Noisy Experimental Data Research Articles

Mode shape-based damage detection in plate structure without baseline data

In this paper, a mode shape curvature-based method for detection and localization of damage in plate-like structures is described. The proposed algorithm requires only the mode shape curvature data of the damaged structure. The damage index is defined as the absolute difference between the measured curvature of the damaged structure and the smoothed polynomial representing the curvature of the healthy structure. To examine the advantages and limitations of the proposed method, several sets of numerical simulations are carried out. Simulated test cases considering different levels of damage severity, measurement noise and sensor sparsity are studied to evaluate the robustness of the method under the noisy experimental data and limited sensor data. Applicability and effectiveness of the proposed damage detection method are further demonstrated experimentally on an aluminium plate containing mill-cut damage. The modal frequencies and the corresponding mode shapes are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer for the experimental study. Copyright © 2016 John Wiley & Sons, Ltd.

The Intrinsic Geometric Structure of Protein-Protein Interaction Networks for Protein Interaction Prediction.

Recent developments in high-throughput technologies for measuring protein-protein interaction (PPI) have profoundly advanced our ability to systematically infer protein function and regulation. However, inherently high false positive and false negative rates in measurement have posed great challenges in computational approaches for the prediction of PPI. A good PPI predictor should be 1) resistant to high rate of missing and spurious PPIs, and 2) robust against incompleteness of observed PPI networks. To predict PPI in a network, we developed an intrinsic geometry structure (IGS) for network, which exploits the intrinsic and hidden relationship among proteins in network through a heat diffusion process. In this process, all explicit PPIs participate simultaneously to glue local infinitesimal and noisy experimental interaction data to generate a global macroscopic descriptions about relationships among proteins. The revealed implicit relationship can be interpreted as the probability of two proteins interacting with each other. The revealed relationship is intrinsic and robust against individual, local and explicit protein interactions in the original network. We apply our approach to publicly available PPI network data for the evaluation of the performance of PPI prediction. Experimental results indicate that, under different levels of the missing and spurious PPIs, IGS is able to robustly exploit the intrinsic and hidden relationship for PPI prediction with a higher sensitivity and specificity compared to that of recently proposed methods.

A phenomenological contact model: Understanding the graft–tunnel interaction in anterior cruciate ligament reconstructive surgery

In this paper, we sought to expand the fidelity of a validated model of the anterior cruciate ligament reconstruction (ACL-R) procedure by incorporating a stick–slip contact model with linear pressure–overclosure relationship at the interface. The suggested model is characterized by three unknown parameters, friction coefficient, shear stress softening and contact stiffness. In the absence of any isolated experiments exploring the graft–tunnel interactions during an aggregate joint load, the calibration data used in this study are derived from a reported biomechanical study. A Bayesian calibration procedure was employed to find the unknown probability distribution function (PDF) of these contact parameters. Initially, the response surface approximations of the predicted graft forces from laxity test simulations was adopted to estimate the likelihood of noisy experimental data reported in the literature. Then, the wide domain of contact parameters was sampled sequentially based on the Marcov Chain Monte Carlo (MCMC) method with acceptance–rejection criteria to search for population of samples in significantly narrower domain of unknown parameters that are associated with the highest occurrence likelihood of noisy experimental data. Our simulations with calibrated contact parameters indicate that pre-tensioning applied at 30° of flexion leads to larger graft force after the joint is fully extended compared to the graft force when the same pre-tensioning force is applied at full extension. Moreover, regardless of the pre-tensioning force, the graft–tunnel contact pressure is larger when the fixation of the graft is performed at full extension, increasing with the pre-tensioning force.

A posteriori determination of the useful data range for small-angle scattering experiments on dilute monodisperse systems.

