This paper analyzes the relationship between the competitive environment faced by depository institutions and the decisions these institutions make regarding the size of their branch networks. Specifically, we consider branches as a sunk investment that potentially increases utility for consumers and examine how local competition and product differentiation affect firms’ decisions regarding whe...

A generalized die is a list (x1; :::; xn) of integers. For integers n 1, a b and s let D(n; a; b; s) be the set of all dice with a x1 ::: xn b and P xi = s. Two dice X and Y are tied if the number of pairs (i; j) with xi < yj equals the number of pairs (i; j) with xi > yj . We prove the following: with one exception (unique up to isomorphism), if X 6= Y 2 D(n; a; b; s) are tied dice neither of ...

For integers n 1, a b and s let D(n; a; b; s) be the set of all lists of integers (x1; :::; xn) with a x1 ::: xn b and P xi = s. There is a graph G(n; a; b; s) with vertex-set D(n; a; b; s) in which two vertices are adjacent if one is stronger than the other in a natural dice game. In The prevalence of “paradoxical” dice [Bull. Inst. Combin. Appl. 45 (2005), 70-76] the dice which are isolated v...

The possible formation of three-stranded RNA and DNA hybrid structures (R-loops) in thousands of functionally important guanine-rich genic and inter-genic regions could suggest their involvement in transcriptional regulation and even development of diseases. Here, we introduce the first freely available R-loop prediction program called Quantitative Model of R-loop Forming Sequence (RLFS) finder...