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Signals analysis for cytometry remains a challenging task that has a significant impact on uncertainty. Conventional cytometers assume that individual measurements are well characterized by simple properties such as the signal area, width, and height. However, these approaches have difficulty distinguishing inherent biological variability from instrument artifacts and operating conditions. As a result, it is challenging to quantify uncertainty in the properties of individual cells and perform tasks such as doublet deconvolution. We address these problems via signals analysis techniques that use scale transformations to: (I) separate variation in biomarker expression from effects due to flow conditions and particle size; (II) quantify reproducibility associated with a given laser interrogation region; (III) estimate uncertainty in measurement values on a per-event basis; and (IV) extract the singlets that make up a multiplet. The key idea behind this approach is to model how variable operating conditions deform the signal shape and then use constrained optimization to "undo" these deformations for measured signals; residuals to this process characterize reproducibility. Using a recently developed microfluidic cytometer, we demonstrate that these techniques can account for instrument and measurand induced variability with a residual uncertainty of less than 2.5% in the signal shape and less than 1% in integrated area. [ABSTRACT FROM AUTHOR]

COVID-19 has highlighted challenges in the measurement quality and comparability of serological binding and neutralization assays. Due to many different assay formats and reagents, these measurements are known to be highly variable with large uncertainties. The development of the WHO international standard (WHO IS) and other pool standards have facilitated assay comparability through normalization to a common material but does not provide assay harmonization nor uncertainty quantification. In this paper, we present the results from an interlaboratory study that led to the development of (1) a novel hierarchy of data analyses based on the thermodynamics of antibody binding and (2) a modeling framework that quantifies the probability of neutralization potential for a given binding measurement. Importantly, we introduced a precise, mathematical definition of harmonization that separates the sources of quantitative uncertainties, some of which can be corrected to enable, for the first time, assay comparability. Both the theory and experimental data confirmed that mAbs and WHO IS performed identically as a primary standard for establishing traceability and bridging across different assay platforms. The metrological anchoring of complex serological binding and neuralization assays and fast turn-around production of an mAb reference control can enable the unprecedented comparability and traceability of serological binding assay results for new variants of SARS-CoV-2 and immune responses to other viruses. [ABSTRACT FROM AUTHOR]

Fentanyl analogs are a class of designer drugs that are particularly challenging to unambiguously identify due to the mass spectral and retention time similarities of unique compounds. In this paper, we use agglomerative hierarchical clustering to explore the measurement diversity of fentanyl analogs and better understand the challenge of unambiguous identifications using analytical techniques traditionally available to drug chemists. We consider four measurements in particular: gas chromatography retention indices, electron ionization mass spectra, electrospray ionization tandem mass spectra, and direct analysis in real time mass spectra. Our analysis demonstrates how simultaneously considering data from multiple measurement techniques increases the observable measurement diversity of fentanyl analogs, which can reduce identification ambiguity. This paper further supports the use of multiple analytical techniques to identify fentanyl analogs (among other substances), as is recommended by the Scientific Working Group for the Analysis of Seized Drugs (SWGDRUG). [ABSTRACT FROM AUTHOR]

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has emphasized the importance and challenges of correctly interpreting antibody test results. Identification of positive and negative samples requires a classification strategy with low error rates, which is hard to achieve when the corresponding measurement values overlap. Additional uncertainty arises when classification schemes fail to account for complicated structure in data. We address these problems through a mathematical framework that combines high dimensional data modeling and optimal decision theory. Specifically, we show that appropriately increasing the dimension of data better separates positive and negative populations and reveals nuanced structure that can be described in terms of mathematical models. We combine these models with optimal decision theory to yield a classification scheme that better separates positive and negative samples relative to traditional methods such as confidence intervals (CIs) and receiver operating characteristics. We validate the usefulness of this approach in the context of a multiplex salivary SARS-CoV-2 immunoglobulin G assay dataset. This example illustrates how our analysis: (i) improves the assay accuracy, (e.g. lowers classification errors by up to 42% compared to CI methods); (ii) reduces the number of indeterminate samples when an inconclusive class is permissible, (e.g. by 40% compared to the original analysis of the example multiplex dataset) and (iii) decreases the number of antigens needed to classify samples. Our work showcases the power of mathematical modeling in diagnostic classification and highlights a method that can be adopted broadly in public health and clinical settings. [ABSTRACT FROM AUTHOR]

