About multiplicities and applications to Bezout numbers

Let $(A,\mathfrak{m},\Bbbk)$ denote a local Noetherian ring and $\mathfrak{q}$ an ideal such that $\ell_A(M/\mathfrak{q}M) < \infty$ for a finitely generated $A$-module $M$. Let \au = a_1,\ldots,a_d denote a system of parameters of $M$ such that $a_i \in \mathfrak{q}^{c_i} \setminus \mathfrak{q}^{c_i+1}$ for $i=1,\ldots,d$. It follows that \chi := e_0(\au;M) - c \cdot e_0(\mathfrak{q};M) \geq 0, where $c = c_1\cdot \ldots \cdot c_d$. The main results of the report are a discussion when $\chi = 0$ resp. to describe the value of $\chi$ in some particular cases. Applications concern results on the multiplicity e_0(\au;M) and applications to Bezout numbers.Comment: 11 pages, to appear Springer INdAM-Series, Vol. 20 (2017

Estimation of Agricultural Production Relations in the LUC Model for China

Chinas demand for feed-grains has been growing fast during the last two decades, largely due to the increasing meat demand. This raises the important question whether China will in the coming years be able to satisfy these increasing needs which has implications that reach far beyond the country itself, especially in the light of Chinas upcoming accession to WTO. The answer depends on many factors, including the policy orientation of the Chinese government, the loss of cropland caused by the ongoing industrialization and urbanization processes, and the effect of climate change on the agricultural potentials of the country. To analyze these issues, the Land Use Change (LUC) Project is engaged in the development of an intertemporal welfare maximizing policy analysis model. The present report presents the input-output relationships for agricultural crops in this model. The specified relationships are geographically explicit and determine the crop output combinations that can be achieved, under the prevailing biophysical conditions across China, from given input combinations in each of some 2040 counties, on the basis of data for 1990. The inputs are chemical and organic fertilizer, labor and machinery. Irrigated and rain-fed land is distinguished as separate land-use types. Distinct relationships are estimated by cross-section for eight economic regions distinguished in the LUC model. The biophysical potential enters as an asymptote in a generalized Mitscherlich-Baule (MB) yield function and is computed on the basis of an agro-ecological assessment of climatic and land resources, including irrigation. The chosen form globally satisfies the required slope and curvature conditions. Estimation results show that all key parameters are significant and are of the expected sign. The calculated elasticities of aggregate output with respect to inputs reflect rather closely the relative scarcity of irrigated land, labor and other inputs across the different regions. It also appears that if account is taken of the distance to main urban centers, the observed cropping patterns are generally consistent with profit maximization. Confirmation is found for the often noted labor surplus in the Southern and South-Eastern regions

Simulating the Socio-Economic and Biogeophysical Driving Forces of Land-Use and Land-Cover Change: The IIASA Land-Use Change Model