Small-angle X-ray and neutron scattering (SAXS and SANS) experiments on solutions provide rapidly decaying scattering curves, often with a poor signal-to-noise ratio, especially at higher angles. On modern instruments, the noise is partially compensated for by oversampling, thanks to the fact that the angular increment in the data is small compared with that needed to describe adequately the local behaviour and features of the scattering curve. Given a (noisy) experimental data set, an important question arises as to which part of the data still contains useful information and should be taken into account for the interpretation and model building. Here, it is demonstrated that, for monodisperse systems, the useful experimental data range is defined by the number of meaningful Shannon channels that can be determined from the data set. An algorithm to determine this number and thus the data range is developed, and it is tested on a number of simulated data sets with various noise levels and with different degrees of oversampling, corresponding to typical SAXS/SANS experiments. The method is implemented in a computer program and examples of its application to analyse the experimental data recorded under various conditions are presented. The program can be employed to discard experimental data containing no useful information in automated pipelines, in modelling procedures, and for data deposition or publication. The software is freely accessible to academic users.

Comparison of different numerical treatments for x-ray phase tomography of soft tissue from differential phase projections

X-ray imaging of soft tissue is made difficult by their low absorbance. The use of x-ray phase imaging and tomography can significantly enhance the detection of these tissues and several approaches have been proposed to this end. Methods such as analyzer-based imaging or grating interferometry produce differential phase projections that can be used to reconstruct the 3D distribution of the sample refractive index. We report on the quantitative comparison of three different methods to obtain x-ray phase tomography with filtered back-projection from differential phase projections in the presence of noise. The three procedures represent different numerical approaches to solve the same mathematical problem, namely phase retrieval and filtered back-projection. It is found that obtaining individual phase projections and subsequently applying a conventional filtered back-projection algorithm produces the best results for noisy experimental data, when compared with other procedures based on the Hilbert transform. The algorithms are tested on simulated phantom data with added noise and the predictions are confirmed by experimental data acquired using a grating interferometer. The experiment is performed on unstained adult zebrafish, an important model organism for biomedical studies. The method optimization described here allows resolution of weak soft tissue features, such as muscle fibers.

Deconvolution of reacting-flow dynamics using proper orthogonal and dynamic mode decompositions.

Analytical and computational studies of reacting flows are extremely challenging due in part to nonlinearities of the underlying system of equations and long-range coupling mediated by heat and pressure fluctuations. However, many dynamical features of the flow can be inferred through low-order models if the flow constituents (e.g., eddies or vortices) and their symmetries, as well as the interactions among constituents, are established. Modal decompositions of high-frequency, high-resolution imaging, such as measurements of species-concentration fields through planar laser-induced florescence and of velocity fields through particle-image velocimetry, are the first step in the process. A methodology is introduced for deducing the flow constituents and their dynamics following modal decomposition. Proper orthogonal (POD) and dynamic mode (DMD) decompositions of two classes of problems are performed and their strengths compared. The first problem involves a cellular state generated in a flat circular flame front through symmetry breaking. The state contains two rings of cells that rotate clockwise at different rates. Both POD and DMD can be used to deconvolve the state into the two rings. In POD the contribution of each mode to the flow is quantified using the energy. Each DMD mode can be associated with an energy as well as a unique complex growth rate. Dynamic modes with the same spatial symmetry but different growth rates are found to be combined into a single POD mode. Thus, a flow can be approximated by a smaller number of POD modes. On the other hand, DMD provides a more detailed resolution of the dynamics. Two classes of reacting flows behind symmetric bluff bodies are also analyzed. In the first, symmetric pairs of vortices are released periodically from the two ends of the bluff body. The second flow contains von Karman vortices also, with a vortex being shed from one end of the bluff body followed by a second shedding from the opposite end. The way in which DMD can be used to deconvolve the second flow into symmetric and von Karman vortices is demonstrated. The analyses performed illustrate two distinct advantages of DMD: (1) Unlike proper orthogonal modes, each dynamic mode is associated with a unique complex growth rate. By comparing DMD spectra from multiple nominally identical experiments, it is possible to identify "reproducible" modes in a flow. We also find that although most high-energy modes are reproducible, some are not common between experimental realizations; in the examples considered, energy fails to differentiate between reproducible and nonreproducible modes. Consequently, it may not be possible to differentiate reproducible and nonreproducible modes in POD. (2) Time-dependent coefficients of dynamic modes are complex. Even in noisy experimental data, the dynamics of the phase of these coefficients (but not their magnitude) are highly regular. The phase represents the angular position of a rotating ring of cells and quantifies the downstream displacement of vortices in reacting flows. Thus, it is suggested that the dynamical characterizations of complex flows are best made through the phase dynamics of reproducible DMD modes.

