Uncertainty-based measurement quality control

According to a simple acceptance decision rule for measurement quality control, a measured value will be accepted if the expanded uncertainty of the measurements is not greater than a preset maximum permissible uncertainty. Otherwise, the measured value will be rejected. The expanded uncertainty may be calculated as the z-based uncertainty (the half-width of the z-interval) when the measurement population standard deviation σ is known or the sample size is large (30 or greater), or by a sample-based uncertainty estimator when σ is unknown and the sample size is small. The decision made based on the z-based uncertainty will be deterministic and may be assumed to be correct. However, the decision made based on a sample-based uncertainty estimator will be uncertain. This paper develops the mathematical formulations for computing the probability of acceptance for two sample-based uncertainty estimators: the t-based uncertainty (the half-width of the t-interval) and an unbiased uncertainty estimator. The risk of incorrect decision-making, in terms of the false acceptance probability and false rejection probability, is derived from the probability of acceptance. The theoretical analyses indicate that the t-based uncertainty may result in significantly high false rejection probability when the sample size is very small (especially for samples of size 2). For some applications, the unbiased uncertainty estimator may be superior to the t-based uncertainty for measurement quality control. Several examples from acoustic Doppler current profiler streamflow measurements are presented to demonstrate the performance of the t-based uncertainty and the unbiased uncertainty estimator.     

Limits of detection and decision. Part 1

Extensive Monte Carlo studies of instrumental limits of detection were performed on a simple univariate chemical measurement system having homoscedastic, Gaussian measurement noise and using ordinary least squares (OLS) processing of tens of millions of independent calibration curve data sets. It was found that prediction interval-based experimental detection limits were significantly negatively biased, in both the net response domain and the chemical content domain, resulting in substantially higher rates of false negatives than specified via customary critical t values. The diagnostic fix for the bias problem provided clear proof that hypothesis-based detection limits need not be unique, even as distributions of random variates, if the alternate hypothesis is non-unique. It was also demonstrated that hypothesis-based decision and detection limits have finite support that does not include the region near zero analyte content, so that both have finite moments and finite confidence intervals.     

Robust curve fitting method for optical spectra by least median squares (LMedS) estimator with particle swarm optimization (PSO).

A curve fitting technique for optical spectra based on a robust estimator, least median squares (LMedS), is introduced in this study. For the effective calculation of LMedS, particle swarm optimization (PSO) is also introduced. Unlike a standard curve fitting method using least squares (LS) estimator, the method based on LMedS estimator is less influenced by outliers in experimental data. Two kinds of data sets, simulated data with outliers and temperature-dependent near-infrared (NIR) spectra of oleic acid (OA) are applied for the demonstration of the proposed method. The results clearly reveal that, compared with the LS estimator, the proposed method can effectively reduce undesirable effects of low SN ratio and can yield more accurate fitting results.     

Robustness properties of a robust partial least squares regression method

The presence of multicollinearity in regression data is no exception in real life examples. Instead of applying ordinary regression methods, biased regression techniques such as principal component regression and ridge regression have been developed to cope with such datasets. In this paper, we consider partial least squares (PLS) regression by means of the SIMPLS algorithm. Because the SIMPLS algorithm is based on the empirical variance-covariance matrix of the data and on least squares regression, outliers have a damaging effect on the estimates. To reduce this pernicious effect of outliers, we propose to replace the empirical variance-covariance matrix in SIMPLS by a robust covariance estimator. We derive the influence function of the resulting PLS weight vectors and the regression estimates, and conclude that they will be bounded if the robust covariance estimator has a bounded influence function. Also the breakdown value is inherited from the robust estimator. We illustrate the results using the MCD estimator and the reweighted MCD estimator (RMCD) for low-dimensional datasets. Also some empirical properties are provided for a high-dimensional dataset.     

