Harmonic analysis of homogeneous networks.

We introduce a generalization of mutually inhibitory networks called homogeneous networks. Such networks have symmetric connection strength matrices that are circulant (one-dimensional case) or block circulant with circulant blocks (two-dimensional case). Fourier harmonics provide universal eigenvectors, and we apply them to several homogeneous examples: k-wta, k-cluster, on/center off/surround, and the assignment problem. We also analyze one nonhomogeneous case: the subset-sum problem. We present the results of 10000 trials on a 50-node k-cluster problem and 100 trials on a 25-node subset-sum problem.

Inhibitory grids and the assignment problem.

A family of symmetric neural networks that solve a simple version of the assignment problem (AP) is analyzed. The authors analyze the suboptimal performance of these networks and compare the results to optimal answers obtained by linear programming techniques. They then use the interactive activation model to define the network dynamics-a model that is closely related to the Hopfield-Tank model. A systematic analysis of hypercube corner stability and eigenspaces of the connection strength matrix leads to network parameters that give feasible solutions 100% of the time and to a projection algorithm that significantly improves performance. Two formulations of the problem are discussed: (i) nearest corner: encode the assignment numbers as initial activations, and (ii) lowest energy corner: encode the assignment numbers as external inputs.

High urine 1-hydroxypyrene glucuronide concentrations in Linxian, China, an area of high risk for squamous oesophageal cancer.

Most squamous cell carcinomas of the oesophagus in low-risk populations are attributable to alcohol and tobacco consumption, but the aetiologic agents in many high-risk populations have yet to be definitively identified. Linxian, China has some of the highest oesophageal cancer rates in the world. Recent studies suggest that an association exists between high-level exposure to carcinogenic polycyclic aromatic hydrocarbons (PAHs), such as benzo[a]pyrene (B[a]P), and the development of oesophageal cancer. The inhabitants of this high-risk region extensively use coal and wood for cooking and heating in unvented stoves, and thus may be exposed to PAHs produced during the incomplete combustion of these fuel sources. High levels of B[a]P were recently detected in staple food samples from Linxian and histopathologic changes that may be associated with PAH exposure have also been identified in oesophagectomy specimens from the region. In an effort to determine whether this high-risk population is exposed to high levels of PAHs, voided urines from non-smokers (n = 22) without occupational exposure were collected and analysed using immunoaffinity chromatography and synchronous fluorescence spectroscopy for 1-hydroxypyrene glucuronide, a PAH metabolite and index biomarker for mixed PAH exposure. The median urine 1-hydroxypyrene glucuronide concentration (2.06 pmol ml(-1)) was equivalent to concentrations detected in current smokers. To the authors' knowledge, this represents the first report of elevated urine 1-hydroxpyrene glucuronide concentrations in Linxian, and the first biologic confirmation that the inhabitants of this rural, non-industrial, high oesophageal cancer risk region are exposed to carcinogenic PAHs.