Search for: All records

ABSTRACT Non‐negative Matrix Factorization (NMF) is an effective algorithm for multivariate data analysis, including applications to feature selection, pattern recognition, and computer vision. Its variant, Semi‐Nonnegative Matrix Factorization (SNF), extends the ability of NMF to render parts‐based data representations to include mixed‐sign data. Graph Regularized SNF builds upon this paradigm by adding a graph regularization term to preserve the local geometrical structure of the data space. Despite their successes, SNF‐related algorithms to date still suffer from instability caused by the Frobenius norm due to the effects of outliers and noise. In this paper, we present a new SNF algorithm that utilizes the noise‐insensitive norm. We provide monotonic convergence analysis of the SNF algorithm. In addition, we conduct numerical experiments on three benchmark mixed‐sign datasets as well as several randomized mixed‐sign matrices to demonstrate the performance superiority of SNF over conventional SNF algorithms under the influence of Gaussian noise at different levels. 

Abstract Ensemble Forecast Sensitivity to Observation (EFSO) is a technique that can efficiently identify the beneficial/detrimental impacts of every observation in ensemble‐based data assimilation (DA). While EFSO has been successfully employed on atmospheric DA, it has never been applied to ocean or coupled DA due to the lack of a suitable error norm for oceanic variables. This study introduces a new density‐based error norm incorporating sea temperature and salinity forecast errors, making EFSO applicable to ocean DA for the first time. We implemented the oceanic EFSO on the CFSv2‐LETKF and investigated the impact of ocean observations under a weakly coupled DA framework. By removing the detrimental ocean observations detected by EFSO, the CFSv2 forecasts were significantly improved, showing the validation of impact estimation and the great potential of EFSO to be extended as a data selection criterion. 

Abstract We introduce two new lowest order methods, a mixed method, and a hybrid discontinuous Galerkin method, for the approximation of incompressible flows. Both methods use divergence-conforming linear Brezzi–Douglas–Marini space for approximating the velocity and the lowest order Raviart–Thomas space for approximating the vorticity. Our methods are based on the physically correct viscous stress tensor of the fluid, involving the symmetric gradient of velocity (rather than the gradient), provide exactly divergence-free discrete velocity solutions, and optimal error estimates that are also pressure robust. We explain how the methods are constructed using the minimal number of coupling degrees of freedom per facet. The stability analysis of both methods are based on a Korn-like inequality for vector finite elements with continuous normal component. Numerical examples illustrate the theoretical findings and offer comparisons of condition numbers between the two new methods. 

Predictive power inference (PPI and PPI++) is a recently developed statistical method for computing confidence intervals and tests. It combines observations with machine-learning predictions. We use this technique to measure the association between the thickness of retinal layers and the time from the onset of Multiple Sclerosis (MS) symptoms. Further, we correlate the former with the Expanded Disability Status Scale, a measure of the progression of MS. In both cases, the confidence intervals provided with PPI++ improve upon standard statistical methodology, showing the advantage of PPI++ for answering inference problems in healthcare. 

Liquid droplet dynamics are widely used in biological and engineering applications, which contain complex interfacial instabilities and pattern formation such as droplet merging, splitting and transport. This paper studies a class of mean field control formulations for these droplet dynamics, which can be used to control and manipulate droplets in applications. We first formulate the droplet dynamics as gradient flows of free energies in modified optimal transport metrics with nonlinear mobilities. We then design an optimal control problem for these gradient flows. As an example, a lubrication equation for a thin volatile liquid film laden with an active suspension is developed, with control achieved through its activity field. Lastly, we apply the primal–dual hybrid gradient algorithm with high-order finite-element methods to simulate the proposed mean field control problems. Numerical examples, including droplet formation, bead-up/spreading, transport, and merging/splitting on a two-dimensional spatial domain, demonstrate the effectiveness of the proposed mean field control mechanism.