Least-squares Procedure Research Articles

Redox-Active 1D Coordination Polymers of Iron-Sulfur Clusters.

Here we describe the combination of an archetypal redox-active metal sulfide cluster, Fe4S4, with an organic linker, 1,4-benzenedithiolate, to prepare coordination polymers containing infinite chains of Fe4S4 clusters. The crystal structures of two solid materials have been solved from synchrotron X-ray powder diffraction data using simulated annealing and refined by a least-squares Rietveld refinement procedure. The electronic properties of these chains have also been characterized by UV-visible and Mössbauer spectroscopies. Additional experiments demonstrated that these chains can be solubilized by variation of the countercation and that the chain structure is maintained in solution. The redox-activity of the Fe4S4 clusters can be accessed with chemical reagents. Introduction of charge carriers by reduction of the Fe4S4 clusters is found to increase the electrical conductivity of the materials by up to 4 orders of magnitude. These results highlight the utility of Fe4S4 clusters as redox-active building blocks in preparing new classes of coordination polymers.

Robust external calibration of terrestrial laser scanner and digital camera for structural monitoring

Abstract In the last two decades, the integration of a terrestrial laser scanner (TLS) and digital photogrammetry, besides other sensors integration, has received considerable attention for deformation monitoring of natural or man-made structures. Typically, a TLS is used for an area-based deformation analysis. A high-resolution digital camera may be attached on top of the TLS to increase the accuracy and completeness of deformation analysis by optimally combining points or line features extracted both from three-dimensional (3D) point clouds and captured images at different epochs of time. For this purpose, the external calibration parameters between the TLS and digital camera needs to be determined precisely. The camera calibration and internal TLS calibration are commonly carried out in advance in the laboratory environments. The focus of this research is to highly accurately and robustly estimate the external calibration parameters between the fused sensors using signalised target points. The observables are the image measurements, the 3D point clouds, and the horizontal angle reading of a TLS. In addition, laser tracker observations are used for the purpose of validation. The functional models are determined based on the space resection in photogrammetry using the collinearity condition equations, the 3D Helmert transformation and the constraint equation, which are solved in a rigorous bundle adjustment procedure. Three different adjustment procedures are developed and implemented: (1) an expectation maximization (EM) algorithm to solve a Gauss-Helmert model (GHM) with grouped t-distributed random deviations, (2) a novel EM algorithm to solve a corresponding quasi-Gauss-Markov model (qGMM) with t-distributed pseudo-misclosures, and (3) a classical least-squares procedure to solve the GHM with variance components and outlier removal. The comparison of the results demonstrates the precise, reliable, accurate and robust estimation of the parameters in particular by the second and third procedures in comparison to the first one. In addition, the results show that the second procedure is computationally more efficient than the other two.

Effect of polyhedron deformation on the 5d energy level of Ce3+ in lanthanide aluminum perovskites.

The crystal-field levels of Ce3+ in a series of lanthanide aluminum perovskites have been investigated with reference to polyhedron deformation. For each compound, the corresponding ideal cuboctahedron is derived through a least-square procedure. The virtual energy levels of Ce3+ in these ideal polyhedrons are then obtained considering both crystal-field splitting and spin-orbit coupling. From comparison to real levels, we have a clear understanding of how polyhedron deformation affects the energy levels of Ce3+ in the perovskites.

The potential application of plant wax markers from alfalfa for estimating the total feed intake of sheep