Flow cytometry is an invaluable technology in biomedical research, but confidence in single-cell measurements remains limited due to a lack of appropriate techniques for uncertainty quantification (UQ). It is particularly challenging to evaluate the potential for different instrumentation designs or operating parameters to influence the measurement physics in ways that change measurement repeatability. Here, we report a direct experimental approach to UQ using a serial flow cytometer that measured each particle more than once along a flow path. The instrument was automated for real-time characterization of measurement precision and operated with particle velocities exceeding 1 m s−1, throughputs above 100 s−1, and analysis yields better than 99.9%. These achievements were enabled by a novel hybrid inertial and hydrodynamic particle focuser to tightly control particle positions and velocities. The cytometer identified ideal flow conditions with fluorescence area measurement precision on the order of 1% and characterized tradeoffs between precision, throughput, and analysis yield. The serial cytometer is anticipated to improve single-cell measurements through estimation (and subsequent control) of uncertainty contributions from various other instrument parameters leading to overall improvements in the ability to better classify sample composition and to find rare events. [ABSTRACT FROM AUTHOR]

1. Motivation and Approach Tomography became an important field about 40 years ago with the application x-rays to human subjects to detect tumors (1). In the classical Computerized Axial Tomography [...]

1. Introduction Given a finite set of real numbers, Y = {(y.sub.1), ..., (y.sub.n)}, the problem of isotonic regression with respect to a complete order is the following quadratic programming [...]

A mathematical algorithm is presented that locates and calculates the area beneath peaks from real data using only reproducible mathematical operations and no user-selected parameters. It makes no assumptions about peak shape and requires no smoothing or preprocessing of the data. In fact, it is shown that for matrix-assisted laser desorption time-of-flight mass spectra noise exists at all frequency ranges making the smoothing of data without distortion of peak areas impossible. The algorithm is based on a time-series segmentation routine that reduces the data set to groups of three strategic points where each group defines the beginning, center, and ending of each peak located. The peak areas are found from the strategic points using a commonplace polygonal area calculation routine. Peaks with statistically insignificant height or area are then discarded. The performance of the algorithm is demonstrated on a polystyrene mass spectrum with varying degrees of noise added either mathematically or experimentally. An on-line implementation of the method, termed MassSpectator, for public use can be found at www.nist.gov/maldi.

Efficiently, robustly, and accurately solving systems of nonlinear differential algebraic equations for dynamic building system simulation is becoming more important due to the increasing need to simulate large-scale problems. The focus of this paper is an investigation of methods for solving the nonlinear algebraic equations encountered in dynamic building system simulations. Dynamic building system simulations employ a myriad of solution techniques, many of which use derivative information. As the problem size grows, so do the memory requirements, leading to challenges in solving large-scale problems. Newton-Krylov methods are a promising candidate for large-scale simulation. The performance of these methods is often improved, sometimes drastically, when employed with a preconditioning technique. Here, a cost-effective preconditioning technique is applied to a Newton-Krylov method and tested on a series of problems. To illustrate the benefits of the approach, comparison is made to the frequently employed Powell's Hybrid Method. [ABSTRACT FROM AUTHOR]

Formulating accurate and robust classification strategies is a key challenge of developing diagnostic and antibody tests. Methods that do not explicitly account for disease prevalence and uncertainty therein can lead to significant classification errors. We present a novel method that leverages optimal decision theory to address this problem. As a preliminary step, we develop an analysis that uses an assumed prevalence and conditional probability models of diagnostic measurement outcomes to define optimal (in the sense of minimizing rates of false positives and false negatives) classification domains. Critically, we demonstrate how this strategy can be generalized to a setting in which the prevalence is unknown by either (i) defining a third class of hold-out samples that require further testing or (ii) using an adaptive algorithm to estimate prevalence prior to defining classification domains. We also provide examples for a recently published SARS-CoV-2 serology test and discuss how measurement uncertainty (e.g. associated with instrumentation) can be incorporated into the analysis. We find that our new strategy decreases classification error by up to a decade relative to more traditional methods based on confidence intervals. Moreover, it establishes a theoretical foundation for generalizing techniques such as receiver operating characteristics by connecting them to the broader field of optimization. [ABSTRACT FROM AUTHOR]

