Method For Estimation Of Constants Research Articles

Identifiability Analysis and Noninvasive Online Estimation of the First-Order Neural Activation Dynamics in the Brain With Closed-Loop Transcranial Magnetic Stimulation.

Neurons demonstrate very distinct nonlinear activation dynamics, influenced by the neuron type, morphology, ion channel expression, and various other factors. The measurement of the activation dynamics can identify the neural target of stimulation and detect deviations, e.g., for diagnosis. This paper describes a tool for closed-loop sequential parameter estimation (SPE) of the activation dynamics through transcranial magnetic stimulation (TMS). The proposed SPE method operates in real time, selects ideal stimulus parameters, detects and processes the response, and concurrently estimates the input-output (IO) curve and the first-order approximation of the activated neural target. To develop a method for concurrent SPE of the first-order activation dynamics and IO curve with closed-loop TMS. First, identifiability of an integrated model of the first-order neural activation dynamics and IO curve is assessed, demonstrating that at least two IO curves need to be acquired with different pulse widths. Then, a two-stage SPE method is proposed. It estimates the IO curve by using Fisher information matrix (FIM) optimization in the first stage and subsequently estimates the membrane time constant as well as the coupling gain in the second stage. The procedure continues in a sequential manner until a stopping rule is satisfied. The results of 73 simulation cases confirm the satisfactory estimation of the membrane time constant and coupling gain with average absolute relative errors (AREs) of 6.2% and 5.3%, respectively, with an average of 344 pulses (172 pulses for each IO curve or pulse width). The method estimates the IO curves' lower and upper plateaus, mid-point, and slope with average AREs of 0.2%, 0.7%, 0.9%, and 14.5%, respectively. The conventional time constant estimation method based on the strength-duration (S-D) curve leads to 33.3% ARE, which is 27.0% larger than 6.2% ARE obtained through the proposed real-time FIM-based SPE method in this paper. SPE of the activation dynamics requires acquiring at least two IO curves with different pulse widths, which needs a controllable TMS (cTMS) device with adjustable pulse duration. The proposed SPE method enhances the cTMS functionality, which can contribute novel insights in research and clinical studies.

Numerical Application of a Proposed Material Constant Estimation Method Based on Ideal Mixing Theory

In large projects such as dams, embankments, and seawalls, it is sometimes important to determine the compressive properties of a mixture containing soil and gravel with particle sizes exceeding 75 mm. The Saemangeum Renewable Energy Vision Proclamation Ceremony, held in October 2018 in Korea, confirmed and promulgated the plan to build a total of 4.0 GW of renewable energy power generation complex in the Saemangeum area. The project will be carried out on an area of 31.95 km2, and a 1.0 GW offshore wind power development plan is in progress. Since most of the Saemangeum area has a soft ground layer that has been reclaimed, a key research institute is absolutely necessary to lead in the stabilization of the supporting structures for power generation facilities and to achieve the renewable energy 3020 policy in extreme environments. Hence, it is meaningful to investigate the effect of gravel content (P) on the ground strength characteristics. However, such investigation cannot be routinely performed due to the limited size of the equipment available. Several equations have been proposed in the literature to modify the compaction properties of gravel-mixed soils containing coarse aggregates. Among these is the proposed equation by Walker and Holtz, which has widely been used. However, the use of this equation in the case of high gravel content is not appropriate because the physical meaning of this equation is not clear and does not apply to materials with gravel content exceeding 40%. Therefore, a better quantitative evaluation method in determining material characteristics according to gravel content must be established through laboratory tests on samples of acceptable particle size for the experimental equipment. To obtain the compressive properties of decomposed granite soil (D-G-S), in this study, the results from large-scale one-dimensional compression tests on samples compacted at various gravel concentrations, constant compaction energy, and constant water content were analyzed. To quantitatively evaluate the properties of D-G-S according to the gravel content, a modified formula based on the two-phase mixing theory was utilized. It was shown that the degree of mixing between the gravel and sand for the conditions of D-G-S used in the experiments was high, at 0.85. To estimate the compression curves of D-G-S at various gravel content, the compression curves of purely sand (P = 0%) and purely gravel (P = 100%) materials, and the value of Rm = 0.85 were utilized, and it was shown that the compression index and swelling index curves estimated using the method presented in this study were in good agreement with the experimental results. To confirm the engineering applicability of the presented method, finite element analysis was performed, and as a result, it was revealed that it can be sufficiently applied in the simulation of embankment settlement. In order to obtain more reliable results in the future, verification using various samples is required.

