Bounds on some van der Waerden numbers

For positive integers s and k₁,k₂,…,ks, the van der Waerden number w(k₁,k₂,…,ks;s) is the minimum integer n such that for every s-coloring of set {1,2,…,n}, with colors 1,2,…,s, there is a ki-term arithmetic progression of color i for some i. We give an asymptotic lower bound for w(k,m;2) for fixed m. We include a table of values of w(k,3;2) that are very close to this lower bound for m=3. We also give a lower bound for w(k,k,…,k;s) that slightly improves previously-known bounds. Upper bounds for w(k,4;2) and w(4,4,…,4;s) are also provided.     

Treatment-related central nervous system toxicity: MR imaging evaluation with CT and clinical correlation

Thirteen patients with abnormal brain MR scans attributable to treatment-induced injury were retrospectively reviewed. All patients were treated with radiation therapy and 62% received chemotherapy. Five patients were graded as having severe white matter (WM) changes, four had moderate WM changes, and four had mild WM changes. CT was generally equivalent to MR in evaluation of severe and moderate WM abnormalities, whereas MR was superior to CT in detection of mild WM abnormalities. In general, the severity of changes depicted by MR/CT correlated with the extent of neurologic dysfunction. The most severe changes were seen in those patients treated with combination irradiation and chemotherapy.     

Journal Review: Cybernetics & Human Knowing: A journal of second-order cybernetics,autopoiesis and cyber-semiotics. Quarterly,Thorverton, UK: Keith Sutherland,Imprint Academic. $55.00. Editor: Søren Brier

Nonlinear Dynamics, Psychology, and Life Sciences -     

A model for the shell current in a reversed field pinch

A model for the shell current in a reversed field pinch which includes the current induced by the motion of the plasma is discussed. This model gives a good approximation to the magnitude and time dependence of a shell current measured experimentally     

Intensity stabilisation of an argon laser using an electro-optic modulator —Performance and limitations

An intensity-stabilisation system for an argon laser using an electro-optic modulator is described. We achieved a degree of stabilisation of up to 40 dB (factor of 100) for intensity fluctuations below a few kHz. The performance in this frequency range did not reach that expected from the available loop gain. We have identified two serious limiting factors to the performance of our system at low frequency: geometrical fluctuations and frequency fluctuations of the laser light.     

Periodic Fermentor Yield and Enhanced Product Enrichment from Autonomous Oscillations

Four decades of work have clearly established the existence of autonomous oscillations in budding yeast culture across a range of operational parameters and in a few strains. Autonomous oscillations impact substrate conversion to biomass and products. Relatively little work has been done to quantify yield in this case. We have analyzed the yield of autonomously oscillating systems, grown under different conditions, and demonstrate that it too oscillates. Using experimental data and mathematical models of yeast growth and division, we demonstrate strategies to increase the efficient recovery of products. The analysis makes advantage of the population structure and synchrony of the system and our ability to target production within the cell cycle. While oscillatory phenomena in culture have generally been regarded with trepidation in the engineering art of bioprocess control, our results provide further evidence that autonomously oscillating systems can be a powerful tool, rather than an obstruction.     

Stereospecific α-methallylation of hydroxyaldehydes by silatropic ene cyclisation

We describe the thermal rearrangement of aldehydes bearing an α-(allyl- or crotylsilyl)oxy substituent. The transformations are best described mechanistically as intramolecular silatropic ene reactions based on stereoselectivity, kinetic and computed transition state data. The overall process constitutes a stereospecific (meth)allylation of α-hydroxyaldehydes, under neutral conditions, in which the hydroxyl protecting group is also the (meth)allylating agent.