Multidimensional Experimental Data Research Articles

Fault diagnosis of EHA with few-shot data augmentation technique

As an emerging object in aerospace actuators, electro-hydrostatic actuator (EHA) has the advantages of heavy load capacity and high reliability. An EHA fault diagnosis method based on a few-shot data augmentation technique is proposed to diagnose and isolate possible faults. The sensitive parameters of typical failure modes are demonstrated based on the mathematical model of EHA. By converting multi-dimensional experimental data into two-dimensional grayscale data and extracting local features, the time series characteristics and correlation between different signals can be highlighted. The Wasserstein deep convolutional generative adversarial network (WDCGAN) is used to enhance the EHA small sample data. The diagnostic model WDCGAN-stacked denoised auto encoder (SDAE) combined with WDCGAN and SDAE is proposed to differentiate between multiple types of EHA failures. Compared with the five commonly used fault classification methods, the proposed method can effectively identify the typical fault modes of EHA, with the highest accuracy of fault classification and strong feature extraction ability.

Nonlinear dynamics of estrogen receptor-positive breast cancer integrating experimental data: A novel spatial modeling approach.

Oncology research has focused extensively on estrogen hormones and their function in breast cancer proliferation. Mathematical modeling is essential for the analysis and simulation of breast cancers. This research presents a novel approach to examine the therapeutic and inhibitory effects of hormone and estrogen therapies on the onset of breast cancer. Our proposed mathematical model comprises a nonlinear coupled system of partial differential equations, capturing intricate interactions among estrogen, cytotoxic T lymphocytes, dormant cancer cells, and active cancer cells. The model's parameters are meticulously estimated through experimental studies, and we conduct a comprehensive global sensitivity analysis to assess the uncertainty of these parameter values. Remarkably, our findings underscore the pivotal role of hormone therapy in curtailing breast tumor growth by blocking estrogen's influence on cancer cells. Beyond this crucial insight, our proposed model offers an integrated framework to delve into the complexity of tumor progression and immune response under hormone therapy. We employ diverse experimental datasets encompassing gene expression profiles, spatial tumor morphology, and cellular interactions. Integrating multidimensional experimental data with mathematical models enhances our understanding of breast cancer dynamics and paves the way for personalized treatment strategies. Our study advances our comprehension of estrogen receptor-positive breast cancer and exemplifies a transformative approach that merges experimental data with cutting-edge mathematical modeling. This framework promises to illuminate the complexities of cancer progression and therapy, with broad implications for oncology.

ОЦІНКА ОСОБЛИВОСТЕЙ БАГАТОВИМІРНИХ ВИПАДКОВИХ ПРОЦЕСІВ НА ОСНОВІ ЇХНІХ ВІЗУАЛЬНИХ ОБРАЗІВ

Despite the wide implementation of information technologies in diagnostic systems, visual control of the processes that characterize the object state remains relevant, especially when the number of such processes is large. An analysis of the possi-bilities of visual control for multidimensional random processes, the realizations of which are processed in measurement infor-mation systems on complex technical objects, was carried out. For this, these processes are transformed into a visual image, that represented a set of curves on a plane, which are obtained for each discrete moment of time. Any curve is the sum of products of the realizations values for each random process at a specified discrete moment of time on the corresponding or-thogonal function that depends on some generalized argument. Lagrangian functions are used in the article.The purpose of the article is to check the effectiveness of a new method of visualizing realizations of a multidimensional random process for extreme cases and to develop proposals for detecting the parameters jumps of one or more processes.For the first time, a method of visual detection of the parameters jumps of realizations for one or more random processes is proposed. The essence of the method is based on the subtraction of a visual image, that is, a set of functions in the absence of a jump of one or more process parameters from a similar image that concludes jumps of parameters. In practice, the first image should be a statistical average for the conditions of normal functioning of the technical object. After subtraction, a new visual image is created, which shows anomalies caused by jumps in process parameters. The usefulness of the method is demonstrated on the example of processing multidimensional experimental data, which were matched with generalized visual images. The functioning of this method is verified also for extreme cases of processing white noise and a deterministic process. The obtained visual images also reveal the features of the behavior of multidimensional random processes.