Estimating the feed intake of grazing herbivores is critical for determining their nutrition, overall productivity and utilization of grassland resources. A 17-day indoor feeding experiment was conducted to evaluate the potential use of Medicago sativa as a natural supplement for estimating the total feed intake of sheep. A total of 16 sheep were randomly assigned to four diets (four sheep per diet) containing a known amount of M. sativa together with up to seven forages common to typical steppes. The diets were: diet 1, M. sativa + Leymus chinensis + Puccinellia distans; diet 2, species in diet 1 + Phragmites australis; diet 3, species in diet 2 + Chenopodium album + Elymus sibiricus; and diet 4, species in diet 3 + Artemisia scoparia + Artemisia tanacetifolia. After faecal marker concentrations were corrected by individual sheep recovery, treatment mean recovery or overall recovery, the proportions of M. sativa and other dietary forages were estimated from a combination of alkanes and long-chain alcohols using a least-square procedure. Total intake was the ratio of the known intake of M. sativa to its estimated dietary proportion. Each dietary component intake was obtained using total intake and the corresponding dietary proportions. The estimated values were compared with actual values to assess the estimation accuracy. The results showed that M. sativa exhibited a distinguishable marker pattern in comparison to the other dietary forage species. The accuracy of the dietary composition estimates was significantly (P < 0.001) affected by both diet diversity and the faecal recovery method. The proportion of M. sativa and total intake across all diets could be accurately estimated using the individual sheep or the treatment mean recovery methods. The largest differences between the estimated and observed total intake were 2.6 g and 19.2 g, respectively, representing only 0.4% and 2.6% of the total intake. However, they were significantly (P < 0.05) biased for most diets when using the overall recovery method. Due to the difficulty in obtaining individual sheep recovery under field conditions, treatment mean recovery is recommended. This study suggests that M. sativa, a natural roughage instead of a labelled concentrate, can be utilized as a dietary supplement to accurately estimate the total feed intake of sheep indoors and further indicates that it has potential to be used in steppe grassland of northern China, where the marker patterns of M. sativa differ markedly from commonly occurring plant species.

Accurate empirical rovibrational energies and transitions of H216O.

Several significant improvements are proposed to the computational molecular spectroscopy protocol MARVEL (Measured Active Rotational-Vibrational Energy Levels) facilitating the inversion of a large set of measured rovibrational transitions to energy levels. The most important algorithmic changes include the use of groups of transitions, blocked by their estimated experimental (source segment) uncertainties, an inversion and weighted least-squares refinement procedure based on sequential addition of blocks of decreasing accuracy, the introduction of spectroscopic cycles into the refinement process, automated recalibration, synchronization of the combination difference relations to reduce residual uncertainties in the resulting dataset of empirical (MARVEL) energy levels, and improved classification of the lines and energy levels based on their accuracy and dependability. The resulting protocol, through handling a large number of measurements of similar accuracy, retains, or even improves upon, the best reported uncertainties of the spectroscopic transitions employed. To show its advantages, the extended MARVEL protocol is applied for the analysis of the complete set of highly accurate H216O transition measurements. As a result, almost 300 highly accurate energy levels of H216O are reported in the energy range of 0-6000 cm-1. Out of the 15 vibrational bands involved in accurately measured rovibrational transitions, the following three have definitely highly accurate empirical rovibrational energies of 8-10 digits of accuracy: (v1v2v3) = (0 0 0), (0 1 0), and (0 2 0), where v1, v2, and v3 stand for the symmetric stretch, bend, and antisymmetric stretch vibrational quantum numbers. The dataset of experimental rovibrational transitions and empirical rovibrational energy levels assembled during this study, both with improved uncertainties, is considerably larger and more accurate than the best previous datasets.

Novel qLPV MPC Design with Least-Squares Scheduling Prediction

The design of a Model Predictive Control (MPC) algorithm for quasi Linear Parameter Varying (qLPV) systems is developed herein. An online Least-Squares procedure that computes the future evolution of the qLPV scheduling parameters is at the core of the proposed method, which enables the replacement of a complex nonlinear optimization by a (much simpler) Quadratic Programming Problem (QP) one. The method also uses contractive terminal set constraints and a Lyapunov-associated terminal cost to the MPC QP, so that the domain of attraction of this controller is enlarged and feasibility is guaranteed. This paper ends with a successful simulation of this technique applied to the control of vehicular suspensions.