Метод возмущений в регуляризации уравнений первого рода и приложения

One of the most common problems of scientific applications is computation of the derivative of a function specified by possibly noisy or imprecise experimental data. Application of conventional techniques for numerically calculating derivatives will amplify the noise making the result useless. We address this typical ill-posed problem by application of perturbation method to linear first kind equations Ax=f with bounded operator A. We assume that we know the operator A and source function f only such as ||A-A||<=b ||f-f||

Variations of Ant Colony Optimization for the Solution of the Structural Damage Identification Problem

In this work the inverse problem of identification of structural stiffness coefficients of a damped spring-mass system is tackled. The problem is solved by using different versions of Ant Colony Optimization (ACO) metaheuristic solely or coupled with the Hooke-Jeeves (HJ) local search algorithm. The evaluated versions of ACO are based on a discretization procedure to deal with the continuous domain design variables together with different pheromone evaporation and deposit strategies and also on the frequency of calling the local search algorithm. The damage estimation is evaluated using noiseless and noisy synthetic experimental data assuming a damage configuration throughout the structure. The reported results show the hybrid method as the best choice when both rank-based pheromone deposit and a new heuristic information based on the search history are used.

Numerical and Experimental Study on the Application of Mode Shape Curvature for Damage Detection in Plate-Like Structures

The paper describes on-going research effort at detecting and localizing damage in plate-like structures using mode shape curvature based damage detection algorithm. The proposed damage index uses data on exclusively mode shape curvature from the damaged structure. This method was originally developed for beam-like structures. The article generalizes the method of plate-like structures characterized by two-dimensional mode shape curvature. To examine limitations of the method, several sets of simulated data are applied and the obtained results of the numerical detection of damage are validated by comparing them with the findings of the case of the experimental test. The simulated test cases include the damage of various levels of severity. In order to ascertain the sensitivity of the proposed method for noisy experimental data, numerical mode shapes are corrupted with different levels of random noise. Modal frequencies and corresponding mode shapes of an aluminium plate containing mill-cut damage are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer (SLV) for the experimental study.

Applying Derivative-Free Optimization to Fit Kinetic Parameters of Viral Capsid Self-Assembly Models from Multi-Source Bulk in vitro Data

Virus capsid assembly has been a powerful model system for biological self-assembly in general due to the combination of experimental tractability but complicated pathway space. Detailed experimental resolution of viral assembly processes, however, has so far proven impossible. Computational approaches have provided a solution, allowing us to learn models of assembly consistent with indirect experimental measures of bulk in vitro assembly and thus fill the gaps between coarse-grained experimental measurements and detailed theoretical models. Nonetheless, accurate simulation predictions rely on building accurate models, which has proven to be a challenging data-fitting problem due to the high computational cost of simulating capsid assembly trajectories, high stochastic noise inherent to the system, and limited and generally noisy experimental data available. Here, we describe progress in learning accurate kinetic models of capsid assembly systems by computationally fitting assembly simulations to experimental data. We previously developed a heuristic optimization approach to learn rate parameters of coat-coat interactions by minimizing the deviation between real and simulated static light scattering measurements. We now show that one can substantially improve fitting to light scattering data using an alternative class of methods called derivative-free optimization, designed to deal with challenges of costly, noisy computations. Simultaneously, simulated exploration of potential alternative sources of experimental data for monitoring bulk assembly (e.g, non-covalent mass spectrometry) suggest that other feasible technologies providing richer data on assembly progress can more precisely pin down true parameters and assembly pathways. Advancing such simulation-based data fitting methods provides a general technology for greatly enhancing our ability to learn fine-scale details of complex assembly processes from experimental data, a strategy with potential application to developing accurate quantitative models of numerous other assembly systems found through biology.

