Nonlinear Least-squares Analysis Research Articles

Lanthanum-Ferrite based cathode: Impedance data interpretation via complex nonlinear least-squares and distribution of relaxation times analyses

Lanthanum Strontium Cobalt Ferrite Oxide (LaSrCoFeO3) has been widely used as cathode material for intermediate-temperature solid oxide fuel cells at the temperature of 500–800 °C. At this temperature range, understanding the electrochemical behavior which is commonly analyzed by complex nonlinear least-squares (CNLS) analysis is very crucial in improving the cathode's performance. However, this analysis shows some limitations in interpreting the electrochemical processes in detail, particularly at the electrode-electrolyte interface. Hence, this study is conducted to compare the electrochemical impedance data analyses by CNLS and the distribution of relaxation times (DRT) of a fabricated LaSrCoFe|BCZY|LaSrCoFe (LaSrCoFeLa0.6Sr0.4Co0.2Fe0.8O3 and BCZY=BaCe0.54Zr0.36Y0.1O2.95) symmetrical cell. Impedance data of the cell is collected at T = 800 °C at two different stabilization times and to further enhance the analysis process, the impedance data of the cell at measurement temperatures of 700 °C and 750 °C are also included. In a Nyquist plot, the cell exhibits depressed semi-circles that represent a few processes occurring at the interface. The DRT analysis is more precise and easily reveals the semi-circles consisting of four different sub-processes (represented by four peaks) than CNLS (represented by four impedance arcs). The extracted responses from both analyses correspond to the oxygen reduction reactions that follow the Adler-Lane-Steele model. The stabilized symmetrical cells for respective 34 h and 17 h show an area-specific resistance (ASR) of (i) 0.22 Ωcm2 and 0.30 Ωcm2 (by CNLS) and (ii) 0.20 Ωcm2 and 0.26 Ωcm2 (by DRT). In addition, the ASR of the cell at T = 700 °C and T = 750 °C after being stabilized for 34 h is (iii) 0.71 Ωcm2 and 0.40 Ωcm2 (by CNLS) and (iv) 0.70 Ωcm2 and 0.44 Ωcm2 (by DRT), accordingly. Conversely, the cell's microstructure is not affected by the applied stabilization periods as observed by a scanning electron microscope.

Head growth in patients with myelomeningocele treated with prenatal and postnatal surgery.

The need for permanent CSF diversion is lower in patients who have undergone prenatal surgery for myelomeningocele (MMC) than in those who have undergone postnatal closure. Differences in brain development and head growth between treatment groups are not known, particularly for those who do not require surgical treatment for hydrocephalus. The objective of this study was to determine differences in head growth and to generate MMC-specific head circumference (HC) growth curves for patients who underwent either prenatal or postnatal surgery. The authors retrospectively identified patients from St. Louis Children's Hospital who were treated for MMC between 2016 and 2021. HC data were obtained from birth until the most recent follow-up or hydrocephalus treatment. Nonlinear least-squares regression analysis was performed to fit the data into four models: two-term power, Gompertz, West ontogenetic, and Weibull. Subsequently, the curves were assessed for their utility in predicting hydrocephalus treatment. Sixty-one patients (29 females [47.5%], 25 [41%] underwent prenatal surgery, mean gestational age at birth 36.6 weeks) were included in the study. The Weibull model best fit the HC data (prenatal adjusted R2 = 0.95, postnatal adjusted R2 = 0.95), while the Gompertz model had the worst fit (prenatal adjusted R2 = 0.56, postnatal adjusted R2 = 0.39) across both cohorts. Prenatal MMC repair patients had significantly larger HC measurements than their postnatal repair counterparts. The 50th percentile of the Weibull curve was determined as a useful threshold for hydrocephalus treatment: children with HC measurements that crossed and remained above this threshold were significantly more likely to have hydrocephalus treatment regardless of time of MMC repair (prenatal relative risk [RR] 10.0 [95% CI 1.424-70.220], sensitivity 85.7% [95% CI 0.499-0.984], and specificity 82.4% [95% CI 0.600-0.948]; postnatal RR 4.750 [95% CI 1.341-16.822], sensitivity 90.5% [95% CI 0.728-0.980], and specificity 75.0% [95% CI 0.471-0.924]). The HC growth curves of the MMC patients treated prenatally were significantly larger than the WHO HC curves (p < 0.001). The Weibull model was identified as the HC growth curve with the best fit for MMC patients and serves as a useful predictor of hydrocephalus treatment. For MMC patients with hydrocephalus, prenatal repair patients fit the model well but postnatal repair patients did not, potentially indicating different mechanisms of hydrocephalus development. Those treated prenatally had significantly larger HC measurements compared with both the general population and those treated postnatally. Further study is needed to understand the long-term cognitive outcomes and optimal management of clinically asymptomatic patients with large HC measurements who were treated prenatally for MMC.

