Nonlinear Least-squares Fitting Research Articles

The Trouble with Free-Water Elimination using Single-Shell Diffusion MRI Data: A Case-Study in Ageing

Abstract Free-water elimination (FWE) modelling for Diffusion Tensor Imaging (DTI) can be used to estimate the free-water (FW) volume fraction, as well as FW-compensated DTI parameters. Single-shell (SS) diffusion MRI acquisitions are more common in clinical cohorts due to time constraints, but the FWE-DTI model is a two-compartment model, hence only well-posed for multi-shell (MS) data. A regularised gradient descent (RGD) method is often applied to SS datasets and has been used to study healthy ageing, Alzheimer’s and Parkinson’s disease, amongst others, largely ignoring the methodological limitations of this approach. In this study, we compared the performance of RGD fitting with SS data, to a non-linear least squares (NLS) fitting applied to MS data, using simulations and data from 620 participants aged 18 to 88 years. Consistent with previous studies, our simulations show that RGD fitting using SS data flattens the relationship between mean diffusivity (MD) estimates and their ground truth values, and introduces an artificial positive correlation between fractional anisotropy (FA) estimates and the underlying tissue ground truth MD. Neither of these biases were observed when NLS fitting was applied to MS data. In human data, a smaller number of significant voxels with positive correlations between MD and age was observed when the RGD SS algorithm was used, which is consistent with the flattening of MD profiles observed in simulations. FW-compensated FA maps produced strikingly different results depending on the method employed: the maps obtained with RGD SS identified some brain areas with a strong positive association with age, while no such positive correlations were found with MS NLS. While similar positive correlations between age and FW-compensated FA maps obtained with SS RGD have been reported, these results are only replicated when the RGD SS was used, suggesting this apparent FA increase was likely an artefact introduced by inappropriate modelling using SS data. Our study, therefore, suggests that previous findings reported in the literature using the RGD approach should be interpreted with extreme care.

Highly accelerated parameter mapping using model-based alternating reconstruction coupling fitting

Objective. A model-based alternating reconstruction coupling fitting, termed Model-based Alternating Reconstruction COupling fitting (MARCO), is proposed for accurate and fast magnetic resonance parameter mapping. Approach. MARCO utilizes the signal model as a regularization by minimizing the bias between the image series and the signal produced by the suitable signal model based on iteratively updated parameter maps when reconstructing. The technique can incorporate prior knowledge of both image series and parameters by adding sparsity constraints. The optimization problem is decomposed into three subproblems and solved through three alternating steps involving reconstruction and nonlinear least-square fitting, which can produce both contrast-weighted images and parameter maps simultaneously. Main results. The algorithm is applied to T 2 mapping with extended phase graph algorithm integrated and validated on undersampled multi-echo spin-echo data from both phantom and in vivo sources. Compared with traditional compressed sensing and model-based methods, the proposed approach yields more accurate T 2 maps with more details at high acceleration factors. Significance. The proposed method provides a basic framework for quantitative MR relaxometry, theoretically applicable to all quantitative MR relaxometry. It has the potential to improve the diagnostic utility of quantitative imaging techniques.

Rapid simultaneous estimation of relaxation rates using multi-echo, multi-contrast MRI

