Minimal vertex covers of random trees

We study minimal vertex covers of trees. Contrarily to the number $N_{vc}(A)$ of minimal vertex covers of the tree $A$, $\log N_{vc}(A)$ is a self-averaging quantity. We show that, for large sizes $n$, $\lim_{n\to +\infty} <\log N_{vc}(A)>_n/n= 0.1033252\pm 10^{-7}$. The basic idea is, given a tree, to concentrate on its degenerate vertices, that is those vertices which belong to some minimal vertex cover but not to all of them. Deletion of the other vertices induces a forest of totally degenerate trees. We show that the problem reduces to the computation of the size distribution of this forest, which we perform analytically, and of the average $$ over totally degenerate trees of given size, which we perform numerically

Asymmetric evolving random networks

We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A node is added at each time step and is connected to the rest of the graph by oriented edges emerging from older nodes. This leads to a statistical asymmetry between incoming and outgoing edges. The law for the number of new edges at each time step is fixed but arbitrary. Thermodynamical behavior is expected when this law has a large time limit. Although (by construction) the incoming degree distributions depend on this law, this is not the case for most qualitative features concerning the size distribution of connected components, as long as the law has a finite variance. As the variance grows above 1/4, the average being <1/2, a giant component emerges, which connects a finite fraction of the vertices. Below this threshold, the distribution of component sizes decreases algebraically with a continuously varying exponent. The transition is of infinite order, in sharp contrast with the case of static graphs. The local-in-time profiles for the components of finite size allow to give a refined description of the system.Comment: 30 pages, 3 figure

Learning curves and changing product attributes: the case of wind turbines

The heuristic concept of learning curves describes cost reductions as a function of cumulative production. A study of the Liberty shipbuilders suggested that product quality and production scale are other relevant factors that affect costs. Significant changes of attributes of a technology must be corrected when assessing the impact of learning-by-doing. We use an engineering-based model to capture the cost changes of wind turbines that can be attributed to changes in turbine size. We estimate the learning curve and turbine size parameters using more than 1500 price points from 1991 to 2003. The fit between model and empirical data confirms the concept

Carbon price and optimal extraction of a polluting fossil fuel with restricted carbon capture

Among technological options to mitigate greenhouse gas (GHG) emissions, Carbon Capture and Storage technology (CCS) seems particularly promising. This technology allows to keep on extracting polluting fossil fuels without drastically increasing CO2 atmospheric concentration. We examine here a two-sector model with two primary energy resources, a polluting exhaustible resource and an expensive carbon-free renewable resource, in which an environmental regulation is imposed through a cap on the atmospheric carbon stock. We assume that only the emissions from one sector can be captured. Previous literature, based on one-sector models in which all emissions are capturable, finds that CCS technology should not be used before the threshold has been reached. We find that, when technical constraints make it impossible to capture emissions from both sectors, this result does not always hold. CCS technology should be used before the ceiling is reached if non capturable emissions are large enough. In that case, we find that energy prices paths must differ between sectors reflecting the difference of social cost of the resource according to its use. Numerical exercise shows that the initial carbon tax should equal 52$/t CO2 and that using CCS before the ceiling is optimal.Nonrenewable Resources, Externalities, Carbon Capture.

Carbon price and optimal extraction of a polluting fossil fuel with restricted carbon capture

Among technological options to mitigate greenhouse gas (GHG) emissions, Carbon Capture and Storage technology (CCS) seems particularly promising. This technology allows to keep on extracting polluting fossil fuels without drastically increasing CO2 atmospheric concentration. We examine here a two-sector model with two primary energy resources, a polluting exhaustible resource and an expensive carbon-free renewable resource, in which an environmental regulation is imposed through a cap on the atmospheric carbon stock. We assume that only the emissions from one sector can be captured. Previous literature, based on one-sector models in which all emissions are capturable, finds that CCS technology should not be used before the threshold has been reached. We find that, when technical constraints make it impossible to capture emissions from both sectors, this result does not always hold. CCS technology should be used before the ceiling is reached if non capturable emissions are large enough. In that case, we find that energy prices paths must differ between sectors reflecting the difference of social cost of the resource according to its use. Numerical exercise show that, when the ceiling is set at 450ppm CO2, the initial carbon tax should equal 52$/tCO2 and that using CCS before the ceiling is optimal.dynamic models ; global warming ; externalities ; nonrenewable resources ; carbon capture ; energy markets

Peace, War and International Security: Economic Theories

This paper considers the economic theories that are relevant for the study of peace war and international security . It presents different levels of generality, starting with the big questions of international security, which are usually the domain of international relations, before moving to general economic theoretical perspectives and then focusing on some specific developments in economics and security. More specifically it reviews the economics of security, distinguishing neoclassical theories, Keynesian and institutional, Marxist, and monopoly capital, before discussing the issues involved in the debate between the schools of thought. The economics of conflict is then considered, starting with the approach economists have taken –mainly neoclassical, before considering more general political economy perspectives.Economics; Peace; war; security;

Peace, War and International Security: Economic Theories (trial entry)

This paper considers the economic theories that are relevant for the study of peace war and international security . It presents different levels of generality, starting with the big questions of international security, which are usually the domain of international relations, before moving to general economic theoretical perspectives and then focusing on some specific developments in economics and security. More specifically it reviews the economics of security, distinguishing neoclassical theories, Keynesian and institutional, Marxist, and monopoly capital, before discussing the issues involved in the debate between the schools of thought. The economics of conflict is then considered, starting with the approach economists have taken –mainly neoclassical, before considering more general political economy perspectives.Economics; Peace; war; security;

The Evolution of the Economic Thought Confronted with World War I and the Reparations’ Issue

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