Classical Least-squares Research Articles

Simulation of flow in deformable fractures using a quasi-Newton based partitioned coupling approach

We introduce a partitioned coupling approach for iterative coupling of flow processes in deformable fractures embedded in a poro-elastic medium that is enhanced by interface quasi-Newton (IQN) methods. In this scope, a unique computational decomposition into a fracture flow and a poro-elastic domain is developed, where communication and numerical coupling of the individual solvers are realized by consulting the open-source library preCICE. The underlying physical problem is introduced by a brief derivation of the governing equations and interface conditions of fracture flow and poro-elastic domain followed by a detailed discussion of the partitioned coupling scheme. We evaluate the proposed implementation and undertake a convergence study to compare a classical interface quasi-Newton inverse least-squares (IQN-ILS) with the more advanced interface quasi-Newton inverse multi-vector Jacobian (IQN-IMVJ) method. These coupling approaches are verified for an academic test case before the generality of the proposed strategy is demonstrated by simulations of two complex fracture networks. In contrast to the development of specific solvers, we promote the simplicity and computational efficiency of the proposed partitioned coupling approach using preCICE and FEniCS for parallel computations of hydro-mechanical processes in complex, three-dimensional fracture networks.

Advances in mixed cell deconvolution enable quantification of cell types in spatial transcriptomic data

Mapping cell types across a tissue is a central concern of spatial biology, but cell type abundance is difficult to extract from spatial gene expression data. We introduce SpatialDecon, an algorithm for quantifying cell populations defined by single cell sequencing within the regions of spatial gene expression studies. SpatialDecon incorporates several advancements in gene expression deconvolution. We propose an algorithm harnessing log-normal regression and modelling background, outperforming classical least-squares methods. We compile cell profile matrices for 75 tissue types. We identify genes whose minimal expression by cancer cells makes them suitable for immune deconvolution in tumors. Using lung tumors, we create a dataset for benchmarking deconvolution methods against marker proteins. SpatialDecon is a simple and flexible tool for mapping cell types in spatial gene expression studies. It obtains cell abundance estimates that are spatially resolved, granular, and paired with highly multiplexed gene expression data.

Chemometrics-Assisted Spectrophotometric Method Development and Validation for Simultaneous Estimation of Emtricitabine, Tenofovir Alafenamide Fumarate, and Dolutegravir Sodium in Dosage Form

Aim: This study aims on the development of a chemometric-assisted spectroscopic method for the analysis of combined dosage form of emtricitabine (EMT), tenofovir alafenamide fumarate (TEN), and dolutegravir sodium (DOL). The use of a multivariate algorithm to analyse spectrophotometric data is a novel approach to estimating drug concentrations in formulations. Materials and Methods: The quantitative estimation of EMT, TEN, and DOL in tablets was carried out using four chemometric approaches: Classical least square (CLS), inverse least square, partial least square, and principal component regression. Thirty-two ternary mixtures of calibration sets and 16 mixtures of validation sets were prepared. The absorbance data matrix was attained by calculating absorbance at 25 different wavelengths in a range of 240–336 nm (Δλ = 4 nm). The chemometric calculations were performed using Matlab2018a and Minitab software. The developed methods were validated. Results: The great accuracy of the current study was justified by the near-perfect recovery values (100%) and low standard deviation. For chemometrics approaches, the root mean square error of calibration (RMSEC), root mean square error of prediction (RMSEP), and root mean square error of cross-validation (RMSECV) outcomes display decent accuracy and precision. Conclusion: The CLS approach yielded the lowest predicted residual error sum of squares, RMSEC, RMSEP, and RMSECV scores. As a result, CLS might be regarded as the best chemometric approach among all techniques utilized. The label claim determined is in excellent accordance with the mean recoveries for EMT, TEN, and DOL. So, it can be used in quality control laboratories.