High-Dimensional Extension of the TICER Algorithm

The TICER (TIme-Constant Equilibration Reduction) algorithm is a well-known resistor-capacitor (RC) network reduction algorithm. It finds wide applications in integrated circuit post-layout simulation tools. However, the original algorithm is one-dimensional in that each step eliminates one circuit node to obtain an approximately equivalent circuit by connecting additional elements to the neighboring nodes after each elimination. This work extends the TICER algorithm to its high-dimensional version in the sense that each step eliminates a subcircuit as a whole to obtain an approximately equivalent circuit, again by connecting extra elements to the neighboring nodes after each elimination. In practice the high-dimensional TICER (HD-TICER) algorithm finds many advantages over the classical one-dimensional TICER (1D-TICER) algorithm, which is a special case of the HD-TICER algorithm. An elegant mathematical derivation of the HD-TICER algorithm is provided by applying the notion of driving point impedance (DPI). The advantages of the HD-TICER algorithm are demonstrated by application to reductions of some purely resistive networks and RC networks. An approximate time constant estimation method is also provided for selection of a subblock circuit to eliminate.

STUDY ON THE RHEOLOGICAL CONSTANTS ESTIMATION METHOD OF CEMENT PASTE BY FLOW TEST

With the improvement of earthquake resistance and large scale of buildings, the number of cases where it is difficult to fill the form work with conventional slump-managed concrete is increasing. In addition, slump flows 45 cm, 50 cm, 55 cm, and 60 cm have been added due to the JIS (Japanese industrial standard) revision made in March 2019. In the future, it is estimated that the use of slump flow managed concrete will increase. Furthermore, in recent years, new admixtures have been actively developed, and it is necessary to correctly grasp the flow characteristics of concrete using these admixtures from a rheological point of view. It is the cement paste in concrete that is most affected by the flow properties of the admixture. Therefore, it is useful to be able to grasp the flow characteristics of cement paste. We have already examined the relationship between the rheology constants obtained from the rheology test and the flow characteristics obtained from the paste flow test, and we proposed a rheology constant estimation method. In this study, we reexamined the rheological constant estimation method based on the correlation analysis findings using the visco-plastic finite element method (FEM). First, flow analysis was performed by FEM using any combination of rheological constant and paste density (yield stress: 10 patterns, plastic viscosity: 7 patterns, paste density: 3 patterns, total 210 patterns) as input values. Next, based on the analysis results, the relationship between the paste flow characteristics (flow value, each flow arrival time, flow stop time) and the rheology constant and paste density was examined by correlation analysis. As a result, it was found that the yield stress can be estimated by the flow value, and the plastic viscosity can be estimated by the multiple regression equation of the paste density and the 150 mm flow arrival time. Furthermore, we proposed a new rheological constant estimation equation using the actual test results of the cement paste for the relationship obtained from the correlation analysis. After that, the rheology constant was estimated from the actual paste flow test results using the rheology constant estimation equation. Finally, a paste flow simulation was performed using the MPS method, which can consider the influence of the flow cone, and it was compared and examined: the actual paste flow test results and MPS analysis results. As a result, the actual paste flow test results could be reproduced by MPS analysis, and the validity of the rheological constant equation was confirmed.

Development of a New Dynamic Elastic Constant Estimation Method for FRP and Its Validation Using The FDTD Method

Development of a New Dynamic Elastic Constant Estimation Method for FRP and Its Validation Using The FDTD Method

Applicability Assessment of Estimation Methods for Baseflow Recession Constants in Small Forest Catchments

In South Korea, since small forest catchments are located upstream of most river basins, the baseflow from these catchments is important for a clean water supply to downstream areas. Baseflow recession analysis is widely recognized as a valuable tool for estimating the baseflow component of the stream hydrograph. However, few studies have applied this tool to small forest catchments. So, this study was conducted to assess the applicability of the recession analysis methods proposed in previous studies. The data used were long-term rainfall-runoff data from 1982 to 2011 in the Gwangneung coniferous (GC) and deciduous (GD) forest catchment in Gyeonggi-do, South Korea. For the applicability assessment, six recession constant estimation methods, which were used by previous studies, were selected. The recession constants of the GC and GD catchments were calculated, and applicability assessments were conducted by comparing the recession predictions and baseflow separations. As a result, the recession constants for GC and GD were 0.8480 and 0.9235, respectively. This clear difference may be due to the different forest cover in each area. The correlation regression line, AR(1) model, and the Vogel and Kroll method showed lower error rates and appropriate baseflow indexes compared with other methods.

