Generating functions for generating trees

Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the object. Generating trees lead to a fast computation of enumeration sequences (sometimes, to explicit formulae as well) and provide efficient random generation algorithms. We investigate the links between the structural properties of the rewriting rules defining such trees and the rationality, algebraicity, or transcendence of the corresponding generating function.Comment: This article corresponds, up to minor typo corrections, to the article submitted to Discrete Mathematics (Elsevier) in Nov. 1999, and published in its vol. 246(1-3), March 2002, pp. 29-5

PICES Press, Vol. 16, No. 2, July 2008

The 2008 Inter-Sessional Science Board Meeting (pp.1-2, pdf, 0.1 Mb) FUTURE – From Science Plan to Implementation Plan (pp. 3-4, pdf, 0.1 Mb) CFAME Task Team Workshop – Linking and Visualising (p. 5, pdf, 0.1 Mb) PICES WG 21 Meets in Busan, Korea: The Database Meeting (pp. 6-7, pdf, 0.1 Mb) ICES-PICES-IOC Symposium on Climate Change (pp. 8-12, pdf, 1.2 Mb) Zooplankton and Climate: Response Modes and Linkages (pp. 13-15, pdf, 0.2 Mb) PICES Fishery Science Committee Workshop in Gijón (pp. 16-18, pdf, 0.1 Mb) The North Pacific Continuous Plankton Recorder Survey (pp. 19-21, pdf, 0.4 Mb) PICES Ecosystem Status Report Wins Design Award (p. 21, pdf, 0.4 Mb) Canada’s Three Oceans (C3O): A Canadian Contribution to the International Polar Year (pp. 22-25, pdf, 0.8 Mb) New Surface Mooring at Station Papa Monitors Climate (pp. 26-27, pdf, 0.2 Mb) The State of the Western North Pacific in the Second Half of 2007 (pp. 28-29, pdf, 0.4 Mb) The Bering Sea: Current Status and Recent Events (pp. 30-31, pdf, 0.4 Mb) Recent Trends in Waters of the Subarctic NE Pacific (pp.32-33, pdf, 0.3 Mb) 2009 Vintage of Fraser River Sockeye Salmon: A Complex Full Bodied Redd with Mysterious Bouquet (p. 34, pdf, 0.1 Mb) Pacific Biological Station Celebrates Centennial Anniversary, 1908–2008 (p. 35, pdf, 0.3 Mb) Marine and Coastal Fisheries: American Fisheries Society Open Access E-journal (p. 36, pdf, 0.1 Mb) Latest and Upcoming PICES Publications (p. 36, pdf, 0.1 Mb

The Evolution of Enterprise Reform in Africa: From State-owned Enterprises to Private Participation in Infrastructure — and Back?

Many African state-owned enterprises (SOEs), particularly those in infrastructure, have a long history of poor performance. From the outset, SOE financial and economic performance generally failed to meet the expectations of their creators and funders. By the late 1970s, the situation was alarming, and by early 1980s, critical. The poor financial performance of SOEs became so burdensome to government budgets that it attracted the attention of the international financial institutions, or IFIs. In response, in the 1980s, the World Bank approved SOE reforms that could be summed up in the term “commercialization”. By the mid-1990s, however, the idea of making SOEs function efficiently and effectively under government management was largely abandoned by the IFIs and privatization and private participation in infrastructure, or PPI became the order of the day. Once more, however, the results were disappointing. PPI has not been as widely adopted as anticipated, nor has it generated the massive resources and changes hoped for, nor has it been widely accepted as beneficial by the African public. The findings of recent studies in Africa suggest that PPI should not be jettisoned, and that the more productive path is to recognize the limitations of the approach, and to work harder at creating the conditions needed to make it function effectively. This will entail, as many have recognized, an end to the view that public and private infrastructure provision is a dichotomy – a case of either-or, one or the other – and a better appreciation of the extent to which the performance of each is dependent on the competence of the other. In other words, for the private sector to perform well, public sector capacity must be enhanced. Moreover, proposed tactics of reform should fit more closely with the expectations and sentiments of the affected government, consumer base, and general population. This broader approach implies, probably, a reduction in the scope and, certainly, a reduction in the planned speed of operations. Improving infrastructure performance is a long-term matter.Africa, Enterprise reform, State-owned enterprises, Privatization

