A transmitter and receiver need to be designed to guarantee reliable communication on any channel belonging to a given family of finite-state channels defined over common finite input, output, and state alphabets. Both the transmitter and receiver are assumed to be ignorant of the channel over which transmission is carried out and also ignorant of its initial state. For this scenario we derive ...

A decision maker (DM) makes choices from different sets of alternatives. The DM is initially fully ignorant of the payoff associated to each alternative, and learns these payoffs only after a large number of choices have been made. We show that, in the presence of an outside option once payoffs are learned, the optimal choice rule from sets of alternatives is one that is as if the DM had strict...

‎given a finite non-cyclic group $g$‎, ‎call $sigma(g)$ the smallest number of proper subgroups of $g$ needed to cover $g$‎. ‎lucchini and detomi conjectured that if a nonabelian group $g$ is such that $sigma(g) < sigma(g/n)$ for every non-trivial normal subgroup $n$ of $g$ then $g$ is textit{monolithic}‎, ‎meaning that it admits a unique minimal normal subgroup‎. ‎in this paper we show how thi...