Sample size planning for classification models

In biospectroscopy, suitably annotated and statistically independent samples (e.g. patients, batches, etc.) for classifier training and testing are scarce and costly. Learning curves show the model performance as function of the training sample size and can help to determine the sample size needed to train good classifiers. However, building a good model is actually not enough: the performance must also be proven. We discuss learning curves for typical small sample size situations with 5–25 independent samples per class. Although the classification models achieve acceptable performance, the learning curve can be completely masked by the random testing uncertainty due to the equally limited test sample size. In consequence, we determine test sample sizes necessary to achieve reasonable precision in the validation and find that 75–100 samples will usually be needed to test a good but not perfect classifier. Such a data set will then allow refined sample size planning on the basis of the achieved performance. We also demonstrate how to calculate necessary sample sizes in order to show the superiority of one classifier over another: this often requires hundreds of statistically independent test samples or is even theoretically impossible. We demonstrate our findings with a data set of ca. 2550 Raman spectra of single cells (five classes: erythrocytes, leukocytes and three tumour cell lines BT-20, MCF-7 and OCI-AML3) as well as by an extensive simulation that allows precise determination of the actual performance of the models in question.     

Comments on the widom Hall effect current formula

Recently Widom has derived a formula for the Hall current. The aim of the following comments is to clarify the relation between Widom's formula and the usual one.     

On Facts and Artefacts: The Difficulty to Evaluate an Artificial Nuclease

A number of promising synthetic catalysts for the hydrolytic degradation of RNA have been developed in recent years. Some of them show remarkable selectivity for pyrimidine nucleotides. The general problem of all these studies is to distinguish between real effects and artefacts caused by traces of contaminating natural ribonucleases. We show that methods representing the current state of the art (diethylpyrocarbonate treatment, sterilization, ultrafiltration, etc.) do not sufficiently protect against severe artefacts. However, an incorruptible assay could be found by comparing the cleavage of RNA and its mirror image. Enantiomeric RNA is completely resistant to enzymatic degradation, whereas achiral nonpeptide catalysts, by fundamental laws of symmetry, cannot distinguish between enantiomers and will induce exactly the same cleavage pattern with both substrates.     

Analytical reliability of carbonyl compound determination using 1,5-dansylhydrazine-derivatization

Solid sorbents coated with the fluorescent reagent 5-dimethylaminonaphthalene-1-sulfohydrazide (dansylhydrazine, DNSH) have been used for derivatization and quantitative determination of airborne carbonyl compounds, for example in investigations on atmospheric pollution. The evaluation of this derivatization reaction presented here revealed that, for several reasons, it may not be recommended when sampling is performed with impingers containing liquid reagent solutions. Derivative yields came out to be strongly influenced by water and phosphoric acid which are essential for sufficient derivatization rates, but also responsible for the degradation of derivatives. Even at water and acid concentrations considered as an optimal compromise between accelerating and degrading effects, the analytical reliability of the method can only be guaranteed under controlled laboratory conditions. The reduced or lacking reactivity of DNSH towards aromatic aldehydes or aliphatic and aromatic ketones is an additional finding discarding the DNSH method for routine air monitoring at least when impingers are used for sampling.     

Application of combined high-performance thin-layer chromatography immunostaining and nanoelectrospray ionization quadrupole time-of-flight tandem mass spectrometry to the structural characterization of high- and low-affinity binding ligands of Shiga toxin 1

Shiga toxin 1 (Stx1) represents an AB5 toxin produced by enterohemorrhagic Escherichia coli, which cause gastrointestinal diseases in humans that are often followed by potentially fatal systemic complications, such as acute encephalopathy and hemolytic uremic syndrome. The expression of the preferential Stx1 receptor, Gb3Cer/CD77 (Gal alpha1-4Gal beta1-4Glc beta1-1Cer), is one of the primary determinants of susceptibility to tissue injury. Due to the clinical importance of this life-threatening toxin, a combined strategy of preparative high-performance thin-layer chromatography (HPTLC) overlay assay and mass spectrometry was developed for the detection and structural characterization of Stx1-binding glycosphingolipids (GSLs). A preparation of neutral GSLs from human erythrocytes, comprising 21.4% and 59.1% of the high- and low-affinity Stx1-binding ligands Gb3Cer/CD77 and Gb4Cer, respectively, was separated on silica gel precoated HPTLC plates and probed for the presence of Stx1 receptors. Stx1 positive on the one hand and anti-Gb3Cer/CD77 and anti-Gb4Cer antibody positive bands from parallel reference runs on the other hand were extracted with chloroform/methanol/water (30/60/8, v/v/v). These crude extracts were used without any further purification for a detailed structural analysis by nanoelectrospray ionization quadrupole time-of-flight mass spectrometry (nanoESI-QTOF-MS) in the negative ion mode. In all extracts investigated, neutral GSLs were detected as singly charged deprotonated molecular ions, [M-H]-, and neither buffer-derived salt adducts nor coextracted contaminants from the overlay assay procedure or the silica gel layer were observed. For the structural characterization of Stx1- and antibody-binding GSLs low-energy collision-induced dissociation (CID) was applied to high and low abundant receptor species of the crude extracts. All MS/MS spectra obtained contained full series of Y-type ions, B-type ions and additional ions generated by ring cleavages of the sugar moiety. Only analytical quantities in the microgram scale of a single GSL species within the complex GSL mixture were required for the structural MS characterization of Stx1 ligands as Gb3Cer/CD77 and Gb4Cer. This effective combined HPTLC/MS procedure offers a broad range of applications, not only for toxins of bacterial origin, but also for any GSL-binding agents such as plant-derived lectins or human proteins with yet unknown binding specificities.     