PRINCIPAL COMPONENT ANALYSIS OF PHOTON COUNTING HISTOGRAMS IN FLUORESCENCE FLUCTUATION SPECTROSCOPY EXPERIMENTS

An integrated approach based on the use of data mining methods has been proposed to improve the efficiency of the analysis of photon counting histograms in the study of the molecular composition of a substance by the method of fluorescence fluctuation spectroscopy. The method of principal components is used to test the hypothesis about the cluster separability of multidimensional experimental data. The reason for the compression of a point cloud into a characteristic nonlinearity, or so-called arc-shaped cloud, in the space of first two principal components is investigated. Examples of simulated data sets on some selected molecular systems of various brightness and concentration are considered. Nonlinear effects complicate interpretation and subsequent quantitative analysis of data. It has been established that the arching of the data cloud is a consequence of the presence of a significant variation in one or more physical parameters. In particular, it is the result of a significant increase in the variation in the parameters of the brightness or concentration of molecules. These parameters can be as additional measure in assessing the quality of the experiments if only one type of molecule is studied, and also can be used for characterizing the system under study in the case of a mixture of molecules of different types. It is proposed to apply the locally weighted scatterplot smoothing normalization to eliminate the nonlinear effects in the space of principal components.

Application of Genomics and Phenomics in Plant Breeding for Climate Resilience

Advances in the fields of genomics and phenomics are currently creating significant foundations for the sustainable intensification of plant breeding initiatives targeting climate resilience. Genomics is a biological study that focuses on architecture, function, editing, mapping, and evolution of genomes. It can be applied extensively in climate resilience breeding for cost-effective, rapid, and high-through put genotyping, phenotyping, and trait mapping. The efficacy of genomics-assisted breeding (GAB) is strongly hinged on the high resolution and robustness of Next Generation Sequencing (NGS) and CRISPR/Cas9-based Gene Editing systems. The integration of genomics and phenomics in crop improvement can upscale the efficiency of breeding systems targeting climate resilience and hasten cultivar release cycle. Phenomics is an interdisciplinary field that focuses on the enhanced measurement of plant performance, growth, and composition. Similarly, phenomics has revolutionized the efficacy of plant breeding off-trial initiatives established to phenotypically characterize and study diversity levels of collected germplasm. Field phenomics tools such as the phenonet, phenomobile, and phenonetwork have proven to be efficient in capturing large sums of multiscale and multidimensional experimental data. The main purpose of this review article is to present a summarized account of the probable applications of integrated systems of genomics and phenomics in plant breeding for climate resilience in major crops.

Graphic method for assessing the margins of resistance to acoustic vibrations in the chambers of rocket engines by combustion noise

An experimental method is proposed for estimating the damping decrements of pressure fluctuations in the combustion chambers of forced rocket engines. The method is based on the statistical processing of noise pressure pulsations in the vicinity of natural resonance frequencies for normal modes of acoustic vibrations of the reaction volume and the subsequent prediction of the instability of the combustion process relative to acoustic vibrations. Based on the theory of statistical regression for multidimensional experimental data, the problem of predicting unknown parameters of sample distributions is solved by asymptotic determination of the correlation coefficient of the damping decrement of pressure vibrations through optimal linear predictors and the Kolmogorov distribution. Keywords rocket engine, combustion chamber, acoustic vibrations, combustion noise, spectral characteristics, Kolmogorov criterion, damping decrement. KniaZ988@mail.ru

ПРОГНОЗИРОВАНИЕ СВОЙСТВ МНОГОКОМПОНЕНТНОЙ КЕРАМИКИ НА ОСНОВЕ САМООРГАНИЗУЮЩЕЙСЯ СЕТИ КОХОНЕНА

Рассмотрены информационные возможности метода прогнозирования значений многомерных экспериментальных данных, определенных на неравномерной сетке. Суть метода заключается в использовании самоорганизующейся сети Кохонена для определения качественного влияния независимых параметров в многокомпонентной керамике на основе оксида олова на коэффициент ее нелинейности в задаче улучшения параметров элементов защиты электрических цепей.

Predicting clinical outcome of neuroblastoma patients using an integrative network-based approach

BackgroundOne of the main current challenges in computational biology is to make sense of the huge amounts of multidimensional experimental data that are being produced. For instance, large cohorts of patients are often screened using different high-throughput technologies, effectively producing multiple patient-specific molecular profiles for hundreds or thousands of patients.ResultsWe propose and implement a network-based method that integrates such patient omics data into Patient Similarity Networks. Topological features derived from these networks were then used to predict relevant clinical features. As part of the 2017 CAMDA challenge, we have successfully applied this strategy to a neuroblastoma dataset, consisting of genomic and transcriptomic data. In particular, we observe that models built on our network-based approach perform at least as well as state of the art models. We furthermore explore the effectiveness of various topological features and observe, for instance, that redundant centrality metrics can be combined to build more powerful models.ConclusionWe demonstrate that the networks inferred from omics data contain clinically relevant information and that patient clinical outcomes can be predicted using only network topological data.ReviewersThis article was reviewed by Yang-Yu Liu, Tomislav Smuc and Isabel Nepomuceno.

