Mixed Poisson approximation of node depth distributions in random binary search trees

We investigate the distribution of the depth of a node containing a specific key or, equivalently, the number of steps needed to retrieve an item stored in a randomly grown binary search tree. Using a representation in terms of mixed and compounded standard distributions, we derive approximations by Poisson and mixed Poisson distributions; these lead to asymptotic normality results. We are particularly interested in the influence of the key value on the distribution of the node depth. Methodologically our message is that the explicit representation may provide additional insight if compared to the standard approach that is based on the recursive structure of the trees. Further, in order to exhibit the influence of the key on the distributional asymptotics, a suitable choice of distance of probability distributions is important. Our results are also applicable in connection with the number of recursions needed in Hoare's [Comm. ACM 4 (1961) 321-322] selection algorithm Find.Comment: Published at http://dx.doi.org/10.1214/105051604000000611 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Immigration and the Canadian Welfare State 2011

This publication provides an estimate of the fiscal burden created by recent immigration into Canada and proposes reforms to existing immigrant selection policies to eliminate the burden. It uses a 2006 Census database to estimate the average incomes and taxes paid on these by immigrants who arrived in Canada over the period from 1987 to 2004. It also estimates other taxes they paid and the value of government services they absorbed. The study concludes that in the fiscal year 2005/06 the immigrants on average received an excess of $6,051 in benefits over taxes paid. Depending on assumptions about the number of recent immigrants in Canada, the fiscal burden in that year is estimated to be between$23.6 billion and $16.3 billion. These estimates are not changed by the consideration of other alleged benefits brought by immigrants. To curtail this growing fiscal burden from immigration, the study proposes that temporary work visas be granted to applicants who have a valid offer for employment from employers, in occupations and at pay levels specified by the federal government and determined in cooperation with private-sector employers. Immediate dependents may accompany successful applicants. The temporary visas are renewable and lead to landed immigrant status if certain specified employment criteria are met.Canadian immigration, fiscal impacts of immigration to Canada, Immigration policy

Internationally Diversified Portfolios: Welfare Gains and Capital Flows

The models of portfolio balance developed by Markowitz and Tobin explain the real world phenomenon of diversified asset holdings elegantly and properly. The models have been criticized, extended, and empirically tested; by now their basic content has become economic orthodoxy. Strangely, however, the analysis has not yet been applied explicitly to the explanation of long-term asset holdings that include claims denominated in foreign currency .The present paper fills this gap and yields some interesting results.First, the international diversification of portfolios is the source of an entirely new kind of world welfare gains from international economic relations, different from both the traditional "gains from trade" and in­ creased productivity flowing from the migration of the factors of pro­ duction. This specific theoretical proposition is illustrated with some calculations based on empirical data drawing on ex post realized rates of return from investment in 11 major stock markets of the world.Second, the theoretical model shows that international capital movements are a function not only of interest rate differentials but also of rates of growth in total asset holdings in two countries. As a result, capital may flow between countries when interest rate differentials are zero or negative and may not flow when a positive interest differential exists.Third, the analysis has some important policy implications in a growing world where monetary and fiscal policies are mixed to achieve internal and external balance

International Trade in Used Cars and Problems of Economic Development

This paper provides a price-theoretic explanation of the well-known phenomenon that automobiles in developing countries depreciate less rapidly and are scrapped at a greater age than they are in industrial countries. This paper then argues that the renewal of barriers to free trade in used cars would lead to substantial welfare gains for developing countries through both capital gains implicit in the arbitrage and positive externalities from car repair industries. Negative externalities from increased car supplies are evaluated and the final part of this paper considers what policies might be needed to develop international trade in used cars on a large scale

Foreign Exchange Earnings and Price Stabilization Schemes

Whether price and output stabilization schemes for primary commodities are likely to increase or decrease foreign exchange earnings from what they would be otherwise is a question of great importance to countries contemplating the formation of such institutional arrangements. This paper sheds some light on this question and clarifies under what circumstances Ragnar Nurkse\u27s assertion is valid that countries will fail to maximize foreign exchange earnings if they do stabilize prices

Ligand and Metal Effects on the CO-Release Reactivity of Metal Acireductone and Flavonolate Complexes

