scholarly journals A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems

2014 ◽  
Vol 48 (6) ◽  
pp. 1777-1806 ◽  
Author(s):  
M. Billaud-Friess ◽  
A. Nouy ◽  
O. Zahm
Keyword(s):  
Approximation Method ◽  
High Dimensional ◽  
Tensor Approximation ◽  
Minimal Residual

scholarly journals Sensitive detection of rare disease-associated cell subsets via representation learning

2016 ◽  
Author(s):  
Eirini Arvaniti ◽  
Manfred Claassen
Keyword(s):  
Single Cell ◽  
Rare Disease ◽  
Peripheral Blood ◽  
Residual Disease ◽  
Representation Learning ◽  
High Dimensional ◽  
Cell Populations ◽  
Learning Approach ◽  
Paracrine Signaling ◽  
Minimal Residual

Rare cell populations play a pivotal role in the initiation and progression of diseases like cancer. However, the identification of such subpopulations remains a difficult task. This work describes CellCnn, a representation learning approach to detect rare cell subsets associated with disease using high dimensional single cell measurements. Using CellCnn, we identify paracrine signaling and AIDS onset associated cell subsets in peripheral blood, and minimal residual disease associated populations in leukemia with frequencies as low as 0.005%.

A Compact High-Dimensional Yield Analysis Method using Low-Rank Tensor Approximation

2022 ◽  
Vol 27 (2) ◽  
pp. 1-23
Author(s):  
Xiao Shi ◽  
Hao Yan ◽  
Qiancun Huang ◽  
Chengzhen Xuan ◽  
Lei He ◽  
...  
Keyword(s):  
Analog Circuits ◽  
Adaptive Sampling ◽  
Sampling Method ◽  
Low Rank ◽  
High Dimensional ◽  
Yield Analysis ◽  
Meta Model ◽  
Polynomial Degree ◽  
Rank Tensor ◽  
Tensor Approximation

“Curse of dimensionality” has become the major challenge for existing high-sigma yield analysis methods. In this article, we develop a meta-model using Low-Rank Tensor Approximation (LRTA) to substitute expensive SPICE simulation. The polynomial degree of our LRTA model grows linearly with the circuit dimension. This makes it especially promising for high-dimensional circuit problems. Our LRTA meta-model is solved efficiently with a robust greedy algorithm and calibrated iteratively with a bootstrap-assisted adaptive sampling method. We also develop a novel global sensitivity analysis approach to generate a reduced LRTA meta-model which is more compact. It further accelerates the procedure of model calibration and yield estimation. Experiments on memory and analog circuits validate that the proposed LRTA method outperforms other state-of-the-art approaches in terms of accuracy and efficiency.

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