Nonlinear Data Fitting Research Articles

3-Arylpropionylhydroxamic acid derivatives as Helicobacter pylori urease inhibitors: Synthesis, molecular docking and biological evaluation

Helicobacter pylori urease is involved in several physiologic responses such as stomach and duodenal ulcers, adenocarcinomas and stomach lymphomas. Thus, inhibition of urease is taken for a good chance to treat H. pylori-caused infections, we have therefore focused our efforts on seeking novel urease inhibitors. Here, a series of arylpropionylhydroxamic acids were synthesized and evaluated for urease inhibition. Out of these compounds, 3-(2-benzyloxy-5-chlorophenyl)-3-hydroxypropionylhydroxamic acid (d24) was the most active inhibitor with IC50 of 0.15±0.05μM, showing a mixed inhibition with both competitive and uncompetitive aspects. Non-linear fitting of kinetic data gives kinetics parameters of 0.13 and 0.12μg·mL−1 for Ki and Ki′, respectively. The plasma protein binding assays suggested that d24 exhibited moderate binding to human and rabbit plasma proteins.

Online Damping Ratio Prediction Using Locally Weighted Linear Regression

In this study, a locally weighted linear regression (LWLR) method is proposed to predict damping ratio of a dominant mode online. The LWLR method, which is nonparametric and data-oriented, is essentially proposed for nonlinear data fitting; therefore, it can track the nonlinear power system operations and help damping ratio prediction in real power systems, which is hardly achieved by the conventional linear regression. To successfully implement this method, the measurement of weighting value and the choice of weighting function as well as its parameter setting, related to prediction accuracy and numerical conditions, are extensively discussed. Simulations are carried out in a two-area four-machine system and a large complex system, China Southern Grid. Both results validate the effectiveness of the proposed method.

Characterization of acid functional groups of carbon dots by nonlinear regression data fitting of potentiometric titration curves

The oxygenated functional groups present on the surface of carbon dots with an average size of 2.7±0.5nm were characterized by a variety of techniques. In particular, we discussed the fit data of potentiometric titration curves using a nonlinear regression method based on the Levenberg–Marquardt algorithm. The results obtained by statistical treatment of the titration curve data showed that the best fit was obtained considering the presence of five Brønsted–Lowry acids on the surface of the carbon dots with constant ionization characteristics of carboxylic acids, cyclic ester, phenolic and pyrone-like groups. The total number of oxygenated acid groups obtained was 5mmolg−1, with approximately 65% (∼2.9mmolg−1) originating from groups with pKa<6. The methodology showed good reproducibility and stability with standard deviations below 5%. The nature of the groups was independent of small variations in experimental conditions, i.e. the mass of carbon dots titrated and initial concentration of HCl solution. Finally, we believe that the methodology used here, together with other characterization techniques, is a simple, fast and powerful tool to characterize the complex acid–base properties of these so interesting and intriguing nanoparticles.

Fast and simplified mapping of mean axon diameter using temporal diffusion spectroscopy.

Mapping axon diameter is of interest for the potential diagnosis and monitoring of various neuronal pathologies. Advanced diffusion-weighted MRI methods have been developed to measure mean axon diameters non-invasively, but suffer major drawbacks that prevent their direct translation into clinical practice, such as complex non-linear data fitting and, more importantly, long scanning times that are usually not tolerable for most human subjects. In the current study, temporal diffusion spectroscopy using oscillating diffusion gradients was used to measure mean axon diameters with high sensitivity to small axons in the central nervous system. Axon diameters have been found to be correlated with a novel metric, DDR⊥ (the rate of dispersion of the perpendicular diffusion coefficient with gradient frequency), which is a model-free quantity that does not require complex data analyses and can be obtained from two diffusion coefficient measurements in clinically relevant times with conventional MRI machines. A comprehensive investigation including computer simulations and animal experiments ex vivo showed that measurements of DDR⊥ agree closely with histological data. In humans in vivo, DDR⊥ was also found to correlate well with reported mean axon diameters in human corpus callosum, and the total scan time was only about 8 min. In conclusion, DDR⊥ may have potential to serve as a fast, simple and model-free approach to map the mean axon diameter of white matter in clinics for assessing axon diameter changes.

