Scalar Factor Research Articles

Permutation Test for Image-on-Scalar Regression With an Application to Breast Cancer.

Image based screening is now routinely available for early detection of cancer and other diseases. Quantitative analysis for effects of risk factors on digital images is important to extract biological insights for modifiable factors in prevention studies and understand pathways for targets in preventive drugs. However, current approaches are restricted to summary measures within the image with the assumption that all relevant features needed to characterize an image can be identified and appropriately quantified. Motivated by data challenges in breast cancer, we propose a nonparametric statistical framework for risk factor screening that uses the whole mammogram image as outcome. The proposed permutation test allows assessment of whether a set of scalar risk factors is associated with the whole image in the presence of correlated residuals across the spatial domain. We provide extensive simulation studies and illustrate an application to the Joanne Knight Breast Health Cohort using the mammogram imaging data.

Data generation and training of surrogate models for friction factor and Nusselt number in low Reynolds number flows through pin fin geometries

Abstract The design of various biomedical, electronics cooling, and microfluidic devices relies on geometry-specific models and empirical correlations for flow and heat transfer through microscale pin fin geometries. Machine learning techniques are being used across many branches of science to develop more generalized surrogate models that can predict such transport processes. To collapse the simulation of flow and thermal properties across many different pin fin surfaces into a single predictive tool, the present study develops machine-learning-based surrogate models for the friction factor and Nusselt number (for constant wall temperature conditions) for fully developed low Reynolds number flow across pin fin geometries of differing cross-section shape (circular, square, triangular) in aligned or staggered arrangements, oriented at any angle to the incoming flow, and for a range of transverse and longitudinal pitches, with water as the working fluid. The model training data are generated using an automated workflow that allows thousands of numerical simulations to be carried out on across different geometric and flow configurations. A total of ~14,800 distinct simulation cases, for both friction factor and Nusselt number, are generated whilst varying the Reynolds number and aforementioned geometric parameters to train and test the machine learning models. The machine learning model architecture takes inputs of both image and vector data, and then outputs a scalar friction factor or Nusselt number. The trained models yield a goodness of fit (R2) value of 0.98 on unseen data.

Fiber Microstructure Quantile (FMQ) Regression: A Novel Statistical Approach for Analyzing White Matter Bundles from Periphery to Core.

The structural connections of the brain's white matter are critical for brain function. Diffusion MRI tractography enables the in-vivo reconstruction of white matter fiber bundles and the study of their relationship to covariates of interest, such as neurobehavioral or clinical factors. In this work, we introduce Fiber Microstructure Quantile (FMQ) Regression, a new statistical approach for studying the association between white matter fiber bundles and scalar factors (e.g., cognitive scores). Our approach analyzes tissue microstructure measures based on quantile-specific bundle regions . These regions are defined according to the quantiles of fractional anisotropy (FA) from the periphery to the core of a population fiber bundle, which pools all individuals' bundles. To investigate how fiber bundle tissue microstructure relates to covariates of interest, we employ the statistical technique of quantile regression. Unlike ordinary regression, which only models a conditional mean, quantile regression models the conditional quantiles of a response variable. This enables the proposed analysis, where a quantile regression is fitted for each quantile-specific bundle region. To demonstrate FMQ Regression, we perform an illustrative study in a large healthy young adult tractography dataset derived from the Human Connectome Project-Young Adult (HCP-YA), focusing on particular bundles expected to relate to particular aspects of cognition and motor function. Importantly, our analysis considers sex-specific effects in brain-behavior associations. In comparison with a traditional method, Automated Fiber Quantification (AFQ), which enables FA analysis in regions defined along the trajectory of a bundle, our results suggest that FMQ Regression is much more powerful for detecting brain-behavior associations. Importantly, FMQ Regression finds significant brain-behavior associations in multiple bundles, including findings unique to males or to females. In both males and females, language performance is significantly associated with FA in the left arcuate fasciculus, with stronger associations in the bundle's periphery. In males only, memory performance is significantly associated with FA in the left uncinate fasciculus, particularly in intermediate regions of the bundle. In females only, motor performance is significantly associated with FA in the left and right corticospinal tracts, with a slightly lower relationship at the bundle periphery and a slightly higher relationship toward the bundle core. No significant relationships are found between executive function and cingulum bundle FA. Our study demonstrates that FMQ Regression is a powerful statistical approach that can provide insight into associations from bundle periphery to bundle core. Our results also identify several brain-behavior relationships unique to males or to females, highlighting the importance of considering sex differences in future research.