Phase aberration compensation for digital holographic microscopy based on double fitting and background segmentation

We propose a purely automatic and accurate phase aberration compensation method in digital holographic microscopy for phase-contrast imaging of living cells. At first, a least-squares fitting procedure is implemented to correct a large proportion of the phase aberrations. Subsequently, the flat phase background is retrieved based on phase gradient and image segmentation. Finally, the residual phase aberrations are eliminated in another least-squares fitting procedure performed within the background region. This method needs no manual intervention or prior knowledge of optical setup. Not only phase curvature but also high order aberrations could be corrected without extra components. It outperforms the phase-variation-minimization method in terms of noise robustness and calculation speed. The performance of the proposed method is demonstrated with simulated and experimental results.

A Fuzzy Least-Squares Estimation of a Hybrid Log-Poisson Regression and Its Goodness of Fit for Optimal Loss Reserves in Insurance

In loss reserving, the log-Poisson regression model is a well-known stochastic model underlying the chain-ladder method which is the most used method for reserving purposes. Mack (ASTIN Bull 21(01):93–109, 1991) proved that the log-Poisson model provides the same estimates as the chain-ladder method. So in this article, our objective is to improve the log-Poisson regression model in loss reserving framework. Thereby, we prove the reliability of hybrid models in loss reserving, especially when the data contain fuzziness, for example when the claims are related to body injures (Straub and Swiss in Non-life insurance mathematics, Springer, Berlin, 1988). Thus, we estimate a hybrid generalized linear model (GLM) (log-Poisson) using the fuzzy least-squares procedures (Celmis in Fuzzy Sets Syst 22(3):245–269, 1987a; Math Model 9(9):669–690, 1987b; D’Urso and Gastaldi in Comput Stat Data Anal 34(4): 427–440, 2000; in: Advances in classification and data analysis, Springer, 2001). We develop a new goodness of fit index to compare this new model and the classical log-Poisson regression (Mack 1991). Both the classical log-Poisson model and the hybrid one are performed on a loss reserving data. According to the goodness of fit index and the mean square error prediction, we prove that the new model provide better results than the classical log-Poisson model. This comparison can be extend to any other GLM in loss reserving.

Hydrodynamic derivative determination based on CFD and motion simulation for a tow-fish

A new methodology to determine hydrodynamic derivatives of a tow-fish underwater vehicle using computational fluid dynamics (CFD) was presented. Hydrodynamic derivatives were derived from a second-order modulus expansion and consist of added mass, linear damping, and nonlinear damping coefficients. Added mass coefficients were analytically obtained using strip theory. All components of linear and nonlinear damping coefficients were determined by CFD simulations without any pre-elimination. The determination procedure for damping coefficients is as follows. First, a series of simulations was prepared for various situations reflecting the actual operating conditions of the tow-fish. Then, actual CFD simulations were performed for each of the cases, and 6 degree-of-freedom (6-DOF) forces and moments acting on the tow-fish were obtained. Finally, all linear and nonlinear damping coefficients were determined by optimized fitting of the CFD results using the least-squares procedure. The effectiveness of the determined hydrodynamic derivatives was demonstrated by reproducing the 6-DOF forces and moments and comparing them with those obtained from the CFD simulations. The relative significance of each coefficient was estimated by a global comparative view of normalized coefficients. To demonstrate the applicability of the current approach, 6-DOF simulations of the tow-fish for three different scenarios (L -, U -, and S -turn scenarios) at various towing speeds were conducted. The efficacy of the current methodology was strengthened by graphical and physical analyses of the virtual simulation results.