Cellulose based cationic adsorbent fabricated via radiation grafting process for treatment of dyes waste water

A cationized adsorbent was prepared from cellulosic cotton fabric waste via a single step-green-radiation grafting process using gamma radiation source, wherein poly[2-(methacryloyloxy) ethyl]trimethylammonium chloride (PMAETC) was covalently attached to cotton cellulose substrate. Radiation grafted (PMAETC-g-cellulose) adsorbent was investigated for removal of acid dyes from aqueous solutions using two model dyes: Acid Blue 25 (AB25) and Acid Blue 74 (AB74). The equilibrium adsorption data was analyzed by Langmuir and Freundlich isotherms, whereas kinetic data was analyzed by pseudo first order, pseudo second order, intra particle diffusion and Boyd's models. The PMAETC-g-cellulose adsorbent with 25% grafting yield exhibited equilibrium adsorption capacities of ∼540.0mg/g and ∼340.0mg/g for AB25 and AB74, respectively. Linear and nonlinear fitting of adsorption data suggested that the equilibrium adsorption process followed Langmuir adsorption isotherm model, whereas, the kinetic adsorption process followed pseudo-second order model. The multi-linearities observed in the intra-particle kinetic plots suggested that the intraparticle diffusion was not the only rate-controlling process in the adsorption of acid dyes on the adsorbent, which was further supported by Boyd's model. The adsorbent could be regenerated by eluting the adsorbed dye from the adsorbent and could be repeatedly used.

Overview of SIMS-Based Experimental Studies of Tracer Diffusion in Solids and Application to Mg Self-Diffusion

Tracer diffusivities provide the most fundamental information on diffusion in materials, and are the foundation of robust diffusion databases that enable the use of the Onsager phenomenological formalism with no major assumptions. Compared to traditional radiotracer techniques that utilize radioactive isotopes, the secondary ion mass spectrometry (SIMS)-based thin-film technique for tracer diffusion is based on the use of enriched stable isotopes that can be accurately profiled using SIMS. An overview of the thin-film method for tracer diffusion studies using stable isotopes is provided. Experimental procedures and techniques for the measurement of tracer diffusion coefficients are presented for pure magnesium, which presents some unique challenges due to the ease of oxidation. The development of a modified Shewmon-Rhines diffusion capsule for annealing Mg and an ultra-high vacuum system for sputter deposition of Mg isotopes are discussed. Optimized conditions for accurate SIMS depth profiling in polycrystalline Mg are provided. An automated procedure for correction of heat-up and cool-down times during tracer diffusion annealing is discussed. The non-linear fitting of a SIMS depth profile data using the thin-film Gaussian solution to obtain the tracer diffusivity along with the background tracer concentration and tracer film thickness is demonstrated. An Arrhenius fit of the Mg self-diffusion data obtained using the low-temperature SIMS measurements from this study and the high-temperature radiotracer measurements of Shewmon and Rhines (Trans. AIME 250:1021-1025, 1954) was found to be a good representation of both types of diffusion data over a broad range of temperatures between 250 and 627 °C (523 and 900 K).

Simulated Analysis of Linear Reversible Enzyme Inhibition with SCILAB

SCILAB is a lesser-known program (than MATLAB) for numeric simulations and has the advantage of being free software. A challenging software-based activity to analyze the most common linear reversible inhibition types with SCILAB is described. Students establish typical values for the concentration of enzyme, substrate, and inhibitor to simulate realistic kinetic data. To extract kinetic parameters, linear and nonlinear (hyperbolic) data fitting are used. The actual distinction between competitive and mixed-type inhibitions and between noncompetitive and mixed-type inhibitions is discussed on the basis of nonlinear data fitting. The activity was performed as a part of an advanced undergraduate course, “Chemical Kinetics”, and added to students’ diverse preexisting knowledge.