Real-time kinetics and affinity analysis of the interaction between protein A and immunoglobulins G derived from different species on silica colloidal crystal films

Kinetic and affinity analysis of protein interactions reveals information on their related activities in biological processes. Herein, we established a system for evaluating the kinetics and affinity of the interaction between protein A and various IgG species on the surface of silica spheres of silica colloidal crystal (SCC) films by the extraordinary optical interference capabilities of 190 nm silica spheres after self-assembly. The equilibrium association constant (KA) was calculated by the equilibrium Langmuir model and nonlinear least-squares analysis of time-dependent data. The relative protein A/IgG binding affinity is human > rabbit >cow >goat. In addition, the competitive interaction of distinct species of IgG with protein A at the interface of SCC films was studied and performed. These findings may help with the use of protein A and other recognition components in a number of sensor types. Furthermore, this research might offer a novel approach to determining the kinetics and affinity of proteins on the surface of spheres particles, which may contribute to the development of the application of spheres particles in pharmaceutical science, biomedical engineering, and other techniques.

Experimental verification of theoretical uncertainties in non-linear least-squares analysis of gamma spectra

Experimental verification of theoretical uncertainties in non-linear least-squares analysis of gamma spectra

1H NMR spectroscopic characterization of inclusion complex of desferrioxamine B chelator and β-cyclodextrin

In this work the complexation between desferioxamine B (DFOB), and β-Cyclodextrin (β-CD) in solution was investigated using 1H NMR spectroscopy. Inclusion compound formation was confirmed by the upfield shifts of H3 and H5 protons, located inside the cavity of β-CD, and downfield shifts of some of the methylene protons of DFOB, observed during NMR titration experiments. Using the continuous variation method, we determined a 1:1 stoichiometry and the association constant was calculated using a nonlinear least-square regression analysis implemented in CONSTEQ, a software developed in our group. A theoretical molecular docking study was additionally performed to ascertain possible conformations of the inclusion complex.

Performance Analysis of Ammonia in Solid Oxide Fuel Cells

The transition of the marine propulsion system towards alternative fuels is mandatory to offset carbon emission. Among the alternative fuels, ammonia is carbon-free and can be produced in sustainable ways. Ammonia has 17.8% hydrogen (wt %) and is easily liquified at 25°C and 8 bar pressure. The two-stroke internal combustion engines currently used in the marine sector reach efficiencies of about 50% but generate substantial polluting emissions. Solid oxide fuel cells generate electricity with efficiencies greater than 50 % and can use ammonia as fuel.In this work, a single-cell SOFC was characterised using in-situ ammonia decomposition reaction (Int-ADR) and compared with ex-situ ammonia decomposition reaction (Ext - ADR; composition - N2:H2 = 1:3), and pure hydrogen (H2 100%; composition - H2 = 100%), between temperatures of 750 °C to 850°C. The constant load tests performed at 750°C with 84% fuel utilization revealed that the LHV efficiency of the ammonia fed SOFC was 58%. The J-V characteristics showed similar performances for the three compositions at different temperatures and flowrates. The open-circuit voltage (OCV) of Int-ADR was similar to that of Ext- ADR, confirming that usage of ammonia as fuel in the Ni-YSZ anode involved two steps, (i) decomposition of ammonia into nitrogen and hydrogen, followed by (ii) electrochemical conversion of the hydrogen into steam.The electrochemical impedance spectroscopy (EIS) results showed that the polarisation resistance (Rp) decreased by 15% over this temperature range. The total flowrate of 80 Nml min -1 of ammonia for Int-ADR, 160 Nml min -1 for Ext ADR and 120 Nml min -1 for H2 100% were chosen after performing distribution of relaxation time (DRT) analysis on changing total flowrates at 775 °C. The DRT coupled with complex nonlinear least-square (CNLS) analysis for the temperature range of 750-850°C revealed that the charge transfer resistance reduced by 66%, while the gas conversion resistance increased by 12% due to better evacuation of steam. The Arrhenius plot of DRT peak resistances revealed that the polarisation activation energy was the same for the three gas compositions, at 16 kJ mol -1 . Figure 1

