Extreme fluctuations in noisy task-completion landscapes on scale-free networks

We study the statistics and scaling of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally-constrained queuing networks, with scale-free topology. In these networks the average size of the fluctuations becomes finite (synchronized state) and the extreme fluctuations typically diverge only logarithmically in the large system-size limit ensuring synchronization in a practical sense. Provided that local fluctuations in the network are short-tailed, the statistics of the extremes are governed by the Gumbel distribution. We present large-scale simulation results using the exact algorithmic rules, supported by mean-field arguments based on a coarse-grained description.Comment: 16 pages, 6 figures, revte

Marx, the labour theory of value and the transformation problem

This article reconsiders what Marx says about the transformation problem in Chapter IX of Capital Volume III, in the light of Marx's claim, made in Capital Volume I, that the value of a commodity is determined by the socially necessary labour time that goes into its production. The article criticises the traditional way of thinking about the transformation problem, according to which what Marx is doing in Chapter IX is considering the transformation of values into prices ('prices of production'). I argue that Marx's prices of production may be thought of as modified values. The discussion in Chapter IX is usually seen as a supplement to the labour theory of value. On this view its purpose is to explain how and why the prices of commodities sometimes deviate from their values. Against this view, the paper argues that Marx's remarks in Chapter IX can be seen as an elaboration on or development of the labour theory of value. It is a refinement of the account offered in Capital Volume I, which takes into consideration what Marx had in mind there when he introduced the notion of socially necessary as opposed to actual labour-time. The paper draws attention to the importance of Marx's distinction between the individual value of a commodity (determined by actual labour-time) and its social value (determined by socially necessary labour-time). It also draws attention to the methodological difficulties that are generated by any attempt to read Marx in this way

Classical Macrodynamics and the Labor Theory of Value

This paper outlines a multisector dynamic model of the convergence of market prices to natural prices in conditions of fixed technology and composition of demand. Prices and quantities adjust in real-time in response to excess supplies and differential profit-rates. Finance capitalists earn interest income by supplying money-capital to fund production. Industrial capitalists, as the owners of firms, are liable for profits and losses. Market prices stabilize to profit-equalizing prices of production proportional to the total coexisting labor required to reproduce commodities. This result resolves the classical problem of the incommensurability between money and labor-value accounts in conditions of profits on stock, i.e. Marx's transformation problem