PurposeMulti-echo, multi-contrast methods are increasingly used in dynamic imaging studies to simultaneously quantify R2∗ and R2. To overcome the computational challenges associated with nonlinear least squares (NLSQ) fitting, we propose a generalized linear least squares (LLSQ) solution to rapidly fit R2∗ and R2. MethodsSpin- and gradient-echo (SAGE) data were simulated across T2∗ and T2 values at high (200) and low (20) SNR. Full (four-parameter) and reduced (three-parameter) parameter fits were implemented and compared with both LLSQ and NLSQ fitting. Fit data were compared to ground truth using concordance correlation coefficient (CCC) and coefficient of variation (CV). In vivo SAGE perfusion data were acquired in 20 subjects with relapsing-remitting multiple sclerosis. LLSQ R2∗ and R2, as well as cerebral blood volume (CBV), were compared with the standard NLSQ approach. ResultsAcross all fitting methods, T2∗ was well-fit at high (CCC = 1, CV = 0) and low (CCC ≥ 0.87, CV ≤ 0.08) SNR. Except for short T2∗ values (5–15 ms), T2 was well-fit at high (CCC = 1, CV = 0) and low (CCC ≥ 0.99, CV ≤ 0.03) SNR. In vivo, LLSQ R2∗ and R2 estimates were similar to NLSQ, and there were no differences in R2∗ across fitting methods at high SNR. However, there were some differences at low SNR and for R2 at high and low SNR. In vivo NLSQ and LLSQ three parameter fits performed similarly, as did NLSQ and LLSQ four-parameter fits. LLSQ CBV nearly matched the standard NLSQ method for R2∗- (0.97 ratio) and R2-CBV (0.98 ratio). Voxel-wise whole-brain fitting was faster for LLSQ (3–4 min) than NLSQ (16–18 h). ConclusionsLLSQ reliably fit for R2∗ and R2 in simulated and in vivo data. Use of LLSQ methods reduced the computational demand, enabling rapid estimation of R2∗ and R2.

The effects of chain-length distributions on starch-related properties in waxy rices

Normal rice starch consists of amylopectin and amylose, whose relative amounts and chain-length distributions (CLDs) are major determinants of the digestibility and rheology of cooked rice, and are related to metabolic health and consumer preference. Here, the mechanism of how molecular structural features of pure amylopectin (waxy) starches affect starch properties was explored. Following debranching, chain-length distributions of seven waxy varieties were measured using size-exclusion chromatography, and parameterized using biosynthesis-based models, which involve breaking up the chain-length distribution into contributions from five enzyme sets covering overlapping ranges of chain length; structure-property correlations involving the fifth set were found to be statistically significant. Digestibility was measured in vitro, and parameters for the slower and longer digestion phase quantified using non-linear least-squares fitting. The coefficient for the significant correlation involving amylopectin fine structure for the fifth set was −0.903, while the amounts of amylopectin short and long chains were found to dominate breakdown viscosity (correlation coefficients 0.801 and − 0.911, respectively). This provides a methodology for finding or developing healthier starch in terms of lower digestion rate, while also having acceptable palatability. As rice breeders can to some extent control CLDs, this can help the development of waxy rices with improved properties.

Bias-reduced neural networks for parameter estimation in quantitative MRI.

To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound. We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications. In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as nonlinear least-squares fitting, while state-of-the-art NNs show larger deviations. The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

Version 8 IMK/IAA MIPAS measurements of CFC-11, CFC-12, and HCFC-22

Abstract. The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) on Envisat provided infrared limb emission spectra, which were used to infer global distributions of CFC-11, CFC-12, and HCFC-22. Spectra were analysed using constrained non-linear least-squares fitting. Changes with respect to earlier data versions refer to the use of version 8 spectra, the altitude range where the background continuum is considered, details of the regularization and microwindow selection, and the occasional joint fitting of interfering species, the use of new spectroscopic data, the joint fit of a tangent-height-dependent spectral offset, and the use of 2D temperature fields. In the lower stratosphere the error budget is dominated by uncertainties in spectroscopic data, while above this measurement noise is the leading error source. The vertical resolution of CFC-11 and CFC-12 is 2–3 km near the tropopause, about 4 km at 30 km altitude, and 6–10 km at 50 km. The vertical resolution of HCFC-22 is somewhat coarser, 3–4 km at the tropopause and 10–12 km at 35 km altitude. In the altitude range of interest, the horizontal resolution is typically limited by the horizontal sampling of the measurements, not by the smearing of the retrievals. Horizontal information displacement does not exceed 150 km, which can become an issue only for comparisons with model simulations with high horizontal resolution or localized in situ observations. Along with the regular data product, an alternative representation of the data on a coarser vertical grid is offered. These data can be used without consideration of the averaging kernels. The new data version provides improvement with respect to reduction of biases and improved consistency between the full- and reduced-resolution mission period of MIPAS.

