MAFFIN: Metabolomics Sample Normalization Using Maximal Density Fold Change with High-Quality Metabolic Features and Corrected Signal Intensities

Sample normalization is a critical step in metabolomics to remove differences in total sample amount or concentration of metabolites between biological samples. Here, we present MAFFIN, an accurate and robust post-acquisition sample normalization workflow that works universally for metabolomics data collected by mass spectrometry (MS)-based platforms. The most important design of MAFFIN is the calculation of normalization factor using maximal density fold change (MDFC) value computed by a kernel density-based approach. MDFC is more accurate than traditional median FC-based normalization, especially when the numbers of up- and down-regulated metabolic features are different. In addition, we showcase two essential steps that are overlooked by conventional normalization methods, and incorporated them into MAFFIN. First, instead of using all detected metabolic features, MAFFIN automatically extracts and uses only the high-quality features to calculate FCs and determine the normalization factor. In particular, multiple orthogonal criteria are proposed to pick up the high-quality features. Second, to guarantee the accuracy of the FCs, the MS signal intensities of the high-quality features are corrected using serial quality control (QC) samples. Using simulated data and urine metabolomics datasets, we demonstrated the critical need of high-quality feature selection, MS signal correction, and MDFC. We also show the superior performance of MAFFIN over other commonly used post-acquisition sample normalization methods. Finally, a biological application on a human saliva metabolomics study shows that MAFFIN provides robust sample normalization, leading to better data separation in principal component analysis (PCA) and the identification of more significantly altered metabolic features.

IMPACT OF THE NORMALIZATION OF THE SPECTRAL RESPONSIVITY ON THE PERFORMANCE OF THE GENERAL V(λ) MISMATCH INDEX

Quality indexes are usually defined for measurement instruments in order to characterize some specific aspect of their performance. The V(λ) spectral mismatch of photometers is evaluated by the general V(λ) mismatch index, f1’, whose value must be correlated with the average measurement error introduced by this spectral mismatch. The objective of this work is to assess the correlation of several indexes of this type with this average error of photometers. The difference between the studied indexes is that the spectral responsivity of the photometer is normalized with different factors to that defined for f1’. From this study, we conclude that the most suitable normalization in the definition of a f1’-type quality index is not determined by the spectral distribution used in the calibration or by those of the light sources to be measured. The normalization factor presenting the best correlation in all studied cases was obtained by numerically minimizing the value of the index instead of by applying an explicit function, as it is done in f1’.

Scattering and absorption sections of Schwarzschild-anti de Sitter with quintessence

In this paper, we study the scattering and absorption sections of the Schwarzschild--anti de Sitter black hole surrounded by quintessence. The critical values of the cosmological constant and the normalization factor are obtained. We describe the event horizons and the extremal condition of the black hole surrounded by quintessence. The effects of quintessence on the classical and semi--classical scattering cross--sections have been estimated. Also, the absorption section is studied with the sinc approximation in the eikonal limit. We consider the quintessence state parameter in the particular cases ω = -2/3 and ω = -1/2.

A Two-Steps-Ahead Estimator for Bubble Entropy

Aims: Bubble entropy (bEn) is an entropy metric with a limited dependence on parameters. bEn does not directly quantify the conditional entropy of the series, but it assesses the change in entropy of the ordering of portions of its samples of length m, when adding an extra element. The analytical formulation of bEn for autoregressive (AR) processes shows that, for this class of processes, the relation between the first autocorrelation coefficient and bEn changes for odd and even values of m. While this is not an issue, per se, it triggered ideas for further investigation. Methods: Using theoretical considerations on the expected values for AR processes, we examined a two-steps-ahead estimator of bEn, which considered the cost of ordering two additional samples. We first compared it with the original bEn estimator on a simulated series. Then, we tested it on real heart rate variability (HRV) data. Results: The experiments showed that both examined alternatives showed comparable discriminating power. However, for values of 10<m<20, where the statistical significance of the method was increased and improved as m increased, the two-steps-ahead estimator presented slightly higher statistical significance and more regular behavior, even if the dependence on parameter m was still minimal. We also investigated a new normalization factor for bEn, which ensures that bEn=1 when white Gaussian noise (WGN) is given as the input. Conclusions: The research improved our understanding of bubble entropy, in particular in the context of HRV analysis, and we investigated interesting details regarding the definition of the estimator.