Assessment of the 153Eu and 154Eu neutron capture cross sections from the integral data assimilation of used nuclear fuel experiments

The purpose of this paper is to make the most of a large set of used nuclear fuel experiments for determining integral trends on the 153Eu(n,γ) and 154Eu(n,γ) reactions cross sections. The assimilation of the integral trends is based on a linear least-square fitting procedure relying on the Bayes’ theorem. Realistic uncertainties are obtained thanks to a marginalization technique. The method is applied to the 153Eu and 154Eu capture cross sections recommended in the evaluated nuclear data library JEFF-3.1.1. Our results indicate an underestimation of both capture cross-sections of approximately 4.9% and 7.1%, respectively. For 153Eu, our study suggests to increase the capture resonance integral from I0 = 1409 barns to I0 = 1502 ± 68 barns. This trend is consistent with the capture resonance integral I0 = 1560 ± 4 barns obtained from recent time-of-flight measurements carried out at the Renssealer Polytechnic Institute. The trend obtained in this work on 154Eu capture cross section is also consistent with a recent analysis that confirms its underestimation.

A kinetic study for the Fenton and photo-Fenton paracetamol degradation in an annular photoreactor

A kinetic model describing Fenton and photo-Fenton degradation of paracetamol (PCT) and consumption of hydrogen peroxide (H2O2) was proposed. A set of Fenton and photo-Fenton experiments (18 runs in total) was performed by fixing the initial concentration of PCT to 40 mg L−1 and varying the initial concentrations of H2O2 and ferrous ion, Fe2+. The experimental set-up was a well-stirred annular photoreactor equipped with an actinic BL TL-DK 36 W/10 1SL lamp. Experimental results highlighted that PCT is no more detected by HPLC analysis within a minimum reaction time of 2.5 and a maximum reaction time of 15.0 min. Besides, a maximum conversion of total organic carbon (TOC) of 68.5% was observed after 75 min of reaction in case of using UV radiation and the highest concentrations of the Fenton reagents. The experimental data were used to fit the kinetic model. The radiation field inside the reactor was taken into account through the local volumetric rate of photon absorption, evaluated by assuming a line source model with spherical and isotropic emission. The kinetic parameters were estimated by using a non-linear least-squares regression procedure and root mean square errors (RMSE) were calculated in order to validate the feasibility of the proposed model. A good agreement between experimental and predicted data was observed and the lowest values of RMSE resulted in 5.84 and 9.59% for PCT and H2O2 normalized concentrations, respectively.

Prediction of primal cuts by using an automatic ultrasonic device as a new method for estimating a pig-carcass slaughter and commercial value

The objective of the present work was to develop regression equations to estimate the percentage, weight (in g) and lean meat content (in %) of the primal cuts of a pig carcass by using Auto-Fom and to estimate the commercial value of the carcass on the slaughter line in a meat-processing plant. The research was conducted on 168 pig carcasses. From the whole pork carcass, only the most valuable cuts (i.e. belly, ham, loin, neck and shoulder) and also meat content in ham and shoulder were weighed at a 100 g accuracy and the percentage of each cut in carcass was calculated. Loin ‘eye’ height and belly-muscle thickness were also measured. The regression equations for the prediction of the primal-cut weights and their percentages in the pig carcasses were derived using the partial least-square procedure. The developed equations include 70 variables that are standard measurements taken with an Auto-Fom device. These equations have a satisfactory accuracy rate and are useful in estimating the yield of the elements, especially for loin, ham and belly content. Belly-muscle thickness (R2 = 0.98) and the percentage of meat in the ham (R2 = 0.93) can be estimated with a high precision. It was confirmed that the developed equations may be used in the current Auto-Fom software.

A new line-shape asymmetry model for wavelength modulation spectroscopy in gaseous flows

Abstract This communication reports technical notes on the development and application of an automated line-shape fitting procedure for wavelength modulation spectroscopy (WMS). Near-infrared transitions of carbon dioxide (CO2) around 1573 nm were measured in vertical cold (nonreacting) flow of CO2 at atmospheric pressure using WMS with demodulation at second harmonic frequency. Semi-empirical model based on the set of so-called Gabor functions was developed and parameters of Lorentzian line-shape profile and its asymmetry resulting from simultaneous frequency and amplitude response of the current-modulated semiconductor laser were determined. Nonlinear least-square fitting procedure employing differential evolution algorithm was successfully utilized for performing this task. Line-shape fitting procedure enabling efficient signal de-noising and background subtraction of wavelength modulation spectra was implemented into an open-source code.