Determination of Two-Steps Acid Dissociation Constants of L-Ascorbic Acid by Capillary Zone Electrophoresis

Two-steps acid dissociation constants of L-ascorbic acid (AA) were determined through the changes in the effective electrophoretic mobility in capillary zone electrophoresis. Although ascorbic acid is oxidatively degradable in an aqueous solution, especially in alkaline conditions, the effective electrophoretic mobility of AA was successfully measured in the pH range between 1.87 and 11.97. In the analysis of the first-step acid dissociation constant (pKa1) at weakly acidic pH conditions, a coated capillary with 1,3-propanesultone and a pressure-assist were utilized to detect anionic AA. In the analysis of the second-step acid dissociation constant (pKa2) at weakly alkaline pH conditions, AA was successfully detected at the pH range up to 11.97 with the help of Cu catalyst to remove the dissolved oxygen in the separation buffer. Acid dissociation constants were independently determined as pKa1 = 4.15±0.01 and pKa2 = 12.07±0.04 by non-linear least-squares analyses. AA did not fully dissociate at the weakly alkaline pH range, and the effective electrophoretic mobility of the dianion form of AA was extrapolated for the analysis.

Estimating the size of COVID-19 epidemic outbreak

In this work, we analyze the epidemic data of cumulative infected cases collected from many countries as reported by the World Health Organization (WHO). Our inspection is motivated by the renormalization group (RG) framework. Here we propose the RG-inspired logistic function of the form as an epidemic strength function with n being asymmetry in the modified logistic function. We perform the non-linear least-squares analysis with data from various countries. The uncertainty for model parameters is computed using the squared root of the corresponding diagonal components of the covariance matrix. We carefully divide countries under consideration into 2 categories based on the estimation of the inflection point: the maturing phase and the growth-dominated phase. We observe that long-term estimations of cumulative infected cases of countries in the maturing phase for both n = 1 and are close to each other. We find from the value of root mean squared error (RMSE) that the RG-inspired logistic model with is slightly preferable in this category. We also argue that n determines the characteristic of the epidemic at an early stage. However, in the second category, the estimated asymptotic number of cumulative infected cases contain rather large uncertainty. Therefore, in the growth-dominated phase, we focus on using n = 1 for countries in this phase. Some of them are in an early stage of an epidemic with an insufficient amount of data leading to a large uncertainty on parameter fits. In terms of the accuracy of the size estimation, the results do strongly depend on limitations on data collection and the epidemic phase for each country.

Loading of nickel phthalocyanine onto functionalized mesoporous KIT-6 solid support: an efficient visible photocatalyst for the degradation of 2,4-dichlorophenol

2,4-Dichlorophenol (DCP) is one of the high-risk sources of contaminating water resources, which is very difficult for biodegradation. In this contribution, sulfonated nickel phthalocyanine (NiPcS) was loaded onto mesoporous KIT-6 through functionalization of the solid support and electrostatic anchorage of the dye. The materials were characterized using standard instrumental methods in every step of the preparation. High catalytic activity was noticed for the degradation of DCP under visible light. The results showed that the photocatalyst had converted nearly 90% of DCP under visible light with optimum operating conditions of 25 mg of catalyst, natural pH (pH 6), and 30 mg L−1 of DCP also, chemical oxygen demand (COD) were determined. The photo-degradation rate of DCP fits well with the pseudo first-order kinetics and, the nonlinear least-squares analysis, which is common for photocatalytic reactions. The catalyst reusing is simple and it was found that it remarkably preserves 94% of its activity following four consecutive cycles of use.

Dissecting the statistical properties of the linear extrapolation method of determining protein stability.