A Simple Method for Estimation of Dielectric Constants and Polarizabilities of Nonpolar and Slightly Polar Hydrocarbons

Many of the liquids that are used as electrical insulators are nonpolar or slightly polar petroleum-derived hydrocarbons, such as the ones used for cable and/or transformer oils. In this work, semi-empirical expressions with no adjustable parameters for the dielectric constant and the polarizability of nonpolar and slightly polar hydrocarbons and their mixtures are proposed and validated. The expressions that were derived using the Vargas–Chapman One-Third rule require the mass density and the molecular weight of the substance of interest. The equations were successfully tested for various hydrocarbons and polymers with dipole moments <0.23 and densities from 500 to 1200 kg $$\cdot $$ $$\hbox {m}^{-3}$$ . The predictions are in good agreement with the experimental data in a wide range of temperatures and pressures. The proposed expressions eliminate the need of extensive experimental data and require less input parameters compared to existing correlations.

Estimation of varying coefficient models with time trend and integrated regressors

In this paper we extend the semiparametric varying coefficient model to contain non-stationary I(1) and time trend as covariates. We show that the local constant kernel estimation method leads to a consistent estimation result. This is in contrast to the semiparametric varying coefficient model with stationary I(0) and time trend covariates where Liang and Li (2012) show that local constant estimation method leads to inconsistent estimation result. The extra variability of the I(1) regressor restore the consistency of the local constant estimation method. We derive the rate of convergence of the local constant estimators, simulations results strongly support our theoretical analysis.

Functional coefficient regression models with time trend

We consider the problem of estimating a varying coefficient regression model when regressors include a time trend. We show that the commonly used local constant kernel estimation method leads to an inconsistent estimation result, while a local polynomial estimator yields a consistent estimation result. We establish the asymptotic normality result for the proposed estimator. We also provide asymptotic analysis of the data-driven (least squares cross validation) method of selecting the smoothing parameters. In addition, we consider a partially linear time trend model and establish the asymptotic distribution of our proposed estimator. Two test statistics are proposed to test the null hypotheses of a linear and of a partially linear time trend models. Simulations are reported to examine the finite sample performances of the proposed estimators and the test statistics.

A jump-detecting procedure based on spline estimation

In a random-design nonparametric regression model, procedures for detecting jumps in the regression function via constant and linear spline estimation method are proposed based on the maximal differences of the spline estimators among neighbouring knots, the limiting distributions of which are obtained when the regression function is smooth. Simulation experiments provide strong evidence that corroborates with the asymptotic theory, while the computing is extremely fast. The detecting procedure is illustrated by analysing the thickness of pennies data set.

A comparative assessment of octanol-water partitioning and distribution constant estimation methods for perfluoroalkyl carboxylates and sulfonates

A comparative assessment of octanol-water partitioning and distribution constant estimation methods for perfluoroalkyl carboxylates and sulfonates

A comparative assessment of octanol-water partitioning and distribution constant estimation methods for perfluoroalkyl carboxylates and sulfonates

AbstractNew experimental data is available in the literature regarding the octanol-water distribution behavior of representative straight chain perfluoroalkyl carboxylate (PFCA) and sulfonate (PFSA) congeners. The current study provides the first investigation into the predictive ability of various software programs for estimating the corresponding octanol-water partitioning (log P) and distribution (log D) constants of PFCAs and PFSAs. Wide predictive variation was found within and between the various methods. Several programs were able to accurately estimate the log P/D fragmental contributions of a -CF~2~- group for PFCAs, as well as the associated Gibbs free energies for partitioning into octanol from water due to the hydrophobic character of the perfluoroalkyl chain (Δ~hydrophobic~G~ow~). Only the SPARC log D method accurately predicted the electrostatic contributions of the carboxylate head group (Δ~electrostatic~G~ow~) towards octanol-water partitioning for PFCAs. Similar log D values and organic carbon normalized sediment-water partitioning coefficients (K~oc~) for PFCAs and PFSAs having equivalent perfluoroalkyl chain lengths suggests potentially equivalent Δ~electrostatic~G~ow~ and Δ~hydrophobic~G~ow~ contributions towards lipophilic partitioning for these two contaminant classes at near neutral pH values, regardless of head group identity. In contrast, there are potentially different Δ~electrostatic~G~ow~ and Δ~hydrophobic~G~ow~ contributions towards proteinophilic partitioning under biologically relevant conditions.