High-precision identification and compensation of nonlinear error in hemispherical resonator gyro

This paper presents a novel nonlinear error identification and compensation method for the Hemispherical Resonator Gyro (HRG) from the signal processing perspective. Firstly, the paper establishes an HRG nonlinear error model that reveals the quantitative correlation between angle measurement error and the amplitude-gap ratio. Subsequently, a dynamic analysis model for gyro drift is developed using nonlinear motion equations. Based on this, a scalar factor nonlinear identification model encompassing assembly and nonlinear errors is proposed. Nonlinear optimization is then used to identify error parameters accurately. Finally, a joint compensation method is devised to mitigate assembly and nonlinear error issues. Empirical findings provide concrete validation for the precision of the identification and compensation method. The experimental results demonstrate that reductions of 97%, 89%, and 40% after the joint compensation are achieved in the fourth harmonic component, scale factor nonlinearity, and bias instability of the gyro, respectively.

Machine learning based tool for the efficient estimation of geometric features of aggregated aerosol particles

While significant progress has been made in developing models for the formation and transport of aerosol aggregates, there is still a need for a simple, versatile tool capable of estimating intrinsic properties of aggregated particles. Scalar friction factor is an important parameter used extensively in the field of aerosol science. The scalar friction factor for non-spherical particles can be computed with the information on two geometric parameters, hydrodynamic radius (Rh) and orientationally averaged projected area (PA), depending on the momentum transfer regime. Although the existing methods for the estimation of these descriptors are efficient, many applications involve frequent estimation of these geometric descriptors, which can be time-consuming. We propose a Machine Learning (ML) based tool that can predict these descriptors using Fractal Dimension, pre-exponential factor, number of monomers and anisotropy factors as the input. An extensive database comprising fractal parameters, anisotropy factors, Rh, and PA is developed for testing and training the ML models. Five ML methods were assessed, with random forest (RF) identified as the most effective. The RF model demonstrated high accuracy in the testing phase, with R-squared value of 0.9875 for Rh and 0.9979 for PA, and average errors of 3.17% and 1.21% for Rh and PA, respectively. The predicted Rh and PA values were then used to estimate other relevant 3-dimensional properties such as mobility diameter, shape factor, and aerodynamic diameter, with the results indicating high accuracy of the prediction tool. Python-based tool offers ease of use, and can be easily integrated with other numerical codes.

The Fatigue and Altered Cognition Scale among SARS-CoV-2 Survivors: Psychometric Properties and Item Correlations with Depression and Anxiety Symptoms.

Background/Objectives: This study examined the psychometric properties of the Fatigue and Altered Cognition Scale (FACs) among adult COVID-19 survivors and its unique ability to assess symptomology not accounted for by measures of depression and anxiety. Methods: COVID-19 survivors completed an online survey that included the FACs, a measure of brain fog and central fatigue with 20 items rated on a digital-analog scale. Useable data from 559 participants were analyzed to test the two-factor structure of the FACs, test for measurement invariance by sex and device was used to complete the survey (hand-held, computer), and item correlations with symptoms of depression and anxiety were examined. Results: The two-factor structure of the FACs replicated, supporting the separate assessments of brain fog and fatigue, χ2(164) = 1028.363, p < 0.001, CFI = 0.934, TLI = 0.923, RMSEA = 0.097, SRMR = 0.053. The FACs exhibited invariance at the scalar level, indicating item and factor integrity regardless of sex and device type. Using a correlation > 0.70 as a criterion (i.e., indicating more than 50% shared variance between two items), items on the FACs (assessing fatigue and lack of energy) were highly correlated with feeling tired or having little energy on the depression measure. No other items correlated with any anxiety symptom larger than 0.70. Conclusions: The FACs appears to be a psychometrically sound and efficient measure for use with COVID-19 survivors, assessing symptoms of brain fog and central fatigue that are not attributable to symptoms assessed by established measures of depression and anxiety.