The Rare Earth Metal-Rich Indides RE 4RhIn ( RE = Gd–Tm, Lu)

The rare earth-transition metal-indides RE ₄RhIn (RE = Gd–Tm, Lu) were prepared by arc-melting of the elements and subsequent annealing. Single crystals were grown via slowly cooling of the samples. The indides were investigated via X-ray powder diffraction and several structures were refined from X-ray single crystal diffractometer data: F[`4]3mF{\bar 4}3m , a = 1370.7(9) pm, wR2 = 0.049, 428 F ² values for Gd₄RhIn, a = 1360.3(6) pm, wR2 = 0.028, 420 F ² values for Tb₄RhIn, a = 1354.5(2) pm, wR2 = 0.041, 380 F ² values for Dy₄RhIn, a = 1349.2(3) pm, wR2 = 0.029, 410 F ² values for Ho₄RhIn, a = 1342.5(5) pm, wR2 = 0.037, 403 F ² values for Er₄RhIn, a = 1337.8(3) pm, wR2 = 0.038, 394 F ² values for Tm₄RhIn with 14 variable parameters per refinement, and a = 1329.7(3) pm for Lu₄RhIn. In this new structure type, the rhodium atoms have a trigonal prismatic rare earth coordination. Condensation of the RhRE ₆ prisms leads to a three-dimensional network which leaves voids that are filled by regular In₄ tetrahedra (317 pm In–In distance) in Gd₄RhIn. The indium atoms have twelve nearest neighbors (3 In + 9 RE) in icosahedral coordination. The gadolinium atoms build up a three-dimensional, adamantane-like network of condensed, face-sharing empty octahedra.     

Syntheses and Structures of RE10Ni9+xIn20 (RE = Tb,Dy) and YbNiIn2

The ternary indides RE₁₀Ni_9+xIn₂₀ (RE = Tb, Dy) were synthesized from the elements by arc‐melting under argon and subsequent annealing. YbNiIn₂ was prepared in a sealed tantalum tube in a water‐cooled sample chamber of a high‐frequency furnace. X‐ray powder and single crystal data revealed isotypism with the tetragonal Ho₁₀Ni₉In₂₀ type structure, space group P4/nmm for the RE₁₀Ni_9+xIn₂₀ compounds: a = 1337.0(2), c = 909.5(2) pm, wR2 = 0.0527, 1795 F² values, 65 variables for RE = Tb, and a = 1333.63(7), c = 907.2(1) pm, wR2 = 0.0590, 1346 F² values, 65 variables for RE = Dy. Both indides show an additional nickel site (Ni4) with partial nickel occupancy leading to the refined compositions Tb₁₀Ni_9.34(2)In₂₀ and Dy₁₀Ni_9.32(2)In₂₀. YbNiIn₂ adopts the orthorhombic MgCuAl₂‐type structure: Cmcm, a = 430.67(9), b = 1033.0(2), c = 758.1(1) pm, wR2 = 0.0262, 424 F² values and 16 variable parameters. The crystal chemistry of the RE₁₀Ni_9+xIn₂₀ and RENiIn₂ compounds is briefly discussed.     

Characterization of cellulose produced by Salmonella enterica serovar Typhimurium

Distinct bacterial species belonging to the family of enterobacteriaceae produce cellulose as an exopolysaccharide. Cellulose produced by Salmonella enterica serovar Typhimurium was isolated by various methods. Subsequently, transmission electron microscopy (TEM) studies of the isolated material revealed novel structural details of enterobacterial cellulose.     

Die Bromokomplexe von Molybdän(IV) [MoBr6]2⊖ und [Mo2Br10]2⊖. Die Kristallstruktur von (PPh3Me)2[MoBr6] · 2 CH2Br2

Bromo Complexes of Molybdenum(IV) [MoBr₆]^2? and [Mo₂Br₁₀]^2?. Crystal Structure of (PPh₃Me)₂[MoBr₆] · 2 CH₂Br₂ The bromomolybdates(IV) (PPh₃Me)₂[MoBr₆] · 2 CH₂Br₂ and (PPh₄)₂[Mo₂Br₁₀] are obtained by reactions of molybdenum tetrabromide with PPh₃MeBr and PPh₄Br, respectively. They form black-brown, hydrolysis sensitive crystal powders. The crystal structure of (PPh₃Me)₂[MoBr₆] · 2 CH₂Br₂ was determined by X-ray diffraction (2376 independent observed reflexions, R = 0.082). Crystal data: a = 1024, b = 1131, c = 1179 pm, α = 108.2°, β = 106.8°, γ = 99.0°, space group P1 , Z = 1. The compound consists of PPh₃Me⁺ ions, CH₂Br₂ molecules and nearly octahedral [MoBr₆]^2? ions with MoBr bond lengths between 252.7 and 254.0 pm.