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     

Patterns in random permutations avoiding the pattern 321

We consider a random permutation drawn from the set of 321 ‐avoiding permutations of length n and show that the number of occurrences of another pattern σ has a limit distribution, after scaling by n^{m + ?} where m is the length of σ and ? is the number of blocks in it. The limit is not normal, and can be expressed as a functional of a Brownian excursion.     

Pattern Avoidance in Alternating Sign Matrices

We generalize the definition of a pattern from permutations to alternating sign matrices. The number of alternating sign matrices avoiding 132 is proved to be counted by the large Schr?der numbers, 1, 2, 6, 22, 90, 394, .... We give a bijection between 132-avoiding alternating sign matrices and Schr?der paths, which gives a refined enumeration. We also show that the 132-, 123-avoiding alternating sign matrices are counted by every second Fibonacci number. Received January 2, 2007     

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.     

Transparent conductive electrodes for electrochromic devices: A review

This paper reviews the optical and electrical performance of thin films that are useful as transparent electrodes in electrochromic devices. The properties of certain heavily doped wide-bandgap semiconductor oxides (especially In₂O₃:Sn) and of certain coinage metal films are discussed.     

The minimal spanning tree in a complete graph and a functional limit theorem for trees in a random graph

The minimal weight of a spanning tree in a complete graph K_n with independent, uniformly distributed random weights on the edges is shown to have an asymptotic normal distribution. The proof uses a functional limit extension of results by Barbour and Pittel on the distribution of the number of tree components of given sizes in a random graph.     

Analysis of thermal radiation from laser-heated nanoparticles formed by laser-induced decomposition of ferrocene

Thermal radiation, originating from laser-heated gas-phase nanoparticles, was detected in the 400–700 nm wavelength range by means of optical emission spectroscopy. The particles were formed upon laser-induced photolytic decomposition of ferrocene (Fe(C₅H₅)₂) and consisted of an iron core surrounded by a carbon shell. The laser-induced excitation was performed as the particles were still within the reactor zone, and the temperature of the particles could be determined from thermal emission. Both the temperature of the nanoparticles and the relative intensity changes of the emission were monitored as a function of time (with respect to the laser pulse), laser fluence and Ar ambient pressure. At high laser fluences, the particles reached high temperatures, and evidence was found for boiling of iron. Modeling of possible energy-releasing mechanisms such as black-body radiation, thermionic electron emission, evaporation and heat transfer by the ambient gas was also performed. The dominant cooling mechanisms at different ranges of temperature were clarified, together with a determination of the accommodation factor for the Ar–nanoparticle collisions. The strong evaporation at elevated temperatures also led to significant iron loss from the produced particles. PACS 61.46.+w; 81.16.Mk; 65.80.+n     

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.     

Long and short paths in uniform random recursive dags

In a uniform random recursive k-directed acyclic graph, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S _n is the shortest path distance from node n to the root, then we determine the constant σ such that S _n /log n→σ in probability as n→∞. We also show that max _1≤i≤n S _i /log n→σ in probability.