Acid–base properties and surface complexation modeling of phosphate anion adsorption by wasted low grade iron ore with high phosphorus

The adsorption phenomena and specific reaction processes of phosphate onto wasted low grade iron ore with high phosphorus (WLGIOWHP) were studied in this work. Zeta potential and Fourier transform infrared spectroscopy (FTIR) analyses were used to elucidate the interaction mechanism between WLGIOWHP and aqueous solution. The results implied that the main adsorption mechanism was the replacement of surface hydroxyl groups by phosphate via the formation of inner-sphere complex. The adsorption process was characterized by chemical adsorption onto WLGIOWHP. The non-electrostatic model (NEM) was used to simulate the surface adsorption of phosphate onto WLGIOWHP. The total surface site density and protonation constants for NEM (NT=1.6×10−4mol/g, Ka1=2.2×10−4, Ka2=6.82×10−9) were obtained by non-linear data fitting of acid–base titrations. In addition, the NEM was used to establish the surface adsorption complexation modeling of phosphate onto WLGIOWHP. The model successfully predicted the adsorption of phosphate onto WLGIOWHP from municipal wastewater.

Doppler Effect removal based on instantaneous frequency estimation and time domain re-sampling for wayside acoustic defective bearing detector system

The phenomenon of Doppler Effect in the acoustic signal recorded by the wayside acoustic defective bearing detector (ADBD) leads to the difficulty for fault diagnosis of train bearings with a high moving speed, which is a barrier that would badly reduce the effectiveness of online defect detection. In order to improve the performance of condition monitoring of the bearings on a passing train with microphones amounted besides the railway, the elimination of the Doppler Effect should be solved firstly. An effective method for removing the Doppler Effect embedded in the source signal is presented in this paper. The Short Time Fourier Transform-Viterbi Algorithm (STFT-VA) is applied to obtain instantaneous frequency estimation of the distorted signal. According to the acoustic theory of Morse, the non-linear data fitting is then carried out to get the fitting instantaneous frequencies. The necessary parameters for time domain interpolation re-sampling, which is totally based on the kinematic analysis, are acquired from the fitting curve and the re-sampling sequence could be established in the time domain. As a result of the preceding steps, the fault diagnosis for the train bearings could be implemented with the restored signal. The effectiveness of this proposed method is verified by means of a simulation with three adjacent frequencies and an experiment with practical acoustic signals of train bearings with a crack on the outer race and the inner race. The results of the simulation and the experiment indicate that the proposed method has an excellent performance in removing Doppler Effect, and could be well employed to the condition monitoring and fault diagnosis of train bearings with a high moving speed.

Performance comparison of adsorption isotherm models for supercritical hydrogen sorption on MOFs

Modeling of adsorption on porous material plays a crucial role in providing a better understanding of adsorption phenomena, isotherms, and isosteric heats, and predicting the thermodynamics of adsorption-based storage systems. In this work, the multicomponent potential theory of adsorption (MPTA) coupled with the modified Dubinin potential (MDP), the modified Dubinin–Astakhov (DA) model, and the Unilan model are compared for their effectiveness in nonlinear least square fitting of experimental hydrogen adsorption data on three prototypical metal–organic frameworks (MOFs) in two temperature ranges: 30K—room temperature (RT) for MOF-5, and 77K—RT for MOF-5, Cu-BTC, and MIL-101. The ability of each model to accurately describe excess adsorption is found to depend on the pore size and the energetic pore heterogeneity of MOFs, and the latter's relation to the assumptions used within each model. The simpler Langmuir-like Unilan model complies best with the monolayer type adsorption mechanism in MOFs with large pores and homogenous pore distribution, such as in MOF-5, while the pore filling models like modified DA and MPTA–MDP better represent the adsorption phenomena in MOFs with smaller pores and heterogeneous pore distributions, such as Cu-BTC and MIL-101. In the vicinity of hydrogen's critical temperature, adsorbed hydrogen inside the pores of MOF-5 undergoes a phase-transition to solid-like phase with densities higher than that of bulk solid hydrogen, which is attributed to the increased force field in the confined pores of MOF-5.

Gaussian processes uncertainty estimates in experimental Sentinel-2 LAI and leaf chlorophyll content retrieval