Multivariate analytical methods for simultaneous estimation of Atenolol and Hydrochlorothiazide in bulk and tablet dosage form

The present study aimed to develop simple, accurate and precise FTIR and UV spectrophotometric methods for the quantification of Atenolol and Hydrochlorothiazide in bulk and tablet dosage forms. FT-IR method like classical least squares (CLS) was developed within the range of 2366.69-3433.44; 1564.40-1673.30 cm- UV methods like Cramer’s matrix method (method-I) and linear regression analysis (Method II) were developed and they are based upon constructing the matrix set by using molar absorptivity values at 275.60 nm and 270.40 nm. The assay values for FTIR- CLS method were 102% and 108 % for Atenololand Hydrochlorothiazide respectively. Cramer’s matrix method results were found to be 95.15% and 104% for Atenolol and Hydrochlorothiazide respectively and for linear regression method they were found to be 98.50% and 106% (w/w).

Induced polarization of the 1630-monogenetic dome, Furnas volcano, São Miguel Island, Azores archipelago

Induced polarization is used to image the feeder dike of a monogenetic dome thanks to the signature of pronounced alteration around these conduits. We performed a 3D tomography of the electrical conductivity and normalized chargeability of the 1630-monogenetic dome located inside the caldera of Furnas, a quiescent stratovolcano in the Eastern side of São Miguel Island (Azores volcanic archipelago, Atlantic Ocean). A total of 2634 apparent resistivity and chargeability data were collected and inverted using a classical regularized least-squares inversion (based on a quasi-Gauss-Newton approach). The 3D tomograms display an area of both high electrical conductivity and normalized chargeability. This area corresponds to the altered subvolume associated with the magmatic feeding conduit of the monogenetic dome. The same conduit can be also observed on a 2D magnetotelluric (MT) section, at least for the first 200 m below the ground surface. Assuming that the in-situ pore water conductivity is the same as in Furnas Lake (∼0.016 S m−1, 25 °C), the electrical conductivity and normalized chargeability are combined to obtain tomograms of the water content and cation exchange capacity of the monogenetic dome. The cation exchange capacity provides a proxy to image alteration associated with the formation of clay minerals and zeolites. This study highlights the usefulness of these techniques to image the structure of monogenetic domes.

Quantification of Raman-Interfering Polyoxoanions for Process Analysis: Comparison of Different Chemometric Models and a Demonstration on Real Hanford Waste.

The Hanford site represents a complicated environmental remediation challenge, remaining from the production of nuclear weapons. Over 100 million gallons of liquid radioactive waste of unknown composition will be chemically processed and vitrified, but the varying chemical composition and highly radioactive nature of the waste preclude the implementation of more developed, offline technologies to determine the composition. The only practical approach to waste treatment will require the significant utilization of real-time, chemometric modeling approaches. Although chemometric approaches have been applied to the analysis of Hanford waste, the models developed were highly tank-specialized, and limited discussion was provided on how models fared with interfering signals. As the tank waste is largely composed of oxoanions, which tend to have interfering Raman spectra, the general question was posed as to what chemometric approach is best suited to accurately quantify analytes in the presence of interfering signals. This was carried out by examining the ability of classical least square (CLS), principal component regression (PCR), partial least square (PLS), and locally weighted regression (LWR) to quantify NO3- and CO32- using their bands around 1050 cm-1. For all samples, the PLS-based model was found to be the most efficient approach from a model building and application perspective.

Towards a High Order Convergent ALE-SPH Scheme with Efficient WENO Spatial Reconstruction

This paper studies the convergence properties of an arbitrary Lagrangian–Eulerian (ALE) Riemann-based SPH algorithm in conjunction with a Weighted Essentially Non-Oscillatory (WENO) high-order spatial reconstruction, in the framework of the DualSPHysics open-source code. A convergence analysis is carried out for Lagrangian and Eulerian simulations and the numerical results demonstrate that, in absence of particle disorder, the overall convergence of the scheme is close to the one guaranteed by the WENO spatial reconstruction. Moreover, an alternative method for the WENO spatial reconstruction is introduced which guarantees a speed-up of 3.5, in comparison with the classical Moving Least-Squares (MLS) approach.

