Discrete Convex Functions on Graphs and Their Algorithmic Applications

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems

Synthetic Culture Media Evaluated for the Detection of Coliform Bacteria in Milk, Cheese and Egg Melange

Simple synthetic culture media of liquid and solid form (X broth and X agar) were tested for selective isolation of coliform bacteria. Selectivity is based on the ability of coliform bacteria to grow when the minimal medium contains simple inorganic substances as nitrogen and carbon supply. Selectivity of the media was tested by inoculation of pure cultures of different microbes belonging to the genera of Staphylococcus, Bacillus and Pseudomonas and the family Enterobacteriaceae and was found to be complete in this range. The comparative investigation of milk, camembert cheese and egg melange samples in the traditional and new media proved good applicability of X broth and X agar for an effective and selective detection of coliform bacteria. When testing pasteurized milk samples, X agar detected coliforms in significantly higher counts than violet red-bile-lactose agar