999 research outputs found
Multiple Instance Learning for Heterogeneous Images: Training a CNN for Histopathology
Multiple instance (MI) learning with a convolutional neural network enables
end-to-end training in the presence of weak image-level labels. We propose a
new method for aggregating predictions from smaller regions of the image into
an image-level classification by using the quantile function. The quantile
function provides a more complete description of the heterogeneity within each
image, improving image-level classification. We also adapt image augmentation
to the MI framework by randomly selecting cropped regions on which to apply MI
aggregation during each epoch of training. This provides a mechanism to study
the importance of MI learning. We validate our method on five different
classification tasks for breast tumor histology and provide a visualization
method for interpreting local image classifications that could lead to future
insights into tumor heterogeneity
Joint and individual analysis of breast cancer histologic images and genomic covariates
A key challenge in modern data analysis is understanding connections between
complex and differing modalities of data. For example, two of the main
approaches to the study of breast cancer are histopathology (analyzing visual
characteristics of tumors) and genetics. While histopathology is the gold
standard for diagnostics and there have been many recent breakthroughs in
genetics, there is little overlap between these two fields. We aim to bridge
this gap by developing methods based on Angle-based Joint and Individual
Variation Explained (AJIVE) to directly explore similarities and differences
between these two modalities. Our approach exploits Convolutional Neural
Networks (CNNs) as a powerful, automatic method for image feature extraction to
address some of the challenges presented by statistical analysis of
histopathology image data. CNNs raise issues of interpretability that we
address by developing novel methods to explore visual modes of variation
captured by statistical algorithms (e.g. PCA or AJIVE) applied to CNN features.
Our results provide many interpretable connections and contrasts between
histopathology and genetics
Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction
We study a singular-limit problem arising in the modelling of chemical
reactions. At finite {\epsilon} > 0, the system is described by a Fokker-Planck
convection-diffusion equation with a double-well convection potential. This
potential is scaled by 1/{\epsilon}, and in the limit {\epsilon} -> 0, the
solution concentrates onto the two wells, resulting into a limiting system that
is a pair of ordinary differential equations for the density at the two wells.
This convergence has been proved in Peletier, Savar\'e, and Veneroni, SIAM
Journal on Mathematical Analysis, 42(4):1805-1825, 2010, using the linear
structure of the equation. In this paper we re-prove the result by using solely
the Wasserstein gradient-flow structure of the system. In particular we make no
use of the linearity, nor of the fact that it is a second-order system. The
first key step in this approach is a reformulation of the equation as the
minimization of an action functional that captures the property of being a
curve of maximal slope in an integrated form. The second important step is a
rescaling of space. Using only the Wasserstein gradient-flow structure, we
prove that the sequence of rescaled solutions is pre-compact in an appropriate
topology. We then prove a Gamma-convergence result for the functional in this
topology, and we identify the limiting functional and the differential equation
that it represents. A consequence of these results is that solutions of the
{\epsilon}-problem converge to a solution of the limiting problem.Comment: Added two sections, corrected minor typos, updated reference
On thermodynamically consistent Stefan problems with variable surface energy
A thermodynamically consistent two-phase Stefan problem with
temperature-dependent surface tension and with or without kinetic undercooling
is studied. It is shown that these problems generate local semiflows in
well-defined state manifolds. If a solution does not exhibit singularities, it
is proved that it exists globally in time and converges towards an equilibrium
of the problem. In addition, stability and instability of equilibria is
studied. In particular, it is shown that multiple spheres of the same radius
are unstable if surface heat capacity is small; however, if kinetic
undercooling is absent, they are stable if surface heat capacity is
sufficiently large.Comment: To appear in Arch. Ration. Mech. Anal. The final publication is
available at Springer via http://dx.doi.org/10.1007/s00205-015-0938-y. arXiv
admin note: substantial text overlap with arXiv:1101.376
Geometric Observers for Dynamically Evolving Curves
This paper proposes a deterministic observer design for visual tracking based on nonparametric implicit (level-set) curve descriptions. The observer is continuous discrete with continuous-time system dynamics and discrete-time measurements. Its state-space consists of an estimated curve position augmented by additional states (e.g., velocities) associated with every point on the estimated curve. Multiple simulation models are proposed for state prediction. Measurements are performed through standard static segmentation algorithms and optical-flow computations. Special emphasis is given to the geometric formulation of the overall dynamical system. The discrete-time measurements lead to the problem of geometric curve interpolation and the discrete-time filtering of quantities propagated along with the estimated curve. Interpolation and filtering are intimately linked to the correspondence problem between curves. Correspondences are established by a Laplace-equation approach. The proposed scheme is implemented completely implicitly (by Eulerian numerical solutions of transport equations) and thus naturally allows for topological changes and subpixel accuracy on the computational grid