In 1990, a well‐known model to predict pure component properties of triglycerides was presented by Wesdorp in "Liquid‐multiple solid phase equilibria in fats: theory and experiments" and has been shown to perform well despite making thermodynamically inconsistent predictions for certain test cases. In this study, the underlying parameter set is improved to deliver more physically consistent predictions, i.e., increasing melting point and enthalpy of fusion with increasing stability of the polymorphs, without deterioration of the primary model quality to describe the available experimental data. Interestingly, when a curated dataset containing only thermodynamically consistent data is compared to a broader dataset, it appears that the model's efficacy is highly dependent on the quantity of data, specifically the number of unsaturated triglycerides data. Quality and thermodynamic consistency of model predictions and the condition of a reliable description of monoacid triglycerides as a subset is discussed, addressing a potential interdependence. [ABSTRACT FROM AUTHOR]

In the field of cell-based therapeutics, there is a great need for high-quality, robust, and validated measurements for cell characterization. Flow cytometry has emerged as a critically important platform due to its high-throughput capability and its ability to simultaneously measure multiple parameters in the same sample. However, to assure the confidence in measurement, well characterized biological reference materials are needed for standardizing clinical assays and harmonizing flow cytometric results between laboratories. To date, the lack of adequate reference materials, and the complexity of the cytometer instrumentation have resulted in few standards. This study was designed to evaluate CD19 expression in three potential biological cell reference materials and provide a preliminary assessment of their suitability to support future development of CD19 reference standards. Three commercially available human peripheral blood mononuclear cells (PBMCs) obtained from three different manufacturers were tested. Variables that could potentially contribute to the differences in the CD19 expression, such as PBMCs manufacturing process, number of healthy donors used in manufacturing each PBMC lot, antibody reagent, operators, and experimental days were included in our evaluation. CD19 antibodies bound per cell (ABC) values were measured using two flow cytometry-based quantification schemes with two independent calibration methods, a single point calibration using a CD4 reference cell and QuantiBrite PE bead calibration. Three lots of PBMC from three different manufacturers were obtained. Each lot of PBMC was tested on three different experimental days by three operators using three different lots of unimolar anti-CD19PE conjugates. CD19 ABC values were obtained in parallel on a selected lot of the PBMC samples using mass spectrometry (CyTOF) with two independent calibration methods, EQ4 and bead-based calibration were evaluated with CyTOF-technology. Including all studied variabilities such as PBMC lot, antibody reagent lot, and operator, the averaged mean values of CD19 ABC for the three PBMC manufacturers (A,B, and C) obtained by flow cytometry were found to be: 7953 with a %CV of 9.0 for PBMC-A, 10535 with a %CV of 7.8 for PBMC-B, and 12384 with a %CV of 16 for PBMC-C. These CD19 ABC values agree closely with the findings using CyTOF. The averaged mean values of CD19 ABC for the tested PBMCs is 9295 using flow cytometry-based method and 9699 using CyTOF. The relative contributions from various sources of uncertainty in CD19 ABC values were quantified for the flow cytometry-based measurement scheme. This uncertainty analysis suggests that the number of antigens or ligand binding sites per cell in each PBMC preparation is the largest source of variability. On the other hand, the calibration method does not add significant uncertainty to the expression estimates. Our preliminary assessment showed the suitability of the tested materials to serve as PBMC-based CD19+ reference control materials for use in quantifying relevant B cell markers in B cell lymphoproliferative disorders and immunotherapy. However, users should consider the variabilities resulting from different lots of PBMC and antibody reagent when utilizing cell-based reference materials for quantification purposes and perform bridging studies to ensure harmonization between the results before switching to a new lot. [ABSTRACT FROM AUTHOR]