Modelling Microbial Dechlorination of Trichloroethene: Investigating the Trade-off Between Quality of Fit and Parameter Reliability

This work puts forth a heuristic approach for investigating compromises between quality of fit and parameter reliability for the Monod-type kinetics employed to model microbial reductive dechlorination of trichloroethene. The methodology is demonstrated with three models of increasing fidelity and complexity. Model parameters were estimated with a stochastic global optimization algorithm, using scarce and inherently noisy experimental data from a mixed anaerobic microbial culture, which dechlorinated trichloroethene to ethene completely. Parameter reliability of each model was assessed using a Monte Carlo technique. Finally, an alternate quantity of applied interest was evaluated in order to assist with model discrimination. Results from the application of our approach suggest that the modeler should examine the implementation of conceptually simple models, even if they are a crude abstraction of reality, as they can be computationally less demanding and adequately accurate when model performance is assessed with criteria of applied interest, such as chloroethene elimination time.

Characterizing spiking in noisy type II neurons.

Understanding the dynamics of noisy neurons remains an important challenge in neuroscience. Here, we describe a simple probabilistic model that accurately describes the firing behavior in a large class (type II) of neurons. To demonstrate the usefulness of this model, we show how it accurately predicts the interspike interval (ISI) distributions, bursting patterns and mean firing rates found by: (1) simulations of the classic Hodgkin-Huxley model with channel noise, (2) experimental data from squid giant axon with a noisy input current and (3) experimental data on noisy firing from a neuron within the suprachiasmatic nucleus (SCN). This simple model has 6 parameters, however, in some cases, two of these parameters are coupled and only 5 parameters account for much of the known behavior. From these parameters, many properties of spiking can be found through simple calculation. Thus, we show how the complex effects of noise can be understood through a simple and general probabilistic model.

ReactomeFIViz: a Cytoscape app for pathway and network-based data analysis.

High-throughput experiments are routinely performed in modern biological studies. However, extracting meaningful results from massive experimental data sets is a challenging task for biologists. Projecting data onto pathway and network contexts is a powerful way to unravel patterns embedded in seemingly scattered large data sets and assist knowledge discovery related to cancer and other complex diseases. We have developed a Cytoscape app called "ReactomeFIViz", which utilizes a highly reliable gene functional interaction network combined with human curated pathways derived from Reactome and other pathway databases. This app provides a suite of features to assist biologists in performing pathway- and network-based data analysis in a biologically intuitive and user-friendly way. Biologists can use this app to uncover network and pathway patterns related to their studies, search for gene signatures from gene expression data sets, reveal pathways significantly enriched by genes in a list, and integrate multiple genomic data types into a pathway context using probabilistic graphical models. We believe our app will give researchers substantial power to analyze intrinsically noisy high-throughput experimental data to find biologically relevant information.

ReactomeFIViz: a Cytoscape app for pathway and network-based data analysis

High-throughput experiments are routinely performed in modern biological studies. However, extracting meaningful results from massive experimental data sets is a challenging task for biologists. Projecting data onto pathway and network contexts is a powerful way to unravel patterns embedded in seemingly scattered large data sets and assist knowledge discovery related to cancer and other complex diseases. We have developed a Cytoscape app called “ReactomeFIViz”, which utilizes a highly reliable gene functional interaction network combined with human curated pathways derived from Reactome and other pathway databases. This app provides a suite of features to assist biologists in performing pathway- and network-based data analysis in a biologically intuitive and user-friendly way. Biologists can use this app to uncover network and pathway patterns related to their studies, search for gene signatures from gene expression data sets, reveal pathways significantly enriched by genes in a list, and integrate multiple genomic data types into a pathway context using probabilistic graphical models. We believe our app will give researchers substantial power to analyze intrinsically noisy high-throughput experimental data to find biologically relevant information.