Spectroscopic Monitoring and Modeling Drug Dissolution for Undergraduate Chemistry Curriculum.

The pharmaceutical and medicine manufacturing industry has become the largest industrial sector for the employment of chemists, indicating a need for experiments with a pharmaceutical sciences context in the undergraduate chemistry curriculum. In the pharmaceutical industry, testing drug dissolution is a key analytical task for solid oral dosage forms that is performed in different phases of drug development to test the release behavior of new formulations, ensure consistency between manufacturing lots, and help predict the in vivo absorption of the drug substance after administration. However, there are a limited number of laboratory experiments in dissolution testing developed for the undergraduate chemistry curriculum. To help students obtain hands-on experience in dissolution testing, a protocol has been developed for an undergraduate chemistry laboratory course for students to build a dissolution apparatus, monitor dissolution processes, model the dissolution to extract kinetic parameters, and evaluate the consistency between dissolution curves with FDA regulated methods. Students successfully collected dissolution curves and completed the modeling analysis with nonlinear least-squares fitting. The designed dissolution protocol has been evaluated to have consistency and reproducibility to be implemented in the undergraduate chemistry laboratory curriculum.

Optimization of suspended particulate transport parameters from measured concentration profiles with a new analytical model

The water body’s suspended concentration reflects many coastal environmental indicators, which is important for predicting ecological hazards. The modeling of any concentration in water requires solving the settling-diffusion equation (SDE), and the values of several key input parameters therein (settling velocity ws, eddy diffusivity Ds, and erosion rates p(t)) directly determine the prediction performance. The time-consuming large-scale simulations would benefit if the parameter values could be estimated through available observations in the target sea area. The present work proposes a new optimization method for synchronously estimating the three parameters from limited concentration observations. First, an analytical solution to the one-dimensional vertical (1DV) SDE for suspended concentrations in an unsteady scenario is derived. Second, the near bottom suspended sediment concentration (SSC) profiles are measured with high-resolution observation. Third, the key parameters are optimized through the best fit of the measured SSC profiles and those modeled with the unsteady solution. Nonlinear least square fitting (NLSF) is introduced to judge the best fits automatically. The high-resolution concentration measurements in a specially-designed cylindrical tank experiment using the Yellow River Delta sediments test the proposed method. The method performs well in the initial period of turbulence generation when sediment resuspension is significant. It optimizes p(t), ws, and Ds with reasonable values and uniqueness of their combination. The proposed theory is a practical tool for quickly estimating key substance transport parameters from limited observations; it also has the potential to construct local parametric models to benefit the 3D modeling of coastal substance transport. Although the present work takes SSC as an example, it can be extended to any suspended particulate concentration in the water.

An improved linear prediction evolution algorithm based on topological opposition-based learning for optimization

Prediction-based evolutionary algorithm is one of the emerging category of meta-heuristic optimization techniques. The improved linear prediction evolution algorithm (ILPE) is a recently developed meta-heuristic optimization technique that draws inspiration from non-linear least-square fitting models. This article implements the concept of topological opposition-based learning, which was first applied in grey prediction evolutionary algorithms to the ILPE. In traditional evolutionary algorithms, after employing the mutation and crossover operator, it generates trial populations. The proposed algorithm constructs a new reproduction operator using the non-linear least square fitting model with topological opposition-based learning to generate trial individuals. This reproduction operator considers the population series as a time series and uses the topological opposition-based non-linear least square fitting model to predict the next generation of populations. The efficiency and accuracy of the algorithm are demonstrated through numerical experiments on CEC2014 and CEC2017 benchmark functions. The results of these experiments show that the proposed algorithm is highly effective in solving optimization problems.•An improved linear prediction evolution algorithm based on topological opposition based learning (TILPE) is proposed.•The proposed strategy treat the the population series as a time series.•To validate the efficacy of TILPE, CEC2014 and CEC2017 benchmark functions are used.