The linear extrapolation method to determine protein stability from denaturant-induced unfolding experiments is based on the observation that the free energy of unfolding is often a linear function of the denaturant concentration. The value in the absence of denaturant is then estimated by extrapolation from this linear relationship. Parameters and their confidence intervals are typically estimated by nonlinear least-squares regression. We have compared different methods for calculating confidence intervals and found that a simple method based on linear theory gives accurate results. We have also compared three different parameterizations of the linear extrapolation method and show that the most commonly used form is problematic since the stability and m-value are correlated in the nonlinear least-squares analysis. Parameter correlation can in some cases causes problems in the estimation of confidence intervals and regions and should be avoided when possible. Two alternative parameterizations show much less correlation between parameters.

Proton nutation spectroscopy. Application to the quantitation of water in a kaolinite sample.

Nutation consists in monitoring the motion of nuclear magnetization under the application of a radio-frequency field. Depending on the amplitude of the rf field, the nutation frequency may be sensitive to the two longitudinal and transverse relaxation rates R1 and R2, hence the possibility of differentiating species having the same resonance frequency in the laboratory frame (the Larmor frequency) but differing by their relaxation rates, as it may occur for the composite proton NMR signal of water in complex systems. Thus, Fourier transform of the nutation curve should provide separate peaks associated with the different species involved in a composite classical NMR signal. As nutation peaks may be close to zero frequency (or even at zero frequency), their full observation requires a complex Fourier transform. This implies a second nutation curve, de-phased by 90° with respect to the first one, achieved here by a second nutation experiment preceded by a 90° hard pulse. Eventually, more accurate parameters are obtained by a non-linear least-squares analysis of the simple nutation experiment. This methodology is applied to water in a natural clay (kaolinite) and reveals the unexpected presence of two peaks which can be characterized by the relaxation rates derived from the line-widths of the nutation signals.

Super-resolution reconstruction of speckle phase in depth-resolved wavelength scanning interference using the total least-squares analysis.

Depth-resolved wavelength scanning interferometry (DRWSI) is a tomographic imaging tool that employs phase measurement to visualize micro-displacement inside a sample. It is well known that the depth resolution of DRWSI is restricted by a wavelength scanning range. Recently, a nonlinear least-squares analysis (NLS) algorithm was proposed to overcome the limitation of the wavelength scanning range to achieve super-resolution; however, the NLS failed to measure speckle surfaces owing to the sensibility of initial values. To the best of our knowledge, the improvement of depth resolution on measuring a speckle surface remains an open issue for DRWSI. For this study, we redesigned the signal processing algorithm for DRWSI to refine the depth resolution when considering the case of speckle phase measurement. It is mathematically shown that the DRWSI's signal is derived as a model of total least-squares analysis (TLSA). Subsequently, a super-resolution of the speckle phase map was obtained using a singular value decomposition. Further, a numerical simulation to measure the micro-displacements for speckle surfaces was performed to validate the TLSA, and the results show that it can precisely reconstruct the displacements of layers whose depth distance is 5μm. This study thus provides an opportunity to improve the DRWSI's depth resolution.

Determination of Desorption Isotherms of Potato Using Gravimetric Method and Fast Isotherm Method

The desorption isotherms of potato (Solanum tuberosum) were determined for a range of temperature 30–60 °C using gravimetric and fast isotherm method over the range of relative humidity 5–85%. The objective of this work is to investigate and document the best practice to perform experiments using both these two methods. The desorption isotherms obtained from the gravimetric method were fitted using three models: GAB, BET, and Oswin. A nonlinear least-square regression analysis was used to evaluate the constants of the three isotherm models. The goodness of the fit was determined by two statistical parameters: standard error and correlation coefficient. GAB model was found to be competent to describe desorption isotherms of potato followed by BET and Oswin model. Also, the sorption behavior of potato obtained from the fast isotherm method was validated to the standard gravimetric method.

Preliminary Sizing Correlations for Fixed-Wing Unmanned Aerial Vehicle Characteristics

A comprehensive set of preliminary sizing correlations can be invaluable in the early design stages of any aircraft or to provide initial characteristics for multidisciplinary optimization. For unmanned aircraft, such a set of correlations is not available. The current paper provides correlations based on data for 856 fixed-wing platforms. Correlations for the main mission, mass, and geometric parameters are derived through a nonlinear least-squares regression analysis. Where needed, a distinction is made between aircraft employing different propulsion systems; and the aircraft are split into five categories: piston-, battery-, turbine-, fuel-cell-, and solar-powered aircraft. Significant trends are revealed, and a closed set of correlations is provided to generate an initial sizing, starting from mission and payload requirements.