The research reported herein involves synthetic metal complexes of relevance to dioxygenase enzymes (Ni(II)-containing acireductone dioxygenase (Ni(II)-ARD) and quercentinase (2,4-flavonol dioxygenase) that promote oxidative carbon-carbon bond cleavage and CO release. The experiments focus on the elucidation of structure-reactivity relationships and evaluation of the conditions under which CO is generated. It had been proposed that hydrogen bond donors in the secondary environment of the active site metal center in Ni(II)-ARD influence the coordination of the acireductone substrate on the nickel center. To evaluate this proposal, we investigated the Ni(II) coordination chemistry of an acireductone-type enolate anion using a supporting chelate ligand having two internal hydrogen bond-donors. The resulting complex exhibited differences in terms of the organic product distribution in a CO release reaction resulting from oxidative C-C bond cleavage of the enolate ligand relative to this reported for the iv hydrophobic, 6-Ph2TPA-supported (6-Ph2TPA = N,N-bis((6-phenyl-2-pyridyl)methyl)- N-((2-pyridyl)methyl)amine) analogue. In another study, we found that changes in the supporting chelate ligand or metal center influenced the coordination chemistry of the acireductone-type enolate anion. This chemistry highlighted the propensity of the enolate to undergo isomerization without CO release in the presence of water. Rigorously excluding water enabled the isolation of a Ni(II) enolate complex of the 6-PhTPA ligand and examination of its oxidative CO release chemistry, as well as the spectroscopic characterization of the first Co(II) complex of an acireductone-type enolate. To elucidate factors influencing the CO-release reactivity of metal-flavonoid complexes, some of which have relevance to quercentinase enzymes, we synthesized and characterized the first series of structurally-related metal-flavonolate complexes [(6- Ph2TPA)M(3-Hfl)]X (M = Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II), Hg(II); X = OTfor ClO4 - ). Exposure of these complexes to UV light initiated photooxidative carboncarbon bond cleavage and CO release in a metal-dependent manner, with closed-shell d 10 metals giving rise to the highest rate of CO release. These studies suggest that metal flavonolate species may be useful as a new type of photo-induced CO release molecules (CORMs). Such species are of current interest for possible therapeutic applications

Towards a Theory of Free Economic Zones

This paper presents a theory capable of analysing the welfare effects of a wide variety of institutional innovations which have in common that they involve the deregulation of, or the lowering of tariffs and taxes on, a range of economic activities that can be effectively separated from the regulated, taxed and protected industries of which they are a part. The partial deregulation of economic activities in this manner will be shown to lead to the expansion of trade, but also to involve potential costs of locational diversion of trade and negative externalities. In the context of the debate over deregulation the development of free economic zones can be seen as a practical compromise that generates powerful local interest groups pushing partial deregulation against the well-known in­ terest groups opposing general deregulation

Canadian Economists' Citation and Publication Records

This paper uses the Social Science Citation Index to count the number of citations received and publications made by all economists teaching at Canadian universities in 1975. It is shown that the top decile of individuals received 72 percent of all citations and 50 percent received none. The University of British Columbia and Simon Fraser Univer- sity departments of economics have the highest and second-highest average citation counts of all Canadian universities, respectively. The age-profile of citations, self-citation propensities and the journals of publication are analysed from a sub-sample of data.Cet article utilise le Social Science Citation Index pour relever le nombre de citations reçues et de publications au crédit de tous les économistes qui enseignaient dans les universités canadiennes durant l'année 1975. Il est démontré que le décile supérieur d'individus a reçu 72 pour cent de toutes les citations et que 50 pour cent en ont reçu aucune. Les départments d'économique des universités de la Colombie-Britanique et Simon Fraser ont respectivement le plus grand et le deuxième plus grand nombres moyens de citations de toutes les universités canadiennes. L'aspect temporel des citations, les propensions à l'auto-citation et les revues de publication sont analisés à l'aide d'un sous-échantillon de données

The Making of Canadian Economists - Results of a Survey of Graduate Students

The responses to questions by 155 students revealed the following, most important facts. The students predominantly came from families with high incomes. They have leftist political leanings, though through their training, more have turned right than left. The students share most strongly the views on fundamental propositions in economics held by U.S. graduate students and less those held by Canadian and U.S. professionals. Students from different Canadian universities hold very similar views on price-theoretic propositions but rather widely differing views on some important issues of macro-economics and income distribution. The most important finding is that, like their U.S. colleagues, Canadian graduate students believe that for professional success it is more important to learn technical skills rather than about institutions, history and policy. As a result they end up poorly prepared for work on economic policy issues and their research tends to lack real world relevance, even though real world and policy problems attracted them to the graduate programs.Les réponses de 155 étudiants révèlent les faits suivants. Les étudiants viennent en majorité de familles de niveau socioéconomique élevé. Leurs idées de base sur la politique sont de gauche, quoiaque, suite a leur entrainement, la majorité pench vers la droite. Les étudiants partagent leurs idées sur les théories économiques fondamentales le plus fortement avec les étudiants post-gradués américains et moins avec les professionnels canadiens ou américains. Les étudiants des différentes universités canadiennes ont des opinions très semblables sur la théorie des prix et ses hypothèses, mais ne s'accordent pas en ce que concerne certains sujets importants en macro-économie et la distribution des revenus. La fait saillant qui ressort de cette étude est que, corne leurs pairs américains, les étudiants post-gradués canadiens croient que pour réussir dans la profession il est plus important d'apprendre certaines techiques plustôt que do connaître les institutions, l'histoire et la politique économique. En conséquence ils sont mal préparés a travailler sur les questions de politique économique. Leurs travaux de recherche ont peu ou pas de portée sur la réalité courante malgré le fait que c'est cette réalité et les problèmes de politique économique qui les ont attirés vers les programmes post-gradués