Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.     

On distributionally regenerative processes

The paper is concerned with characterization results for distributional regeneration. It is shown that distributional regeneration is equivalent to renewal representation of the associated (shift) Markov operator. A sufficient condition for the distributional regeneration of the transfer operator in terms of variation is also formulated. Finally, a minorization condition is formulated and proved to be sufficient for recurrent co-Feller operators.     

The kink of cellular automaton rule 18 performs a random walk

We give an exact characterization of the movement of a single kink in the elementary cellular automaton Rule 18. It is a random walk with independent increments as well as independent delay times. Its statistical parameters are computed to confirm the earlier simulation results by Grassberger.     

Electron impact ionization mass spectra of 2,4,5,5-tetrasubstituted 1,2,4-triazolidine-3-thiones. The effect of the ethoxycarbonyl group at position 4

The electron impact ionization mass spectra of 2,4,5,5-tetrasubstituted 1,2,4-triazolidine-3-thiones studied confirmed that the substituent at position 4 has the most dramatic influence on the fragmentation pattern. When the substituent is a methylallyl group the molecular ions exhibit four main routes of fragmentation, but when it is an ethoxycarbonyl/acetyl or a methyl group these direct decompositions of the molecular ion become less abundant. Interestingly all 4-ethoxycarbonyl derivatives and the 4-acetyl derivative exhibited the ions [M-R⁴-COOC₂H₄]⁺ and [M-R⁴-COCH₂]⁺, respectively, with the same composition.     

Cytochrome c–dimyristoylphosphatidylglycerol interactions studied by asymmetrical flow field-flow fractionation

Lipid membranes are well recognized ligands that bind peripheral and integral proteins in a specific manner and regulate their function. Cytochrome c (cyt c) is one of the partner peripheral protein that binds to the lipid membranes via electrostatic and hydrophobic interactions. In this study, asymmetrical flow field-flow fractionation (AsFlFFF) was used to compare the interactions of cyt c with the acidic phospholipid 1,2-dimyristoyl-sn-glycero-3-phospho-rac-glycerol (DMPG), oleic acid (OA), and sodium dodecyl sulfate (SDS). The influence of pH and the cyt c–lipid molar mass ratios were evaluated by monitoring the diffusion coefficients and particle diameter distributions obtained for the free and lipid-bound protein. The hydrodynamic particle diameter of cyt c (pI 10) was 4.1 nm at pH 11.4 and around 4.2 nm at pH 7.0 and 8.0. Standard molar mass marker proteins were used for calibration to obtain the molar masses of free cyt c and its complexes with lipids. AsFlFFF revealed the binding of cyt c to DMPG and to OA to be mainly electrostatic. In the absence of electrostatic interactions, minor complex formation occurred, possibly due to the extended lipid anchorage involving the hydrophobic cavity of cyt c and the hydrocarbon chains of DMPG or SDS. The possibility of the formation of the molten globule state of cyt c, induced by the interaction between cyt c and lipids, is discussed.Electronic Supplementary Material Supplementary material is available for this article at     

Alnumycins A2 and A3: new inverse-epimeric pairs stereoisomeric to alnumycin A1

Two new pairs of stereoisomeric alnumycin As, A2 {(2)-(1R,1′RS,4′SR,5′SR)} and A3 {(2)-(1R,1′RS,4′SR,5′RS)}, are described. Similar to alnumycin A1 {(2)-(1R,1′RS,4′RS,5′SR)}, each of these naturally occurring compounds is also a pair of C-1 inverse epimers. The relative configurations of the dioxane ring sidechains were assigned on the basis of ¹H NMR NOE contacts and molecular modeling using density functional theory (DFT) at the M06-2X/6-31G(d) level of theory. The absolute configurations of C-1 and the determination of inverse epimeric relationships were achieved by experimental electronic circular dichroism (ECD) measurements, with both aspects confirmed by using the chiral derivatizing agent (CDA) Mosher′s acid chloride {α-methoxy-α-trifluorophenylacetyl chloride (MTPACl)} to effect enantiodifferentiation. The absolute configurations of the dioxane ring using the CDA could only be effected in the case of alnumycin A1, the results of which were in agreement with previous assignments. The dioxane ring conformational mobility and the likely interaction between the MTPA groups coupled with the structural novelty of the diols in the dioxane ring with respect to CDA analysis precluded an absolute configuration assignment for alnumycins A2 and A3 based on empirical comparisons or by computational analysis of through-space NMR shieldings (TSNMRS) emanating from the phenyl groups of the MTPA moieties.     