Modelling methane production kinetics of complex poultry slaughterhouse wastes using sigmoidal growth functions

The kinetic evaluation of the methane potential from poultry slaughterhouse waste streams was performed using modified sigmoidal bacterial growth curve equations (Richards, logistic, Gompertz) in order to investigate their suitability to describe the degradation patterns associated with complex substrates, primarily composed of fats. The methane potential and degradation patterns under mesophilic conditions were assessed using Biochemical Methane Potential (BMP) assays. A nonlinear least-square regression analysis was performed to fit the sigmoidal functions to the cumulative methane production curves with respect to time generated from the BMP assays. In the cases modelled the Gompertz and logistic, three parameter models, sufficiently described the methane generation of the simple substrates (dissolved air flotation sludge) with no sign of acute inhibition due to high fat contents. When dealing with more complex degradation patterns of the substrates with a higher fat content (soft offals) and increased bioavailability of the organics, the three parameter models became insufficient in describing the experimental data due to features of the original growth functions, in particularly their fixed points of inflection. In such cases the fourth parameter afforded in the Richards model became critical allowing variability in the point of inflection allowing a much better fit to the experimental curves.

Li+ Local Structure in Li–Tetraglyme Solvate Ionic Liquid Revealed by Neutron Total Scattering Experiments with the 6/7Li Isotopic Substitution Technique

Equimolar mixtures of lithium bis(trifluoromethanesulfonyl)amide (LiTFSA) and tetraglyme (G4: CH3O-(CH2CH2O)4-CH3) yield the solvate (or chelate) ionic liquid [Li(G4)][TFSA], which is a homogeneous transparent solution at room temperature. Solvate ionic liquids (SILs) are currently attracting increasing research interest, especially as new electrolytes for Li-sulfur batteries. Here, we performed neutron total scattering experiments with (6/7)Li isotopic substitution to reveal the Li(+) solvation/local structure in [Li(G4)][TFSA] SILs. The experimental interference function and radial distribution function around Li(+) agree well with predictions from ab initio calculations and MD simulations. The model solvation/local structure was optimized with nonlinear least-squares analysis to yield structural parameters. The refined Li(+) solvation/local structure in the [Li(G4)][TFSA] SIL shows that lithium cations are not coordinated to all five oxygen atoms of the G4 molecule (deficient five-coordination) but only to four of them (actual four-coordination). The solvate cation is thus considerably distorted, which can be ascribed to the limited phase space of the ethylene oxide chain and competition for coordination sites from the TFSA anion.

An Investigation of Protonic and Oxide Ionic Conductivities at the Interfacial Layers in SDC-LNC Composite Electrolytes

SDC (Sm0.2Ce0.8O1.9)-LNC ((Li0.52Na0.48)2CO3) nanocomposites with various LNC volume fractions (0.0, 0.3, 0.4, 0.5, 0.6, 0.7 and 1.0) and MgO-50LNC composites were prepared by prefiring and sintering at different temperatures. The XRD, FESEM and TEM techniques were employed to characterize their phase components and microstructures. The AC impedance spectroscopy and DC polarization method were used to measure their electrical conductivities under different conditions. It has been found that the carbonate phase in the MgO-LNC composites is homogeneously crystallized, whereas amorphous carbonate is always identified in the SDC-LNC composites and shown to form an interface layer of ∼6nm in thickness at the surface of SDC crystallites due to the strong interactions between SDC and LNC phases. The protonic, oxide ionic and overall ionic conductivities of LNC phase were measured at the different temperatures from 450 to 650°C and then adopted to study the contributions of the interfacial interaction between SDC and LNC phase to the enhanced electrical conductivity of SDC-50LNC composites. The interfacial interactions were found to significantly enhance the protonic and oxide ionic conductivities in the SDC-LNC composites regardless of the remarkable suppressing effect on the migrations of metal ions as the majority mobile charged species in the molten LNC phase. Furthermore, based on a microstructural model of randomly-packed SDC/LNC composite particles and the Maxwell-Garnet mixture rule, the protonic and oxide ionic conductivities of the interface layer was successfully found to reach as high as 97mS/cm and 46mS/cm at 650°C, respectively, through a non-linear least-squares data analysis.