Complex Sellmeier equation for the refractive index of semiconductors in the opaque region

Modeling the dispersion relation of semiconductors using a complex Sellmeier equation is reported for the first time. For this purpose, the refractive indices of GaAs and InAsBi were measured using spectroscopic ellipsometry. The complex Sellmeier coefficients were then obtained by a least-square fitting procedure. Simulation results demonstrate that complex Sellmeier equations can accurately model the refractive index dispersion of different semiconductors at wavelengths shorter than the band gap wavelengths, where the conventional Sellmeier equations are not applicable.

Modeling Properties with Artificial Neural Networks and Multilinear Least-Squares Regression: Advantages and Drawbacks of the Two Methods

The mean molecular connectivity indices (MMCI) proposed in previous studies are used in conjunction with well-known molecular connectivity indices (MCI) to model eleven properties of organic solvents. The MMCI and MCI descriptors selected by the stepwise multilinear least-squares (MLS) procedure were used to perform artificial neural network (ANN) computations, with the aim of detecting the advantages and limits of the ANN approach. The MLS procedure can replicate the obtained results for as long as is needed, a characteristic not shared by the ANN methodology, which, on the one hand increases the quality of a description, and on the other hand also results in overfitting. The present study also reveals how ANN methods prefer MCI relatively to MMCI descriptors. Four types of ANN computations show that: (i) MMCI descriptors are preferred with properties with a small number of points, (ii) MLS is preferred over ANN when the number of ANN weights is similar to the number of regression coefficients and, (iii) in some cases, the MLS modeling quality is similar to the modeling quality of ANN computations. Both the common training set and an external randomly chosen validation set were used throughout the paper.

Floating nurseries? Scyphozoan jellyfish, their food and their rich symbiotic fauna in a tropical estuary.

BackgroundThe anthropogenic modification of trophic pathways is seemingly prompting the increase of jellyfish populations at the expense of planktivorous fishes. However, gross generalizations are often made because the most basic aspects of trophic ecology and the diverse interactions of jellyfish with fishes remain poorly described. Here we inquire on the dynamics of food consumption of the medusoid stage of the scyphozoan jellyfish Stomolophus meleagris and characterize the traits and diversity of its symbiotic community.MethodsS. meleagris and their associated fauna were sampled in surface waters between November 2015 and April 2017 in Málaga Bay, an estuarine system at the Colombian Pacific. Stomach contents of medusae were examined and changes in prey composition and abundance over time analysed using a multivariate approach. The associated fauna was identified and the relationship between the size of medusae and the size those organisms tested using least-square fitting procedures.ResultsThe presence of S. meleagris medusa in surface waters was seasonal. The gut contents analysis revealed that algae, copepods and fish early life stages were the more abundant items, and PERMANOVA analysis showed that the diet differed within the seasons (P(perm) = 0.001) but not between seasons (P(perm) = 0.134). The majority of the collected medusae (50.4%) were associated with individuals of 11 symbiotic species, 95.3% of them fishes, 3.1% crustaceans and 1.6% molluscs. Therefore, this study reports 10 previously unknown associations. The bell diameter of S. meleagris was positively related to the body sizes of their symbionts. However, a stronger fit was observed when the size relationship between S. meleagris and the fish Hemicaranx zelotes was modelled.DiscussionThe occurrence of S. meleagris was highly seasonal, and the observed patterns of mean body size through the seasons suggested the arrival of adult medusae to the estuary from adjacent waters. The diet of S. meleagris in the study area showed differences with previous reports, chiefly because of the abundance of algae that are seemingly ingested but not digested. The low number of zooplanktonic items in gut contents suggest the contribution of alternative food sources not easily identifiable. The observed changes in the composition of food in the guts probably reflect seasonal changes in the availability of prey items. The regular pattern in the distribution of symbionts among medusae (a single symbiont per host) and the positive host-symbiont size relationship reflects antagonistic intraspecific and interspecific behaviour of the symbiont. This strongly suggest that medusa represent an “economically defendable resource” that potentially increases the survival and recruitment of the symbionts to the adult population. We argue that, if this outcome of the symbiotic association can be proven, scyphozoan jellyfish can be regarded as floating nurseries.