Thalamocortical Connectivity Correlates with Phenotypic Variability in Dystonia
Dystonia is a brain disorder characterized by abnormal involuntary movements without defining neuropathological changes. The disease is often inherited as an autosomal-dominant trait with incomplete penetrance. Individuals with dystonia, whether inherited or sporadic, exhibit striking phenotypic variability, with marked differences in the somatic distribution and severity of clinical manifestations. In the current study, we used magnetic resonance diffusion tensor imaging to identify microstructural changes associated with specific limb manifestations. Functional MRI was used to localize specific limb regions within the somatosensory cortex. Microstructural integrity was preserved when assessed in subrolandic white matter regions somatotopically related to the clinically involved limbs, but was reduced in regions linked to clinically uninvolved (asymptomatic) body areas. Clinical manifestations were greatest in subjects with relatively intact microstructure in somatotopically relevant white matter regions. Tractography revealed significant phenotype-related differences in the visualized thalamocortical tracts while corticostriatal and corticospinal pathways did not differ between groups. Cerebellothalamic microstructural abnormalities were also seen in the dystonia subjects, but these changes were associated with genotype, rather than with phenotypic variation. The findings suggest that the thalamocortical motor system is a major determinant of dystonia phenotype. This pathway may represent a novel therapeutic target for individuals with refractory limb dystonia
Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension
The qualitative behavior of a thermodynamically consistent two-phase Stefan
problem with surface tension and with or without kinetic undercooling is
studied. It is shown that these problems generate local semiflows in
well-defined state manifolds. If a solution does not exhibit singularities in a
sense made precise below, it is proved that it exists globally in time and its
orbit is relatively compact. In addition, stability and instability of
equilibria is studied. In particular, it is shown that multiple spheres of the
same radius are unstable, reminiscent of the onset of Ostwald ripening.Comment: 56 pages. Expanded introduction, added references. This revised
version is published in Arch. Ration. Mech. Anal. (207) (2013), 611-66
The visual perception of natural motion: abnormal task-related neural activity in DYT1 dystonia
Although primary dystonia is defined by its characteristic motor manifestations, non-motor signs and symptoms have increasingly been recognized in this disorder. Recent neuroimaging studies have related the motor features of primary dystonia to connectivity changes in cerebello-thalamo-cortical pathways. It is not known, however, whether the non-motor manifestations of the disorder are associated with similar circuit abnormalities. To explore this possibility, we used functional magnetic resonance imaging to study primary dystonia and healthy volunteer subjects while they performed a motion perception task in which elliptical target trajectories were visually tracked on a computer screen. Prior functional magnetic resonance imaging studies of healthy subjects performing this task have revealed selective activation of motor regions during the perception of \u27natural\u27 versus \u27unnatural\u27 motion (defined respectively as trajectories with kinematic properties that either comply with or violate the two-thirds power law of motion). Several regions with significant connectivity changes in primary dystonia were situated in proximity to normal motion perception pathways, suggesting that abnormalities of these circuits may also be present in this disorder. To determine whether activation responses to natural versus unnatural motion in primary dystonia differ from normal, we used functional magnetic resonance imaging to study 10 DYT1 dystonia and 10 healthy control subjects at rest and during the perception of \u27natural\u27 and \u27unnatural\u27 motion. Both groups exhibited significant activation changes across perceptual conditions in the cerebellum, pons, and subthalamic nucleus. The two groups differed, however, in their responses to \u27natural\u27 versus \u27unnatural\u27 motion in these regions. In healthy subjects, regional activation was greater during the perception of natural (versus unnatural) motion (P \u3c 0.05). By contrast, in DYT1 dystonia subjects, activation was relatively greater during the perception of unnatural (versus natural) motion (P \u3c 0.01). To explore the microstructural basis for these functional changes, the regions with significant interaction effects (i.e. those with group differences in activation across perceptual conditions) were used as seeds for tractographic analysis of diffusion tensor imaging scans acquired in the same subjects. Fibre pathways specifically connecting each of the significant functional magnetic resonance imaging clusters to the cerebellum were reconstructed. Of the various reconstructed pathways that were analysed, the ponto-cerebellar projection alone differed between groups, with reduced fibre integrity in dystonia (P \u3c 0.001). In aggregate, the findings suggest that the normal pattern of brain activation in response to motion perception is disrupted in DYT1 dystonia. Thus, it is unlikely that the circuit changes that underlie this disorder are limited to primary sensorimotor pathways
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