Performance assessment of linear iterative optimization technology (IOT) for Raman chemical mapping of pharmaceutical tablets

Raman chemical mapping is an inherently slow analysis tool. Accurate and robust multivariate analysis algorithms, which require least amount of time and effort in method development are desirable. Calibration-free regression and resolution approaches such as classical least squares (CLS) and multivariate curve resolution using alternating least squares (MCR-ALS), respectively, help in reducing the resources required for method development. However, conventional CLS does not consider appropriate constraints, which may result in negative and/or greater than 100 % Raman concentration scores, while MCR-ALS may not always be as accurate as regression-based algorithms. Linear iterative optimization technology (IOT) is another calibration-free algorithm, which with appropriate constraints has previously shown promise in online and offline pharmaceutical mixture composition determination. This paper aims to evaluate the performance of the linear IOT algorithm for Raman chemical mapping of the active pharmaceutical ingredient (API), diluent, and lubricant in pharmaceutical tablets. Two pre-processing strategies were applied to the raw Raman mapping spectra. The results were compared with CLS (current reference method) and MCR-ALS. Special emphasis was given to mapping at low Raman exposure times to enable feasible total acquisition times (< 5 h). The quality of IOT/CLS/MCR-ALS estimated Raman concentration predictions were assessed by calculating a correlation factor between the spectrum corresponding to the maximum predicted concentration (or resolved spectra) of a component for IOT/CLS (or MCR-ALS) and the pure powder component spectrum. The Raman chemical maps were visualized, and the average Raman concentrations scores were compared. The results demonstrated the utility of IOT in Raman chemical mapping of pharmaceutical tablets. The diluent (lactose) and API (semi-fine APAP) used in this study were reliably estimated by IOT at relatively short Raman exposure times. On the other hand, as expected, the lubricant (magnesium stearate) could not be detected in any of the cases investigated here, irrespective of the algorithm used. Overall, for the API and diluent used in this formulation as well as the chemical mapping conditions, linear IOT seemed to better estimate the pure spectrum intensities and the average Raman scores (closer to CLS) in comparison to MCR-ALS. Moreover, application of appropriate constraints in linear IOT avoided the presence of negative and/or greater than 100 % Raman concentration scores, as observed in CLS-based Raman chemical maps.

Application of alternating trilinear decomposition-assisted multivariate curve resolution to gas chromatography-mass spectrometric data for the quantification of polycyclic aromatic hydrocarbons in aerosols.

For the first time, alternating trilinear decomposition-assisted multivariate curve resolution (ATLD-MCR) was applied to analyse complex gas chromatography–mass spectrometric (GC-MS) data with severe baseline drifts, serious co-elution peaks and slight retention time shifts for the simultaneous identification and quantification of polycyclic aromatic hydrocarbons (PAHs) in aerosols. It was also compared with the classic multivariate curve resolution-alternating least-squares (MCR-ALS) and the GC-MS-based external standard method. In validation samples, average recoveries of five PAHs were within the range from (96.2 ± 6.8)% to (106.5 ± 4.1)% for ATLD-MCR, near to the results of MCR-ALS ((98.0 ± 1.5)% to (106.7 ± 4.3)%). In aerosol samples, the concentrations of pyrene provided by ATLD-MCR were not significantly different from those of MCR-ALS. The other four PAHs including chrysene, benzo[a]anthracene, fluoranthene and benzo[b]fluoranthene were not detected by ATLD-MCR and the GC-MS-based external standard method. The results of figures of merit further demonstrated that ATLD-MCR achieved high sensitivities (8.9 × 104 to 1.7 × 106 mAU ml µg−1) and low limits of detection (0.003 to 0.087 µg ml−1), which were better than or similar to MCR-ALS, presenting a great choice to deal with complex GC-MS data for the simultaneous determination of targeted PAHs in aerosols.

