Image analysis and chemical information in images

Image analysis and its different aspects are presented with emphasis on the difference between technology, conceptual modelling (psychology) and chemical information. An overview is given of how the information in image analysis is presented. The distinction between univariate and multivariate image analysis is taken up. The different data analysis techniques that are in common in both chemometrics and image analysis play a major role here.     

Multiple excitations in the core photoelectron spectrum of acetylene

A high-resolution core photoelectron spectrum of free acetylene is presented. Configuration interaction and complete active space SCF calculations were carried out for assignment and prediction of energies and intensities in the spectrum. The shake-up structure is found to be strongly dominated by intervalence π_g to π_g transitions for which multiple 2-, 3- and 4-fold excitations are important.     

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     

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     

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     

Average-case results on heapsort

A new algorithm for rearranging a heap is presented and analysed in the average case. The average case upper bound for deleting the maximum element of a random heap is improved, and is shown to be less than [logn]+0.299+M(n) comparisons, *) whereM(n) is between 0 and 1. It is also shown that a heap can be constructed using 1.650n+O(logn) comparisons with this algorithm, the best result for any algorithm which does not use any extra space. The expected time to sortn elements is argued to be less thann logn+0.670n+O(logn), while simulation result points at an average case ofn log n+0.4n which will make it the fastest in-place sorting algorithm. The same technique is used to show that the average number of comparisons when deleting the maximum element of a heap using Williams' algorithm for rearrangement is 2([logn]–1.299+L(n)) whereL(n) also is between 0 and 1, and the average cost for Floyd-Williams Heapsort is at least 2nlogn–3.27n, counting only comparisons. An analysis of the number of interchanges when deleting the maximum element of a random heap, which is the same for both algorithms, is also presented.     

Statistical molecular design of peptoid libraries

Statistical experimental design provides an efficient approach for selecting the building blocks to span the structural space and increase the information content in a combinatorial library. A set of renin-inhibitors, hexapeptoids, is used to illustrate the approach. Multivariate quantitative structure-activity relationships (MQSARs) were developed relating renin inhibition to the peptoid sequences variation, parametrized by the z-scales. By using the information from the models, the number of building block sets could be reduced from six to three. Using a statistical molecular design (SMD) reduces the number of compounds from more than 100 000 down to 90. A second SMD was used for comparison, based on less prior knowledge. This gave a reduction from over 2 billion to 120 compounds.     

Ionic bonding in free nanoscale NaCl clusters as seen by photoelectron spectroscopy

The free neutral nanoscale NaCl clusters have been produced in a beam and studied with x-ray photoelectron spectroscopy. High resolution spectra simultaneously containing cluster and molecular-monomer, featuring in both the valence and core-level Na 2p and Cl 2p regions, have been obtained. Cluster-level energy shifts of around 3 eV toward lower binding energy for Na 2p and ≈1 eV toward higher binding energy for Cl 2p relative to the monomer levels have been unambiguously established. To rationalize the core-level energy shifts of the nanoscale NaCl clusters, the ionic model taking into account all charge-charge and polarization interactions has been developed and implemented. A satisfactory agreement between the experimental and model results has been obtained. The model calculations have also shed additional light on the size- and site-specific cluster responses.     

Duality in inhomogeneous random graphs,and the cut metric

The classical random graph model G(n, c/n) satisfies a “duality principle”, in that removing the giant component from a supercritical instance of the model leaves (essentially) a subcritical instance. Such principles have been proved for various models; they are useful since it is often much easier to study the subcritical model than to directly study small components in the supercritical model. Here we prove a duality principle of this type for a very general class of random graphs with independence between the edges, defined by convergence of the matrices of edge probabilities in the cut metric. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 399–411, 2011