A Novel Method for Quantifying Human In Situ Whole Brain Deformation under Rotational Loading Using Sonomicrometry.

Traumatic brain injuries (TBI) are one of the least understood injuries to the body. Finite element (FE) models of the brain have been crucial for understanding concussion and for developing injury mitigation systems; however, the experimental brain deformation data currently used to validate these models are limited. The objective of this study was to develop a methodology for the investigation of in situ three-dimensional brain deformation during pure rotational loading of the head, using sonomicrometry. Sonomicrometry uses ultrasonic pulses to measure the dynamic distances between piezoelectric crystals implanted in any sound-transmitting media. A human cadaveric head-neck specimen was acquired 14 h postmortem and was instrumented with an array of 32 small sonomicrometry crystals embedded in the head: 24 crystals were implanted in the brain, and 8 were fixed to the inner skull. A dynamic rotation was then applied to the head using a closed-loop controlled test device. Four pulses with different severity levels were applied around three orthogonal anatomical axes of rotation. A repeated test of the highest severity rotation was conducted in each axis to assess repeatability. All tests were completed within 56 h postmortem. Overall, the combined experimental and sonomicrometry methods were demonstrated to reliably and repeatedly capture three-dimensional dynamic deformation of an intact human brain. These methods provide a framework for using sonomicrometry to acquire multidimensional experimental data required for FE model development and validation, and will lend insight into the deformations sustained by the brain during impact.

Development of wall and interfacial friction models for two-dimensional film flow with local measurement methods

Abstract Based on the advancement of computational capability, high-precision analyses of multi-dimensional thermal hydraulic phenomena in nuclear power plants have been carried out. One of the multi-dimensional phenomena is two-phase flow in the upper downcomer. The quantification of momentum transfer between a downward liquid flow and a transverse gas flow in the reflood phase is significant because it determines the bypass flow rate of the emergency core coolant (ECC). Multi-dimensional modules of thermal-hydraulic analysis codes have been used to simulate this multi-dimensional two-phase flow. However, the model and correlations incorporated in the multi-dimensional modules are ones developed from one-dimensional experimental results. Because the characteristics of multi-dimensional phenomena are different from one-dimensional conditions, the implemented models and correlations might produce inaccurate results. Therefore, new models based on multi-dimensional experimental data should be developed. This study involved the twodimensional, two-phase experiments performed using 1/10 and 1/5 scale facilities. These were simplified unfolded downcomers of the Advanced Power Reactor 1400 (APR1400). The local measurement methods, pitot tubes, ultrasonic thickness gauge, and depth-averaged PIV, were applied to measure local variables: air velocity, liquid film velocity, and liquid film thickness. Local experimental data on the two-dimensional film flow were used to produce the wall and to inform interfacial friction factors from two-dimensional, two-phase momentum conservation equations. New wall and interfacial friction models were developed incorporating newly proposed physical concepts.

An averaging based tube model for deformation induced anisotropic stress softening of filled elastomers

In this paper, a micromechanically based constitutive model capturing anisotropic stress softening in reinforced elastomers under quasi-static loading is presented. A novel spatial distribution function of polymer chains taking into account its deformation induced anisotropic alignment is proposed. By this means, the anisotropic network averaging over the unit sphere can be evaluated analytically. The anisotropic alignment of polymer chains introduces non-affine deformation in the model. Furthermore, the anisotropic evolution of the Mullins effect and hysteresis are also derived analytically, so that no numerical integration is applied here. The model includes very few physically motivated material parameters and demonstrates good agreement with multi-dimensional experimental data as well as with molecular dynamics simulations.

Acceleratingk-nearest-neighbor searches

The search for whichkpoints are closest to a given probe point in a space ofNknown points, the `k-nearest-neighbor' or `KNN' problem, is a computationally challenging problem of importance in many disciplines, such as the design of numerical databases, analysis of multi-dimensional experimental data sets, multi-particle simulations and data mining. A standard approach is to preprocess the data into a tree and make use of the triangle inequality to prune the search time to the order of the logarithm ofNfor a single nearest point in a well balanced tree. All known approaches suffer from the `curse of dimensionality', which causes the search to explore many more branches of the tree than one might wish as the dimensionality of the problem increases, driving search times closer to the order ofN. Looking forknearest points can sometimes be done in approximately the time needed to search for one nearest point, but more often it requiresksearches because the results are distributed widely. The result is very long search times, especially when the search radius is large andkis large, and individual distance calculations are very expensive, because the same probe-to-data-point distance calculations need to be executed repeatedly as the top of the tree is re-explored. Combining two acceleration techniques was found to improve the search time dramatically: (i) organizing the search into nested searches in non-overlapping annuli of increasing radii, using an estimation of the Hausdorff dimension applicable to this data instance from the results of earlier annuli to help set the radius of the next annulus; and (ii) caching all distance calculations involving the probe point to reduce the cost of repeated use of the same distances. The result of this acceleration in a search of the combined macromolecular and small-molecule data in a combined six-dimensional database of nearly 900 000 entries has been an improvement in the overall time of the searches by one to two orders of magnitude.