A mathematical model for simulating biological field effect transistor (Bio-FET) experiments is introduced. It takes the form of a nonlinear equation that describes evolution of reacting species concentration at the boundary coupled to a diffusion equation. Using analytic techniques, this coupled system of equations is reduced to a singular integrodifferential equation (IDE). A numerical approximation of this equation is developed that achieves greater than firstorder accuracy in time and greater than second-order accuracy in space, despite the presence of a singular temporal convolution kernel and a discontinuous boundary condition. The mathematical model was validated using Bio-FET data, and stochastic regression was employed to separate signal from noise. Results show that our IDE provides a robust way of estimating important parameters such as diffusion coefficients and kinetic rate constants. [ABSTRACT FROM AUTHOR]

The problem of choosing an optimal signal set for non-Gaussian detection was reduced to a smooth inequality constrained mini-max nonlinear programming prob1cm by Gockenbach and Kearsley. Here we consider the [...]

Serology testing can identify past infection by quantifying the immune response of an infected individual providing important public health guidance. Individual immune responses are time-dependent, which is reflected in antibody measurements. Moreover, the probability of obtaining a particular measurement from a random sample changes due to changing prevalence (i.e., seroprevalence, or fraction of individuals exhibiting an immune response) of the disease in the population. Taking into account these personal and population-level effects, we develop a mathematical model that suggests a natural adaptive scheme for estimating prevalence as a function of time. We then combine the estimated prevalence with optimal decision theory to develop a time-dependent probabilistic classification scheme that minimizes the error associated with classifying a value as positive (history of infection) or negative (no such history) on a given day since the start of the pandemic. We validate this analysis by using a combination of real-world and synthetic SARS-CoV-2 data and discuss the type of longitudinal studies needed to execute this scheme in real-world settings. • Personal antibody levels and global disease prevalence depend on time. • Time dependence as a convolution of dual timeline effects. • Estimate prevalence using the unbiased estimator, then classify. • Optimal classification domains change with time. • Can be applied in a low prevalence setting and for different assays, infections. [ABSTRACT FROM AUTHOR]

Significance: Performance improvements in microfluidic systems depend on accurate measurement and fluid control on the micro- and nanoscales. New applications are continuously leading to lower volumetric flow rates. Aim: We focus on improving an optofluidic system for measuring and calibrating microflows to the sub-nanoliter per minute range. Approach: Measurements rely on an optofluidic system that delivers excitation light and records fluorescence in a precise interrogation region of a microfluidic channel. Exploiting a scaling relationship between the flow rate and fluorescence emission after photobleaching, the system enables real-time determination of flow rates. Results: Here, we demonstrate improved calibration of a flow controller to 1% uncertainty. Further, the resolution of the optofluidic flow meter improved to less than 1 nL / min with 5% uncertainty using a molecule with a 14-fold smaller diffusion coefficient than our previous report. Conclusions: We demonstrate new capabilities in sub-nanoliter per minute flow control and measurement that are generalizable to cutting-edge light-material interaction and molecular diffusion for chemical and biomedical industries. [ABSTRACT FROM AUTHOR]

Abstract: Monge–Kantorovich mass transfer theory is employed to obtain an existence and uniqueness result for solutions to Fokker–Planck Equations with time dependent point control. Existence for an approximate problem is established together with a convergence analysis in the Wasserstein distance through equivalence with weak- convergence. [Copyright &y& Elsevier]

Abstract: The new generation of mass spectrometers produces an astonishing amount of high-quality data in a brief period of time, leading to inevitable data analysis bottlenecks. Automated data analysis algorithms are required for rapid and repeatable processing of mass spectra containing hundreds of peaks, the part of the spectra containing information. New data processing algorithms must work with minimal user input, both to save operator time and to eliminate inevitable operator bias. Toward this end an accurate mathematical algorithm is presented that automatically locates and calculates the area beneath peaks. The promising numerical performance of this algorithm applied to raw data is presented. [Copyright &y& Elsevier]

