8,147 research outputs found
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 and random additive fitness , with rate . For we find the connectivity distribution is power law with exponent . In the second model (B), the network is built by connecting nodes to nodes of connectivity , random additive fitness and random multiplicative fitness with rate . 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 , incoming links and outgoing links gains a new incoming link with rate , and a new outgoing link with rate . The distributions of the number of incoming and outgoing links both scale as power laws, with inverse logarithmic corrections
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
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
Spectral Density of Complex Networks with a Finite Mean Degree
In order to clarify the statistical features of complex networks, the
spectral density of adjacency matrices has often been investigated. Adopting a
static model introduced by Goh, Kahng and Kim, we analyse the spectral density
of complex scale free networks. For that purpose, we utilize the replica method
and effective medium approximation (EMA) in statistical mechanics. As a result,
we identify a new integral equation which determines the asymptotic spectral
density of scale free networks with a finite mean degree . In the limit , known asymptotic formulae are rederived. Moreover, the
corrections to known results are analytically calculated by a perturbative
method.Comment: 18 pages, 1 figure, minor corrections mad
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 and 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 contributions
to gravity which can be associated with the anomaly. We comment on the
relationship to gravitational monopoles.Comment: 14 page
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