Modeling stochastic phenotype switching and bet‐hedging in bacteria: stochastic nonlinear dynamics and critical state identification

Fluctuating environments pose tremendous challenges to bacterial populations. It is observed in numerous bacterial species that individual cells can stochastically switch among multiple phenotypes for the population to survive in rapidly changing environments. This kind of phenotypic heterogeneity with stochastic phenotype switching is generally understood to be an adaptive bet‐hedging strategy. Mathematical models are essential to gain a deeper insight into the principle behind bet‐hedging and the pattern behind experimental data. Traditional deterministic models cannot provide a correct description of stochastic phenotype switching and bet‐hedging, and traditional Markov chain models at the cellular level fail to explain their underlying molecular mechanisms. In this paper, we propose a nonlinear stochastic model of multistable bacterial systems at the molecular level. It turns out that our model not only provides a clear description of stochastic phenotype switching and bet‐hedging within isogenic bacterial populations, but also provides a deeper insight into the analysis of multidimensional experimental data. Moreover, we use some deep mathematical theories to show that our stochastic model and traditional Markov chain models are essentially consistent and reflect the dynamic behavior of the bacterial system at two different time scales. In addition, we provide a quantitative characterization of the critical state of multistable bacterial systems and develop an effective data‐driven method to identify the critical state without resorting to specific mathematical models.

A Three-Dimensional Inverse Finite Element Analysis of the Heel Pad

Quantification of plantar tissue behavior of the heel pad is essential in developing computational models for predictive analysis of preventive treatment options such as footwear for patients with diabetes. Simulation based studies in the past have generally adopted heel pad properties from the literature, in return using heel-specific geometry with material properties of a different heel. In exceptional cases, patient-specific material characterization was performed with simplified two-dimensional models, without further evaluation of a heel-specific response under different loading conditions. The aim of this study was to conduct an inverse finite element analysis of the heel in order to calculate heel-specific material properties in situ. Multidimensional experimental data available from a previous cadaver study by Erdemir et al. ("An Elaborate Data Set Characterizing the Mechanical Response of the Foot," ASME J. Biomech. Eng., 131(9), pp. 094502) was used for model development, optimization, and evaluation of material properties. A specimen-specific three-dimensional finite element representation was developed. Heel pad material properties were determined using inverse finite element analysis by fitting the model behavior to the experimental data. Compression dominant loading, applied using a spherical indenter, was used for optimization of the material properties. The optimized material properties were evaluated through simulations representative of a combined loading scenario (compression and anterior-posterior shear) with a spherical indenter and also of a compression dominant loading applied using an elevated platform. Optimized heel pad material coefficients were 0.001084 MPa (μ), 9.780 (α) (with an effective Poisson's ratio (ν) of 0.475), for a first-order nearly incompressible Ogden material model. The model predicted structural response of the heel pad was in good agreement for both the optimization (<1.05% maximum tool force, 0.9% maximum tool displacement) and validation cases (6.5% maximum tool force, 15% maximum tool displacement). The inverse analysis successfully predicted the material properties for the given specimen-specific heel pad using the experimental data for the specimen. The modeling framework and results can be used for accurate predictions of the three-dimensional interaction of the heel pad with its surroundings.

Study on Linear Correlation Coefficient and Nonlinear Correlation Coefficient in Mathematical Statistics

In the two-dimensional or multidimensional experimental data in the traditional statistics, there is usually a linear relationship, or a similar linear relationship between independent variables and the dependent variable. Commonly the linear correlation coefficient is used to measure the degree of linear between the independent variables and the dependent variable. However, for the two-dimensional or multidimensional experimental data, there may be a simple linear relationship between independent variables and the dependent variable, or a simple non-linear relationship, or both linear and non-linear relationship. Article [1] found that the traditional correlation coefficient (linear correlation coefficient) r is only suitable for simple linear relationship. On the basis of article [1] , this article discusses the linear correlation coefficient r , analyzes nonlinear correlation coefficient r nl , and gives a new definition of the correlation coefficient R . The new correlation coefficient R can not only describe the case of a simple linear relationship, but also describe the case of a simple nonlinear relationship and the case of both simple linear relationship and nonlinear relationship. That is to say, the new correlation coefficient R can describe the internal law of any experimental data.

