A large number n of sensors (finite connected intervals) are placed randomly on the real line so that the distances between the consecutive midpoints are independent random variables with expectation inversely proportional to n. In this work we address two fundamental sensor allocation problems. Interference problem tries to reallocate the sensors from their initial positions so as to eliminate...

Let κ be an uncountable cardinal with κ = κ. In this paper we introduce Rκ, a Cauchy-complete real closed field of cardinality 2. We will prove that Rκ shares many features with R which have a key role in real analysis and computable analysis. In particular, we will prove that the Intermediate Value Theorem holds for a non-trivial subclass of continuous functions over Rκ. We propose Rκ as a can...