Unified Bayesian network for uncertainty quantification of physiological parameters in dynamic contrast enhanced (DCE) MRI of the liver

Objective. Physiological parameter estimation is affected by intrinsic ambiguity in the data such as noise and model inaccuracies. The aim of this work is to provide a deep learning framework for accurate parameter and uncertainty estimates for DCE-MRI in the liver. Approach. Concentration time curves are simulated to train a Bayesian neural network (BNN). Training of the BNN involves minimization of a loss function that jointly minimizes the aleatoric and epistemic uncertainties. Uncertainty estimation is evaluated for different noise levels and for different out of distribution (OD) cases, i.e. where the data during inference differs strongly to the data during training. The accuracy of parameter estimates are compared to a nonlinear least squares (NLLS) fitting in numerical simulations and in vivo data of a patient suffering from hepatic tumor lesions. Main results. BNN achieved lower root-mean-squared-errors (RMSE) than the NLLS for the simulated data. RMSE of BNN was on overage of all noise levels lower by 33% ± 1.9% for k trans, 22% ± 6% for v e and 89% ± 5% for v p than the NLLS. The aleatoric uncertainties of the parameters increased with increasing noise level, whereas the epistemic uncertainty increased when a BNN was evaluated with OD data. For the in vivo data, more robust parameter estimations were obtained by the BNN than the NLLS fit. In addition, the differences between estimated parameters for healthy and tumor regions-of-interest were significant (p < 0.0001). Significance. The proposed framework allowed for accurate parameter estimates for quantitative DCE-MRI. In addition, the BNN provided uncertainty estimates which highlighted cases of high noise and in which the training data did not match the data during inference. This is important for clinical application because it would indicate cases in which the trained model is inadequate and additional training with an adapted training data set is required.

Novel approach to reducing uncertainty of drift estimate in international comparisons of relative humidity scales

International comparisons of relative humidity scales at the highest level are often challenging because of significant drift of the impedance-based transfer standard, which reduces the accuracy of comparison. Comparisons that are shorter or have fewer participants may be less affected by drift, but ultimately require more inter-linking with their inherent irreproducibility to compare all scales internationally. We addressed these issues in a large comparison of 21 laboratories from the European association of national metrology institutes (EURAMET), covering a range from 10%rh to 95%rh at air temperatures from 10 °C to 70 °C. In it, nine state-of-the-art transfer standards drifted on average between 0,6%rh and 1,8%rh, depending on the measurement point, while the participants can achieve calibration uncertainties on average between 0,2%rh and 1,5%rh. To produce useful comparison data even with significantly drifting transfer standards, we carefully planned the topology of the comparison and the number of transfer standards to be able to partly compensate for drift. This paper focuses on the approach we took in analysing the results to minimise the impact of instrument drift on the comparison outcome. We combined the estimated drift of the transfer standards together with the links drawn between the loops into so-called between-set variability. To calculate the reference value, we used an adjusted Paule-Mandel estimate where we modified the model equations to account for the three interlinked loops and solved for them using a non-linear least-squares fitting. This approach reduced the uncertainty in the drift estimates and the uncertainty in evaluated degrees of equivalence at most, but not all, of the measured values. We discuss the advantages of this approach to consider its applicability in future interlaboratory comparisons.

A new tool to derive simultaneously exponent and extremes of power-law distributions

ABSTRACT Many experimental quantities show a power-law distribution p(x) ∝ x−α. In astrophysics, examples are: size distribution of dust grains or luminosity function of galaxies. Such distributions are characterized by the exponent α and by the extremes xminxmax where the distribution extends. There are no mathematical tools that derive the three unknowns at the same time. In general, one estimates a set of α corresponding to different guesses of xminxmax. Then, the best set of values describing the observed data is selected a posteriori. In this paper, we present a tool that finds contextually the three parameters based on simple assumptions on how the observed values xi populate the unknown range between xmin and xmax for a given α. Our tool, freely downloadable, finds the best values through a non-linear least-squares fit. We compare our technique with the maximum likelihood estimators for power-law distributions, both truncated and not. Through simulated data, we show for each method the reliability of the computed parameters as a function of the number N of data in the sample. We then apply our method to observed data to derive: (i) the slope of the core mass function in the Perseus star-forming region, finding two power-law distributions: α = 2.576 between $1.06\, \mathrm{M}_{\odot }$ and $3.35\, \mathrm{M}_{\odot }$, α = 3.39 between $3.48\, \mathrm{M}_{\odot }$ and $33.4\, \mathrm{M}_{\odot }$; (ii) the slope of the γ-ray spectrum of the blazar J0011.4+0057, extracted from the Fermi-LAT archive. For the latter case, we derive α = 2.89 between 1484 MeV and 28.7 GeV; then we derive the time-resolved slopes using subsets of 200 photons each.