Robust penalized spline estimation with difference penalties

Penalized spline estimation with discrete difference penalties (P-splines) is a popular estimation method for semiparametric models, but the classical least-squares estimator is highly sensitive to deviations from its ideal model assumptions. To remedy this deficiency, a broad class of P-spline estimators based on general loss functions is introduced and studied. Robust estimators are obtained by well-chosen loss functions, such as the Huber or Tukey loss function. A preliminary scale estimator can also be included in the loss function. It is shown that this class of P-spline estimators enjoys the same optimal asymptotic properties as least-squares P-splines, thereby providing strong theoretical motivation for its use. The proposed estimators may be computed very efficiently through a simple adaptation of well-established iterative least squares algorithms and exhibit excellent performance even in finite samples, as evidenced by a numerical study and a real-data example.

Assessment of the uncertainty in spatial-correlation models for earthquake ground motion due to station layout and derivation method

The evaluation of the aggregate risks to spatially distributed infrastructures and portfolios of buildings requires quantification of the estimated shaking over a region. To characterize the spatial dependency of ground motion intensity measures (e.g. peak ground acceleration), a common geostatistical tool is the semivariogram. Over the past decades, different fitting approaches have been proposed in the geostatistics literature to fit semivariograms and thus characterize the correlation structure. A theoretically optimal approach has not yet been identified, as it depends on the number of observations and configuration layout. In this article, we investigate estimation methods based on the likelihood function, which, in contrast to classical least-squares methods, straightforwardly define the correlation without needing further steps, such as computing the experimental semivariogram. Our outcomes suggest that maximum-likelihood based approaches may outperform least-squares methods. Indeed, the former provides correlation estimates, that do not depend on the bin size, unlike ordinary and weighted least-squares regressions. In addition, maximum-likelihood methods lead to lower percentage errors and dispersion, independently of both the number of stations and their layout as well as of the underlying spatial correlation structure. Finally, we propose some guidelines to account for spatial correlation uncertainty within seismic hazard and risk assessments. The consideration of such dispersion in regional assessments could lead to more realistic estimations of both the ground motion and corresponding losses.

Ultraviolet Spectroscopic Detection of Nitrate and Nitrite in Seawater Simultaneously Based on Partial Least Squares.

A direct, reagent-free, ultraviolet spectroscopic method for the simultaneous determination of nitrate (NO3−), nitrite (NO2−), and salinity in seawater is presented. The method is based on measuring the absorption spectra of the raw seawater range of 200–300 nm, combined with partial least squares (PLS) regression for resolving the spectral overlapping of NO3−, NO2−, and sea salt (or salinity). The interference from chromophoric dissolved organic matter (CDOM) UV absorbance was reduced according to its exponential relationship between 275 and 295 nm. The results of the cross-validation of calibration and the prediction sets were used to select the number of factors (4 for NO3−, NO2−, and salinity) and to optimize the wavelength range (215–240 nm) with a 1 nm wavelength interval. The linear relationship between the predicted and the actual values of NO3−, NO2−, salinity, and the recovery of spiked water samples suggest that the proposed PLS model can be a valuable alternative method to the wet chemical methods. Due to its simplicity and fast response, the proposed PLS model can be used as an algorithm for building nitrate and nitrite sensors. The comparison study of PLS and a classic least squares (CLS) model shows both PLS and CLS can give satisfactory results for predicting NO3− and salinity. However, for NO2− in some samples, PLS is superior to CLS, which may be due to the interference from unknown substances not included in the CLS algorithm. The proposed method was applied to the analysis of NO3−, NO2−, and salinity in the Changjiang (Yangtze River) estuary water samples and the results are comparable with that determined by the colorimetric Griess assay.