Non-linear Normalization for Non-UMI Single Cell RNA-Seq

Single cell RNA-seq data, like data from other sequencing technology, contain systematic technical noise. Such noise results from a combined effect of unequal efficiencies in the capturing and counting of mRNA molecules, such as extraction/amplification efficiency and sequencing depth. We show that such technical effects are not only cell-specific, but also affect genes differently, thus a simple cell-wise size factor adjustment may not be sufficient. We present a non-linear normalization approach that provides a cell- and gene-specific normalization factor for each gene in each cell. We show that the proposed normalization method (implemented in “SC2P" package) reduces more technical variation than competing methods, without reducing biological variation. When technical effects such as sequencing depths are not balanced between cell populations, SC2P normalization also removes the bias due to uneven technical noise. This method is applicable to scRNA-seq experiments that do not use unique molecular identifier (UMI) thus retain amplification biases.

Approximation of positive operators by analytic vectors

We give the estimates of approximation errors while approximating of a positive operator $A$ in a Banach space by analytic vectors. Our main results are formulated in the form of Bernstein and Jackson type inequalities with explicitly calculated constants. We consider the classes of invariant subspaces ${\mathcal E}_{q,p}^{\nu,\alpha}(A)$ of analytic vectors of $A$ and the special scale of approximation spaces $\mathcal {B}_{q,p,\tau}^{s,\alpha}(A)$ associated with the complex degrees of positive operator. The approximation spaces are determined by $E$-functional, that plays a similar role as the module of smoothness. We show that the approximation spaces can be considered as interpolation spaces generated by $K$-method of real interpolation. The constants in the Bernstein and Jackson type inequalities are expressed using the normalization factor.

Multiloop contributions to the on-shell-$$ \overline{{\mathrm{MS}}}$$ heavy quark mass relation in QCD and the asymptotic structure of the corresponding series: the updated consideration

The asymptotic structure of the QCD perturbative relation between the on-shell and $$\overline{{\mathrm{MS}}}$$ MS ¯ heavy quark masses is studied. We estimate the five and six-loop contributions to this relation by three different techniques. First, the effective charges motivated approach in two variants is used. Second, the results following from the large-$$\beta _0$$ β 0 approximation are analyzed. Finally, the consequences of applying the asymptotic renormalon-based formula are investigated. We show that all approaches lead to corrections which are qualitatively consistent in order of magnitude. Their sign-alternating character in powers of the number of massless quarks is demonstrated. We emphasize that there is no contradiction in the behavior of the fine structure of the renormalon-based estimates with other approaches if one use the detailed information about the normalization factor included in the renormalon asymptotic formula. The obtained five- and six-loop estimates indicate that in the case of the b-quark the asymptotic character of the studied relation manifests itself above the fourth order of PT, whereas for the t-quark it starts to reveal itself after the seventh order. This allows to conclude that like the running masses, the pole masses of the b and especially t-quark in principle may be used in the phenomenologically-oriented studies.

Different folding models for 6Li+28Si elastic scattering

In this work, the elastic scattering of 6Li+[Formula: see text]Si system at wide range energies from 76 to 318[Formula: see text]MeV is analyzed. The analysis is carried out in the framework of the optical model (OM). Two different methods are adopted for nuclear optical potential of this system. The first method is the double folding cluster (DFC) for the real part supplied with an imaginary part in the Woods–Saxon (WS) form. In the second one, the double folding (DF) model based upon São Paulo potential (SPP) is used as real and imaginary parts each multiplied by a corresponding normalization factor. For [Formula: see text]Si, the full [Formula: see text]-cluster density is considered while the [Formula: see text]-deuteron ([Formula: see text]–[Formula: see text]) structure is considered for 6Li. Therefore, the DFC real central part is calculated by folding both [Formula: see text]–[Formula: see text] and [Formula: see text]–[Formula: see text] effective interaction between target and nuclei over the cluster densities of the target and projectile. The derived renormalized potentials give a successful description of the data. The present results are in good agreement with the previous work. This agreement confirms the validity of the present methods to generate nucleus–nucleus optical potentials.

Erratum to: Hints of unitarity at large N in the O(N)3 tensor field theory

The measure in equation (2.11) contains a wrong normalization factor, and it should be multiplied by 21−dΓ(d − 1)/Γ(d/2)2.