Precision electron measurements in the solar wind at 1 au from NASA’s Wind spacecraft

Context. The non-equilibrium characteristics of electron velocity distribution functions (eVDFs) in the solar wind are key to understanding the overall plasma thermodynamics as well as the origin of the solar wind. More generally, they are important in understanding heat conduction and energy transport in all weakly collisional plasmas. Solar wind electrons are not in local thermodynamic equilibrium, and their multicomponent eVDFs develop various non-thermal characteristics, such as velocity drifts in the proton frame and temperature anisotropies as well as suprathermal tails and heat fluxes along the local magnetic field direction. Aims. This work aims to characterize precisely and systematically the nonthermal characteristics of the eVDF in the solar wind at 1 au using data from the Wind spacecraft. Methods. We present a comprehensive statistical analysis of solar wind electrons at 1 au using the electron analyzers of the 3D-Plasma instrument on board Wind. This work uses a sophisticated algorithm developed to analyze and characterize separately the three populations – core, halo and strahl – of the eVDF up to super-halo energies (2 keV). This algorithm calibrates these electron measurements with independent electron parameters obtained from the quasi-thermal noise around the electron plasma frequency measured by Wind’s Thermal Noise Receiver (TNR). The code determines the respective set of total electron, core, halo, and strahl parameters through non-linear least-square fits to the measured eVDF, properly taking into account spacecraft charging and other instrumental effects, such as the incomplete sampling of the eVDF by particle detectors. Results. We use four years, approximately 280 000 independent measurements, of core, halo, and strahl electron parameters to investigate the statistical properties of these different populations in the slow and fast solar wind. We discuss the distributions of their respective densities, drift velocities, temperature, and temperature anisotropies as functions of solar wind speed. We also show distributions with solar wind speed of the total density, temperature, temperature anisotropy, and heat flux of the total eVDF, as well as those of the proton temperature, proton-to-electron temperature ratio, proton-β and electron-β. Intercorrelations between some of these parameters are also discussed. Conclusions. The present data set represents the largest, high-precision collection of electron measurements in the pristine solar wind at 1 au. It provides a new wealth of information on electron microphysics. Its large volume will enable future statistical studies of parameter combinations and their dependences under different plasma conditions.

Model-based reconstructions for intravoxel incoherent motion and diffusion tensor imaging parameter map estimations.

Intravoxel incoherent motion (IVIM) imaging and diffusion tensor imaging (DTI) facilitate noninvasive quantification of tissue perfusion and diffusion. Both are promising biomarkers in various diseases and a combined acquisition is therefore desirable. This comes with challenges, including noisy parameter maps and long scan times, especially for the perfusion fraction f and pseudo-diffusion coefficient D*. A model-based reconstruction has the potential to overcome these challenges. As a first step, our goal was to develop a model-based reconstruction framework for IVIM and combined IVIM-DTI parameter estimation. The IVIM and IVIM-DTI models were implemented in the PyQMRI model-based reconstruction framework and validated with simulations and in vivo data. Commonly used voxel-wise nonlinear least-squares fitting was used as the reference. Simulations with the IVIM and IVIM-DTI models were performed with 100 noise realizations to assess accuracy and precision. Diffusion-weighted data were acquired for IVIM reconstruction in the liver (n = 5), as well as for IVIM-DTI in the kidneys (n = 5) and lower-leg muscles (n = 6) of healthy volunteers. The median and interquartile range (IQR) values of the IVIM and IVIM-DTI parameters were compared to assess bias and precision. With model-based reconstruction, the parameter maps exhibited less noise, which was most pronounced in the f and D* maps, both in the simulations and in vivo. The bias values in the simulations were comparable between model-based reconstruction and the reference method. The IQR was lower with model-based reconstruction compared with the reference for all parameters. In conclusion, model-based reconstruction is feasible for IVIM and IVIM-DTI and improves the precision of the parameter estimates, particularly for f and D* maps.

