1,693 research outputs found
Varying Coefficient Tensor Models for Brain Imaging
We revisit a multidimensional varying-coefficient model (VCM), by allowing regressor coefficients to vary smoothly in more than one dimension, thereby extending the VCM of Hastie and Tibshirani. The motivating example is 3-dimensional, involving a special type of nuclear magnetic resonance measurement technique that is being used to estimate the diffusion tensor at each point in the human brain. We aim to improve the current state of the art, which is to apply a multiple regression model for each voxel separately using information from six or more volume images. We present a model, based on P-spline tensor products, to introduce spatial smoothness of the estimated diffusion tensor. Since the regression design matrix is space-invariant, a 4-dimensional tensor product model results, allowing more efficient computation with penalized array regression
Space-Varying Coefficient Models for Brain Imaging
The methodological development and the application in this paper originate from diffusion tensor imaging (DTI), a powerful nuclear magnetic resonance technique enabling diagnosis and monitoring of several diseases as well as reconstruction of neural pathways. We reformulate the current analysis framework of separate voxelwise regressions as a 3d space-varying coefficient model (VCM) for the entire set of DTI images recorded on a 3d grid of voxels. Hence by allowing to borrow strength from spatially adjacent voxels, to smooth noisy observations, and to estimate diffusion tensors at any location within the brain, the three-step cascade of standard data processing is overcome simultaneously. We conceptualize two VCM variants based on B-spline basis functions: a full tensor product approach and a sequential approximation, rendering the VCM numerically and computationally feasible even for the huge dimension of the joint model in a realistic setup. A simulation study shows that both approaches outperform the standard method of voxelwise regressions with subsequent regularization. Due to major efficacy, we apply the sequential method to a clinical DTI data set and demonstrate the inherent ability of increasing the rigid grid resolution by evaluating the incorporated basis functions at intermediate points. In conclusion, the suggested fitting methods clearly improve the current state-of-the-art, but ameloriation of local adaptivity remains desirable
Fermi Surface of KFeAs from Quantum Oscillations in Magnetostriction
We present a study of the Fermi surface of KFeAs single crystals.
Quantum oscillations were observed in magnetostriction measured down to 50 mK
and in magnetic fields up to 14 T. For , the calculated
effective masses are in agreement with recent de Haas-van Alphen and ARPES
experiments, showing enhanced values with respect to the ones obtained from
previous band calculations. For , we observed a small orbit at a
cyclotron frequency of 64 T, characterized by an effective mass of , supporting the presence of a three-dimensional pocket at the Z-point.Comment: SCES Conference, Tokyo 201
Improved Dynamic Predictions from Joint Models of Longitudinal and Survival Data with Time-Varying Effects using P-splines
In the field of cardio-thoracic surgery, valve function is monitored over
time after surgery. The motivation for our research comes from a study which
includes patients who received a human tissue valve in the aortic position.
These patients are followed prospectively over time by standardized
echocardiographic assessment of valve function. Loss of follow-up could be
caused by valve intervention or the death of the patient. One of the main
characteristics of the human valve is that its durability is limited.
Therefore, it is of interest to obtain a prognostic model in order for the
physicians to scan trends in valve function over time and plan their next
intervention, accounting for the characteristics of the data.
Several authors have focused on deriving predictions under the standard joint
modeling of longitudinal and survival data framework that assumes a constant
effect for the coefficient that links the longitudinal and survival outcomes.
However, in our case this may be a restrictive assumption. Since the valve
degenerates, the association between the biomarker with survival may change
over time.
To improve dynamic predictions we propose a Bayesian joint model that allows
a time-varying coefficient to link the longitudinal and the survival processes,
using P-splines. We evaluate the performance of the model in terms of
discrimination and calibration, while accounting for censoring
The ordered K-theory of a full extension
Let A be a C*-algebra with real rank zero which has the stable weak
cancellation property. Let I be an ideal of A such that I is stable and
satisfies the corona factorization property. We prove that 0->I->A->A/I->0 is a
full extension if and only if the extension is stenotic and K-lexicographic. As
an immediate application, we extend the classification result for graph
C*-algebras obtained by Tomforde and the first named author to the general
non-unital case. In combination with recent results by Katsura, Tomforde, West
and the first author, our result may also be used to give a purely
K-theoretical description of when an essential extension of two simple and
stable graph C*-algebras is again a graph C*-algebra.Comment: Version IV: No changes to the text. We only report that Theorem 4.9
is not correct as stated. See arXiv:1505.05951 for more details. Since
Theorem 4.9 is an application to the main results of the paper, the main
results of this paper are not affected by the error. Version III comments:
Some typos and errors corrected. Some references adde
Bilinear modulation models for seasonal tables of counts
We propose generalized linear models for time or age-time tables of seasonal counts, with the goal of better understanding seasonal patterns in the data. The linear predictor contains a smooth component for the trend and the product of a smooth component (the modulation) and a periodic time series of arbitrary shape (the carrier wave). To model rates, a population offset is added. Two-dimensional trends and modulation are estimated using a tensor product B-spline basis of moderate dimension. Further smoothness is ensured using difference penalties on the rows and columns of the tensor product coefficients. The optimal penalty tuning parameters are chosen based on minimization of a quasi-information criterion. Computationally efficient estimation is achieved using array regression techniques, avoiding excessively large matrices. The model is applied to female death rate in the US due to cerebrovascular diseases and respiratory diseases
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