Application of simca multivariate data analysis to the classification of gas chromatographic profiles of human brain tissues

Sixteen samples of three types (classes) of brain tissue were characterized by capillary gas chromatography (g.c.). Each sample is thus characterized by the peak heights of 105 peaks in each g.c. profile. SIMCA pattern recognition is used to analyze the 16 × 105 data matrix in order to differentiate between the three classes on the basis of the g.c. data only. The SIMCA method is therefore applicable even when the number of variables (105) exceeds the number of objects (16). The results indicate that g.c. profiles are useful for the identification of brain tissue type.     

The lower tail: Poisson approximation revisited

The well‐known “Janson's inequality” gives Poisson‐like upper bounds for the lower tail probability when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations, this inequality is optimal whenever X is approximately Poisson, i.e., when the dependencies are weak. We also present correlation‐based approaches that, in certain symmetric applications, yield related conclusions when X is no longer close to Poisson. As an illustration we, e.g., consider subgraph counts in random graphs, and obtain new lower tail estimates, extending earlier work (for the special case ) of Janson, ?uczak and Ruciński. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 219–246, 2016     

Retention of opioids and their glucuronides on a combined zwitterion and hydrophilic interaction stationary phase

A stationary phase combining zwitterionic ion chromatography and hydrophilic interaction chromatography (ZIC-HILIC) from SeQuant was evaluated for the chromatography of some opiates and their polar metabolites. The effects of mobile phase constitution on retention and resolution were extensively evaluated. Different aspects of mobile phase constitution such as ion strength and type of buffer, type and amount of organic modifier and pH were examined. The selectivity and retention of the opiates compared to their glucuronides could be substantially altered with small changes of the mobile phase, especially when the type of buffer, i.e., formate or acetate and organic modifier, i.e., acetonitrile or methanol were changed. The retention on the ZIC-HILIC was dominated by hydrophilic interaction chromatography (HILIC) but considerable effects on the selectivity was observed, possibly caused by an ion exchange mechanism due to interactions with the charges on the stationary phase.     

Size dependent fragmentation of argon clusters in the soft x-ray ionization regime

Photofragmentation of argon clusters of average size ranging from 10 up to 1000 atoms is studied using soft x-ray radiation below the 2p threshold and multicoincidence mass spectroscopy technique. For small clusters (=10), ionization induces fast fragmentation with neutral emission imparting a large amount of energy. While the primary dissociation takes place on a picosecond time scale, the fragments undergo slow degradation in the spectrometer on a microsecond time scale. For larger clusters ( >or=100) we believe that we observe the fragmentation pattern of multiply charged species on a time-scale which lasts a few hundred nanoseconds. The reason for these slower processes is the large number of neutral atoms which act as an efficient cooling bath where the excess energy ("heat") dissipates among all degrees of freedom. Further degradation of the photoionic cluster in spectrometer then takes place on the microsecond time scale, similar to small clusters.     

The electronic structure of free aluminum clusters: metallicity and plasmons

The electronic structure of free aluminum clusters with ～3-4 nm radius has been investigated using synchrotron radiation-based photoelectron and Auger electron spectroscopy. A beam of free clusters has been produced using a gas-aggregation source. The 2p core level and the valence band have been probed. Photoelectron energy-loss features corresponding to both bulk and surface plasmon excitation following photoionization of the 2p level have been observed, and the excitation energies have been derived. In contrast to some expectations, the loss features have been detected at energies very close to those of the macroscopic solid. The results are discussed from the point of view of metallic properties in nanoparticles with a finite number of constituent atoms.     

A regular decomposition of the edge-product space of phylogenetic trees

We investigate the topology and combinatorics of a topological space called the edge-product space that is generated by the set of edge-weighted finite labelled trees. This space arises by multiplying the weights of edges on paths in trees, and is closely connected to tree-indexed Markov processes in molecular evolutionary biology. In particular, by considering combinatorial properties of the Tuffley poset of labelled forests, we show that the edge-product space has a regular cell decomposition with face poset equal to the Tuffley poset.     

Random cutting and records in deterministic and random trees

We study random cutting down of a rooted tree and show that the number of cuts is equal (in distribution) to the number of records in the tree when edges (or vertices) are assigned random labels. Limit theorems are given for this number, in particular when the tree is a random conditioned Galton–Watson tree. We consider both the distribution when both the tree and the cutting (or labels) are random and the case when we condition on the tree. The proofs are based on Aldous' theory of the continuum random tree. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

Parity Splits by Triple Point Distances in X-Trees

At the conference Dress defined parity split maps by triple point distance and asked for a characterisation of such maps coming from binary phylogenetic X-trees. This article gives an answer to that question. The characterisation for X-trees can be easily described as follows: If all restrictions of a split map to sets of five or fewer elements is a parity split map for an X-tree, then so is the entire map. To ensure that the parity split map comes from an X-tree which is binary and phylogenetic, we add two more technical conditions also based on studying at most five points at a time. Received August 27, 2004     

Dense Packing of Patterns in a Permutation

We study the length L _k of the shortest permutation containing all patterns of length k. We establish the bounds e ⁻² k ² < L _k ≤ (2/3 + o(1))k ². We also prove that as k → ∞, there are permutations of length (1/4 + o(1))k ² containing almost all patterns of length k. Received January 2, 2007