2,016 research outputs found
Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions
We consider the finite element solution of the vector Laplace equation on a
domain in two dimensions. For various choices of boundary conditions, it is
known that a mixed finite element method, in which the rotation of the solution
is introduced as a second unknown, is advantageous, and appropriate choices of
mixed finite element spaces lead to a stable, optimally convergent
discretization. However, the theory that leads to these conclusions does not
apply to the case of Dirichlet boundary conditions, in which both components of
the solution vanish on the boundary. We show, by computational example, that
indeed such mixed finite elements do not perform optimally in this case, and we
analyze the suboptimal convergence that does occur. As we indicate, these
results have implications for the solution of the biharmonic equation and of
the Stokes equations using a mixed formulation involving the vorticity
Personalized Prediction of Future Lesion Activity and Treatment Effect in Multiple Sclerosis from Baseline MRI
Precision medicine for chronic diseases such as multiple sclerosis (MS)
involves choosing a treatment which best balances efficacy and side
effects/preferences for individual patients. Making this choice as early as
possible is important, as delays in finding an effective therapy can lead to
irreversible disability accrual. To this end, we present the first deep neural
network model for individualized treatment decisions from baseline magnetic
resonance imaging (MRI) (with clinical information if available) for MS
patients. Our model (a) predicts future new and enlarging T2 weighted (NE-T2)
lesion counts on follow-up MRI on multiple treatments and (b) estimates the
conditional average treatment effect (CATE), as defined by the predicted future
suppression of NE-T2 lesions, between different treatment options relative to
placebo. Our model is validated on a proprietary federated dataset of 1817
multi-sequence MRIs acquired from MS patients during four multi-centre
randomized clinical trials. Our framework achieves high average precision in
the binarized regression of future NE-T2 lesions on five different treatments,
identifies heterogeneous treatment effects, and provides a personalized
treatment recommendation that accounts for treatment-associated risk (e.g. side
effects, patient preference, administration difficulties).Comment: Accepted to MIDL 202
Spatial and temporal variability of cadmium in Gulf Stream warm-core rings and associated waters
Seawater samples were collected and analyzed for cadmium during four cruises studying Gulf Stream warm-core rings and associated waters. Warm-core ring (WCR) 82-B was sampled in April (approximately two months after formation), in June (after seasonal stratification), and in August (during its interaction with the Gulf Stream). The September–October cruise studied closure and separation of a meander that formed ring 82-H. The depth of the cadmium maximum varied with the depth of the main thermocline; the maximum occurred at a potential temperature of 7.8 ± 0.5°C and sigma-theta 27.4 ± 0.05 in the Slope Water, Gulf Stream, and Sargasso Sea stations. As the upper 100 m of the ring progressed from vertically well-mixed in April to seasonally stratified in June, the mole-ratios of cadmium/nutrient removal in the mixed layer were similar to the calculated slopes of the linear regressions of cadmium with phosphate, nitrate and silicate calculated from spatial distributions. Lateral mixing processes near the boundaries of WCR 82-B markedly influenced the vertical cadmium distribution via intrusions of Shelf/Slope water containing elevated levels of cadmium. Comparison of ASV-labile and total dissolvable cadmium from the August WCR 82-B station indicated essentially 100% ASV-labile cadmium in the waters within and below the main thermocline but non-detectable (\u3c0.010 nmol kg−1) ASV-labile cadmium in the waters above the thermocline
Supraglacial lakes on the Larsen B ice shelf, Antarctica, and at Paakitsoq, West Greenland:A Comparative Study
This is the accepted manuscript. The final version is available from Ingenta Connect at http://www.ingentaconnect.com/content/igsoc/agl/2014/00000055/00000066/art00001.Supraglacial meltwater lakes trigger ice-shelf break-up and modulate seasonal ice\ud
sheet flow, and are thus agents by which warming is transmitted to the Antarctic\ud
and Greenland ice sheets. To characterize supraglacial lake variability we perform a\ud
comparative analysis of lake geometry and depth in two distinct regions, one on the\ud
pre-collapse (2002) Larsen B Ice Shelf, and the other in the ablation zone of\ud
Paakitsoq, a land-terminating region of the Greenland Ice Sheet. Compared to\ud
Paakitsoq, lakes on the Larsen B Ice Shelf cover a greater proportion of surface area\ud
(5.3% vs. 1%), but are shallower and more uniform in area. Other aspects of lake\ud
geometry, such as eccentricity, degree of convexity (solidity) and orientation, are\ud
relatively similar between the two regions. We attribute the notable difference in\ud
lake density and depth between ice-shelf and grounded ice to the fact that ice shelves\ud
have flatter surfaces and less distinct drainage basins. Ice shelves also possess more\ud
stimuli to small-scale, localized surface elevation variability due to the various\ud
structural features that yield small variations in thickness and which float at\ud
different levels by Archimedes? principle.We acknowledge the support of the U.S. National Science Foundation under grant ANT-0944248
Counterfactual Image Synthesis for Discovery of Personalized Predictive Image Markers
The discovery of patient-specific imaging markers that are predictive of
future disease outcomes can help us better understand individual-level
heterogeneity of disease evolution. In fact, deep learning models that can
provide data-driven personalized markers are much more likely to be adopted in
medical practice. In this work, we demonstrate that data-driven biomarker
discovery can be achieved through a counterfactual synthesis process. We show
how a deep conditional generative model can be used to perturb local imaging
features in baseline images that are pertinent to subject-specific future
disease evolution and result in a counterfactual image that is expected to have
a different future outcome. Candidate biomarkers, therefore, result from
examining the set of features that are perturbed in this process. Through
several experiments on a large-scale, multi-scanner, multi-center multiple
sclerosis (MS) clinical trial magnetic resonance imaging (MRI) dataset of
relapsing-remitting (RRMS) patients, we demonstrate that our model produces
counterfactuals with changes in imaging features that reflect established
clinical markers predictive of future MRI lesional activity at the population
level. Additional qualitative results illustrate that our model has the
potential to discover novel and subject-specific predictive markers of future
activity.Comment: Accepted to the MIABID workshop at MICCAI 202
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