scholarly journals Understanding cardiac alternans: A piecewise linear modeling framework

2010 ◽  
Vol 20 (4) ◽  
pp. 045102 ◽  
Author(s):  
R. Thul ◽  
S. Coombes
Keyword(s):  
Piecewise Linear ◽  
Linear Modeling ◽  
Modeling Framework ◽  
Cardiac Alternans

Canonical piecewise-linear modeling

1986 ◽  
Vol 33 (5) ◽  
pp. 511-525 ◽  
Author(s):  
L. Chua ◽  
An-Chang Deng
Keyword(s):  
Piecewise Linear ◽  
Linear Modeling

scholarly journals Kernel Regression Imputation in Manifolds via Bi-Linear Modeling: The Dynamic-MRI Case

2021 ◽  
Author(s):  
Konstantinos Slavakis ◽  
Gaurav Shetty ◽  
Loris Cannelli ◽  
Gesualdo Scutari ◽  
Ukash Nakarmi ◽  
...  
Keyword(s):  
Reproducing Kernel ◽  
Kernel Regression ◽  
Dynamic Mri ◽  
Efficient Solutions ◽  
Training Data ◽  
Superior Performance ◽  
Linear Modeling ◽  
Modeling Framework ◽  
Geometric Information ◽  
Regression Imputation

This paper introduces a non-parametric kernel-based modeling framework for imputation by regression on data that are assumed to lie close to an unknown-to-the-user smooth manifold in a Euclidean space. The proposed framework, coined kernel regression imputation in manifolds (KRIM), needs no training data to operate. Aiming at computationally efficient solutions, KRIM utilizes a small number of ``landmark'' data-points to extract geometric information from the measured data via parsimonious affine combinations (``linear patches''), which mimic the concept of tangent spaces to smooth manifolds and take place in functional approximation spaces, namely reproducing kernel Hilbert spaces (RKHSs). Multiple complex RKHSs are combined in a data-driven way to surmount the obstacle of pin-pointing the ``optimal'' parameters of a single kernel through cross-validation. The extracted geometric information is incorporated into the design via a novel bi-linear data-approximation model, and the imputation-by-regression task takes the form of an inverse problem which is solved by an iterative algorithm with guaranteed convergence to a stationary point of the non-convex loss function. To showcase the modular character and wide applicability of KRIM, this paper highlights the application of KRIM to dynamic magnetic resonance imaging (dMRI), where reconstruction of high-resolution images from severely under-sampled dMRI data is desired. Extensive numerical tests on synthetic and real dMRI data demonstrate the superior performance of KRIM over state-of-the-art approaches under several metrics and with a small computational footprint.<br>

scholarly journals Using Single Nucleotide Variations in Single-Cell RNA-Seq to Identify Subpopulations and Genotype-phenotype Linkage

2016 ◽  
Author(s):  
Olivier Poirion ◽  
Xun Zhu ◽  
Travers Ching ◽  
Lana X. Garmire
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Single Cells ◽  
Transcript Abundance ◽  
Rna Seq ◽  
Linear Modeling ◽  
Modeling Framework ◽  
Single Nucleotide ◽  
Single Nucleotide Variations

AbstractDespite its popularity, characterization of subpopulations with transcript abundance is subject to a significant amount of noise. We propose to use effective and expressed nucleotide variations (eeSNVs) from scRNA-seq as alternative features for tumor subpopulation identification. We developed a linear modeling framework, SSrGE, to link eeSNVs associated with gene expression. In all the datasets tested, eeSNVs achieve better accuracies than gene expression for identifying subpopulations. Previously validated cancer-relevant genes are also highly ranked, confirming the significance of the method. Moreover, SSrGE is capable of analyzing coupled DNA-seq and RNA-seq data from the same single cells, demonstrating its value in integrating multi-omics single cell techniques. In summary, SNV features from scRNA-seq data have merits for both subpopulation identification and linkage of genotype-phenotype relationship. The method SSrGE is available at https://github.com/lanagarmire/SSrGE.

Understanding the Relationships between Demand for Shared Ride Modes: Case Study using Open Data from New York City

2019 ◽  
Vol 2673 (12) ◽  
pp. 30-39 ◽  
Author(s):  
Raymond Gerte ◽  
Karthik C. Konduri ◽  
Nalini Ravishanker ◽  
Amit Mondal ◽  
Naveen Eluru
Keyword(s):  
New York ◽  
New York City ◽  
York City ◽  
Transportation Network ◽  
Temporal Trends ◽  
Primary Objective ◽  
Linear Modeling ◽  
Modeling Framework ◽  
Exogenous Factors ◽  
Citi Bike

The concept of shared travel, making trips with other users via a common vehicle, is far from novel. However, a changing technological climate has laid the tracks for new dynamically shared modes in the form of transportation network companies (TNCs), to substantially impact travel behavior. The current body of research on how these modal offerings impact the demand for existing shared modes (e.g., bikeshare, transit) is growing. However, a comprehensive investigation of the temporal evolution of the demand for TNCs and their relationship to other shared modes, is lacking. This research tackles this important limitation by analyzing ridership data for TNCs, taxi, subway, and Citi Bike in New York City using daily ridership data from January 2015 through June 2017. The primary objective was to understand the relationship between TNCs and other shared modal offerings while accounting for the influence of temporal trends and other exogenous factors. A dynamic linear modeling framework was formulated to accommodate time-dependent trends, periodicity, and time-varying exogenous factors on the demand for TNCs. As a preliminary work, the findings of this study reinforce the observed substitution relationship between taxis and TNCs. The results may also indicate a substitutional relationship between TNCs and Citi Bike, and a complementary relationship with subway, however these results still need to be explored further. With potentially impactful findings for planning and policymakers, the predictive model developed in the study can be used to carry out forecasting in support of short- and long-term operations and planning applications.

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