SVM classifier to predict genes important for self-renewal and pluripotency of mouse embryonic stem cells

BackgroundMouse embryonic stem cells (mESCs) are derived from the inner cell mass of a developing blastocyst and can be cultured indefinitely in-vitro. Their distinct features are their ability to self-renew and to differentiate to all adult cell types. Genes that maintain mESCs self-renewal and pluripotency identity are of interest to stem cell biologists. Although significant steps have been made toward the identification and characterization of such genes, the list is still incomplete and controversial. For example, the overlap among candidate self-renewal and pluripotency genes across different RNAi screens is surprisingly small. Meanwhile, machine learning approaches have been used to analyze multi-dimensional experimental data and integrate results from many studies, yet they have not been applied to specifically tackle the task of predicting and classifying self-renewal and pluripotency gene membership.ResultsFor this study we developed a classifier, a supervised machine learning framework for predicting self-renewal and pluripotency mESCs stemness membership genes (MSMG) using support vector machines (SVM). The data used to train the classifier was derived from mESCs-related studies using mRNA microarrays, measuring gene expression in various stages of early differentiation, as well as ChIP-seq studies applied to mESCs profiling genome-wide binding of key transcription factors, such as Nanog, Oct4, and Sox2, to the regulatory regions of other genes. Comparison to other classification methods using the leave-one-out cross-validation method was employed to evaluate the accuracy and generality of the classification. Finally, two sets of candidate genes from genome-wide RNA interference screens are used to test the generality and potential application of the classifier.ConclusionsOur results reveal that an SVM approach can be useful for prioritizing genes for functional validation experiments and complement the analyses of high-throughput profiling experimental data in stem cell research.

Deming least-squares fit to multiple hyperplanes

A method is derived to fit a set of multidimensional experimental data points having a priori uncertainties and possibly also covariances in all coordinates to a straight line, plane, or hyperplane of any dimensionality less than the number of coordinates. The least-squares formulation used is that of Deming, which treats all coordinates on an equal basis. Experimentalists needing to fit a linear model to data of this kind have usually performed multiple independent fits in subspaces of the full data space such that each fit has only one dependent coordinate. That procedure does not guarantee mutual consistency of the fits. The present method can be thought of as providing multiple such hyperplane fits in a single simultaneous and therefore consistent solution. As examples, the method is applied to a straight-line fit in three dimensions to synthetic data and to an analysis of xenon isotopes in a lunar rock.

Quantifying the contributions of structure to annulus fibrosus mechanical function using a nonlinear, anisotropic, hyperelastic model

The annulus fibrosus of the intervertebral disc is comprised of concentric lamella of oriented collagen fibers embedded in a hydrated proteoglycan matrix with smaller amounts of minor collagens, elastin, and small proteoglycans. Its structure and composition enable the disc to withstand complex loads and result in inhomogeneous, anisotropic, and nonlinear mechanical behaviors. The specific contributions of the annulus fibrosus constituent structures to mechanical function remain unclear. Therefore, the objective of this study was to use a structurally motivated, anisotropic, nonlinear strain energy model of annulus fibrosus to determine the relative contributions of its structural components to tissue mechanical behavior. A nonlinear, orthotropic hyperelastic model was developed for the annulus fibrosus. Terms to describe fibers, matrix, and interactions between annulus fibrosus structures (shear and normal to the fiber directions) were explicitly included. The contributions of these structures were analyzed by including or removing terms and determining the effect on the fit to multidimensional experimental data. Correlation between experimental and model-predicted stress, a Bland-Altman analysis of bias and standard deviation of residuals, and the contribution of structural terms to overall tissue stress were calculated. Both shear and normal interaction terms were necessary to accurately model multidimensional behavior. Inclusion of shear interactions more accurately described annulus fibrosus nonlinearity. Fiber stretch and shear interactions dominated contributions to circumferential direction stress, while normal and shear interactions dominated axial stress. The results suggest that interactions between fibers and matrix, perhaps facilitated by crosslinks, elastin, or minor collagens, augment traditional (i.e., fiber-uncrimping) models of nonlinearity.

Simple method for smoothing multidimensional experimental data with application to the CHF and postdryout look-up tables

Simple method for smoothing multidimensional experimental data with application to the CHF and postdryout look-up tables