Solutions to the Inverse LQR Problem with Application to Biological Systems Analysis.

In this paper, we present a set of techniques for finding a cost function to the time-invariant Linear Quadratic Regulator (LQR) problem in both continuous- and discrete-time cases. Our methodology is based on the solution to the inverse LQR problem, which can be stated as: does a given controller K describe the solution to a time-invariant LQR problem, and if so, what weights Q and R produce K as the optimal solution? Our motivation for investigating this problem is the analysis of motion goals in biological systems. We first describe an efficient Linear Matrix Inequality (LMI) method for determining a solution to the general case of this inverse LQR problem when both the weighting matrices Q and R are unknown. Our first LMI-based formulation provides a unique solution when it is feasible. Additionally, we propose a gradient-based, least-squares minimization method that can be applied to approximate a solution in cases when the LMIs are infeasible. This new method is very useful in practice since the estimated gain matrix K from the noisy experimental data could be perturbed by the estimation error, which may result in the infeasibility of the LMIs. We also provide an LMI minimization problem to find a good initial point for the minimization using the proposed gradient descent algorithm. We then provide a set of examples to illustrate how to apply our approaches to several different types of problems. An important result is the application of the technique to human subject posture control when seated on a moving robot. Results show that we can recover a cost function which may provide a useful insight on the human motor control goal.

ReactomeFIViz: the Reactome FI Cytoscape app for pathway and network-based data analysis

High-throughput experiments are routinely performed in modern biological studies. However, extracting meaningful results from massive experimental data sets is a challenging task for biologists. Projecting data onto pathway and network contexts is a powerful way to unravel patterns embedded in seemingly scattered large data sets and assist knowledge discovery related to cancer and other complex diseases. We have developed a Cytoscape app called “ReactomeFIViz”, which utilizes a highly reliable gene functional interaction network and human curated pathways from Reactome and other pathway databases. This app provides a suite of features to assist biologists in performing pathway- and network-based data analysis in a biologically intuitive and user-friendly way. Biologists can use this app to uncover network and pathway patterns related to their studies, search for gene signatures from gene expression data sets, reveal pathways significantly enriched by genes in a list, and integrate multiple genomic data types into a pathway context using probabilistic graphical models. We believe our app will give researchers substantial power to analyze intrinsically noisy high-throughput experimental data to find biologically relevant information.

Understanding the sub-cellular dynamics of silicon transportation and synthesis in diatoms using population-level data and computational optimization.

Controlled synthesis of silicon is a major challenge in nanotechnology and material science. Diatoms, the unicellular algae, are an inspiring example of silica biosynthesis, producing complex and delicate nano-structures. This happens in several cell compartments, including cytoplasm and silica deposition vesicle (SDV). Considering the low concentration of silicic acid in oceans, cells have developed silicon transporter proteins (SIT). Moreover, cells change the level of active SITs during one cell cycle, likely as a response to the level of external nutrients and internal deposition rates. Despite this topic being of fundamental interest, the intracellular dynamics of nutrients and cell regulation strategies remain poorly understood. One reason is the difficulties in measurements and manipulation of these mechanisms at such small scales, and even when possible, data often contain large errors. Therefore, using computational techniques seems inevitable. We have constructed a mathematical model for silicon dynamics in the diatom Thalassiosira pseudonana in four compartments: external environment, cytoplasm, SDV and deposited silica. The model builds on mass conservation and Michaelis-Menten kinetics as mass transport equations. In order to find the free parameters of the model from sparse, noisy experimental data, an optimization technique (global and local search), together with enzyme related penalty terms, has been applied. We have connected population-level data to individual-cell-level quantities including the effect of early division of non-synchronized cells. Our model is robust, proven by sensitivity and perturbation analysis, and predicts dynamics of intracellular nutrients and enzymes in different compartments. The model produces different uptake regimes, previously recognized as surge, externally-controlled and internally-controlled uptakes. Finally, we imposed a flux of SITs to the model and compared it with previous classical kinetics. The model introduced can be generalized in order to analyze different biomineralizing organisms and to test different chemical pathways only by switching the system of mass transport equations.