Collision of C2 with NH and deuterated analogs in the interstellar medium. Scattering calculations

ABSTRACT Shephard’s interpolation potential energy surface and isotopic substitution were used to understand the mechanisms of chemical reactions; the NH + C2 reaction potential energy surface was constructed in this research and evaluated using ab-initio calculations. Classical trajectory simulations were used to calculate the reaction probability and cross-section. In addition, the rate constant by the nonlinear least-squares fitting was calculated. These were determined as a function of cross-section. In non-reactive trajectories for inelastic collisions, the scattering angle was estimated. The effects of the impact parameter and the relative velocity of particles on the reaction probability, transmitted energy, and dispersion angle were investigated. In addition, Isotopic substitution in the NH radical was evaluated for the effect of the mass of the target and incident particles on the cross-section, reaction probability, dispersion angle, and reaction rate. To calculate the kinetic isotope effect, the influence of the mass of colliding molecules on the observable properties was studied. Deuterated imidogen reacted faster than hydrogenated imidogen. These observations provided valuable insights into the details of the mechanisms, possible reactions of ND and NH + C2 , and deuterium fractionation.

Waveform inversion via reduced order modeling

We introduce a novel approach to waveform inversion based on a data-driven reduced order model (ROM) of the wave operator. The presentation is for the acoustic wave equation, but the approach can be extended to elastic or electromagnetic waves. The data are time resolved measurements of the pressure wave gathered by an acquisition system that probes the unknown medium with pulses and measures the generated waves. We propose to solve the inverse problem of velocity estimation by minimizing the square misfit between the ROM computed from the recorded data and the ROM computed from the modeled data, at the current guess of the velocity. We give a step by step computation of the ROM, which depends nonlinearly on the data and yet can be obtained from them in a noniterative fashion, using efficient methods from linear algebra. We also explain how to make the ROM robust to data inaccuracy. The ROM computation requires the full array response matrix gathered with colocated sources and receivers. However, we find that the computation can deal with an approximation of this matrix, obtained from towed-streamer data using interpolation and reciprocity on-the-fly. Although the full-waveform inversion approach of nonlinear least-squares data fitting is challenging without low-frequency information, due to multiple minima of the data fit objective function, we find that the ROM misfit objective function has better behavior, even for a poor initial guess. We also find by explicit computation of the objective functions in a simple setting that the ROM misfit objective function has convexity properties, whereas the least-squares data fit objective function displays multiple local minima.

FCSNet and ImFCSNet, convolutional neural network approaches to FCS data analysis.

Fluorescence Correlation Spectroscopy (FCS) is a widely used tool to analyse molecular dynamics in biological samples. It analyses the correlation function of the fluorescence fluctuations in a defined observation volume to extract information about the underlying molecular processes. However, FCS faces a number of challenges. First, it requires the use of theoretical fit models that often cannot be solved exactly and thus require approximations. Second, the measurement times for FCS are comparatively long, on the order of a minute, to obtain accurate parameter estimates. Third, the data analysis can be computationally quite time consuming. We therefore explore deep learning approaches to address these issues. For this purpose, we focus on Imaging FCS, a camera-based FCS modality, that provides correlation functions at or between any pixels on a camera, without loss of generality. We developed two convolutional neural networks (CNNs). FCSNet and ImFCSNet use either correlation functions or raw intensity traces as input, respectively. Both networks are trained on simulated, synthetic data, as it is difficult to obtain ground truth data for FCS over wide parameter ranges. More importantly, it allows us to use arbitrary experimental geometries and molecular processes, even when analytic models are not available for conventional fitting, thus solving the first problem. We demonstrate that the two CNNs perform well on synthetic and experimental data and outperform conventional nonlinear least squares (NLS) fits by a) requiring about one order of magnitude less data, b) providing higher precision for parameter estimates, and c) being two orders of magnitude faster. To demonstrate the power of CNNs we present comparisons of data evaluations by conventional NLS fitting on lipid bilayers and cells and on data recorded on total internal reflection and light sheet microscopes.

