Hyperopic Cops and Robbers

We introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the corresponding analogue of the cop number, and we investigate bounds and other properties of this parameter. We characterize the cop-win graphs for this variant, along with graphs with the largest possible hyperopic cop number. We analyze the cases of graphs with diameter 2 or at least 3, focusing on when the hyperopic cop number is at most one greater than the cop number. We show that for planar graphs, as with the usual cop number, the hyperopic cop number is at most 3. The hyperopic cop number is considered for countable graphs, and it is shown that for connected chains of graphs, the hyperopic cop density can be any real number in $[0,1/2].

Common adversaries form alliances: modelling complex networks via anti-transitivity

Anti-transitivity captures the notion that enemies of enemies are friends, and arises naturally in the study of adversaries in social networks and in the study of conflicting nation states or organizations. We present a simplified, evolutionary model for anti-transitivity influencing link formation in complex networks, and analyze the model's network dynamics. The Iterated Local Anti-Transitivity (or ILAT) model creates anti-clone nodes in each time-step, and joins anti-clones to the parent node's non-neighbor set. The graphs generated by ILAT exhibit familiar properties of complex networks such as densification, short distances (bounded by absolute constants), and bad spectral expansion. We determine the cop and domination number for graphs generated by ILAT, and finish with an analysis of their clustering coefficients. We interpret these results within the context of real-world complex networks and present open problems

The Social Impact of the Banking Sector in Colombia, 1995 – 2002

This document studies the impact of the banking sector on social variables in Colombia, and tries to identify how the difference in banking institutions’ development at the municipal levels influences economic and social prosperity of low income households and firms. One part of the literature emphasizes the role of the financial system in promoting this type of agents’ economic performance as long as it attracts them to the use of financial intermediation, making available to them the use of financial services and technologies, both in deposits and credit. Another trend in the literature studies specific characteristics of liquidity constrained agents. This study empirically identifies how bancarization influences poverty and investment on education, in the case of families; and economic performance and the number of firms, in the municipal level in Colombia for the period 1995-2002. When studying these effects we control for local variables such as public spending in investment, homicide rate and guerrilla conflict. The period of study was characterized by the end of an economic boom and recession, which influences our econometric results. This study shows that banking developments affect households’ education decisions and firms’ performance at the municipal level; it was also found that non performing loans are associated with the decrease in the number of firms, but a relationship between loans and the creation of firms was not present.