Variational Bayesian Learning of SMoGs: Modelling and Their Application to Synthetic Aperture Radar

We show how modern Bayesian Machine Learning tools can be effectively used in order to develop efficient methods for filtering Earth Observation signals. Bayesian statistical methods can be thought of as a generalization of the classical least-squares adjustment methods where both the unknown signals and the parameters are endowed with probability distributions, the priors. Statistical inference under this scheme is the derivation of posterior distributions, that is, distributions of the unknowns after the model has seen the data. Least squares can then be thought of as a special case that uses Gaussian likelihoods, or error statistics. In principle, for most non-trivial models, this framework requires performing integration in high-dimensional spaces. Variational methods are effective tools for approximate inference in Statistical Machine Learning and Computational Statistics. In this paper, after introducing the general variational Bayesian learning method, we apply it to the modelling and implementation of sparse mixtures of Gaussians (SMoG) models, intended to be used as adaptive priors for the efficient representation of sparse signals in applications such as wavelet-type analysis. Wavelet decomposition methods have been very successful in denoising real-world, non-stationary signals that may also contain discontinuities. For this purpose we construct a constrained hierarchical Bayesian model capturing the salient characteristics of such sets of decomposition coefficients. We express our model as a Dirichlet mixture model. We then show how variational ideas can be used to derive efficient methods for bypassing the need for integration: the task of integration becomes one of optimization. We apply our SMoG implementation to the problem of denoising of Synthetic Aperture Radar images, inherently affected by speckle noise, and show that it achieves improved performance compared to established methods, both in terms of speckle reduction and image feature preservation.

Quantification of Acetaminophen, Caffeine and Ibuprofen in Solid Dosage Forms by UV Spectroscopy coupled with Multivariate analysis

Quantification of acetaminophen, caffeine and ibuprofen in ternary mixtures was studied by using UV spectroscopy coupled with multivariate analysis [tri-linear regression-calibration (TLRC), classical least squares (CLS) and multi linear regression calibration (MLRC)]. To validate UV spectroscopic methods, the wavelength range of 215 – 290nm and a matrix (composed of 21 standard solutions containing acetaminophen 20-32.5mg/L, caffeine 1-3.5mg/L and ibuprofen 12-32mg/L) were selected. With the exception of TLRC, CLS and MLRS algorithms proved to be relevant for obtaining UV spectroscopic assay results and dissolution profile of acetaminophen, caffeine and ibuprofen in their combined capsules and tablets, with precision (RSD &lt; 3%) and accuracy (98.3 – 101.9% recovery). It is also suggested that these UV spectroscopic methods could replace UHPLC analysis in the routine quality control of these compounds in their solid pharmaceutical dosage forms (p &gt; 0.05).

Criticalquality attribute assessment of big brand traditional Chinese medicine: visualization method for quality control of Ginkgo Leaves Tablets based on spatial distribution uniformity

Spatial distribution uniformity is the critical quality attribute(CQA) of Ginkgo Leaves Tablets, a variety of big brand traditional Chinese medicine. The evaluation of the spatial distribution uniformity of active pharmaceutical ingredients(APIs) in Ginkgo Leaves Tablets is important in ensuring their stable and controllable quality. In this study, hyperspectral imaging technology was used to construct the spatial distribution map of API concentration based on three prediction models, further to realize the visualization research on the spatial distribution uniformity of Ginkgo Leaves Tablets. The region of interest(ROI) was selected from each Ginkgo Leaves Tablet, with length and width of 50 pixels, and a total of 2 500 pixels. Each pixel had 288 spectral channels, and the number of content prediction data could reach 1×10~5 for a single sample. The results of the three models showed that the Partial Least Squares(PLS) model had the highest prediction accuracy, with calibration set determination coefficient R_(pre)~2 of 0.987, prediction set determination coefficient R_(pre)~2 of 0.942, root mean square error of calibration(RMSEC) of 0.160%, and root mean square error of prediction(RMSEP) of 0.588%. The classical least-squares(CLS) model had a greater prediction error, with the RMSEP of 0.867%. Multivariate Curve Resolution-Alternating Least Square(MCR-ALS) model showed the worst predictive ability among the three models, and it couldn't realize content prediction. Based on the prediction results of PLS and CLS models, the spatial distribution map of APIs concentration was obtained through three-dimensional data reconstruction. Furthermore, histogram method was used to evaluate the spatial distribution uniformity of API. The data showed that the spatial distribution of APIs in Ginkgo Leaves Tablets was relatively uniform. The study explored the feasibility of visualization of spatial distribution of Ginkgo Leaves Tablets based on three models. The results showed that PLS model had the highest prediction accuracy, and MCR-ALS model had the lowest prediction accuracy. The research results could provide a new strategy for the visualization method of quality control of Ginkgo Leaves Tablets.