Untangling the Diverse Interior and Multiple Exterior Guest Interactions of a Supramolecular Host by the Simultaneous Analysis of Complementary Observables.

The entropic and enthalpic driving forces for encapsulation versus sequential exterior guest binding to the [Ga4L6](12-) supramolecular host in solution are very different, which significantly complicates the determination of these thermodynamic parameters. The simultaneous use of complementary techniques, such as NMR, UV-vis, and isothermal titration calorimetry, enables the disentanglement of such multiple host-guest interactions. Indeed, data collected by each technique measure different components of the host-guest equilibria and together provide a complete picture of the solution thermodynamics. Unfortunately, commercially available programs do not allow for global analysis of different physical observables. We thus resorted to a novel procedure for the simultaneous refinement of multiple parameters (ΔG°, ΔH°, and ΔS°) by treating different observables through a weighted nonlinear least-squares analysis of a constrained model. The refinement procedure is discussed for the multiple binding of the Et4N(+) guest, but it is broadly applicable to the deconvolution of other intricate host-guest equilibria.

Kinetic Analysis as a Tool to Distinguish Pathway Complexity in Molecular Assembly: An Unexpected Outcome of Structures in Competition.

While the sensitive dependence of the functional characteristics of self-assembled nanofibers on the molecular structure of their building blocks is well-known, the crucial influence of the dynamics of the assembly process is often overlooked. For natural protein-based fibrils, various aggregation mechanisms have been demonstrated, from simple primary nucleation to secondary nucleation and off-pathway aggregation. Similar pathway complexity has recently been described in synthetic supramolecular polymers and has been shown to be intimately linked to their morphology. We outline a general method to investigate the consequences of the presence of multiple assembly pathways, and show how kinetic analysis can be used to distinguish different assembly mechanisms. We illustrate our combined experimental and theoretical approach by studying the aggregation of chiral bipyridine-extended 1,3,5-benzenetricarboxamides (BiPy-1) in n-butanol as a model system. Our workflow consists of nonlinear least-squares analysis of steady-state spectroscopic measurements, which cannot provide conclusive mechanistic information but yields the equilibrium constants of the self-assembly process as constraints for subsequent kinetic analysis. Furthermore, kinetic nucleation-elongation models based on one and two competing pathways are used to interpret time-dependent spectroscopic measurements acquired using stop-flow and temperature-jump methods. Thus, we reveal that the sharp transition observed in the aggregation process of BiPy-1 cannot be explained by a single cooperative pathway, but can be described by a competitive two-pathway mechanism. This work provides a general tool for analyzing supramolecular polymerizations and establishing energetic landscapes, leading to mechanistic insights that at first sight may seem unexpected and counterintuitive.

Thermodynamic study of complex formation between Ce3+ and cryptand 222 in some binary mixed nonaqueous solvents

The stoichiometry, stability and the thermodynamic parameters of complex formation between cerium(III) cation and cryptand 222 (4,7,13,16,21,24-hexaoxa-1,10-diazabycyclo[8.8.8]-hexacosane) were studied by conductometric titration method in some binary solvent mixtures of dimethylformamide (DMF), 1,2-dichloroethane (DCE), ethyl acetate (EtOAc) and methyl acetate (MeOAc) with methanol (MeOH), at 288, 298, 308, and 318 K. A model based on 1: 1 stoichiometry has been used to analyze the conductivity data. The data have been fitted according to a non-linear least-squares analysis that provide the stability constant, K f, for the cation-ligand inclusion complex. The results revealed that the stability order of [Ce(cryptand 222)]3+ complex changes with the nature and composition of the solvent system. A non-linear relationship was observed between the stability constant (logK f) of [Ce(cryptand 222)]3+ complex versus the composition of the binary mixed solvent. Standard thermodynamic values were obtained from temperature dependence of the stability constant of the complex, show that the studied complexation process is mainly entropy governed and are influenced by the nature and composition of the binary mixed solvent solutions.