ESA’s upcoming Sentinel-2 (S2) Multispectral Instrument (MSI) foresees to provide continuity to land monitoring services by relying on optical payload with visible, near infrared and shortwave infrared sensors with high spectral, spatial and temporal resolution. This unprecedented data availability leads to an urgent need for developing robust and accurate retrieval methods, which ideally should provide uncertainty intervals for the predictions. Statistical learning regression algorithms are powerful candidats for the estimation of biophysical parameters from satellite reflectance measurements because of their ability to perform adaptive, nonlinear data fitting. In this paper, we focus on a new emerging technique in the field of Bayesian nonparametric modeling. We exploit Gaussian process regression (GPR) for retrieval, which is an accurate method that also provides uncertainty intervals along with the mean estimates. This distinct feature is not shared by other machine learning approaches. In view of implementing the regressor into operational monitoring applications, here the portability of locally trained GPR models was evaluated. Experimental data came from the ESA-led field campaign SPARC (Barrax, Spain). For various simulated S2 configurations (S2-10m, S2-20m and S2-60m) two important biophysical parameters were estimated: leaf chlorophyll content (LCC) and leaf area index (LAI). Local evaluation of an extended training dataset with more variation over bare soil sites led to improved LCC and LAI mapping with reduced uncertainties. GPR reached the 10% precision required by end users, with for LCC a NRMSE of 3.5–9.2% (r2: 0.95–0.99) and for LAI a NRMSE of 6.5–7.3% (r2: 0.95–0.96). The developed GPR models were subsequently applied to simulated Sentinel images over various sites. The associated uncertainty maps proved to be a good indicator for evaluating the robustness of the retrieval performance. The generally low uncertainty intervals over vegetated surfaces suggest that the locally trained GPR models are portable to other sites and conditions.

Fast evaluation of enantioselective drug metabolism by electrophoretically mediated microanalysis: Application to fluoxetine metabolism by CYP2D6

In this work, a capillary electrophoretic methodology for the enantioselective in vitro evaluation of drugs metabolism is applied to the evaluation of fluoxetine (FLX) metabolism by cytochrome 2D6 (CYP2D6). This methodology comprises the in-capillary enzymatic reaction and the chiral separation of FLX and its major metabolite, norfluoxetine enantiomers employing highly sulfated β-CD and the partial filling technique. The methodology employed in this work is a fast way to obtain a first approach of the enantioselective in vitro metabolism of racemic drugs, with the additional advantage of an extremely low consumption of enzymes, CDs and all the reagents involved in the process. Michaelis-Menten kinetic parameters (Km and Vmax ) for the metabolism of FLX enantiomers by CYP2D6 have been estimated by nonlinear fitting of experimental data to the Michaelis-Menten equation. Km values have been found to be 30 ± 3 μM for S-FLX and 39 ± 5 μM for R-FLX. Vmax estimations were 28.6 ± 1.2 and 34 ± 2 pmol·min(-1) ·(pmol CYP)(-1) for S- and R-FLX, respectively. Similar results were obtained using a single enantiomer (R-FLX), indicating that the use of the racemate is a good option for obtaining enantioselective estimations. The results obtained show a slight enantioselectivity in favor of R-FLX.

Synthesis and characterization of resorcinol formaldehyde carbon cryogel as efficient sorbent for imidacloprid removal

AbstractCarbon cryogel (CC) has been prepared through sol gel polycondensation of resorcinol with formaldehyde in basic aqueous solution followed by freeze-drying and carbonization. Porous properties of CC analyzed by gravimetric McBain method confirmed the expected surface area and degree of mesoporosity. Obtained powdered material was used for the removal of pesticide imidacloprid from aqueous solutions under regular batch adsorption procedure. A set of several isotherm models including Langmuir, Freundlich, Temkin, Dubinin–Radushkevich, Brouers–Sotolongo, Redlich–Peterson, Sips, Toth, Jovanovic, Hurkins–Jura, Halsey and Radke–Prausnitz model was used for nonlinear fitting of equilibrium data. Several models fitted with quite high correlation coefficients. Bangham and Elovich model fitted suitably for kinetic study indicating that pesticide diffusion into carbons pores is important step which dictates the process rate. Suitability of kinetic models decreased with the increase in adsorbent dosage. Imidac...

Determination of the kinematic viscosity by the liquid rise in a capillary tube

We discuss first the valid time interval of a formula found in the literature which gives the theoretical distance run by a liquid which rises along a capillary tube as a function of time. A non-linear least square fitting of experimental data to this theoretical curve allows the measurement of the kinematic viscosity of the liquid. The goodness of the fitting for three different sets of experimental data given in the literature is above 99%.