Exploring cutoff points and measurement invariance of the Brunnsviken brief quality of life inventory.

Quality of life (QoL) can be defined as the goodness of life, beyond simply absence of disease or functional impairments, self-rating scales of which capture valuable information beyond change in primary outcomes. This study (n = 3,384) validated the Brunnsviken Brief Quality of Life Inventory (BBQ) across divergent groups by evaluating its measurement invariance (MI). We hypothesized measurement invariance for the BBQ across age groups, genders, depression, and anxiety severity. Potential cutoff points for the BBQ were also explored. Confirmatory factor analysis (CFA) models were fit to sample data obtained from an ongoing study on transdiagnostic internet-based treatment modules. Parameters were successively constrained to assess configural, metric, scalar, and residual invariance factor structures across different groups. The BBQ demonstrated MI at the metric level and partial MI at the scalar level across all these groups, which remained stable at the strict-residual level for all groups except for genders. These results remained stable after correcting for unbalanced group sizes for gender, clinical-subclinical levels of depression, and clinical-subclinical levels of anxiety. A cutoff point analysis revealed that a BBQ total scores below 39 was associated with notable psychopathology. The BBQ is a reliable measure of QoL that is applicable for various divergent groups (e.g., vulnerable persons), and thus a viable instrument for use in healthcare and research with minimal aversive impact.Clinical trial registration: NCT05016843.

Bauer’s spectral factorization method for low order multiwavelet filter design

Para-Hermitian polynomial matrices obtained by matrix spectral factorization lead to functions useful in control theory systems, basis functions in numerical methods or multiscaling functions used in signal processing. We introduce a fast algorithm for matrix spectral factorization based on Bauer’s method. We convert Bauer’s method into a nonlinear matrix equation (NME). The NME is solved by two different numerical algorithms (Fixed Point Iteration and Newton’s Method) which produce approximate scalar or matrix factors, as well as a symbolic algorithm which produces exact factors in closed form for some low-order scalar or matrix polynomial matrices, respectively. Convergence rates of the two numerical algorithms are investigated for a number of singular and nonsingular scalar and matrix polynomials taken from different areas. In particular, one of the singular examples leads to new orthogonal multiscaling and multiwavelet filters. Since the NME can also be solved as a Generalized Discrete Time Algebraic Riccati Equation (GDARE), numerical results using built-in routines in Maple 17.0 and six Matlab versions are presented.

Analysis of the Influence of the Parametric Scalar Factor in the Viscoplastic Equation for Determining Intragranular Shear Rates on the Response in Multilevel Constitutive Models of Metals

Analysis of the Influence of the Parametric Scalar Factor in the Viscoplastic Equation for Determining Intragranular Shear Rates on the Response in Multilevel Constitutive Models of Metals

CONSTRUCTION OF THE SOLUTION OF THE SYSTEM OF SINGULARLY PERTURBATED DIFFERENTIAL EQUATIONS WITH A DIFFERENTIAL TURNING POINT

In this work, a system of singularly perturbed differential equations of the 4th order with a small parameter at the highest derivative and a turning point is considered. The turning point x=0 is located in the end of the segment [-l;0] under consideration. The coefficients of a given matrix are infinitely differentiable functions on a given interval. The goal is to construct a uniform solution asymptotics for a system of singularly perturbed differential equations with a differential turning point on the segment [-l;0]. In this case, the spectrum of the limit operator contains multiple and identically zero elements. The uniform asymptotic solution is constructed by the method of essential-singular functions using the Airy functions [0;l] and their derivatives. Studies have shown that the Apparatus of Airy functions and model equations is quite effective for constructing a uniform asymptotic solution of problems with turning points. It was also established that in order to select these functions along with the independent variable it is necessary to introduce a new variable t of the segment [0;l]. As a result, an extended problem will be obtained, which will make it possible to formally find the solution in the form of series with a small parameter. The constructions of the solutions are obtained by sequentially solving the systems of iterative equations, which at a certain step of the iterations make it possible to determine all the components of the sought-after vector functions with an accuracy of two scalar factors that form an arbitrary vector. The regularizing function Bi(t) is chosen in such a way that the function increases indefinitely when t approaches the infinity. The conducted studies showed that for any ratio of the signs of the matrix coefficient near which the inflection point is located, it is not possible to write down a smooth solution in the form of a single analytical expression. The solution of a degenerate vector equation in the general case has a discontinuity of the second kind at the inflection point, so it cannot be used explicitly to construct the asymptotic solution of this problem. For this purpose, a technique from the classical theory of linear differential equations was applied and solutions for a degenerate equation of the 2nd order were obtained.