A comparative assessment of octanol-water partitioning and distribution constant estimation methods for perfluoroalkyl carboxylates and sulfonates

AbstractNew experimental data is available in the literature regarding the octanol-water distribution behavior of representative straight chain perfluoroalkyl carboxylate (PFCA) and sulfonate (PFSA) congeners. The current study provides the first investigation into the predictive ability of various software programs for estimating the corresponding octanol-water partitioning (log P) and distribution (log D) constants of PFCAs and PFSAs. Wide predictive variation was found within and between the various methods. Several programs were able to accurately estimate the log P/D fragmental contributions of a -CF~2~- group for PFCAs, as well as the associated Gibbs free energies for partitioning into octanol from water due to the hydrophobic character of the perfluoroalkyl chain (Δ~hydrophobic~G~ow~). Only the SPARC log D method accurately predicted the electrostatic contributions of the carboxylate head group (Δ~electrostatic~G~ow~) towards octanol-water partitioning for PFCAs. Similar log D values and organic carbon normalized sediment-water partitioning coefficients (K~oc~) for PFCAs and PFSAs having equivalent perfluoroalkyl chain lengths suggests potentially equivalent Δ~electrostatic~G~ow~ and Δ~hydrophobic~G~ow~ contributions towards lipophilic partitioning for these two contaminant classes, regardless of head group identity. In contrast, there are potentially different Δ~electrostatic~G~ow~ and Δ~hydrophobic~G~ow~ contributions towards proteinophilic partitioning.

Cross‐validation and non‐parametric k nearest‐neighbour estimation

Summary In this paper we consider the problem of estimating a non-parametric regression function using the k nearest-neighbour method. We provide asymptotic theories for the least-squares cross validation (CV) selected smoothing parameter k for both local constant and local linear estimation methods. We also establish the asymptotic normality results for the resulting non-parametric regression function estimators. Some limited Monte Carlo experiments show that the CV method performs well in finite sample applications.

Measurement and Estimation of Rate Constants for the Reactions of Hydroxyl Radical with Several Alkanes and Cycloalkanes

Relative rate experiments were used to measure ratios of chemical kinetics rate constants as a function of temperature for the reactions of OH with isobutane, isopentane, 2-methylpentane, 3-methylpentane, 2,3-dimethylbutane, 2,3-dimethylpentane, 2,4-dimethylpentane, 2,3,4-trimethylpentane, n-heptane, n-octane, cyclopentane, cyclohexane, and cycloheptane. The results have been used to calibrate a structure-reactivity rate constant estimation method for k(298 K) which, when combined with previously determined relationships between k(298 K) and the Arrhenius parameters, is capable of determining the temperature dependence accurately. The estimation method reproduces most of the observed rate data within experimental accuracy but appears to fail for 2,3-dimethylbutane, which has an anomalously high rate constant. Curvature in the Arrhenius plots at low temperatures is not present for compounds with a single type of C-H bond and, for compounds with different C-H bonds, is shown to be consistent with effects due to different group sites on the molecule.

Maximum Likelihood Estimation of Ion Channel Kinetics from Macroscopic Currents

We describe a maximum likelihood method for direct estimation of rate constants from macroscopic ion channel data for kinetic models of arbitrary size and topology. The number of channels in the preparation, and the mean and standard deviation of the unitary current can be estimated, and a priori constraints can be imposed on rate constants. The method allows for arbitrary stimulation protocols, including stimuli with finite rise time, trains of ligand or voltage steps, and global fitting across different experimental conditions. The initial state occupancies can be optimized from the fit kinetics. Utilizing arbitrary stimulation protocols and using the mean and the variance of the current reduce or eliminate problems of model identifiability (Kienker, 1989). The algorithm is faster than a recent method that uses the full autocovariance matrix (Celentano and Hawkes, 2004), in part due to the analytical calculation of the likelihood gradients. We tested the method with simulated data and with real macroscopic currents from acetylcholine receptors, elicited in response to brief pulses of carbachol. Given appropriate stimulation protocols, our method chose a reasonable model size and topology.