In 1995, a new project Modeling Land-Use and Land-Cover Changes in Europe and Northern Asia (LUC) was established at IIASA with the objective of analyzing the spatial characteristics, temporal dynamics, and environmental consequences of land-use and land-cover changes that have occurred in Europe and Northern Asia over the period 1900 to 1990 as a result of a range of socio-economic and biogeophysical driving forces. The analysis will then be used to project plausible future changes in land use and land cover for the period 1990 to 2050 under different assumptions of future demographic, economic, technological, social and political development. The study region, Europe and Northern Asia, has been selected because of its diversity in social, economic and political organization, the rapid changes in recent history, and the significant implications for current and future land-use and land-cover change. Land-cover change is driven by a multitude of processes. Natural processes, such as vegetation dynamics, involve alterations in cover due to natural changes in climate and soils. However, changes of land cover driven by anthropogenic forcing are currently the most important and most rapid of all changes (Turner et al. 1990). Therefore, any sound effort to project the future state of land cover must consider the determinants of human requirements and activities, e.g., demand for land-based products such as food, fiber and fuel, or use of land for recreation. In the past, major land-cover conversions have occurred as a consequence of deforestation to convert land for crop and livestock production; removal of wood for fuel and timber; conversion of wetlands to agricultural and other uses; conversion of land for habitation, infrastructure and industry; and conversion of land for mineral extraction (Turner et al. 1993). These human-induced conversions of land cover, particularly during the past two centuries, have resulted in a net release of CO2 to the atmosphere, changes in the characteristics of land surfaces (e.g., albedo and roughness), and decreased biodiversity. More subtle processes, termed land-cover modifications, affect the character of the land cover without changing its overall classification. For instance, land-cover degradation through erosion, overgrazing, desertification, salinization and acidification, is currently considered a major environmental problem. Although the effects of land-cover modifications may be small at local scales, their aggregate impact may be considerable. For example, use of fertilizers locally has no significance for atmospheric concentrations of greenhouse gases. However, when practiced frequently in many locations, nitrogen fertilizer can make a significant contribution to emissions of nitrous oxide (N2O) globally. The implementation of a comprehensive land-use change model poses a number of methodological challenges. These include the complexity of the issues involved and the large number of interacting agents and factors; the nonlinear interactions between prices, the supply of and the demand for land-based commodities and resources; the importance of intertemporal aspects; the intricacy of biogeophysical feedbacks; and the essential role of uncertainty in the overall evaluation of strategies. The interaction mechanisms between biophysical cycles and economic processes have mainly been studied in dynamic simulation models that follow recursive chains of causation, where the past and present events determine what will happen tomorrow. Not surprisingly, many of these studies have led to dramatic predictions, basically because the agents whose behavior is described within the model are themselves assumed to be unable to predict at all. By contrast, in micro-economics it is usually assumed that agents do have the capacity to make informed predictions and to plan so as to avoid the probability of disaster in the future. However, even full information and rationality of individual choice are not always sufficient to avoid disaster. The coordination mechanisms that prevail among economic agents often tend to be of decisive importance. The aim of this paper is to summarize the LUC project approach and to extend our earlier writings on modeling of land-use and land-cover change dynamics. We discuss the adequacy and applicability of welfare analysis as a conceptual framework for the LUC project at IIASA. We recognize from the outset the complexity of socio-economic and environmental driving forces and the fundamental uncertainties involved in their spatial and temporal interactions (and outcomes). Unlike physical particles, economic agents have the ability to anticipate, and they possess the freedom to change their behavior. This inherent unpredictability, in particular the multiplicity of possible outcomes, calls for a normative approach, and for comparative policy analysis rather than exact prediction. Therefore, we adopt an approach that enables the explicit representation of various policy measures, thus providing a means to search for "better futures", i.e., for trajectories of future development that may alleviate environmental stresses while improving human welfare

Scheduling Jobs in Flowshops with the Introduction of Additional Machines in the Future

This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier and can be found at: http://www.journals.elsevier.com/expert-systems-with-applications/.The problem of scheduling jobs to minimize total weighted tardiness in flowshops,\ud with the possibility of evolving into hybrid flowshops in the future, is investigated in\ud this paper. As this research is guided by a real problem in industry, the flowshop\ud considered has considerable flexibility, which stimulated the development of an\ud innovative methodology for this research. Each stage of the flowshop currently has\ud one or several identical machines. However, the manufacturing company is planning\ud to introduce additional machines with different capabilities in different stages in the\ud near future. Thus, the algorithm proposed and developed for the problem is not only\ud capable of solving the current flow line configuration but also the potential new\ud configurations that may result in the future. A meta-heuristic search algorithm based\ud on Tabu search is developed to solve this NP-hard, industry-guided problem. Six\ud different initial solution finding mechanisms are proposed. A carefully planned\ud nested split-plot design is performed to test the significance of different factors and\ud their impact on the performance of the different algorithms. To the best of our\ud knowledge, this research is the first of its kind that attempts to solve an industry-guided\ud problem with the concern for future developments

Hunger: Beyond the Reach of the Invisible Hand

The work described in this report differs from many others in that the analysis of policies is based on a common integrated framework. It shows why hunger persists, why many policies advanced in popular literature do not work, and what kind of policies can work. Although based on analyses using a quantitative, sophisticated system of models, the book is addressed to the nontechnical layman and to the general reader. The arguments go beyond economic and technical analysis and deal with political and moral aspects. The authors show that solutions that rely only on the market mechanism do not work to eliminate hunger rapidly enough. This analysis shows that even policies that try to intervene, modify, and distort the market do not help to reduce hunger effectively if they rely on the market mechanism

UV/IR duality in noncommutative quantum field theory

We review the construction of renormalizable noncommutative euclidean phi(4)-theories based on the UV/IR duality covariant modification of the standard field theory, and how the formalism can be extended to scalar field theories defined on noncommutative Minkowski space.Comment: 12 pages; v2: minor corrections, note and references added; Contribution to proceedings of the 2nd School on "Quantum Gravity and Quantum Geometry" session of the 9th Hellenic School on Elementary Particle Physics and Gravity, Corfu, Greece, September 13-20 2009. To be published in General Relativity and Gravitatio

