scholarly journals Motion tomography via occupation kernels

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Benjamin P. Russo ◽  
Rushikesh Kamalapurkar ◽  
Dongsik Chang ◽  
Joel A. Rosenfeld
Keyword(s):  
Flow Field ◽  
Marked Improvement ◽  
Contraction Mapping ◽  
Simulated Data ◽  
Ground Truth ◽  
Trajectory Data ◽  
Established Method ◽  
Contraction Mapping Theorem ◽  
Error Metrics ◽  
Predictor Corrector

<p style='text-indent:20px;'>The goal of motion tomography is to recover a description of a vector flow field using measurements along the trajectory of a sensing unit. In this paper, we develop a predictor corrector algorithm designed to recover vector flow fields from trajectory data with the use of occupation kernels developed by Rosenfeld et al. [<xref ref-type="bibr" rid="b9">9</xref>,<xref ref-type="bibr" rid="b10">10</xref>]. Specifically, we use the occupation kernels as an adaptive basis; that is, the trajectories defining our occupation kernels are iteratively updated to improve the estimation in the next stage. Initial estimates are established, then under mild assumptions, such as relatively straight trajectories, convergence is proven using the Contraction Mapping Theorem. We then compare the developed method with the established method by Chang et al. [<xref ref-type="bibr" rid="b5">5</xref>] by defining a set of error metrics. We found that for simulated data, where a ground truth is available, our method offers a marked improvement over [<xref ref-type="bibr" rid="b5">5</xref>]. For a real-world example, where ground truth is not available, our results are similar results to the established method.</p>

scholarly journals Multibody Kinematics Optimization for the Estimation of Upper and Lower Limb Human Joint Kinematics: A Systematized Methodological Review

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Mickaël Begon ◽  
Michael Skipper Andersen ◽  
Raphaël Dumas
Keyword(s):  
Degrees Of Freedom ◽  
Inertial Sensors ◽  
Model Development ◽  
Simulated Data ◽  
Ground Truth ◽  
Joint Kinematics ◽  
Sensitivity Analyses ◽  
Geometrical Parameters ◽  
Joint Models ◽  
Human Joint

Multibody kinematics optimization (MKO) aims to reduce soft tissue artefact (STA) and is a key step in musculoskeletal modeling. The objective of this review was to identify the numerical methods, their validation and performance for the estimation of the human joint kinematics using MKO. Seventy-four papers were extracted from a systematized search in five databases and cross-referencing. Model-derived kinematics were obtained using either constrained optimization or Kalman filtering to minimize the difference between measured (i.e., by skin markers, electromagnetic or inertial sensors) and model-derived positions and/or orientations. While hinge, universal, and spherical joints prevail, advanced models (e.g., parallel and four-bar mechanisms, elastic joint) have been introduced, mainly for the knee and shoulder joints. Models and methods were evaluated using: (i) simulated data based, however, on oversimplified STA and joint models; (ii) reconstruction residual errors, ranging from 4 mm to 40 mm; (iii) sensitivity analyses which highlighted the effect (up to 36 deg and 12 mm) of model geometrical parameters, joint models, and computational methods; (iv) comparison with other approaches (i.e., single body kinematics optimization and nonoptimized kinematics); (v) repeatability studies that showed low intra- and inter-observer variability; and (vi) validation against ground-truth bone kinematics (with errors between 1 deg and 22 deg for tibiofemoral rotations and between 3 deg and 10 deg for glenohumeral rotations). Moreover, MKO was applied to various movements (e.g., walking, running, arm elevation). Additional validations, especially for the upper limb, should be undertaken and we recommend a more systematic approach for the evaluation of MKO. In addition, further model development, scaling, and personalization methods are required to better estimate the secondary degrees-of-freedom (DoF).

scholarly journals Evaluating the reproducibility of single-cell gene regulatory network inference algorithms

2020 ◽  
Author(s):  
Yoonjee Kang ◽  
Denis Thieffry ◽  
Laura Cantini
Keyword(s):  
Single Cell ◽  
Network Inference ◽  
Simulated Data ◽  
Ground Truth ◽  
Real Data ◽  
Gene Regulatory Network Inference ◽  
Sequencing Platform ◽  
Cell Network ◽  
Inference Algorithms ◽  
Inference Methods

AbstractNetworks are powerful tools to represent and investigate biological systems. The development of algorithms inferring regulatory interactions from functional genomics data has been an active area of research. With the advent of single-cell RNA-seq data (scRNA-seq), numerous methods specifically designed to take advantage of single-cell datasets have been proposed. However, published benchmarks on single-cell network inference are mostly based on simulated data. Once applied to real data, these benchmarks take into account only a small set of genes and only compare the inferred networks with an imposed ground-truth.Here, we benchmark four single-cell network inference methods based on their reproducibility, i.e. their ability to infer similar networks when applied to two independent datasets for the same biological condition. We tested each of these methods on real data from three biological conditions: human retina, T-cells in colorectal cancer, and human hematopoiesis.GENIE3 results to be the most reproducible algorithm, independently from the single-cell sequencing platform, the cell type annotation system, the number of cells constituting the dataset, or the thresholding applied to the links of the inferred networks. In order to ensure the reproducibility and ease extensions of this benchmark study, we implemented all the analyses in scNET, a Jupyter notebook available at https://github.com/ComputationalSystemsBiology/scNET.

scholarly journals Quantifying accuracy and heterogeneity in single-molecule super-resolution microscopy

