Models for the size distribution of businesses in a price driven market

A microscopic model of aggregation and fragmentation is introduced to investigate the size distribution of businesses. In the model, businesses are constrained to comply with the market price, as expected by the customers, while customers can only buy at the prices offered by the businesses. We show numerically and analytically that the size distribution scales like a power-law. A mean-field version of our model is also introduced and we determine for which value of the parameters the mean-field model agrees with the microscopic model. We discuss to what extent our simple model and its results compare with empirical data on company sizes in the U.S. and debt sizes in Japan. Finally, possible extensions of the mean-field model are discussed, to cope with other empirical data.Comment: 12 pages, 2 figures, submitted for publicatio

Applications of W-algebras to BF theories, QCD and 4D Gravity

We are able to show that BF theories naturally emerge from the coadjoint orbits of $W_2$ and $w_\infty$ algebras which includes a Kac-Moody sector. Since QCD strings can be identified with a BF theory, we are able to show a relationship between the orbits and monopole-string solutions of QCD. Furthermore, we observe that when 4D gravitation is cast into a BF form through the use of Ashtekar variables, we are able to get order $\hbar$ contributions to gravity which can be associated with the $W_2$ anomaly. We comment on the relationship to gravitational monopoles.Comment: 14 page

W∞W_\infty and Anomalies of Self-Dual Einstein Theories

This manuscripts corrects some minor error in the paper, Mod. Phys. Lett. A 6 1893 (1991)Comment: (revised due to TeXnical errors), 11 page

Growing random networks with fitness

Three models of growing random networks with fitness dependent growth rates are analysed using the rate equations for the distribution of their connectivities. In the first model (A), a network is built by connecting incoming nodes to nodes of connectivity $k$ and random additive fitness $\eta$, with rate $(k-1)+ \eta$. For $\eta >0$ we find the connectivity distribution is power law with exponent $\gamma=+2$. In the second model (B), the network is built by connecting nodes to nodes of connectivity $k$, random additive fitness $\eta$ and random multiplicative fitness $\zeta$ with rate $\zeta(k-1)+\eta$. This model also has a power law connectivity distribution, but with an exponent which depends on the multiplicative fitness at each node. In the third model (C), a directed graph is considered and is built by the addition of nodes and the creation of links. A node with fitness $(\alpha, \beta)$, $i$ incoming links and $j$ outgoing links gains a new incoming link with rate $\alpha(i+1)$, and a new outgoing link with rate $\beta(j+1)$. The distributions of the number of incoming and outgoing links both scale as power laws, with inverse logarithmic corrections

Erodibility of hill peat

peer-reviewedThe project was funded by the European Union Structural Funds EAGGF distributed under the Department of Agriculture and Food Stimulus Fund.The energy necessary to entrain soil in water depends on the soil strength. Once entrained, the settling velocity of the eroded soil in water is of fundamental importance to the processes of sediment transport and deposition. In this paper, stream power theory and transport concepts coupled with the equation of continuity were used to derive a transport-limited peat concentration. The ratio of the log of the actual sediment concentration in surface run-off to the log of the transport-limited sediment concentration was the index of erosion used. The value of this index is a measure of the sensitivity of peat to erosion by sheet flow. Four peats were subjected to a range of overland flow rates under two slopes in a laboratory flume. The peats represented peat farmed in a sustainable manner (Leenane), overgrazed peat (Maam), peat undergoing erosion (Newport) and peat which had undergone weathering following exposure by a landslip (Croagh Patrick). Both in situ and surface damaged slabs were studied. The results indicate that shearing and remoulding of a wet peat surface (e.g., by animal treading) and weathering of exposed drained peat surfaces predispose peat to erosion. Defoliation by overgrazing is considered to be of secondary importance.Department of Agriculture, Food and the MarineEuropean Union Structural Funds EAGG

Strategy Selection in the Minority Game

We investigate the dynamics of the choice of an active strategy in the minority game. A history distribution is introduced as an analytical tool to study the asymmetry between the two choices offered to the agents. Its properties are studied numerically. It allows us to show that the departure from uniformity in the initial attribution of strategies to the agents is important even in the efficient market. Also, an approximate expression for the variance of the number of agents at one side in the efficient phase is proposed. All the analytical propositions are supported by numerical simulations of the system.Comment: Latex file, 17 page, 4 figure