2,258 research outputs found
Cellular Models for River Networks
A cellular model introduced for the evolution of the fluvial landscape is
revisited using extensive numerical and scaling analyses. The basic network
shapes and their recurrence especially in the aggregation structure are then
addressed. The roles of boundary and initial conditions are carefully analyzed
as well as the key effect of quenched disorder embedded in random pinning of
the landscape surface. It is found that the above features strongly affect the
scaling behavior of key morphological quantities. In particular, we conclude
that randomly pinned regions (whose structural disorder bears much physical
meaning mimicking uneven landscape-forming rainfall events, geological
diversity or heterogeneity in surficial properties like vegetation, soil cover
or type) play a key role for the robust emergence of aggregation patterns
bearing much resemblance to real river networks.Comment: 7 pages, revtex style, 14 figure
Modeling urban street patterns
Urban streets patterns form planar networks whose empirical properties cannot
be accounted for by simple models such as regular grids or Voronoi
tesselations. Striking statistical regularities across different cities have
been recently empirically found, suggesting that a general and
details-independent mechanism may be in action. We propose a simple model based
on a local optimization process combined with ideas previously proposed in
studies of leaf pattern formation. The statistical properties of this model are
in good agreement with the observed empirical patterns. Our results thus
suggests that in the absence of a global design strategy, the evolution of many
different transportation networks indeed follow a simple universal mechanism.Comment: 4 pages, 5 figures, final version published in PR
The Fractal Properties of Internet
In this paper we show that the Internet web, from a user's perspective,
manifests robust scaling properties of the type where n
is the size of the basin connected to a given point, represents the density
of probability of finding n points downhill and s a
characteristic universal exponent. This scale-free structure is a result of the
spontaneous growth of the web, but is not necessarily the optimal one for
efficient transport. We introduce an appropriate figure of merit and suggest
that a planning of few big links, acting as information highways, may
noticeably increase the efficiency of the net without affecting its robustness.Comment: 6 pages,2 figures, epl style, to be published on Europhysics Letter
Local minimal energy landscapes in river networks
The existence and stability of the universality class associated to local
minimal energy landscapes is investigated. Using extensive numerical
simulations, we first study the dependence on a parameter of a partial
differential equation which was proposed to describe the evolution of a rugged
landscape toward a local minimum of the dissipated energy. We then compare the
results with those obtained by an evolution scheme based on a variational
principle (the optimal channel networks). It is found that both models yield
qualitatively similar river patterns and similar dependence on . The
aggregation mechanism is however strongly dependent on the value of . A
careful analysis suggests that scaling behaviors may weakly depend both on
and on initial condition, but in all cases it is within observational
data predictions. Consequences of our resultsComment: 12 pages, 13 figures, revtex+epsfig style, to appear in Phys. Rev. E
(Nov. 2000
Network Structures from Selection Principles
We present an analysis of the topologies of a class of networks which are
optimal in terms of the requirements of having as short a route as possible
between any two nodes while yet keeping the congestion in the network as low as
possible. Strikingly, we find a variety of distinct topologies and novel phase
transitions between them on varying the number of links per node. Our results
suggest that the emergence of the topologies observed in nature may arise both
from growth mechanisms and the interplay of dynamical mechanisms with a
selection process.Comment: 4 pages, 5 figure
An Analytical and Numerical Study of Optimal Channel Networks
We analyze the Optimal Channel Network model for river networks using both
analytical and numerical approaches. This is a lattice model in which a
functional describing the dissipated energy is introduced and minimized in
order to find the optimal configurations. The fractal character of river
networks is reflected in the power law behaviour of various quantities
characterising the morphology of the basin. In the context of a finite size
scaling Ansatz, the exponents describing the power law behaviour are calculated
exactly and show mean field behaviour, except for two limiting values of a
parameter characterizing the dissipated energy, for which the system belongs to
different universality classes. Two modified versions of the model,
incorporating quenched disorder are considered: the first simulates
heterogeneities in the local properties of the soil, the second considers the
effects of a non-uniform rainfall. In the region of mean field behaviour, the
model is shown to be robust to both kinds of perturbations. In the two limiting
cases the random rainfall is still irrelevant, whereas the heterogeneity in the
soil properties leads to new universality classes. Results of a numerical
analysis of the model are reported that confirm and complement the theoretical
analysis of the global minimum. The statistics of the local minima are found to
more strongly resemble observational data on real rivers.Comment: 27 pages, ps-file, 11 Postscript figure
Scale-free Networks from Optimal Design
A large number of complex networks, both natural and artificial, share the
presence of highly heterogeneous, scale-free degree distributions. A few
mechanisms for the emergence of such patterns have been suggested, optimization
not being one of them. In this letter we present the first evidence for the
emergence of scaling (and smallworldness) in software architecture graphs from
a well-defined local optimization process. Although the rules that define the
strategies involved in software engineering should lead to a tree-like
structure, the final net is scale-free, perhaps reflecting the presence of
conflicting constraints unavoidable in a multidimensional optimization process.
The consequences for other complex networks are outlined.Comment: 6 pages, 2 figures. Submitted to Europhysics Letters. Additional
material is available at http://complex.upc.es/~sergi/software.ht
Pricing Rainfall Based Futures Using Genetic Programming
Rainfall derivatives are in their infancy since starting trading on the Chicago Mercantile Exchange (CME) since 2011. Being a relatively new class of financial instruments there is no generally recognised pricing framework used within the literature. In this paper, we propose a novel framework for pricing contracts using Genetic Programming (GP). Our novel framework requires generating a risk-neutral density of our rainfall predictions generated by GP supported by Markov chain Monte Carlo and Esscher transform. Moreover, instead of having a single rainfall model for all contracts, we propose having a separate rainfall model for each contract. We compare our novel framework with and without our proposed contract-specific models for pricing against the pricing performance of the two most commonly used methods, namely Markov chain extended with rainfall prediction (MCRP), and burn analysis (BA) across contracts available on the CME. Our goal is twofold, (i) to show that by improving the predictive accuracy of the rainfall process, the accuracy of pricing also increases. (ii) contract-specific models can further improve the pricing accuracy. Results show that both of the above goals are met, as GP is capable of pricing rainfall futures contracts closer to the CME than MCRP and BA. This shows that our novel framework for using GP is successful, which is a significant step forward in pricing rainfall derivatives
Simple models for scaling in phylogenetic trees
Many processes and models --in biological, physical, social, and other
contexts-- produce trees whose depth scales logarithmically with the number of
leaves. Phylogenetic trees, describing the evolutionary relationships between
biological species, are examples of trees for which such scaling is not
observed. With this motivation, we analyze numerically two branching models
leading to non-logarithmic scaling of the depth with the number of leaves. For
Ford's alpha model, although a power-law scaling of the depth with tree size
was established analytically, our numerical results illustrate that the
asymptotic regime is approached only at very large tree sizes. We introduce
here a new model, the activity model, showing analytically and numerically that
it also displays a power-law scaling of the depth with tree size at a critical
parameter value.Comment: 7 pages, 4 figures. A new figure, with example trees, has been added.
To appear in Int. J. Bifurcation and Chao
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