2019 ◽  
Author(s):  
Hesam Mazidi ◽  
Tianben Ding ◽  
Arye Nehorai ◽  
Matthew D. Lew
Keyword(s):  
Single Molecule ◽  
Computational Models ◽  
Amyloid Fibrils ◽  
Imaging System ◽  
Simulated Data ◽  
Super Resolution ◽  
Ground Truth ◽  
Localization Algorithm ◽  
Reconstruction Algorithms ◽  
Imaging Data

The resolution and accuracy of single-molecule localization micro-scopes (SMLMs) are routinely benchmarked using simulated data, calibration “rulers,” or comparisons to secondary imaging modalities. However, these methods cannot quantify the nanoscale accuracy of an arbitrary SMLM dataset. Here, we show that by computing localization stability under a well-chosen perturbation with accurate knowledge of the imaging system, we can robustly measure the confidence of individual localizations without ground-truth knowledge of the sample. We demonstrate that our method, termed Wasserstein-induced flux (WIF), measures the accuracy of various reconstruction algorithms directly on experimental 2D and 3D data of microtubules and amyloid fibrils. We further show that WIF confidences can be used to evaluate the mismatch between computational models and imaging data, enhance the accuracy and resolution of recon-structed structures, and discover hidden molecular heterogeneities. As a computational methodology, WIF is broadly applicable to any SMLM dataset, imaging system, and localization algorithm.

scholarly journals A New Existence and Uniqueness Theorem for Continuous Games

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Seamus D Hogan
Keyword(s):  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Jacobian Matrix ◽  
Iterative Sequence ◽  
Response Functions ◽  
Unique Equilibrium ◽  
Contraction Mapping Theorem ◽  
Best Response ◽  
General Sufficient Condition ◽  
General Game

This paper derives a general sufficient condition for existence and uniqueness in continuous games using a variant of the contraction mapping theorem applied to mappings from a subset of the real line on to itself. We first prove this contraction mapping variant, and then show how the existence of a unique equilibrium in the general game can be shown by proving the existence of a unique equilibrium in an iterative sequence of games involving such mappings. Finally, we show how a general condition for this to occur is that a matrix derived from the Jacobian matrix of best-response functions has positive leading principal minors, and how this condition generalises some existing uniqueness theorems for particular games. In particular, we show how the same conditions used in those theorems to show uniqueness, also guarantee existence in games with unbounded strategy spaces.

Simulation of Two-Dimensional Turbulent Recirculating Flow Field Behind a V-Shaped Bluff Body

1994 ◽  
Author(s):  
Z. Gu ◽  
M. A. R. Sharif
Keyword(s):  
Flow Field ◽  
Bluff Body ◽  
Flame Stabilization ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Combustion Chambers ◽  
Recirculating Flow ◽  
Conservative Form ◽  
Curvilinear Grid ◽  
Predictor Corrector

Abstract The two-dimensional turbulent recirculating flow fields behind a V-shaped bluff body have been investigated numerically. Similar bluff bodies are used in combustion chambers for flame stabilization. The governing transport equations in conservative form are solved by a pressure based predictor-corrector method. The standard k-ϵ turbulence closure model and a boundary fitted multi-block curvilinear grid system are used in the computation. The code is validated against turbulent flow over a backward facing step problem. The predicted flow field behind the bluff body is also compared with experiment. It is found that while the qualitative features of the flow are well predicted, there is quantitative disagreement between the measurement and prediction. This disagreement can be partially attributed to the k-ϵ turbulence model which is known to be inadequate for recirculating flows. Parametric investigation of the flow field by varying the shape and size of the bluff body is also performed and the results are reported.

scholarly journals Brain Tissue Conductivity Measurements with MR-Electrical Properties Tomography: An In Vivo Study

2020 ◽  
Author(s):  
Stefano Mandija ◽  
Petar I. Petrov ◽  
Jord J. T. Vink ◽  
Sebastian F. W. Neggers ◽  
Cornelis A. T. van den Berg
Keyword(s):  
Electrical Properties ◽  
Healthy Subjects ◽  
Ex Vivo ◽  
Simulated Data ◽  
Ground Truth ◽  
In Vivo Study ◽  
Conductivity Measurements ◽  
Tissue Conductivity ◽  
Before And After

AbstractFirst in vivo brain conductivity reconstructions using Helmholtz MR-Electrical Properties Tomography (MR-EPT) have been published. However, a large variation in the reconstructed conductivity values is reported and these values differ from ex vivo conductivity measurements. Given this lack of agreement, we performed an in vivo study on eight healthy subjects to provide reference in vivo brain conductivity values. MR-EPT reconstructions were performed at 3 T for eight healthy subjects. Mean conductivity and standard deviation values in the white matter, gray matter and cerebrospinal fluid (σWM, σGM, and σCSF) were computed for each subject before and after erosion of regions at tissue boundaries, which are affected by typical MR-EPT reconstruction errors. The obtained values were compared to the reported ex vivo literature values. To benchmark the accuracy of in vivo conductivity reconstructions, the same pipeline was applied to simulated data, which allow knowledge of ground truth conductivity. Provided sufficient boundary erosion, the in vivo σWM and σGM values obtained in this study agree for the first time with literature values measured ex vivo. This could not be verified for the CSF due to its limited spatial extension. Conductivity reconstructions from simulated data verified conductivity reconstructions from in vivo data and demonstrated the importance of discarding voxels at tissue boundaries. The presented σWM and σGM values can therefore be used for comparison in future studies employing different MR-EPT techniques.

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