China's agricultural prospects and challenges

The report describes prospects and challenges for Chinese agriculture until 2030 under different scenarios, using the Chinagro welfare model. A scenario is defined as a coherent set of assumptions about exogenous driving forces (farm land, population, non-agricultural growth, world prices etc.), derived from the literature and own assessments. Under these assumptions, simulations with the Chinagro model analyze the price-based interaction between the supply behavior of farmers, the demand behavior of consumers and the determination of trade flows by merchants. The outcomes from the "Baseline scenario" seem reassuring in that foreign imports remain moderate relative to Chinas size, though quite large as fraction of world trade. It would be possible to feed people as well as animals without excessive imports. There is even a potential for significant export flows of vegetables and fruits. Regarding concerns, the trends in per capita agricultural value added are problematic, because they stay in all regions behind per capita value added outside agriculture, albeit that they are rising steadily. This leads to growing disparity in per capita incomes within and across regions. The mounting environmental pressure from fertilizer losses and unused manure surpluses is another cause of concern. The second scenario, the Trade liberalization scenario, appears to hurt farm incomes more than it benefits them and to raise the gap with non-agriculture, also because food becomes cheaper in urban areas. Hence, it highlights the difficult choice between economic efficiency and poverty alleviation that agricultural policy makers often face. The "High income growth scenario" reinforces the national food self-sufficiency result of the baseline simulation. Even with meat demand higher than under the baseline, levels of imports remain manageable. The "High R&D scenario" shows that a considerable reduction in dependence on agricultural imports is possible. However, a substantial part of the gains will accrue to consumers rather than to farmers, due to price reductions. Finally, the "Enhanced irrigation scenario" shows outcomes similar to those of the high R&D scenario. Here also the agricultural trade balance improves and consumer welfare improves, but farmers have to cope with drops in prices, and those who do not benefit from land improvement, only experience losses through falling prices. The present report is written at the onset of the CATSEI-project that will analyze policy packages with more specificity and detail after implementing the following model improvements. First, the impact of Chinas imports and exports on world markets will be represented explicitly. Second, the developments outside agriculture in rural areas will be accounted for endogenously, particularly to represent farm revenue from off-farm employment. Third, the trade and transportation margins between farm-gates and markets will be made dependent on the relative flexibility of the actors (farmers, processors, traders) along the chain. Finally, the various techniques to identify more efficient and more sustainable use of scarce water and nutrients and to address health risks will appear more explicitly

Een onderzoeksagenda naar de relatie tussen voedselrisico en consumentengedrag

Current government policy is striving to reduce the microbial contamination of foods to zero level. However, it is possible that consumers who perceive lower risks of contracting foodborne diseases will take less care of foods. A literature study was carried out to review scientific knowledge about the consequences of the reduction of foodborne infections to a zero level for consumer cooking behaviour. A workshop was then organised to determine the research agenda for this subjec

Tree-based Coarsening and Partitioning of Complex Networks

Many applications produce massive complex networks whose analysis would benefit from parallel processing. Parallel algorithms, in turn, often require a suitable network partition. For solving optimization tasks such as graph partitioning on large networks, multilevel methods are preferred in practice. Yet, complex networks pose challenges to established multilevel algorithms, in particular to their coarsening phase. One way to specify a (recursive) coarsening of a graph is to rate its edges and then contract the edges as prioritized by the rating. In this paper we (i) define weights for the edges of a network that express the edges' importance for connectivity, (ii) compute a minimum weight spanning tree $T^m$ with respect to these weights, and (iii) rate the network edges based on the conductance values of $T^m$'s fundamental cuts. To this end, we also (iv) develop the first optimal linear-time algorithm to compute the conductance values of \emph{all} fundamental cuts of a given spanning tree. We integrate the new edge rating into a leading multilevel graph partitioner and equip the latter with a new greedy postprocessing for optimizing the maximum communication volume (MCV). Experiments on bipartitioning frequently used benchmark networks show that the postprocessing already reduces MCV by 11.3%. Our new edge rating further reduces MCV by 10.3% compared to the previously best rating with the postprocessing in place for both ratings. In total, with a modest increase in running time, our new approach reduces the MCV of complex network partitions by 20.4%