Capacitance-based droplet position estimator for digital microfluidic devices

Digital microfluidic (DMF) devices manipulate minuscule droplets through basic fluidic operations including droplet transport, mixing and splitting commonly known as the building blocks for complete laboratory analyses on a single device. A DMF device can house various chemical species and confine chemical reactions within the volume of a droplet much like a micro-reactor. The automation of fluidic protocols requires a feedback controller whose sensor is capable of locating droplets independent of liquid composition (or previous knowledge of liquid composition). In this research, we present an estimator that tracks the continuous displacement of a droplet between electrodes of a DMF device. The estimator uses a dimensionless ratio of two electrode capacitances to approximate the position of a droplet, even, in the domain between two adjacent electrodes. This droplet position estimator significantly enhances the control precision of liquid handling in DMF devices compared to that of the techniques reported in the literature. It captures the continuous displacement of a droplet; valuable information for a feedback controller to execute intricate fluidic protocols including droplet positioning between electrodes, droplet velocity and acceleration control. We propose a state estimator for tracking the continuous droplet displacement between two adjacent electrodes. The dimensionless nature of this estimator means that any droplet composition can be sensed. Thus, no calibration for each chemical species within a single DMF device is required. We present theoretical and experimental results that demonstrate the efficacy of the position estimator in approximating the position of the droplet in the interval between two electrodes.     

Waste-recycling Monte Carlo with optimal estimates: application to free energy calculations in alloys

The estimator proposed recently by Delmas and Jourdain for waste-recycling Monte Carlo achieves variance reduction optimally with respect to a control variate that is evaluated directly using the simulation data. Here, the performance of this estimator is assessed numerically for free energy calculations in generic binary alloys and is compared to those of other estimators taken from the literature. A systematic investigation with varying simulation parameters of a simplified system, the anti-ferromagnetic Ising model, is first carried out in the transmutation ensemble using path-sampling. We observe numerically that (i) the variance of the Delmas-Jourdain estimator is indeed reduced compared to that of other estimators; and that (ii) the resulting reduction is close to the maximal possible one, despite the inaccuracy in the estimated control variate. More extensive path-sampling simulations involving an FeCr alloy system described by a many-body potential additionally show that (iii) gradual transmutations accommodate the atomic frustrations; thus, alleviating the numerical ergodicity issue present in numerous alloy systems and eventually enabling the determination of phase coexistence conditions.     

Resolution method for overlapping peaks based on the fractional-order differential

Equations between the differential order and the maximum of the fractional-order differential for the specified peak signals are developed based on the variation of the maximum of the specified peak signals at different orders. Also, equations between the differential order and the zero-crossing of the fractional-order differential of the specified peak signals are proposed according to the variation of the zero-crossing of the specified peak signals at different orders. Characteristic paramters of the Gaus- sian peak, Lorentzian peak, and Tsallis peak can be estimated using estimator I and estimator II which are obtained by the equations above. As a result, a new method is presented to resolve the overlapped peaks signal. Firstly, a fractional-order differential of the specified peak signals is obtained with the fractional-order differentiation filter. Then, characteristic paramters of the specified peak signals can be extracted using estimator I and estimator II. Finally, the Tsallis peak is used as a model to assign the overlapping peak signals correctly. Experimental results show that the proposed method is efficient and effective for the simulated overlapping peaks and detected overlapping voltammetric peak signals.     

Fuzzy robust estimation of central location

The problem of a new robust algorithm for estimation of central location has been described in a mathematically simpler way using the fuzzy sets theory. It was compared with ordinary mean estimator and other robust estimators - median, 5% trimmed mean and Huber-, Tukey-, Hampel-, and Andrews-type M-estimators. The performance of Fuzzy 1-means algorithm (FM) proposed is demonstrated by applying it to different data sets from published literature and has been shown to exceed that of conventional ordinary mean estimator and equals or often exceeds that of the most robust estimators.     

Path-integral virial estimator for reaction-rate calculation based on the quantum instanton approximation

The quantum instanton approximation is a type of quantum transition-state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low-order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat-capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial (-type) estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.     

Partial averaging and the centroid virial estimator for stereographic projection path-integral simulations in curved spaces

We develop and test three different partial averaging theories for the stereographic projection path integral in curved spaces. Additionally, we adapt and test the centroid virial estimator for the kinetic energy in curved spaces. We tested both a confining as well as a nonconfining potential for the particle in a ring. All three partial averaging theories are demonstrated to converge linearly in the asymptotic region with k(-2)max, the number of Fourier coefficients. We use an error estimator to determine the optimal parameters for an extrapolation to infinite kmax. We verify that the centroid virial estimator (derived from the primitive DeWitt path-integral formula) converges to the kinetic energy for both confining and nonconfining potentials.     

Measuring surface topography by scanning electron microscopy. II. Analysis of three estimators of surface roughness in second dimension and third dimension.