Synthetic white balancing for intra-operative hyperspectral imaging.

Hyperspectral imaging shows promise for surgical applications to non-invasively provide spatially resolved, spectral information. For calibration purposes, a white reference image of a highly reflective Lambertian surface should be obtained under the same imaging conditions. Standard white references are not sterilizable and so are unsuitable for surgical environments. We demonstrate the necessity for in situ white references and address this by proposing a novel, sterile, synthetic reference construction algorithm. The use of references obtained at different distances and lighting conditions to the subject were examined. Spectral and color reconstructions were compared with standard measurements qualitatively and quantitatively, using and normalized RMSE, respectively. The algorithm forms a composite image from a video of a standard sterile ruler, whose imperfect reflectivity is compensated for. The reference is modeled as the product of independent spatial and spectral components, and a scalar factor accounting for gain, exposure, and light intensity. Evaluation of synthetic references against ideal but non-sterile references is performed using the same metrics alongside pixel-by-pixel errors. Finally, intraoperative integration is assessed though cadaveric experiments. Improper white balancing leads to increases in all quantitative and qualitative errors. Synthetic references achieve median pixel-by-pixel errors lower than 6.5% and produce similar reconstructions and errors to an ideal reference. The algorithm integrated well into surgical workflow, achieving median pixel-by-pixel errors of 4.77% while maintaining good spectral and color reconstruction. We demonstrate the importance of in situ white referencing and present a novel synthetic referencing algorithm. This algorithm is suitable for surgery while maintaining the quality of classical data reconstruction.

Dynamics of cosmological model with domain walls and massive scalar fields in f(R,T) gravity

A spatially homogenous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I space-time is considered in the presence of a massive scalar field containing domain walls in the framework of the [Formula: see text] gravity proposed by Harko et al. [Phys. Rev. D 84, 024020, (2011)]. Solving the field equations of the model using a relation between metric potentials and power law between the scalar field and average scale factor of the model, an anisotropic cosmological model with massive scalar fields and domain walls in [Formula: see text] theory is presented. These conditions result in a model solution that provides a dynamic deceleration parameter. The model’s geometrical and physical properties are also examined. The universe exhibits a smooth transition from its early decelerated phase to its current accelerated phase, as shown by the study of the deceleration parameter. The statefinder plane corresponds to the Chaplygin gas era and the model finally approaches [Formula: see text]CDM model.

Day-ahead photovoltaic power forecasting using hybrid K-Means++ and improved deep neural network

The relationship between environmental factors with the power output of photovoltaic (PV) stations is unclear due to the non-linear characteristics of PV systems, which is challenging for PV power forecasting technology. To cope with these challenges, a hybrid forecasting approach called hybrid K-Means++ and Deep Neural Network with input and output adjusting structures (K-IAOA-DNN) is proposed to accurately predict PV power output. The proposed forecasting approach designs several features for K-Means++ to search for similar samples, reducing the complexity of the following forecasting model. Due to changeable environmental conditions and characteristics of PV systems like degradation, the prediction result of a forecasting model may deviate from the expected one. Therefore, IAOA-DNN model is developed by using a DNN adopting the two proposed structures e.g., the input adjusting structure and the output adjusting structure. The input adjusting structure uses several trainable parameters to determine the importance of each meteorological input for further feature extracting by DNN. The output structure in the prediction model is used for analyzing features extracted from DNN to generate a scalar factor fine-tuning the output of DNN. Additionally, the proposed method provides more accurate forecasting results with average RMSE, NRMSE, and MAE values of 14.43, 0.048, and 9.53 kW, respectively.