Experimental and theoretical investigation of the mass transfer controlled regime in catalytic monoliths

We show that an accurate description of the mass transfer controlled regime in long catalytic monolith channels in which the flow is fully developed and laminar, requires the knowledge of two constants, namely, the asymptotic Sherwood number ( Sh ∞, or dimensionless mass transfer coefficient) and the first normalized Fourier weight, α 1. While the first of these has received considerable attention in the literature, the second factor has been assumed to be unity. Because of this systematic error (of about 20% for common channel geometries), literature data and correlations for mass transfer in monoliths have large uncertainties. We present new experimental data that corroborates the theory and a new method for experimental estimation of the asymptotic constants for any arbitrary channel shape. For the case of a square channel we obtain experimental values for the constants of Sh ∞=2.92±0.16 and α 1=0.78±0.09, which are in excellent agreement with the theoretical values ( Sh ∞=2.977 and α 1=0.8074). Using the asymptotic solutions of the convection–diffusion equation, we develop new correlations for mass transfer coefficients for the case of developing laminar flow that agree with numerical solutions of the Navier–Stokes equations, and theory in the limits.

Simultaneous estimation of the association constants of glycoprotein glycoforms to a common protein by capillary electrophoresis

The efficacy of our capillary electrophoresis method for simultaneous estimation of the association constants of glycoprotein glycoforms to a common target protein was demonstrated using ribonuclease and ovalbumin glycoforms as glycoform models and Lens culinaris agglutinin (LCA) as a protein model. The ribonuclease glycoforms were fairly well separated in the absence of LCA at pH 5.8, but the peaks were retarded without any change of separation profile in the presence of LCA, the retardation becoming greater as LCA concentration increased. The estimated values of apparent association constant ( K a) were at the 10 6 M −1 level for all the ribonuclease glycoforms, and there was no significant difference among glycoforms. The high-mannose-type N-glycans released from a mixture of ribonuclease glycoforms gave lower values of K a at the 10 4–10 5 M −1 level to the same protein, and the glycans having a larger number of the mannose residue gave larger K a values. These results imply that the glycan moiety in this glycoprotein might contribute to its binding to the protein, but the polypeptide core played the major role. In contrast, ovalbumin glycoforms gave poorly resolved peaks in the absence of LCA, but they were separated into several peaks in the presence of LCA, which were tentatively assigned based on the knowledge of affinity to this lectin, and K a values were estimated simultaneously. The estimated K a values were smaller than those of the ribonuclease glycoforms, suggesting the major role of the N-glycan moiety. Thus, capillary electrophoresis allowed simultaneous estimation of K a values under common conditions using small amounts of glycoform mixtures and proteins without prior isolation and purification. Comparison of the obtained values will provide useful information on the glycan structure–affinity correlation.

Estimates of atmospheric lifetimes and ozone depletion potentials for the bromopentafluoropropane isomers

Bromopentafluoropropane (C3H2BrF5) has come under consideration as a potential replacement compound for ozone‐depleting chlorofluorocarbons and Halons. No rate constants for the reaction of the isomers of C3H2BrF5 with hydroxyl radical in the atmosphere have yet been measured. The existing ozone depletion potential recommendations, which are based on estimated reaction rate constants for the C3H2BrF5 isomers, are not in agreement. In this study, we seek to clarify the ozone depletion potential of the C3H2BrF5 isomers. First, we apply two hydroxyl reaction rate constant estimation methods to a series of bromofluorocarbons likely to have similar reactivity to C3H2BrF5 in order to select one estimation method to apply to C3H2BrF5. We then predict hydroxyl reaction rate constants using that estimation method for the C3H2BrF5 isomers and calculate both atmospheric lifetimes and ozone depletion potentials through semiempirical methods. This study obtains C3H2BrF5 atmospheric lifetimes ranging from 1.4 to 59 years and ozone depletion potentials ranging from 0.30 to 12, which reflects the strong dependence of hydroxyl reactivity on the isomeric structure of the potential replacement compound.

A generalized method for estimation of critical constants

A generalized and simple method is proposed to estimate critical temperature, pressure and volume of both polar and non-polar compounds. The input parameters are normal boiling point, density and relative molar mass. The proposed procedure was used to estimate critical properties of more than 250 compounds including hydrocarbons (C 1–C 18), acids, sulfur compounds, nitriles, oxide gases, alcohols, halogenated compounds, ethers, amines and water. Average absolute deviations for estimation of critical temperature, pressure and volume for the proposed method are 0.9, 2.8 and 1.8%, respectively.