Enumeration of graphs by degree sequence

The degree sequence (d₀, d₁, …, d_p-1) of a graph G of order p is defined by d_k = the number of points of G of degree k. Methods of Robinson are extended to produce a generating function F(x₀, x₁, x₂, …) where the coefficient of x…x is the number of graphs of order p having degree sequence (d₀, …, d_p-1).     

On the Betti Numbers of Chessboard Complexes

In this paper we study the Betti numbers of a type of simplicial complex known as a chessboard complex. We obtain a formula for their Betti numbers as a sum of terms involving partitions. This formula allows us to determine which is the first nonvanishing Betti number (aside from the 0-th Betti number). We can therefore settle certain cases of a conjecture of Björner, Lovász, Vreica, and ivaljevi in [2]. Our formula also shows that all eigenvalues of the Laplacians of the simplicial complexes are integers, and it gives a formula (involving partitions) for the multiplicities of the eigenvalues.     

On the number of alignments ofk sequences

Numerous studies by molecular biologists concern the relationships between several long DNA sequences, which are listed in rows with some gaps inserted and with similar positions aligned vertically. This motivates our interest in estimating the number of possible arrangements of such sequences. We say that ak sequence alignment of sizen is obtained by inserting some (or no) 0's intok sequences ofn 1's so that every sequence has the same length and so that there is no position which is 0 in allk sequences. We show by a combinatorial argument that for any fixedk1, the numberf(k, n) ofk alignments of lengthn grows like (c _k ) ⁿ as n , wherec _k = (2^1/k – 1) ^-k . A multi-dimensional saddle-point method is used to give a more precise estimate forf(k, n). Research supported in part by the National Science FoundationResearch supported in part by the System Development FoundationResearch supported in part by the National Institute of Health     

Deposition measurement of particulate matter in connection with corrosion studies

A new passive particle collector (inert surrogate surface) that collects particles from all directions has been developed. It was used to measure particle deposition at 35 test sites as part of a project that examined corrosion of materials in order that variation in particulate material could be used in development of dose–response functions in a modern multi-pollutant environment. The project, MULTI-ASSESS, was funded by the EU to examine the effects of air pollution on cultural heritage. Passive samplers were mounted rain-protected, and both in wind-protected and wind-exposed positions, to match the exposure of the samples for corrosion studies. The particle mass and its chemical content (nitrate, ammonium, sulfate, calcium, sodium, chloride, magnesium and potassium) were analysed. The loss of light reflectance on the surrogate surface was also measured. Very little ammonium and potassium was found, and one or more anions are missing in the ion balance. There were many strong correlations between the analysed species. The mass of analysed water-soluble ions was fairly constant at 24% of the total mass. The particle mass deposited to the samplers in the wind-protected position was about 25% of the particles deposited to an openly exposed sampler. The Cl⁻/Na⁺ ratios indicate a reaction between HNO₃ and NaCl. The deposited nitrate flux corresponds to the missing chloride. The Ca²⁺ deposition equals the deposition and the anion deficiency. The deposition most likely originates from SO₂ that has reacted with basic calcium-containing particles either before or after they were deposited. The particle depositions at the urban sites were much higher than in nearby rural sites. The deposited mass correlated surprisingly well with the PM₁₀ concentration, except at sites very close to traffic.     

Near-infrared Fluorescence Spectroscopy Detects Alzheimer's Disease In Vitro

The purpose of this study was to investigate whether near-infrared (NIR) fluorescence spectroscopy could be used to detect Alzheimer's disease (AD) by brain tissue autofluorescence. Unfixed temporal cortex specimens from AD cases and age-matched, non-AD controls were frozen at autopsy and then thawed just prior to spectral measurement. Spectra of intrinsic tissue fluorescence induced by 647 nm light were recorded from 650 to 850 nm. We used principal component analysis of the tissue spectra from 17 AD cases and 5 non-AD control cases in a calibration study to establish a diagnostic algorithm. Retrospectively applied to the calibration set, the algorithm correctly classified 23 of 24 specimens. In a prospective study of 19 specimens from 5 AD brains and 2 non-AD control brains, 3 of the 4 control specimens and all AD specimens were correctly diagnosed. Both the excitation light used and the measured brain tissue autofluorescence are at NIR wavelengths that can propagate through skull and overlying tissue. Therefore, our results demonstrate an optical spectroscopic technique that carries direct molecular level information about disease. This is the first step toward a clinical tool that has the potential to be applied to the noninvasive diagnosis of AD in living patients.