A fuzzy max-flow min-cut theorem

Interval-valued versions of the max-flow min-cut theorem and Karp-Edmonds algorithm are developed and provide robustness estimates for flows in networks in an imprecise or uncertain environment. These results are extended to networks with fuzzy capacities and flows. (C) 2001 Elsevier Science B.V. All rights reserved.

On the decay rates of buffers in continuous flow lines

Consider a tandem system of machines separated by infinitely large buffers. The machines process a continuous flow of products, possibly at different speeds. The life and repair times of the machines are assumed to be exponential. We claim that the overflow probability of each buffer has an exponential decay, and provide an algorithm to determine the exact decay rates in terms of the speeds and the failure and repair rates of the machines. These decay rates provide useful qualitative insight into the behavior of the flow line. In the derivation of the algorithm we use the theory of Large Deviations.

Acute otitis media

A 3-year-old girl is brought to your office by her mother because she has a fever and complains that her ear hurts. She has no significant medical history. The child is not pleased to be in the physician's office and has been crying. Her mother explains that she developed a cold about 3 days ago with sniffles. Her temperature is 37.8 degreesC (100 degreesF), and the rest of the physical examination is completed with some difficulty. The only abnormalities are slight redness of the throat. a nose full of thick green mucus, and injected tympanic membranes. You wonder what findings other than red tympanic membranes should lead you to diagnose otitis media and also consider the recent controversy about whether to treat acute otitis media (AOM) with antibiotics.