380 research outputs found
Exact solution of a generalized model for surface deposition
We consider a model for surface deposition in one dimension, in the presence of both precursor-layer diffusion and desorption. The model is a generalization that includes random sequential adsorption (RSA), accelerated RSA, and growth-and-coalescence models as special cases. Exact solutions are obtained for the model for both its lattice and continuum versions. Expressions are obtained for physically important quantities such as the surface coverage, average island size, mass-adsorption efficiency, and the process efficiency. The connection between a limiting case of the model and epidemic models is discussed
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Exact solution of a model for crowding and information transmission in financial markets
An exact solution is presented to a model that mimics the crowding effect in financial markets which arises when groups of agents share information. We show that the size distribution of groups of agents has a power law tail with an exponential cut-off. As the size of these groups determines the supply and demand balance, this implies heavy tails in the distribution of price variation. The moments of the distribution are calculated, as well as the kurtosis. We find that the kurtosis is large for all model parameter values and that the model is not self-organizing
Democracy versus dictatorship in self-organized models of financial markets
Models to mimic the transmission of information in financial markets are introduced. As an attempt to generate the demand process, we distinguish between dictatorship associations, where groups of agents rely on one of them to make decision, and democratic associations, where each agent takes part in the group decision. In the dictatorship model, agents segregate into two distinct populations, while the democratic model is driven towards a critical state where groups of agents of all sizes exist. Hence, both models display a level of organization, but only the democratic model is self-organized. We show that the dictatorship model generates less-volatile markets than the democratic model
Transition from coherence to bistability in a model of financial markets
We present a model describing the competition between information transmission and decision
making in financial markets. The solution of this simple model is recalled, and possible variations discussed.
It is shown numerically that despite its simplicity, it can mimic a size effect comparable to a crash. Two
extensions of this model are presented that allow to simulate the demand process. One of these extensions
has a coherent stable equilibrium and is self-organized, while the other has a bistable equilibrium, with a
spontaneous segregation of the population of agents. A new model is introduced to generate a transition
between those two equilibriums. We show that the coherent state is dominant up to an equal mixing of the
two extensions. We focuss our attention on the microscopic structure of the investment rate, which is the
main parameter of the original model. A constant investment rate seems to be a very good approximation
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Eigenvalue distribution of large dilute random matrices
We study the eigenvalue distribution of dilute N3N random matrices HN that in
the pure ~undiluted! case describe the Hopfield model. We prove that for the fixed
dilution parameter a the normalized counting function ~NCF! of HN converges as
N!` to a unique sa(l). We find the moments of this distribution explicitly,
analyze the 1/a correction, and study the asymptotic properties of sa(l) for large
ulu. We prove that sa(l) converges as a !` to the Wigner semicircle distribution
~SCD!. We show that the SCD is the limit of the NCF of other ensembles of dilute
random matrices. This could be regarded as evidence of stability of the SCD to
dilution, or more generally, to random modulations of large random matrices
Efficiency and persistence in models of adaptation
A cut-and-paste model which mimics a trial-and-error process of adaptation is introduced and solved. The model, which can be thought of as a diffusion process with memory, is characterized by two properties, efficiency and persistence. We establish a link between these properties and determine two transitions for each property, a percolation transition and a depinning transition. If the adaptation process is iterated, the antipersistent state becomes an attractor of the dynamics. Extensions to higher dimensions are briefly discussed
Packet transport on scale free networks
We introduce a model of information packet transport on networks in which the packets are posted by a given rate and move in parallel according to a local search algorithm. By performing a number of simulations we investigate the major kinetic properties of the transport as a function of the network geometry, the packet input rate and the buffer size. We find long-range correlations in the power spectra of arriving packet density and the network's activity bursts. The packet transit time distribution shows a power-law dependence with average transit time increasing with network size. This implies dynamic queueing on the network, in which many interacting queues are mutually driven by temporally correlated packet stream
A model of macroevolution with a natural system size
We describe a simple model of evolution which incorporates the branching and extinction of species lines, and also includes abiotic influences. A first principles approach is taken in which the probability for speciation and extinction are defined purely in terms of the fitness landscapes of each species. Numerical simulations show that the total diversity fluctuates around a natural system size which only weakly depends upon the number of connections per species. This is in agreement with known data for real multispecies communities. The numerical results are confirmed by approximate mean field analysi
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A power law distribution in patients' lengths of stay in hospital
The distribution of patients' lengths of stay in English hospitals is measured by using routinely
collected data from 11 years. It is found to be well approximated by a power law distribution
spanning over more than 3 decades. To explain this observation, a theoretical resource allocation
model is presented. It is based on iterative long-term scheduling of hospital beds, and its main
assumption is that future beds are allocated preferentially. This represents a situation where
di®erent parts of the health care system compete for resources, with bargaining powers proportional
to current resource levels
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Complex networks
This chapter contains a brief introduction to complex networks, and in particular to small world and scale free networks. We show how to apply the replica method developed to analyse random matrices in statistical physics to calculate the spectral densities of the adjacency and Laplacian matrices of a scale free network. We use the effective medium approximation to treat networks with finite mean degree and discuss the local properties of random matrices associated with complex networks
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