Total variation denoising and Euclidean distance based distributed temperature monitoring in Brillouin optical time-domain analysis sensors

The performance of Brillouin optical time domain analysis (BOTDA) sensors is largely deteriorated due to the poor signal-to-noise ratio (SNR) of Brillouin gain spectra (BGSs) collected from the BOTDA experiment. The fast monitoring of distributed temperature using BOTDA sensors is also vital for many longdistant applications. To cope with these requirements, this paper proposes total variation denoising (TVD) and Euclidean distance-based pattern recognition (TEPR) for high-performance BOTDA sensors. The performances of TEPR are analyzed explicitly, and rigorous comparisons have been made with traditional nonlinear least squares fitting (NLSF). The experimentally demonstrated results signify that the proposed TEPR can improve the measurement uncertainty by up to ~55% compared to NLSF without worsening the experimental spatial resolution. The signal processing for using TEPR is also ~4 times faster than that for using NLSF. Hence, the proposed technique is an efficient and reliable alternative for the fast and accurate monitoring of distributed temperature in BOTDA sensors. J. Bangladesh Acad. Sci. 46(2); 193-202: December 2022

A Stochastic Mathematical Model for Understanding the COVID-19 Infection Using Real Data

Natural symmetry exists in several phenomena in physics, chemistry, and biology. Incorporating these symmetries in the differential equations used to characterize these processes is thus a valid modeling assumption. The present study investigates COVID-19 infection through the stochastic model. We consider the real infection data of COVID-19 in Saudi Arabia and present its detailed mathematical results. We first present the existence and uniqueness of the deterministic model and later study the dynamical properties of the deterministic model and determine the global asymptotic stability of the system for R0≤1. We then study the dynamic properties of the stochastic model and present its global unique solution for the model. We further study the extinction of the stochastic model. Further, we use the nonlinear least-square fitting technique to fit the data to the model for the deterministic and stochastic case and the estimated basic reproduction number is R0≈1.1367. We show that the stochastic model provides a good fitting to the real data. We use the numerical approach to solve the stochastic system by presenting the results graphically. The sensitive parameters that significantly impact the model dynamics and reduce the number of infected cases in the future are shown graphically.

An unsupervised convolutional neural network method for estimation of intravoxel incoherent motion parameters

Objective. Intravoxel incoherent motion (IVIM) imaging obtained by fitting a biexponential model to multiple b-value diffusion-weighted magnetic resonance imaging (DW-MRI) has been shown to be a promising tool for different clinical applications. Recently, several deep neural network (DNN) methods were proposed to generate IVIM imaging. Approach. In this study, we proposed an unsupervised convolutional neural network (CNN) method for estimation of IVIM parameters. We used both simulated and real abdominal DW-MRI data to evaluate the performance of the proposed CNN-based method, and compared the results with those obtained from a non-linear least-squares fit (TRR, trust-region reflective algorithm) and a feed-forward backward-propagation DNN-based method. Main results. The simulation results showed that both the DNN- and CNN-based methods had lower coefficients of variation than the TRR method, but the CNN-based method provided more accurate parameter estimates. The results obtained from real DW-MRI data showed that the TRR method produced many biased IVIM parameter estimates that hit the upper and lower parameter bounds. In contrast, both the DNN- and CNN-based methods yielded less biased IVIM parameter estimates. Overall, the perfusion fraction and diffusion coefficient obtained from the DNN- and CNN-based methods were close to literature values. However, compared with the CNN-based method, both the TRR and DNN-based methods tended to yield increased pseudodiffusion coefficients (55%–180%). Significance. Our preliminary results suggest that it is feasible to estimate IVIM parameters using CNN.