Determining the linear correlation between dielectric spectroscopy and viable biomass concentration in filamentous fungal fermentations

ObjectivesDielectric spectroscopy is commonly used for online monitoring of biomass growth. It is however not utilized for biomass concentration measurements due to poor correlation with Cell Dry Weight (CDW). A calibration methodology is developed that can directly measure viable biomass concentration in a commercial filamentous process using dielectric values, without recourse to independent and challenging viability determinations.ResultsThe methodology is applied to samples from the industrial scale fermentation of a filamentous fungus, Acremonium fusidioides. By mixing fresh and heat-killed samples, linear responses were verified and sample viability could be fitted with the dielectric Delta C values and total solids concentration. The study included a total of 26 samples across 21 different cultivations, with a legacy at-line viable cell analyzer requiring 2 ml samples, and a modern on-line probe operated at-line with 2 different sample presentation volumes, one compatible with the legacy analyzer, a larger sample volume of 100 ml being compatible with calibration for on-line operation. The linear model provided an {R}^{2} value of 0.99 between Delta C and viable biomass across the sample set using either instrument. The difference in ∆C when analyzing 100 mL and 2 mL samples with an in-line probe can be adjusted by a scalar factor of 1.33 within the microbial system used in this study, preserving the linear relation with {R}^{2} of 0.97.ConclusionsIt is possible to directly estimate viable biomass concentrations utilizing dielectric spectroscopy without recourse to extensive and difficult to execute independent viability studies. The same method can be applied to calibrate different instruments to measure viable biomass concentration. Small sample volumes are appropriate as long as the sample volumes are kept consistent.

Exact Bianchi type-I inflationary model with non-minimally coupled scalar field

In the present work, we try to build up an inflationary model within the framework of Bianchi type-I spacetime using a non-minimally coupled, homogeneous, self-interacting canonical scalar field. Specifically, using the Lie symmetry method, we are able to find some novel exact solutions to the Einstein field equations by assuming a power-law relationship between the scalar field and average scale factor. These symmetry-based solutions have been used to derive the values of some important parameters of the anisotropic universe. In this anisotropic model, we find that the volume of space expands with time in an inflationary scenario, depicting the Universe’s accelerating phases. An important characteristic of this model is that it initially represents anisotropic spacetime and then isotropizes the spacetime as time goes on, which favors recent cosmological observations.

Asymptotics of matrix valued orthogonal polynomials on [−1,1

We analyze the large degree asymptotic behavior of matrix valued orthogonal polynomials (MVOPs), with a weight that consists of a Jacobi scalar factor and a matrix part. Using the Riemann–Hilbert formulation for MVOPs and the Deift–Zhou method of steepest descent, we obtain asymptotic expansions for the MVOPs as the degree tends to infinity, in different regions of the complex plane (outside the interval of orthogonality, on the interval away from the endpoints and in neighborhoods of the endpoints), as well as for the matrix coefficients in the three-term recurrence relation for these MVOPs. The asymptotic analysis follows the work of Kuijlaars, McLaughlin, Van Assche and Vanlessen on scalar Jacobi-type orthogonal polynomials, but it also requires several different factorizations of the matrix part of the weight, in terms of eigenvalues/eigenvectors and using a matrix Szegő function. We illustrate the results with two main examples, MVOPs of Jacobi and Gegenbauer type, coming from group theory.

Factor models for high‐dimensional functional time series II: Estimation and forecasting

This article is the second one in a set of two laying the theoretical foundations for a high‐dimensional functional factor model approach in the analysis of large cross‐sections (panels) of functional time series (FTS). Part I establishes a representation result by which, under mild assumptions on the covariance operator of the cross‐section, any FTS admits a canonical representation as the sum of a common and an idiosyncratic component; common components are driven by a finite and typically small number of scalar factors loaded via functional loadings, while idiosyncratic components are only mildly cross‐correlated. Building on that representation result, Part II is dealing with the identification of the number of factors, their estimation, the estimation of their loadings and the common components, and the resulting forecasts. We provide a family of information criteria for identifying the number of factors, and prove their consistency. We provide average error bounds for the estimators of the factors, loadings, and common components; our results encompass the scalar case, for which they reproduce and extend, under weaker conditions, well‐established similar results. Under slightly stronger assumptions, we also provide uniform bounds for the estimators of factors, loadings, and common components, thus extending existing scalar results. Our consistency results in the asymptotic regime where the number of series and the number of time points diverge thus extend to the functional context the ‘blessing of dimensionality’ that explains the success of factor models in the analysis of high‐dimensional (scalar) time series. We provide numerical illustrations that corroborate the convergence rates predicted by the theory, and provide a finer understanding of the interplay between and for estimation purposes. We conclude with an application to forecasting mortality curves, where our approach outperforms existing methods.