Imaging and characterization of bioengineered blood vessels within a bioreactor using free‐space and catheter‐based OCT

Regenerative medicine involves the bioengineering of a functional tissue or organ by seeding living cells on a biodegradable scaffold cultured in a bioreactor. A major barrier to creating functional tissues, however, has been the inability to monitor the dynamic and complex process of scaffold maturation in real time, making control and optimization extremely difficult. Current methods to assess maturation of bioengineered constructs, such as histology or organ bath physiology, are sample-destructive. Optical coherence tomography (OCT) has recently emerged as a key modality for structural assessment of native blood vessels as well as engineered vessel mimics. The objective of this study was to monitor and assess in real time the development of a bioengineered blood vessel using a novel approach of combining both free-space and catheter-based OCT imaging in a new quartz-walled bioreactor. Development of the blood vessel was characterized by changes in thickness and scattering coefficient over a 30-day period. We constructed a novel blood vessel bioreactor utilizing a rotating cylindrical quartz cuvette permitting free-space OCT imaging of an installed vessel's outer surface. A vascular endoscopic OCT catheter was used to image the lumen of the vessels. The quartz cuvette permits 360 degree, free-space OCT imaging of the blood vessel. Bioengineered blood vessels were fabricated using biodegradable polymers (15% PCL/collagen, ∼300 µm thick) and seeded with CH3 10t1/2 mesenchymal stem cells. A swept-source OCT imaging system comprised of a 20 kHz tunable laser (Santec HSL2000) with 1,300 nm central wavelength and 110 nm FWHM bandwidth was used to assess the vessels. OCT images were obtained at days 1, 4, 7, 14, 21, and 30. Free-space (exterior surface) OCT images were co-registered with endoscopic OCT images to determine the vessel wall thickness. DAPI-stained histological sections, acquired at same time point, were evaluated to quantify wall thickness and cellular infiltration. Non-linear curve fitting of free-space OCT data to the extended Huygen-Fresnel model was performed to determine optical scattering properties. Vessel wall thickness increased from 435 ± 15 µm to 610 ± 27 µm and Vessel scattering coefficient increased from 3.73 ± 0.32 cm⁻¹ to 5.74 ± 0.06 cm⁻¹ over 30 days. Histological studies showed cell migration from the scaffold surface toward the lumen and cell proliferation over the same time course. The imaging procedure did not have any significant impact on scaffold dimensions, cell migration, or cell proliferation. This study suggests that combination of free-space and catheter-based OCT for blood vessel imaging provides accurate structural information of the developing blood vessel. We determined that free-space OCT images could be co-registered with catheter-based OCT images to monitor structural features such as wall thickness or delamination of the developing tissue-engineered blood vessel within a bioreactor. Structural parameters and optical properties obtained from OCT imaging correlate with histological sections of the blood vessel and could potentially be used as markers to non-invasively and non-destructively assess regeneration of engineered tissues in real time.

In-line capillary electrophoretic evaluation of the enantioselective metabolism of verapamil by cytochrome P3A4

In this paper a methodology for the in-line evaluation of enantioselective metabolism by capillary electrophoresis has been developed and applied to the study of verapamil metabolism by cytochrome P3A4. The developed methodology comprises an in-capillary reaction step carried out by electrophoretically mediated microanalysis and a separation step in which highly sulfated β-cyclodextrin with partial filling technique has been employed as chiral selector for verapamil and norverapamil enantiomers resolution, joining the advantages of both methodologies in a unique assay. Kinetic parameters of the enzymatic reaction (Km and Vmax) have been evaluated for both verapamil enantiomers by non-linear fitting of experimental data obtained under intermediate precision conditions to Michaelis–Menten equation. Km and Vmax estimated values were 51±9μM and 22±2pmolmin−1(pmolCYP)−1 for S-VER and 47±9μM and 21±2pmolmin−1(pmolCYP)−1 for R-VER. Consequently, slight enantioselectivity was found for the CYP3A4 metabolism of verapamil. However, since confidence intervals of estimates overlap, we cannot assure a significant enantioselectivity. Intrinsic clearance values were also estimated from Km and Vmax for both enantiomers.

