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.

Branching Densities of Cube-Free and Square-Free Words

Binary cube-free language and ternary square-free language are two “canonical” representatives of a wide class of languages defined by avoidance properties. Each of these two languages can be viewed as an infinite binary tree reflecting the prefix order of its elements. We study how “homogenious” these trees are, analysing the following parameter: the density of branching nodes along infinite paths. We present combinatorial results and an efficient search algorithm, which together allowed us to get the following numerical results for the cube-free language: the minimal density of branching points is between 3509/9120≈0.38476 and 13/29≈0.44828, and the maximal density is between 0.72 and 67/93≈0.72043. We also prove the lower bound 223/868≈0.25691 on the density of branching points in the tree of the ternary square-free language.

211 Biosecurity practices associated with antimicrobial usage in farrow-to-finish pig farms

The objective of this study was to identify biosecurity practices associated with antimicrobial usage (AMU, mg/live body weight, BW) in pig farms. Biosecurity practices were assessed using the Biocheck.UGentTM questionnaire in 54 Irish farrow-to-finish pig farms. For each farm, information on antimicrobial usage in-feed and water and critically important antimicrobials (CIA) usage was collected. Data were analysed using univariable general linear models in PROC GLM of SAS v9.4. Results are presented as least square means ± SE. In-feed AMU was lower in farms where farm staff wore farm specific clothing and shoes, and washed their hands before entering the stables (55.1±19.12 vs. 159.4±31.49 mg/BW; P=0.007) and it tended (P< 0.10) to be lower in farms where animals were loaded for transport from a centrally located corridor, rather than from separately located corridor (69.5±18.79 vs. 148.4±41.07 mg/BW) and had a maximal density of 0.7 m2/pig in the finisher stage (66.5±29.819.152 vs. 145.1±36.98 mg/BW). Similarly, in water AMU was 14.6 mg/BW lower in farms where farm staff wore farm specific clothing and shoes, and washed their hands before entering the stables and 11 mg/BW lower in farms where carcass storage was regularly cleaned (P< 0.05) compared with farms that did not carry out these practices. Wearing gloves when manipulating carcasses (0.3±0.14 vs. 1.0±0.25 mg/BW having footbaths at the entrance of each building (0.2±0.17 vs. 0.7±0.17 mg/BW), loading animals for transport from a central corridor (0.3±0.13 vs. 1.2±0.28 mg/BW) and a maximal density of 0.7 m2/pig in the finisher stage (0.3±0.13 vs. 1.1±0.25 mg/BW) were associated with lower CIA usage (P< 0.05). The implementation of biosecurity practices was associated with lower AMU. Many of these practices could easily be implemented on farms with relatively low costs. Our results highlight the usefulness of cleaning, disinfections and farm compartmentalization to reduce AMU in pig farms.

Square-Free Partial Words with Many Wildcards

We contribute to the study of square-free words. The classical notion of a square-free word has a natural generalization to partial words, studied in several papers since 2008. We prove that the maximal density of wildcards in the ternary infinite square-free partial word is surprisingly big: [Formula: see text]. Further we show that the density of wildcards in a finitary infinite square-free partial words is at most [Formula: see text] and this bound is reached by a quaternary word. We demonstrate that partial square-free words can be viewed as “usual” square-free words with some letters replaced by wildcards and introduce the corresponding characteristic of infinite square-free words, called flexibility. The flexibility is estimated for some important words and classes of words; an interesting phenomenon is the existence of “rigid” square-free words, having no room for wildcards at all.

Motzkin’s Maximal Density and Related Chromatic Numbers

This paper concerns the problem of determining or estimating the maximal upper density of the sets of nonnegative integers S whose elements do not differ by an element of a given set M of positive integers. We find some exact values and some bounds for the maximal density when the elements of M are generalized Fibonacci numbers of odd order. The generalized Fibonacci sequence of order r is a generalization of the well known Fibonacci sequence, where instead of starting with two predetermined terms, we start with r predetermined terms and each term afterwards is the sum of r preceding terms. We also derive some new properties of the generalized Fibonacci sequence of order r. Furthermore, we discuss some related coloring parameters of distance graphs generated by the set M.

Horoball packings related to the 4-dimensional hyperbolic 24 cell honeycomb {3,4,3,4}

In this paper we study the horoball packings related to the hyperbolic 24 cell honeycomb by Coxeter-Schl?fli symbol {3,4,3,4} in the extended hyperbolic 4-spaceH 4 where we allow horoballs in different types centered at the various vertices of the 24 cell. Introducing the notion of the generalized polyhedral density function, we determine the locally densest horoball packing arrangement and its density with respect to the above regular tiling. The maximal density is ? 0:71645 which is equal to the known greatest horoball packing density in hyperbolic 4-space, given in [13].