Efficient iterative solutions to complex-valued nonlinear least-squares problems with mixed linear and antilinear operators

We consider a setting in which it is desired to find an optimal complex vector {mathbf {x}}in {mathbb {C}}^N that satisfies {mathcal {A}}({mathbf {x}}) approx {mathbf {b}} in a least-squares sense, where {mathbf {b}} in {mathbb {C}}^M is a data vector (possibly noise-corrupted), and {mathcal {A}}(cdot ): {mathbb {C}}^N rightarrow {mathbb {C}}^M is a measurement operator. If {mathcal {A}}(cdot ) were linear, this reduces to the classical linear least-squares problem, which has a well-known analytic solution as well as powerful iterative solution algorithms. However, instead of linear least-squares, this work considers the more complicated scenario where {mathcal {A}}(cdot ) is nonlinear, but can be represented as the summation and/or composition of some operators that are linear and some operators that are antilinear. Some common nonlinear operations that have this structure include complex conjugation or taking the real-part or imaginary-part of a complex vector. Previous literature has shown that this kind of mixed linear/antilinear least-squares problem can be mapped into a linear least-squares problem by considering {mathbf {x}} as a vector in {mathbb {R}}^{2N} instead of {mathbb {C}}^N. While this approach is valid, the replacement of the original complex-valued optimization problem with a real-valued optimization problem can be complicated to implement, and can also be associated with increased computational complexity. In this work, we describe theory and computational methods that enable mixed linear/antilinear least-squares problems to be solved iteratively using standard linear least-squares tools, while retaining all of the complex-valued structure of the original inverse problem. An illustration is provided to demonstrate that this approach can simplify the implementation and reduce the computational complexity of iterative solution algorithms.

Improvement of a computer-aided alignment algorithm for the nonsymmetric off-axis reflective telescope

Due to complications of the off-axis three-mirror anastigmat (TMA) telescope, each optical element in the off-axis TMA telescope is introduced with theoretical eccentricity and tilt. Moreover, the introduction of freeform surfaces and other optical elements with complex surface features generally causes the initial alignment accuracy of the optical path to be low. A large initial alignment error amplifies the sensitivity of the misalignment calculation accuracy to the measurement error of the Zernike coefficient, resulting in difficulty obtaining convergence results for a computer-aided alignment algorithm. Considering the above issues, the alignment sensitivity of each component in the optical path is analyzed in this. The large conditional number of the sensitivity matrix results in poor algorithm robustness. Thus, an adaptive damping factor least-squares algorithm model is proposed and derived to improve the efficiency of the classical least-squares algorithm. A method for piecewise optimization of the damping factor is also deduced. Experiments based on a 0.6 m off-axis TMA telescope verify the effectiveness of the algorithm. Simulation and integration experiments show that the proposed method can reduce the accuracy requirements of the initial alignment and improve the adaptability of Zernike coefficient measurement noise. The alignment procedure is carried out for three iterations, and the average of the five field-of-view wave aberration values is enhanced from 2.1λ (RMS; λ=632.8nm) to 0.09λ (average). The improved algorithm can solve the large initial alignment error of a nonsymmetrical off-axis reflective optical system with a freeform surface as well as the problem of the low success rate of the misalignment value due to low Zernike coefficient measurement accuracy.