Scanning electron microscopy (SEM) is widely used in surface studies and continuous efforts are carried out in the search of estimators of different surface characteristics. By using the variogram, we developed two of these estimators that were used to characterize the surface roughness from the SEM image texture. One of the estimators is related to the crossover between fractal region at low scale and the periodic region at high scale, whereas the other estimator characterizes the periodic region. In this work, a full study of these estimators and the fractal dimension in two dimensions (2D) and three dimensions (3D) was carried out for emery papers. We show that the obtained fractal dimension with only one image is good enough to characterize the roughness surface because its behavior is similar to those obtained with 3D height data. We show also that the estimator that indicates the crossover is related to the minimum cell size in 2D and to the average particle size in 3D. The other estimator has different values for the three studied emery papers in 2D but it does not have a clear meaning, and these values are similar for those studied samples in 3D. Nevertheless, it indicates the formation tendency of compound cells. The fractal dimension values from the variogram and from an area versus step log-log graph were studied with 3D data. Both methods yield different values corresponding to different information from the samples.     

Path-integral virial estimator based on the scaling of fluctuation coordinates: application to quantum clusters with fourth-order propagators

We first show that a simple scaling of fluctuation coordinates defined in terms of a given reference point gives the conventional virial estimator in discretized path integral, where different choices of the reference point lead to different forms of the estimator (e.g., centroid virial). The merit of this procedure is that it allows a finite-difference evaluation of the virial estimator with respect to temperature, which totally avoids the need of higher-order potential derivatives. We apply this procedure to energy and heat-capacity calculations of the (H(2))(22) and Ne(13) clusters at low temperature using the fourth-order Takahashi-Imada [J. Phys. Soc. Jpn. 53, 3765 (1984)] and Suzuki [Phys. Lett. A 201, 425 (1995)] propagators. This type of calculation requires up to third-order potential derivatives if analytical virial estimators are used, but in practice only first-order derivatives suffice by virtue of the finite-difference scheme above. From the application to quantum clusters, we find that the fourth-order propagators do improve upon the primitive approximation, and that the choice of the reference point plays a vital role in reducing the variance of the virial estimator.     

Evaluation of false positive responses by mass spectrometry and ion mobility spectrometry for the detection of trace explosives in complex samples

Secondary electrospray ionization-ion mobility-time of flight mass spectrometry (SESI-IM-TOFMS) was used to evaluate common household products and food ingredients for any mass or mobility responses that produced false positives for explosives. These products contained ingredients which shared the same mass and mobility drift time ranges as the analyte ions for common explosives. The results of this study showed that the vast array of compounds in these products can cause either mass or mobility false positive responses. This work also found that two ingredients caused either enhanced or reduced ionization of the target analytes. Another result showed that an IMS can provide real-time separation of ion species that impede accurate mass identifications due to overlapping isotope peak patterns. The final result of this study showed that, when mass and mobility values were used to identify an ion, no false responses were found for the target explosives. The wider implication of these results is that the possibility exists for even greater occurrences of false responses from complex mixtures found in common products. Neither IMS nor MS alone can provide 100% assurance from false responses. IMS, due to its low cost, ease of operation, rugged reliability, high sensitivity and tunable selectivity, will remain the field method of choice for the near future but, when combined with MS, can also reduce the false positive rate for explosive analyses.     

A maximum likelihood estimator to distinguish single molecules by their fluorescence decays

We have developed a maximum likelihood estimator to distinguish between similar molecules at the single molecule level based upon fluorescence decay measurements. Time resolved fluorescence measurements for single Rhodamine 6G and tetramethylrhodamine isothiocyanate molecules in fluid flow are derived from time-correlated single photon counting. A maximum likelihood estimator is developed and applied to data from a mixture of molecules. Single molecules are identified and distinguished by their fluorescence time decays. Comparison is made between identification error rates and theoretical predictions. To our knowledge, this is the first reported example of single molecule identification by fluorescence decay in a mixture.     

Gas chromatography-mass spectrometry determination of the pentafluorobenzoyl derivative of methylhydrazine in false morel (Gyromitra esculenta) as a monitor for the content of the toxin gyromitrin

The main toxic compound found in false morel (Gyromitra esculenta) is acetaldehyde-N-methyl-N-formylhydrazone (gyromitrin). This paper describes a method of determining the total hydrazones content based on acid hydrolysis of gyromitrin and other related hydrazones in air-dried false morel followed by derivatisation of methylhydrazine with pentafluorobenzoyl chloride. The derivative, tris-pentafluorobenzoyl methylhydrazine (tris-PFB-MH) is analyzed by gas chromatography-mass spectrometry. The overall precision of the method is better than 10% (relative standard deviation) for 0.5 ng/microl methylhydrazine in solution. The minimum detectable concentration of methylhydrazine (tris-PFB-MH) by this method is estimated to be approximately 12 pg/microl, which is equal to 0.3 microg/g dry matter (DM) of false morel.     