The prediction capability of the kinetic models extracted from isothermal data in non-isothermal conditions for an epoxy prepreg

In this article, the kinetic behavior of a glass/epoxy prepreg, HexPly® 1454, has been investigated using differential scanning calorimetry data. The kinetic parameters of three different kinetic models have been calculated using non-linear curve fitting of isothermal differential scanning calorimetry data. Curve fitting was done based on genetic algorithm to allow to obtain a unique value for each kinetic parameter. The non-isothermal differential scanning calorimetry experiments were predicted using the obtained models. Prediction results demonstrated that only model with the minimum number of kinetic parameters and unique value for each of them can correctly predict non-isothermal experiments at all heating rates.

Application of a Frequency Distribution Method for Determining Instars of the Beet Armyworm (Lepidoptera: Noctuidae) From Widths of Cast Head Capsules

Instar determination of field-collected insect larvae has generally been based on the analysis of head capsule width frequency distributions or bivariate plotting, but few studies have tested the validity of such methods. We used head capsules from exuviae of known instars of the beet armyworm, Spodoptera exigua (Hübner) (Lepidoptera: Noctuidae), to determine the larval instars with the frequency distribution method and Dyar's rule. Head capsule widths of S. exigua ranged from 0.313 to 1.446 mm. The number of instars from the analytical method matched that from the observed data. Based on misclassification rules derived from nonlinear least square fitting of the head capsule width data, the theoretical misclassification rates ranged from 0.62 to 1.92%. Comparing the theoretical distribution to the observed data, the observational misclassification probabilities ranged from 1.18 to 3.03%. There were also 10 head capsules, eight third instars and two fourth instars, not classified into any of the known instars based on the theoretical distributions. Dyar's growth ratios of successive instars ranged from 1.41 to 1.65, and those based on the observed data and theoretical distribution were similar. Both approaches yielded a linear relationship between the natural logarithm of the mean head capsule width and the instar number, which indicates full representation of the larval instars. The results demonstrated that the frequency distribution-based method was robust, although we recommend caution when using such methods to classify head capsules into specific instar classes. Application of computer algorithms should also be accompanied by visual inspection to determine instars from the frequency distribution.

Equivalent circuit models and analysis of impedance spectra of solid electrolyte Na0.25Li0.75Zr2(PO4)3

Two RC model circuits are connected in series in order to analyze the electrical and dielectric behaviour of mixed alkali Na0.25Li0.75Zr2(PO4)3 NASICON compound. However, the data obtained could best be described by one RC circuit representing the grain boundary resistance () and capacitance () in the temperature and frequency range 300-600 K and 300 kHz to 1GHz, respectively. The values of the grain boundary activation energy obtained by fitting to the Arrhenius equation in a plot is ~ 0.40 eV, which is close to the bulk activation energy for electrical conduction. The maximum conductivity obtained is 0.3 S/m at 590 K. A non Debye character was observed in the dielectric permitivity in its frequency dependence. However, the temperature dependence of followed a linear behaviour at low temperatures and frequencies but decreased at higher temperatures. Complex non linear least squares fitting of impedance data using a composite circuit shows good fitting results with relative standard deviation less than 0.2 for all the free parameters which is indicative of the accuracy of data obtained. Similar good fitting results, using a generic battery model, suggest the applicability of the material in rechargeable lithium ion batteries.

A Robust Static Decoupling Algorithm for 3-Axis Force Sensors Based on Coupling Error Model and ε-SVR

Coupling errors are major threats to the accuracy of 3-axis force sensors. Design of decoupling algorithms is a challenging topic due to the uncertainty of coupling errors. The conventional nonlinear decoupling algorithms by a standard Neural Network (NN) are sometimes unstable due to overfitting. In order to avoid overfitting and minimize the negative effect of random noises and gross errors in calibration data, we propose a novel nonlinear static decoupling algorithm based on the establishment of a coupling error model. Instead of regarding the whole system as a black box in conventional algorithm, the coupling error model is designed by the principle of coupling errors, in which the nonlinear relationships between forces and coupling errors in each dimension are calculated separately. Six separate Support Vector Regressions (SVRs) are employed for their ability to perform adaptive, nonlinear data fitting. The decoupling performance of the proposed algorithm is compared with the conventional method by utilizing obtained data from the static calibration experiment of a 3-axis force sensor. Experimental results show that the proposed decoupling algorithm gives more robust performance with high efficiency and decoupling accuracy, and can thus be potentially applied to the decoupling application of 3-axis force sensors.