Chemometry‐assisted UV‐spectrophotmetric methods for the simultaneous determination of paritaprevir, ritonavir, and ombitasvir in their combined tablet dosage forms: A comparative study

AbstractThe ternary mixture under study is a recent hepatitis‐C antiviral medicine composed of three new directly acting antiviral drugs, namely, ombitasvir, paritaprevir, and ritonavir. They are co‐formulated as a single‐dose combined tablet dosage form. With more than 170 million infected patients worldwide, a large production scales of antivirals medicine is expected, and hence, new simple and fast methodologies are required to cover millions of analyses that are done routinely in the different pharmaceutical quality control and research laboratories. Ultraviolet spectrophotometry represents sensitive, fast, and cheap tool of analysis in all research and quality control laboratories that can cover the massive quality control of these regimens. However, the simultaneous determination of these three drugs using multivariate chemometric methods represents a high challenge as their spectra are strongly overlapping besides the large difference in their potency within the same tablet. In this research paper, four new different multivariate chemometric methods were developed for their simultaneous determination, namely, classical least square (CLS), principal component regression (PCR), partial least squares (PLS), and genetic algorithm‐partial least squares (GA‐PLS) techniques. The validated methods do not require extraction, separation, or derivatization steps. A comparative study was conducted among the four developed methods. All methods provided satisfactory results, whereas GA‐PLS showed better analytical performance as it had the lowest error with good higher correlation coefficient. The methods were applied in the simultaneous determination of the three drugs in pure form and in their combined tablet dosage form. The comparison confirmed agreement of the values obtained for all techniques.

Hydration of the Zwitterionic and Protonated Forms of Glycine Betaine Probed by Soft X-ray Emission Spectroscopy Coupled with Chemometrics.

Soft X-ray absorption and emission spectra of glycine betaine (GB) have been measured at the O K-edge in neutral and strongly acidic solutions. The absorption spectra of the neutral solutions have a resonance peak at 532.6 eV, assigned to the transition to the π* orbital, whereas in the acidic solutions, the peak is shifted by -0.3 eV. The emission spectra taken as a function of the GB concentration have been analyzed by means of a modified classical least-squares regression method to obtain the hydration number of the solute. The analysis is successful when the emission spectra have been acquired at the energy of a slightly detuned resonance, giving 28 and 24 as the minimum values for the zwitterionic and protonated GB, respectively. The number of 28 accords with the reported values for the number of water molecules in the first hydration layer of the zwitterion and is greater than that obtained by other experimental techniques. The obtained numbers are used to discuss the hydration structure of GB with the aid of ab initio molecular orbital calculations. The hydration structure of the protonated form of GB is explored for the first time.

Robust Ellipse Fitting Using Hierarchical Gaussian Mixture Models.

Fitting ellipses from unrecognized data is a fundamental problem in computer vision and pattern recognition. Classic least-squares based methods are sensitive to outliers. To address this problem, in this paper, we present a novel and effective method called hierarchical Gaussian mixture models (HGMM) for ellipse fitting in noisy, outliers-contained, and occluded settings on the basis of Gaussian mixture models (GMM). This method is crafted into two layers to significantly improve its fitting accuracy and robustness for data containing outliers/noise and has been proven to effectively narrow down the iterative interval of the kernel bandwidth, thereby speeding up ellipse fitting. Extensive experiments are conducted on synthetic data including substantial outliers (up to 60%) and strong noise (up to 200%) as well as on real images including complex benchmark images with heavy occlusion and images from versatile applications. We compare our results with those of representative state-of-the-art methods and demonstrate that our proposed method has several salient advantages, such as its high robustness against outliers and noise, high fitting accuracy, and improved performance.