Application of classical versus bayesian statistical control charts to on-line radiological monitoring

False positive and false negative incidence rates of radiological monitoring data from classical and Bayesian statistical process control chart techniques are compared. The on-line monitoring for illicit radioactive material with no false positives or false negatives is the goal of homeland security monitoring, but is unrealistic. However, statistical fluctuations in the detector signal, short detection times, large source to detector distances, and shielding effects make distinguishing between a radiation source and natural background particularly difficult. Experimental time series data were collected using a 1″ × 1″ LaCl₃(Ce) based scintillation detector (Scionix, Orlando, FL) under various simulated conditions. Experimental parameters include radionuclide (gamma-ray) energy, activity, density thickness (source to detector distance and shielding), time, and temperature. All statistical algorithms were developed using MATLAB™. The Shewhart (3-σ) control chart and the cumulative sum (CUSUM) control chart are the classical procedures adopted, while the Bayesian technique is the Shiryayev–Roberts (S–R) control chart. The Shiryayev–Roberts method was the best method for controlling the number of false positive detects, followed by the CUSUM method. However, The Shiryayev–Roberts method, used without modification, resulted in one of the highest false negative incidence rates independent of the signal strength. Modification of The Shiryayev–Roberts statistical analysis method reduced the number of false negatives, but resulted in an increase in the false positive incidence rate.     

AGBNP: an analytic implicit solvent model suitable for molecular dynamics simulations and high-resolution modeling

We have developed an implicit solvent effective potential (AGBNP) that is suitable for molecular dynamics simulations and high-resolution modeling. It is based on a novel implementation of the pairwise descreening Generalized Born model for the electrostatic component and a new nonpolar hydration free energy estimator. The nonpolar term consists of an estimator for the solute-solvent van der Waals dispersion energy designed to mimic the continuum solvent solute-solvent van der Waals interaction energy, in addition to a surface area term corresponding to the work of cavity formation. AGBNP makes use of a new parameter-free algorithm to calculate the scaling coefficients used in the pairwise descreening scheme to take into account atomic overlaps. The same algorithm is also used to calculate atomic surface areas. We show that excellent agreement is achieved for the GB self-energies and surface areas in comparison to accurate, but much more expensive, numerical evaluations. The parameter-free approach used in AGBNP and the sensitivity of the AGBNP model with respect to large and small conformational changes makes the model suitable for high-resolution modeling of protein loops and receptor sites as well as high-resolution prediction of the structure and thermodynamics of protein-ligand complexes. We present illustrative results for these kinds of benchmarks. The model is fully analytical with first derivatives and is computationally efficient. It has been incorporated into the IMPACT molecular simulation program.     

Accurate and unbiased estimation of power-law exponents from single-emitter blinking data

Single emitter blinking with a power-law distribution for the on and off times has been observed on a variety of systems including semiconductor nanocrystals, conjugated polymers, fluorescent proteins, and organic fluorophores. The origin of this behavior is still under debate. Reliable estimation of power exponents from experimental data is crucial in validating the various models under consideration. We derive a maximum likelihood estimator for power-law distributed data and analyze its accuracy as a function of data set size and power exponent both analytically and numerically. Results are compared to least-squares fitting of the double logarithmically transformed probability density. We demonstrate that least-squares fitting introduces a severe bias in the estimation result and that the maximum likelihood procedure is superior in retrieving the correct exponent and reducing the statistical error. For a data set as small as 50 data points, the error margins of the maximum likelihood estimator are already below 7%, giving the possibility to quantify blinking behavior when data set size is limited, e.g., due to photobleaching.     

Scoring hidden Markov models to discriminate beta-barrel membrane proteins

A new method is presented for identification of beta-barrel membrane proteins. It is based on a hidden Markov model (HMM) with an architecture obeying these proteins' construction principles. Once the HMM is trained, log-odds score relative to a null model is used to discriminate beta-barrel membrane proteins from other proteins. The method achieves only 10% false positive and false negative rates in a six-fold cross-validation procedure. The results compare favorably with existing methods. This method is proposed to be a valuable tool to quickly scan proteomes of entirely sequenced organisms for beta-barrel membrane proteins.