Negative index Jacobi forms and quantum modular forms

In this paper, we consider the Fourier coefficients of a special class of meromorphic Jaocbi forms of negative index. Much recent work has been done on such coefficients in the case of Jacobi forms of positive index, but almost nothing is known for Jacobi forms of negative index. In this paper we show, from two different perspectives, that their Fourier coefficients have a simple decomposition in terms of partial theta functions. The first perspective uses the language of Lie super algebras, and the second applies the theory of elliptic functions. In particular, we find a new infinite family of rank-crank type PDEs generalizing the famous example of Atkin and Garvan. We then describe the modularity properties of these coefficients, showing that they are "mixed partial theta functions", along the way determining a new class of quantum modular partial theta functions which is of independent interest.Comment: 29 pages, minor correction

Framework development and application in waste generation prediction

He, R., Sandoval-reyes, M., Scott, I., Semeano, R., Ferrão, P., Matthews, S., & Small, M. J. (2022). Global knowledge base for municipal solid waste management: Framework development and application in waste generation prediction. Journal of Cleaner Production, 377(December), 1-11. [134501]. https://doi.org/10.1016/j.jclepro.2022.134501--- This research is supported by the Mao Yisheng Fellowship of Carnegie Mellon University to Rui He, and through the CMU-Portugal project “Bee2Waste Crypto” (IDT-COP 45933). The authors would like to thank other members of the Bee2Waste Crypto project consortium for their support and inputs to this paper.Increasing municipal solid waste (MSW) generation has become not only a major sustainability challenge and a considerable financial burden for municipalities across the globe, but also an opportunity to promote a circular economy, provided adequate information is made available. Data and information on MSW generation, characterization, and management practices are prerequisites to studying and optimizing solid waste management systems (SWMS). However, such data and information are usually dispersed, unsystematized, and suffering from various availability and quality issues. This study aims to assemble and provide access to the current landscape of MSW data by establishing a comprehensive framework for understanding the interconnectedness of various sub-domains of MSW knowledge. Existing databases and governmental reports were reviewed to compile 1720 records of MSW generation, composition, management practices, and socioeconomic contexts for 219 countries and 410 cities. Multivariate linear regression and additive models were built to relate MSW generation, composition, and recovery rates to demographics, economic development, and climate patterns of cities and regions. These models generate new insights into the complex nature of SWMS and provide an evidence-based decision-making tool to future researchers and policy makers. Specifically, economic development (GDP), density factors (population, population density, and household size), sustainability initiatives, education, and regulation are all identified as positive drivers toward the targets of United Nations Sustainable Development Goal 12.publishersversionpublishersversionpublishersversionepub_ahead_of_prin

Clustering properties of rectangular Macdonald polynomials

The clustering properties of Jack polynomials are relevant in the theoretical study of the fractional Hall states. In this context, some factorization properties have been conjectured for the $(q,t)$-deformed problem involving Macdonald polynomials. The present paper is devoted to the proof of this formula. To this aim we use four families of Jack/Macdonald polynomials: symmetric homogeneous, nonsymmetric homogeneous, shifted symmetric and shifted nonsymmetric.Comment: 43 pages, 2 figure

From Divergence to Convergence: Re-evaluating the History Behind China's Economic Boom

China's long-term economic dynamics pose a formidable challenge to economic historians. The Qing Empire (1644-1911), the world's largest national economy prior to the 19th century, experienced a tripling of population during the 17th and 18th centuries with no signs of diminishing per capita income. In some regions, the standard of living may have matched levels recorded in advanced regions of Western Europe. However, with the Industrial Revolution a vast gap emerged between newly rich industrial nations and China's lagging economy. Only with an unprecedented growth spurt beginning in the late 1970s has the gap separating China from the global leaders been substantially diminished, and China regained its former standing among the world's largest economies. This essay develops an integrated framework for understanding this entire history, including both the long period of divergence and the more recent convergent trend. The analysis sets out to explain how deeply embedded political and economic institutions that had contributed to a long process of extensive growth subsequently prevented China from capturing the benefits associated with new technologies and information arising from the Industrial Revolution. During the 20th century, the gradual erosion of these historic constraints and of new obstacles created by socialist planning eventually opened the door to China's current boom. Our analysis links China's recent economic development to important elements of its past, while using the success of the last three decades to provide fresh perspectives on the critical obstacles undermining earlier modernization efforts, and their removal over the last century and a half.