scholarly journals Data-driven selection of stiff chemistry ODE solver in operator-splitting schemes

2020 ◽  
Vol 220 ◽  
pp. 133-143
Author(s):  
Simon Lapointe ◽  
Sudeepta Mondal ◽  
Russell A. Whitesides
Keyword(s):  
Operator Splitting ◽  
Data Driven ◽  
Splitting Schemes ◽  
Selection Of

scholarly journals Incorporating radiomics into clinical trials: expert consensus on considerations for data-driven compared to biologically driven quantitative biomarkers

2021 ◽  
Author(s):  
Laure Fournier ◽  
Lena Costaridou ◽  
Luc Bidaut ◽  
Nicolas Michoux ◽  
Frederic E. Lecouvet ◽  
...  
Keyword(s):  
Clinical Trials ◽  
Quantitative Imaging ◽  
A Priori ◽  
External Validation ◽  
Data Driven ◽  
Imaging Biomarkers ◽  
Clinical Validation ◽  
Biological Processes ◽  
Imaging Data ◽  
Selection Of

Abstract Existing quantitative imaging biomarkers (QIBs) are associated with known biological tissue characteristics and follow a well-understood path of technical, biological and clinical validation before incorporation into clinical trials. In radiomics, novel data-driven processes extract numerous visually imperceptible statistical features from the imaging data with no a priori assumptions on their correlation with biological processes. The selection of relevant features (radiomic signature) and incorporation into clinical trials therefore requires additional considerations to ensure meaningful imaging endpoints. Also, the number of radiomic features tested means that power calculations would result in sample sizes impossible to achieve within clinical trials. This article examines how the process of standardising and validating data-driven imaging biomarkers differs from those based on biological associations. Radiomic signatures are best developed initially on datasets that represent diversity of acquisition protocols as well as diversity of disease and of normal findings, rather than within clinical trials with standardised and optimised protocols as this would risk the selection of radiomic features being linked to the imaging process rather than the pathology. Normalisation through discretisation and feature harmonisation are essential pre-processing steps. Biological correlation may be performed after the technical and clinical validity of a radiomic signature is established, but is not mandatory. Feature selection may be part of discovery within a radiomics-specific trial or represent exploratory endpoints within an established trial; a previously validated radiomic signature may even be used as a primary/secondary endpoint, particularly if associations are demonstrated with specific biological processes and pathways being targeted within clinical trials. Key Points • Data-driven processes like radiomics risk false discoveries due to high-dimensionality of the dataset compared to sample size, making adequate diversity of the data, cross-validation and external validation essential to mitigate the risks of spurious associations and overfitting. • Use of radiomic signatures within clinical trials requires multistep standardisation of image acquisition, image analysis and data mining processes. • Biological correlation may be established after clinical validation but is not mandatory.

scholarly journals Embedded Zassenhaus Expansion to Splitting Schemes: Theory and Multiphysics Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jürgen Geiser
Keyword(s):  
Fluid Dynamics ◽  
Convergence Rates ◽  
Operator Splitting ◽  
Main Idea ◽  
Computation Time ◽  
Product Formula ◽  
Splitting Methods ◽  
Splitting Schemes ◽  
Operator Splitting Methods ◽  
Multiphysics Problems

We present some operator splitting methods improved by the use of the Zassenhaus product and designed for applications to multiphysics problems. We treat iterative splitting methods that can be improved by means of the Zassenhaus product formula, which is a sequential splitting scheme. The main idea for reducing the computation time needed by the iterative scheme is to embed fast and cheap Zassenhaus product schemes, since the computation of the commutators involved is very cheap, since we are dealing with nilpotent matrices. We discuss the coupling ideas of iterative and sequential splitting techniques and their convergence. While the iterative splitting schemes converge slowly in their first iterative steps, we improve the initial convergence rates by embedding the Zassenhaus product formula. The applications are to multiphysics problems in fluid dynamics. We consider phase models in computational fluid dynamics and analyse how to obtain higher order operator splitting methods based on the Zassenhaus product. The computational benefits derive from the use of sparse matrices, which arise from the spatial discretisation of the underlying partial differential equations. Since the Zassenhaus formula requires nearly constant CPU time due to its sparse commutators, we have accelerated the iterative splitting schemes.

Data driven selection of DRX for energy efficient 5G RAN

2017 ◽  
Author(s):  
Diarmuid Corcoran ◽  
Loghman Andimeh ◽  
Andreas Ermedahl ◽  
Per Kreuger ◽  
Christian Schulte
Keyword(s):  
Energy Efficient ◽  
Data Driven ◽  
Selection Of

Operator-splitting Schemes for Solving Unsteady Elasticity Problems

2001 ◽  
Vol 1 (2) ◽  
pp. 188-198 ◽  
Author(s):  
Francisco J. Lisbona ◽  
Pert N. Vabishchevich
Keyword(s):  
Displacement Vector ◽  
Operator Splitting ◽  
Numerical Algorithms ◽  
General Concept ◽  
Rectangular Domain ◽  
Time Level ◽  
Splitting Schemes ◽  
Strongly Coupled ◽  
Elasticity Equations ◽  
Elasticity Problems

AbstractIn this paper we consider the numerical approximation of the solution of the 2D unsteady Lame equations on a rectangular domain. The basic problems that appear, using both finite difference and finite element methods, are connected with the fact that these equations are strongly coupled. Thus it is natural to design computational algorithms in such a way that they allow one to consider boundary value problems only for uncoupled equations. To implement this general concept, some special (unconditionally stable) operator-splitting schemes are constructed. Its major peculiarity is that transition to the next time level is performed by solving separate elliptic problems for each component of the displacement vector. The previous results make it possible to design efficient numerical algorithms for elasticity equations.

scholarly journals Precision Medicine

2019 ◽  
Vol 6 (1) ◽  
pp. 263-286 ◽  
Author(s):  
Michael R. Kosorok ◽  
Eric B. Laber
Keyword(s):  
Health Care ◽  
Precision Medicine ◽  
Decision Rules ◽  
Data Driven ◽  
Care Process ◽  
Treatment Regimes ◽  
Specific Diet ◽  
Recommended Action ◽  
Selection Of

Precision medicine seeks to maximize the quality of health care by individualizing the health-care process to the uniquely evolving health status of each patient. This endeavor spans a broad range of scientific areas including drug discovery, genetics/genomics, health communication, and causal inference, all in support of evidence-based, i.e., data-driven, decision making. Precision medicine is formalized as a treatment regime that comprises a sequence of decision rules, one per decision point, which map up-to-date patient information to a recommended action. The potential actions could be the selection of which drug to use, the selection of dose, the timing of administration, the recommendation of a specific diet or exercise, or other aspects of treatment or care. Statistics research in precision medicine is broadly focused on methodological development for estimation of and inference for treatment regimes that maximize some cumulative clinical outcome. In this review, we provide an overview of this vibrant area of research and present important and emerging challenges.

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