California Institute of Technology

About: California Institute of Technology is a education organization based out in Pasadena, California, United States. It is known for research contribution in the topics: Galaxy & Redshift. The organization has 57649 authors who have published 146691 publications receiving 8620287 citations. The organization is also known as: Caltech & Cal Tech.

Matrix Completion With Noise

Abstract: On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be incomplete, and perhaps even corrupted, information. In its simplest form, the problem is to recover a matrix from a small sample of its entries, and comes up in many areas of science and engineering including collaborative filtering, machine learning, control, remote sensing, and computer vision to name a few. This paper surveys the novel literature on matrix completion, which shows that under some suitable conditions, one can recover an unknown low-rank matrix from a nearly minimal set of entries by solving a simple convex optimization problem, namely, nuclear-norm minimization subject to data constraints. Further, this paper introduces novel results showing that matrix completion is provably accurate even when the few observed entries are corrupted with a small amount of noise. A typical result is that one can recover an unknown n x n matrix of low rank r from just about nr log^2 n noisy samples with an error which is proportional to the noise level. We present numerical results which complement our quantitative analysis and show that, in practice, nuclear norm minimization accurately fills in the many missing entries of large low-rank matrices from just a few noisy samples. Some analogies between matrix completion and compressed sensing are discussed throughout.

Mutant presenilins specifically elevate the levels of the 42 residue β-amyloid peptide in vivo: evidence for augmentation of a 42-specific γ secretase

Abstract: Amyloid precursor protein (APP) is endoproteolytically processed by BACE1 and γ-secretase to release amyloid peptides (Aβ40 and 42) that aggregate to form senile plaques in the brains of patients with Alzheimer's disease (AD). The C-terminus of Aβ40/42 is generated by γ-secretase, whose activity is dependent upon presenilin (PS 1 or 2). Missense mutations in PS1 (and PS2) occur in patients with early-onset familial AD (FAD), and previous studies in transgenic mice and cultured cell models demonstrated that FAD-PS1 variants shift the ratio of Aβ40 : 42 to favor Aβ42. One hypothesis to explain this outcome is that mutant PS alters the specificity of γ-secretase to favor production of Aβ42 at the expense of Aβ40. To test this hypothesis in vivo, we studied Aβ40 and 42 levels in a series of transgenic mice that co-express the Swedish mutation of APP (APPswe) with two FAD-PS1 variants that differentially accelerate amyloid pathology in the brain. We demonstrate a direct correlation between the concentration of Aβ42 and the rate of amyloid deposition. We further show that the shift in Aβ42 : 40 ratios associated with the expression of FAD-PS1 variants is due to a specific elevation in the steady-state levels of Aβ42, while maintaining a constant level of Aβ40. These data suggest that PS1 variants do not simply alter the preferred cleavage site for γ-secretase, but rather that they have more complex effects on the regulation of γ-secretase and its access to substrates.

Micro-electro-mechanical-systems (mems) and fluid flows

Abstract: The micromachining technology that emerged in the late 1980s can provide micron-sized sensors and actuators. These micro transducers are able to be integrated with signal conditioning and processing circuitry to form micro-electromechanical-systems (MEMS) that can perform real-time distributed control. This capability opens up a new territory for flow control research. On the other hand, surface effects dominate the fluid flowing through these miniature mechanical devices because of the large surface-to-volume ratio in micron-scale configurations. We need to reexamine the surface forces in the momentum equation. Owing to their smallness, gas flows experience large Knudsen numbers, and therefore boundary conditions need to be modified. Besides being an enabling technology, MEMS also provide many challenges for fundamental flow-science research.