Factor models for high‐dimensional functional time series I: Representation results

In this article, which consists of two parts (Part I: representation results; Part II: estimation and forecasting methods), we set up the theoretical foundations for a high‐dimensional functional factor model approach in the analysis of large cross‐sections (panels) of functional time series (FTS). In Part I, we establish a representation result stating that, under mild assumptions on the covariance operator of the cross‐section, we can represent each FTS as the sum of a common component driven by scalar factors loaded via functional loadings, and a mildly cross‐correlated idiosyncratic component. Our model and theory are developed in a general Hilbert space setting that allows for mixed panels of functional and scalar time series. We then turn, in Part II, to the identification of the number of factors, and the estimation of the factors, their loadings, and the common components. We provide a family of information criteria for identifying the number of factors, and prove their consistency. We provide average error bounds for the estimators of the factors, loadings, and common components; our results encompass the scalar case, for which they reproduce and extend, under weaker conditions, well‐established similar results. Under slightly stronger assumptions, we also provide uniform bounds for the estimators of factors, loadings, and common components, thus extending existing scalar results. Our consistency results in the asymptotic regime where the number of series and the number of time observations diverge thus extend to the functional context the ‘blessing of dimensionality’ that explains the success of factor models in the analysis of high‐dimensional (scalar) time series. We provide numerical illustrations that corroborate the convergence rates predicted by the theory, and provide a finer understanding of the interplay between and for estimation purposes. We conclude with an application to forecasting mortality curves, where we demonstrate that our approach outperforms existing methods.

Robust Unscented Kalman Filter-Based Decentralized Multisensor Information Fusion for INS/GNSS/CNS Integration in Hypersonic Vehicle Navigation

INS/GNSS/CNS (inertial navigation system/global navigation satellite system/celestial navigation system) integration is a favourable navigation mode for hypersonic vehicles. However, since the measurements from GNSS and CNS are easily interfered during highly dynamic maneuvers, this integration is very difficult to achieve optimal navigation solution with existing information fusion techniques. This paper proposes a new method of decentralized multi-sensor information fusion based on robust UKF (unscented Kalman filter) for INS/GNSS/CNS integration to solve the above issue. Firstly, a fault detection-based robust UKF is established for local state estimation, in which a hypothesis test is constructed via the Mahalanobis distance of innovation to detect abnormal measurements in GNSS and CNS; and subsequently, a scalar factor is determined and further introduced into the innovation covariance to decrease the Kalman gain to improve the UKF robustness against abnormal measurements. Secondly, the traditional multi-sensor optimal data fusion technique is extended to nonlinear systems by use of unscented transformation in the framework of minimum variance estimation to fuse the local state estimations from INS/GNSS and INS/CNS subsystems. The proposed information fusion method can achieve the globally optimal fusion estimation results against abnormal measurements for hypersonic vehicle navigation with INS/GNSS/CNS integration. Semi-physical simulations and comparison analysis have validated the superior performance of the proposed method.

Anisotropic massive scalar field model with domain walls in f(R, T) gravity

The Bianchi type-V universe with massive scalar fields and domain walls examined within f(R, T) theory of gravity described by Harko et al. (Phys. Rev. D. 84, 024020, 2011). Solving the field equations of the theory using a power law relation between the scalar field and average scale factor of the model we have presented an anisotropic massive scalar field model in this modified theory of gravity. In light of the recent scenario of the universe expanding at an accelerated rate and cosmological observations, we computed the cosmological parameters like energy density, pressure, deceleration parameter (q), statefinder parameters (r,s), and r-q plane of our model and discussed their physical significance.