We analyze quantitatively several strategies for better utilization of the {em cache} or the {em {fast access}} memory in computers. We define a performance factor $alpha$ that denotes the fraction of the cache area utilized when the main memory is accessed at random. We calculate $alpha$ exactly for different competing strategies, including the hash-rehash and the skewed-associative strategies which were earlier analyzed via simulations.

If one places N cities on a continuum in an unit area, extensive numerical results and their analysis (scaling, etc.) suggest that the best normalized optimal travel distance becomes 0.72 for the Euclidean metric and 0.92 for the Manhattan metric. The analytic bounds, we discuss here, give 0.5 and 0.92 as the lower and upper bounds for the Euclidean metric, and 0.64 and 1.17 for the Manhattan metric. When the cities are randomly placed on a lattice with concentration p, we find that the normalized optimal travel distance vary monotonically with p. For p=1, the values in both Euclidean and Manhattan metric are 1, and as p tends to zero, the values are 0.72 and 0.92 in the Euclidean and Manhattan metrics respectively.The problem is trivial for p=1 but it reduces to the continuum TSP as p tends to zero. We do not get any irregular behaviour at any intermediate point, e.g., the percolation point. The crossover from the triviality to the NP- hard problem seems to occur at p<1.

We report the spatio-temporal response of {it Bacillus subtilis} growing on a nutrient-rich layer of agar to ultra-violet (UV) radiation. Below a crossover temperature, the bacteria are confined to regions that are shielded from UV radiation. A forced convection of the population is effected by rotating a UV radiation shield relative to the petri dish. The extinction speed at which the bacterial colony lags behind the shield is found to be qualitatively similar to the front velocity of the colony growing in the absence of the hostile environment as predicted by the model of Dahmen, Nelson and Shnerb. A quantitative comparison is not possible without considering the slow dynamics and the time-dependent interaction of the population with the hostile environment.