A One‐Pot Synthesis of N‐Aryl‐2‐Oxazolidinones and Cyclic Urethanes by the Lewis Base Catalyzed Fixation of Carbon Dioxide into Anilines and Bromoalkanes

The multicomponent assembly of pharmaceutically relevant N‐aryl‐oxazolidinones through the direct insertion of carbon dioxide into readily available anilines and dibromoalkanes is described. The addition of catalytic amounts of an organosuperbase such as Barton's base enables this transformation to proceed with high yields and exquisite substrate functional‐group tolerance under ambient CO₂ pressure and mild temperature. This report also provides the first proof‐of‐principle for the single‐operation synthesis of elusive seven‐membered ring cyclic urethanes.     

On applicability of PCA,voxel-wise variance normalization and dimensionality assumptions for sliding temporal window sICA in resting-state fMRI

Subject-level resting-state fMRI (RS-fMRI) spatial independent component analysis (sICA) may provide new ways to analyze the data when performed in the sliding time window. However, whether principal component analysis (PCA) and voxel-wise variance normalization (VN) are applicable pre-processing procedures in the sliding-window context, as they are for regular sICA, has not been addressed so far. Also model order selection requires further studies concerning sliding-window sICA. In this paper we have addressed these concerns. First, we compared PCA-retained subspaces concerning overlapping parts of consecutive temporal windows to answer whether in-window PCA and VN can confound comparisons between sICA analyses in consecutive windows. Second, we compared the PCA subspaces between windowed and full data to assess expected comparability between windowed and full-data sICA results. Third, temporal evolution of dimensionality estimates in RS-fMRI data sets was monitored to identify potential challenges in model order selection in a sliding-window sICA context. Our results illustrate that in-window VN can be safely used, in-window PCA is applicable with most window widths and that comparisons between windowed and full data should not be performed from a subspace similarity point of view. In addition, our studies on dimensionality estimates demonstrated that there are sustained, periodic and very case-specific changes in signal-to-noise ratio within RS-fMRI data sets. Consequently, dimensionality estimation is needed for well-founded model order determination in the sliding-window case. The observed periodic changes correspond to a frequency band of ≤ 0.1 Hz, which is commonly associated with brain activity in RS-fMRI and become on average most pronounced at window widths of 80 and 60 time points (144 and 108 s, respectively). Wider windows provided only slightly better comparability between consecutive windows, and 60 time point or shorter windows also provided the best comparability with full-data results. Further studies are needed to determine the cause for dimensionality variations.     

Multivariate Association of Graph-Theoretic Variables and Physicochemical Properties

Abstract

We used canonical correlation analysis to examine the multivariate association between two distinct data sets commonly measured or calculated for approximately 600 chemicals: (1) measured or calculated values of select physieochemical properties (i.e., K _ow, boiling point, heat of vaporization, molecular weight, water solubility, molecular volume, hydrogen bonding potential, and vapor pressure) and (2) calculated algorithmically-derived variables (i.e., topological and neighborhood indices derived from graph theory). Canonical correlation analysis identified eight highly significant associations between linear combinations of graph-theoretic variables and linear combinations of physicochemical properties. The set of graph theoretic variables was significantly related to all physieochemical properties, explaining 55% to 99% of the variation in these properties.