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Motivated by the current COVID-19 health crisis, we consider data analysis for quantitative polymerase chain-reaction (qPCR) measurements. We derive a theoretical result specifying the conditions under which all qPCR amplification curves (including their plateau phases) are identical up to an affine transformation, i.e. a multiplicative factor and horizontal shift. We use this result to develop a data analysis procedure for determining when an amplification curve exhibits characteristics of a true signal. The main idea behind this approach is to invoke a criterion based on constrained optimization that assesses when a measurement signal can be mapped to a master reference curve. We demonstrate that this approach: (i) can decrease the fluorescence detection threshold by up to a decade; and (ii) simultaneously improve confidence in interpretations of late-cycle amplification curves. Moreover, we demonstrate that the master curve is transferable reference data that can harmonize analyses between different labs and across several years. Application to reverse-transcriptase qPCR measurements of a SARS-CoV-2 RNA construct points to the usefulness of this approach for improving confidence and reducing limits of detection in diagnostic testing of emerging diseases. Graphical Abstract Left: a collection of qPCR amplification curves. Right: Example of data collapse after affine transformation.

A mass spectral library search algorithm that identifies compounds that differ from library compounds by a single "inert" structural component is described. This algorithm, the Hybrid Similarity Search, generates a similarity score based on matching both fragment ions and neutral losses. It employs the parameter DeltaMass, defined as the mass difference between query and library compounds, to shift neutral loss peaks in the library spectrum to match corresponding neutral loss peaks in the query spectrum. When the spectra being compared differ by a single structural feature, these matching neutral loss peaks should contain that structural feature. This method extends the scope of the library to include spectra of "nearest-neighbor" compounds that differ from library compounds by a single chemical moiety. Additionally, determination of the structural origin of the shifted peaks can aid in the determination of the chemical structure and fragmentation mechanism of the query compound. A variety of examples are presented, including the identification of designer drugs and chemical derivatives not present in the library.

Current methods for aligning biological sequences are based on dynamic programming algorithms. If large numbers of sequences or a number of long sequences are to be aligned, the required computations are expensive in memory and central processing unit (CPU) time. In an attempt to bring the tools of large-scale linear programming (LP) methods to bear on this problem, we formulate the alignment process as a controlled Markov chain and construct a suggested alignment based on policies that minimise the expected total cost of the alignment. We discuss the LP associated with the total expected discounted cost and show the results of a solution of the problem based on a primal-dual interior point method. Model parameters, estimated from aligned sequences, along with cost function parameters are used to construct the objective and constraint conditions of the LP problem. This article concludes with a discussion of some alignments obtained from the LP solutions of problems with various cost function parameter values.

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]

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. [ABSTRACT FROM AUTHOR]

MassSpectator is a novel suite of numerical algorithms that accurately locates and calculates the area beneath peaks from real mass spectral data by using only reproducible mathematical operations. It requires no user-selected parameters but does require a background spectrum to determine instrumental noise. Such a fully automated algorithm is useful for rapid and repeatable processing of mass spectral data containing hundreds of peaks. MassSpectator represents a first attempt to create an unbiased method using time series segmentation to analyze mass spectral data.

Abstract: Estimating time delays for signal alignment is important for many applications. This paper extends a successful frequency domain cost function minimization algorithm capable of estimating time delays to within a fraction of sampling periods. Since the function has a narrow basin of attraction around the global minimum, this method often diverges when initial time delay estimates are not sufficiently close to the desired optimal time delays. We propose a second order successive minimization method with reduced sensitivity to initial guesses. Both an analytic expression for the cost function Hessian matrix and a condition guaranteeing positive-definiteness are presented. This condition facilitates the construction of sequentially modified cost functions whose nested minimization increases the basin of attraction around the global minimum. This successive minimization technique is more robust and yields higher accuracy when compared to the original method and the well-known method of Cross Correlator (CC). [Copyright &y& Elsevier]