Quantitative and robust serology assays are critical measurements underpinning global COVID-19 response to diagnostic, surveillance, and vaccine development. Here, we report a proof-of-concept approach for the development of quantitative, multiplexed flow cytometry-based serological and neutralization assays. The serology assays test the IgG and IgM against both the full-length spike antigens and the receptor binding domain (RBD) of the spike antigen. Benchmarking against an RBD-specific SARS-CoV IgG reference standard, the anti-SARS-CoV-2 RBD antibody titer was quantified in the range of 37.6 µg/mL to 31.0 ng/mL. The quantitative assays are highly specific with no correlative cross-reactivity with the spike proteins of MERS, SARS1, OC43 and HKU1 viruses. We further demonstrated good correlation between anti-RBD antibody titers and neutralizing antibody titers. The suite of serology and neutralization assays help to improve measurement confidence and are complementary and foundational for clinical and epidemiologic studies. [ABSTRACT FROM AUTHOR]

This paper presents a practical numerical method for separating and estimating growth and mortality coefficients in stage- or size-structured populations using only observations of the relative or absolute abundance of each stage. The method involves writing a system of linear ordinary differential equations (ODEs) modelling the rate of change of abundance. The solution of the differential system can be numerically approximated using standard (e.g. sixth-order Runge-Kutta-Felhberg) methods. An optimization problem whose solutions yield ‘optimal’ coefficients for a given model is formulated. The ODE numerical integration technique can then be employed to furnish required function and gradient information to the optimization algorithm. The data-fitting software package ODRPACK is then successfully employed to estimate optimal coefficients for the ODE population model. Simulation experiments with four- and eight-stage model populations illustrate that the method results in the successful estimation of coefficients of mortality and growth from abundance data. [ABSTRACT FROM PUBLISHER]

Fluorescence-based measurements are a standard tool for characterizing the thermodynamic properties of DNA systems. Nonetheless, experimental melt data obtained from polymerase chain-reaction (PCR) machines (for example) often leads to signals that vary significantly between datasets. In many cases, this lack of reproducibility has led to difficulties in analyzing results and computing reasonable uncertainty estimates. To address this problem, we propose a data analysis procedure based on constrained, convex optimization of affine transformations, which can determine when and how melt curves collapse onto one another. A key aspect of this approach is its ability to provide a reproducible and more objective measure of whether a collection of datasets yields a consistent "universal" signal according to an appropriate model of the raw signals. Importantly, integrating this validation step into the analysis hardens the measurement protocol by allowing one to identify experimental conditions and/or modeling assumptions that may corrupt a measurement. Moreover, this robustness facilitates extraction of thermodynamic information at no additional cost in experimental time. We illustrate and test our approach on experiments of Förster resonance energy transfer (FRET) pairs used study the thermodynamics of DNA loops. Image 1 • Objective analysis for PCR fluorescence data that removes background effects. • Tool that facilitates reproducibility. • Method that identifies a universal fluorescence signal. [ABSTRACT FROM AUTHOR]

In the previous two manuscripts we outlined the general theory of heat and mass transport in a cell-liquid-ice system with general boundaries and nonideal and nondilute assumptions. Here we simplify the models considerably by presenting a reduction to a spherically symmetric system—a spherical cell with an encroaching spherical ice front. We also reduce to linear approximations of the nonideal nondilute models, essentially assuming dilute and ideal conditions. We derive the resulting nondimensional combined heat and mass transport model for a ternary solution and present numerical solutions. We include an analysis of the effects of varying some nondimensional parameters on rates of ice growth with comments on the necessity of models that account for spatially varying quantities in cryobiology. [ABSTRACT FROM AUTHOR]

Modeling coupled heat and mass transport in biological systems is critical to the understanding of cryobiology. In Part I of this series we derived the transport equation and presented a general thermodynamic derivation of the critical components needed to use the transport equation in cryobiology. Here we refine to more cryobiologically relevant instances of a double free-boundary problem with multiple species. In particular, we present the derivation of appropriate mass and heat transport constitutive equations for a system consisting of a cell or tissue with a free external boundary, surrounded by liquid media with an encroaching free solidification front. This model consists of two parts–namely, transport in the "bulk phases" away from boundaries, and interfacial transport. Here we derive the bulk and interfacial mass, energy, and momentum balance equations and present a simplification of transport within membranes to jump conditions across them. We establish the governing equations for this cell/liquid/solid system whose solution in the case of a ternary mixture is explored in Part III of this series. [ABSTRACT FROM AUTHOR]