Reply to the Comment by H. Tephany and J. Nahmias on “Percolation in real wildfires” by G. Caldarelli
                    <i>et al.</i>

Caldarelli, Guido; Frondoni, Raffaella; Gabrielli, Andrea; Montuori, M.; Retzlaff, Rebecca; Ricotta, Carlo

doi:10.1209/epl/i2002-00151-4

Cited by 5 publications

(9 citation statements)

References 8 publications

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“…These results may prove useful to some of the large spectrum of physical and interdisciplinary topics where the percolation theory may be applied like forest fires spreading [20,28], immunology [29], liquid migration in porous media [30], econophysics [31], and sociophysics [32].…”

Section: Discussionmentioning

confidence: 99%

Square-lattice site percolation at increasing ranges of neighbor bonds

Malarz

Galam

2005

Phys. Rev. E

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We report site percolation thresholds for square lattice with neighbor bonds at various increasing ranges. Using Monte Carlo techniques we found that nearest neighbors (NN), next-nearest neighbors (NNN), next-next-nearest neighbors (4N), and fifth-nearest neighbors (6N) yield the same pc = 0.592... . The fourth-nearest neighbors (5N) give pc = 0.298... . This equality is proved to be mathematically exact using symmetry argument. We then consider combinations of various kinds of neighborhoods with (NN+NNN), (NN+4N), (NN+NNN+4N), and (NN+5N). The calculated associated thresholds are respectively pc = 0.407..., 0.337..., 0.288..., and 0.234... . The existing Galam-Mauger universal formula for percolation thresholds does not reproduce the data showing dimension and coordination number are not sufficient to build a universal law which extends to complex lattices.

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Section: Discussionmentioning

confidence: 99%

Square-lattice site percolation at increasing ranges of neighbor bonds

Malarz

Galam

2005

Phys. Rev. E

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“…We note that "energy dissipation" in this model is achieved through the birth costs b I and the self-competition terms M II . Equivalent effects could have been produced by making the positive M IJ smaller than the corresponding negative ones by an "ecological efficiency" factor between zero and unity, as in the Webworld model [8,14,15].…”

Section: Modelmentioning

confidence: 99%

“…Early contributions were simulations of parapatric and sympatric speciation [11] and the coupled NK model with population dynamics [12,13]. More recent work includes the Webworld model [8,14,15], the tangled-nature model [16,17,18] and simplified versions of the latter [19,20,21], as well as network models [22,23]. Recently, large individual-based simulations have also been performed of parapatric and sympatric speciation [24,25] and of adaptive radiation [26].…”

Section: Introductionmentioning

confidence: 99%

Individual-based predator-prey model for biological coevolution: Fluctuations, stability, and community structure

Rikvold

Sevi̇m

2007

Phys. Rev. E

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We study an individual-based predator-prey model of biological coevolution, using linear stability analysis and large-scale kinetic Monte Carlo simulations. The model exhibits approximate 1/f noise in diversity and population-size fluctuations, and it generates a sequence of quasisteady communities in the form of simple food webs. These communities are quite resilient toward the loss of one or a few species, which is reflected in different power-law exponents for the durations of communities and the lifetimes of species. The exponent for the former is near -1 , while the latter is close to -2 . Statistical characteristics of the evolving communities, including degree (predator and prey) distributions and proportions of basal, intermediate, and top species, compare reasonably with data for real food webs.

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“…The use of complex networks and graph theory to describe complex systems ranging from the WWW to protein interaction networks is by now well-established (different book and reviews are available about this topic [1,2,3,4,5]). A large class of these systems attains complexity by means of their internal dynamics [6], which is often revealed by computer simulations. One example of such systems is the folding of proteins for which simulations have been extensively used in structural biology.…”

Section: Introductionmentioning

confidence: 99%

Uncovering the topology of configuration space networks

et al. 2007

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The configuration space network ͑CSN͒ of a dynamical system is an effective approach to represent the ensemble of configurations sampled during a simulation and their dynamic connectivity. To elucidate the connection between the CSN topology and the underlying free-energy landscape governing the system dynamics and thermodynamics, an analytical solution is provided to explain the heavy tail of the degree distribution, neighbor connectivity, and clustering coefficient. This derivation allows us to understand the universal CSN topology observed in systems ranging from a simple quadratic well to the native state of the beta3s peptide and a two-dimensional lattice heteropolymer. Moreover, CSNs are shown to fall in the general class of complex networks described by the fitness model.

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Reply to the Comment by H. Tephany and J. Nahmias on “Percolation in real wildfires” by G. Caldarelli et al.

Cited by 5 publications

References 8 publications

Square-lattice site percolation at increasing ranges of neighbor bonds

Square-lattice site percolation at increasing ranges of neighbor bonds

Individual-based predator-prey model for biological coevolution: Fluctuations, stability, and community structure

Uncovering the topology of configuration space networks

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