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Previous research has shown that neural networks can model survival data in situations in which some patients' death times are unknown, e.g. right-censored. However, neural networks have rarely been shown to outperform their linear counterparts such as the Cox proportional hazards model. In this paper, we run simulated experiments and use real survival data(More)
We present an algorithm to solve the two-dimensional Fredholm integral of the first kind with tensor product structure from a limited number of measurements, with the goal of using this method to speed up nuclear magnetic resonance spectroscopy. This is done by incorporating compressive sensing–type arguments to fill in missing measurements, using a priori(More)
We discuss approximation of functions using deep neural nets. Given a function f on a d-dimensional manifold Γ ⊂ R m , we construct a sparsely-connected depth-4 neural network and bound its error in approximating f. The size of the network depends on dimension and curvature of the manifold Γ, the complexity of f , in terms of its wavelet description, and(More)
Potential applications of 2D relaxation spectrum NMR and MRI to characterize complex water dynamics (e.g., compartmental exchange) in biology and other disciplines have increased in recent years. However, the large amount of data and long MR acquisition times required for conventional 2D MR relaxometry limits its applicability for in vivo preclinical and(More)
As new sensing modalities emerge and the presence of multiple sensors per platform becomes widespread, it is vital to develop new algorithms and techniques which can fuse this data. Many of previous attempts to deal with the problem of heterogeneous data integration for the applications in data classification were either highly data dependent or relied on(More)
In [1], Cloninger, Czaja, Bai, and Basser developed an algorithm for compressive sampling based data acquisition for the solution of 2D Fredholm equations. We extend the algorithm to N dimensional data, by randomly sampling in 2 dimensions and fully sampling in the remaining N-2 dimensions. This new algorithm has direct applications to 3-dimensional nuclear(More)
The Hildreth's algorithm is a row action method for solving large systems of inequalities. This algorithm is efficient for problems with sparse matrices, as opposed to direct methods such as Gaussian elimination or QR-factorization. We apply the Hildreth's algorithm, as well as a randomized version, along with prioritized selection of the inequalities, to(More)
We aim to understand and characterize embeddings of datasets with small anomalous clusters using the Laplacian Eigenmaps algorithm. To do this, we characterize the order in which eigenvectors of a disjoint graph Laplacian emerge and the support of those eigenvectors. We then extend this characterization to weakly connected graphs with clusters of differing(More)