dimensional elliptic equation, where the theory of random fluctuations is
well understood. We develop a fluctuation theory for the multi-scale algorithms
in the presence of random environments with short-range and long-range
correlations. What we find is that the computationally more expensive method
MsFEM captures the random fluctuations both for short-range and long-range
oscillations in the medium. The less expensive method HMM correctly captures
the fluctuations for long-range oscillations and strongly amplifies their size
in media with short-range oscillations. We present a modified scheme with an
intermediate computational cost that captures the random fluctuations in all
cases.Comment: 41 page
Multiplicative Noise: Applications in Cosmology and Field Theory
Physical situations involving multiplicative noise arise generically in
cosmology and field theory. In this paper, the focus is first on exact
nonlinear Langevin equations, appropriate in a cosmologica setting, for a
system with one degree of freedom. The Langevin equations are derived using an
appropriate time-dependent generalization of a model due to Zwanzig. These
models are then extended to field theories and the generation of multiplicative
noise in such a context is discussed. Important issues in both the cosmological
and field theoretic cases are the fluctuation-dissipation relations and the
relaxation time scale. Of some importance in cosmology is the fact that
multiplicative noise can substantially reduce the relaxation time. In the field
theoretic context such a noise can lead to a significant enhancement in the
nucleation rate of topological defects.Comment: 21 pages, LaTex, LA-UR-93-210
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