This paper presents a graph-theoretic characterization of idempotent Boolean relation matrices of finite order. A relation-theoretic point of view is adopted in the paper. Idempotent matrices appear in the sequence of powers of any Boolean relation matrix, and are of purely theoretical as well as applied interest in connection with issues of convergence. The results provide a detailed description of the connectivity and cyclic structure of the directed graphs of idempotent matrices. The study is basically motivated by certain connectivity and flow problems which arise in the analysis of largescale information systems. The formal results are exemplified in an investigation of the asymptotic forms of a recursive model of an information system which affords a conjoin t representation of processes of communication and derivation of information. A second principal application is given in a process formulation for the generation of cons istent rank orderings. The relation between system des ign and idempotent forms is exhibited in the two applications.
This edition reviews the long-term performance of economic growth and productivity in the region. It then draws on research from the Inter-American Development Banks Connectivity, Markets, and Finance Division that estimates how much investment in digital infrastructure is needed for countries across Latin America and the Caribbean to reach the levels of advanced economies. This research also estimates both the potential economic benefits associated with that investment and its costs, highlighting the potentially large multipliers associated with closing digital infrastructure gaps. The highlights of the analysis are as follows. It is estimated that closing the digital access gap between Caribbean economies and members countries of the Organization for Economic Co-operation and Development (OECD) could potentially increase the regions GDP by about 6 to 12 percent over the medium term, depending on the country. These gains are multiples of the estimated costs, ranging from about 2 times to nearly 50 times those estimated costs. Productivity gains represent about 80 percent of the estimated improvements in GDP. As is typical with the Caribbean Quarterly Bulletin, the Regional Overview is followed by country sections that provide more detailed analysis for each of the countries covered.
Countries around the world have endured over a year of extreme uncertainty in the context of the COVID-19 crisis, and economies in the Caribbean have suffered more than most. But with the increasing availability of vaccines and prospects for a resumption of international travel, light is emerging at the end of the Pandemic tunnel. With this in mind, The Inter-American Development Bank Caribbean1 Departments most recent Quarterly Bulletin reviews the latest available information regarding the crisis impacts on citizens, their economies, and key factors that will determine the speed and depth of recovery. As also discussed in previous editions, prospects for tourism-dependent economies will depend heavily on vaccine penetration and border normalization in source countries particularly the United States and Western Europe, while commodity-intensive economies could benefit from upward revisions to global demand growth estimates. All countries in the region can do much to support a rapid recovery through forward-looking policies aimed at ensuring they are well positioned to take advantage of post-Pandemic preferences with respect to travel and tourism, services trade, and investment. Our latest report considers these issues, what may lie ahead, and how counties can best position themselves for a recovery in 2021 and beyond.
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