Sensitivity analysis and variance reduction in a stochastic non-destructive testing problem

In this paper, we present a framework to deal with uncertainty quantification in case where the ranges of variability of the random parameters are ill-known. Namely the physical properties of the corrosion product (magnetite) which frequently clogs the tube support plate of steam generator, which is inaccessible in nuclear power plants. The methodology is based on polynomial chaos (PC) for the direct approach and on Bayesian inference for the inverse approach. The direct non-intrusive spectral projection (NISP) method is first employed by considering prior probability densities and therefore constructing a PC surrogate model of the large-scale non-destructive testing finite element model. To face the prohibitive computational cost underlying the high-dimensional random space, an adaptive sparse grid technique is applied on NISP resulting in drastic time reduction. The PC surrogate model, with reduced dimensionality, is used as a forward model in the Bayesian procedure. The posterior probability densities are then identified by inferring from few noisy experimental data. We demonstrate effectiveness of the approach by identifying the most influential parameter in the clogging detection as well as a variability range reduction.

Assessing uncertainty in model parameters based on sparse and noisy experimental data.

To perform parametric identification of mathematical models of biological events, experimental data are rare to be sufficient to estimate target behaviors produced by complex non-linear systems. We performed parameter fitting to a cell cycle model with experimental data as an in silico experiment. We calibrated model parameters with the generalized least squares method with randomized initial values and checked local and global sensitivity of the model. Sensitivity analyses showed that parameter optimization induced less sensitivity except for those related to the metabolism of the transcription factors c-Myc and E2F, which are required to overcome a restriction point (R-point). We performed bifurcation analyses with the optimized parameters and found the bimodality was lost. This result suggests that accumulation of c-Myc and E2F induced dysfunction of R-point. We performed a second parameter optimization based on the results of sensitivity analyses and incorporating additional derived from recent in vivo data. This optimization returned the bimodal characteristics of the model with a narrower range of hysteresis than the original. This result suggests that the optimized model can more easily go through R-point and come back to the gap phase after once having overcome it. Two parameter space analyses showed metabolism of c-Myc is transformed as it can allow cell bimodal behavior with weak stimuli of growth factors. This result is compatible with the character of the cell line used in our experiments. At the same time, Rb, an inhibitor of E2F, can allow cell bimodal behavior with only a limited range of stimuli when it is activated, but with a wider range of stimuli when it is inactive. These results provide two insights; biologically, the two transcription factors play an essential role in malignant cells to overcome R-point with weaker growth factor stimuli, and theoretically, sparse time-course data can be used to change a model to a biologically expected state.

Quantifying the multi-scale performance of network inference algorithms.

Graphical models are widely used to study complex multivariate biological systems. Network inference algorithms aim to reverse-engineer such models from noisy experimental data. It is common to assess such algorithms using techniques from classifier analysis. These metrics, based on ability to correctly infer individual edges, possess a number of appealing features including invariance to rank-preserving transformation. However, regulation in biological systems occurs on multiple scales and existing metrics do not take into account the correctness of higher-order network structure. In this paper novel performance scores are presented that share the appealing properties of existing scores, whilst capturing ability to uncover regulation on multiple scales. Theoretical results confirm that performance of a network inference algorithm depends crucially on the scale at which inferences are to be made; in particular strong local performance does not guarantee accurate reconstruction of higher-order topology. Applying these scores to a large corpus of data from the DREAM5 challenge, we undertake a data-driven assessment of estimator performance. We find that the "wisdom of crowds" network, that demonstrated superior local performance in the DREAM5 challenge, is also among the best performing methodologies for inference of regulation on multiple length scales.