Low-range thermal investigation of zincblende-type ZnS by combined extended X-ray absorption fine structure and X-ray diffraction techniques

Extended X-ray absorption fine structure (EXAFS) has been measured at the zinc K edge in zinc sulfide (ZnS), in the temperature range of 20 K–300 K, in order to investigate the local structure and temperature effect in a zincblende-type ZnS compound. X-ray Diffraction (XRD) data have been carried out at the temperature range of 100 K–300 K for the investigation of the crystallographic local structure of ZnS. The cumulant method and the least-square fitting procedures are used in the EXAFS technique whereas the Rietveld method is used for the refinement of the XRD experimental data. The temperature dependence and the thermal expansion of the first bond distance and the Debye-Waller factor are exhibited and discussed in terms of anisotropy. The difference between the first bond distance measured by EXAFS and XRD is discussed. The Einstein frequencies are compared to the vibrational densities of states (VDOS) due to: the transverse acoustic mode, longitudinal acoustic and/or optic phonon modes; while the force constants have been correlated with the valence force field (VFF) models.

Modeling of Longitudinal Human Walking Force Using Self-Sustained Oscillator

The paper proposes a self-sustained single-degree-of-freedom oscillator to accurately generate the longitudinal contact force between a pedestrian’s feet and the supporting flat rigid surface. The model is motivated from the self-sustained nature of pedestrian walking, i.e. a pedestrian produces the required internal energy to maintain a repetitive body motion. It is derived by adding two nonlinear terms to the conventional Rayleigh oscillator to yield odd as well as even harmonics, as observed in experimentally recorded longitudinal force data. For the dynamic analysis of the oscillator, two methods are adopted: the energy balance method and the Lindstedt–Poincare perturbation technique. Moreover, the least-squares identification procedure is used to identify values of the oscillator parameters from the force records of 12 different pedestrians walking on an instrumented treadmill at 10 walking speeds. The results generated by the proposed oscillator agree well with the experimental data.

Dispersive Radon transform

Dispersion results in the spreading and overlapping of the wave-packets, which often limits the capability of signal interpretation; on the other hand, such a phenomenon can also be used for structure or media evaluation. In this study, the authors propose an original dispersive Radon transform (DRT), which is formulated as integration transform along a set of dispersion curves. Multichannel dispersive signals of each individual mode can be concentrated to a well localized region in the DRT domain. The proposed DRT establishes the sparse projection of the dispersive components and provides an efficient solution for mode separation, noise filtering, and missing data reconstruction. Particularly the DRT method allows projecting the temporal signals of dispersive waves on the space of parameters of interest, which can be used to solve the inverse problem for waveguide or media property estimation. The least-square procedure and sparse scheme of the DRT are introduced. A high-resolution DRT is designed based on an iterative reweighting inversion scheme, which resembles the infinite-aperture velocity gather. The proposed method is applied by analyzing ultrasonic guided waves in plate-like structures and in a human radius specimen. The results suggest that the DRT method can significantly enhance the interpretation of dispersive signals.

Phasing via pure crystallographic least squares: an unexpected feature.

Crystallographic least-squares techniques, the main tool for crystal structure refinement of small and medium-size molecules, are for the first time used for ab initio phasing. It is shown that the chief obstacle to such use, the least-squares severe convergence limits, may be overcome by a multi-solution procedure able to progressively recognize and discard model atoms in false positions and to include in the current model new atoms sufficiently close to correct positions. The applications show that the least-squares procedure is able to solve many small structures without the use of important ancillary tools: e.g. no electron-density map is calculated as a support for the least-squares procedure.