Species lifetime distribution for simple models of ecologies

Interpretation of empirical results based on a taxa's lifetime distribution shows apparently conflicting results. Species' lifetime is reported to be exponentially distributed, whereas higher order taxa, such as families or genera, follow a broader distribution, compatible with power law decay. We show that both these evidences are consistent with a simple evolutionary model that does not require specific assumptions on species interaction. The model provides a zero-order description of the dynamics of ecological communities and its species lifetime distribution can be computed exactly. Different behaviors are found: an initial $t^{-3/2}$ power law, emerging from a random walk type of dynamics, which crosses over to a steeper $t^{-2}$ branching process-like regime and finally is cutoff by an exponential decay which becomes weaker and weaker as the total population increases. Sampling effects can also be taken into account and shown to be relevant: if species in the fossil record were sampled according to the Fisher log-series distribution, lifetime should be distributed according to a $t^{-1}$ power law. Such variability of behaviors in a simple model, combined with the scarcity of data available, cast serious doubts on the possibility to validate theories of evolution on the basis of species lifetime data.Comment: 19 pages, 2 figure

Reply to Comment on ``Thermal Model for Adaptive Competition in a Market''

We reply to the Comment of Challet et al. [cond-mat/0004308] on our paper [Phys. Rev. Lett. 83, 4429 (1999)]. We show that the claim of the Comment that the effects of the temperature in the Thermal Minority Game ``can be eliminated by time rescaling'' and consequently the behaviour is ``independent of T'' has no general validity.Comment: 1 page, 1 figur

Laplacian Fractal Growth in Media with Quenched Disorder

We analyze the combined effect of a Laplacian field and quenched disorder for the generation of fractal structures with a study, both numerical and theoretical, of the quenched dielectric breakdown model (QDBM). The growth dynamics is shown to evolve from the avalanches of invasion percolation (IP) to the smooth growth of Laplacian fractals, i. e. diffusion limited aggregation (DLA) and the dielectric breakdown model (DBM). The fractal dimension is strongly reduced with respect to both DBM and IP, due to the combined effect of memory and field screening. This implies a specific relation between the fractal dimension of the breakdown structures (dielectric or mechanical) and the microscopic properties of disordered materials.Comment: 11 pages Latex (revtex), 3 postscript figures included. Submitted to PR

From Minority Games to real markets

We address the question of market efficiency using the Minority Game (MG) model. First we show that removing unrealistic features of the MG leads to models which reproduce a scaling behavior close to what is observed in real markets. In particular we find that i) fat tails and clustered volatility arise at the phase transition point and that ii) the crossover to random walk behavior of prices is a finite size effect. This, on one hand, suggests that markets operate close to criticality, where the market is marginally efficient. On the other it allows one to measure the distance from criticality of real market, using cross-over times. The artificial market described by the MG is then studied as an ecosystem with different_species_ of traders. This clarifies the nature of the interaction and the particular role played by the various populations.Comment: 9 pages, 7 figures, to appear in Quantitative Financ

The iso-Nazarov reaction

The construction of five-membered rings is essential in organic chemistry. In this context, pentannulation reactions that provide a straightforward access to cyclopentenones are of particular interest, as these structures are not only embedded in important molecules such as some prostaglandins, but also serve as versatile building blocks in organic synthesis. This review documents the acid-promoted cycloisomerization of conjugated dienals and linearly-conjugated dienones for the construction of cyclopentenones, a transformation that has been largely eclipsed by the well-known Nazarov reaction, i.e. the acid-promoted cycloisomerization of cross-conjugated ketones.Fil: Riveira, Martín Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Química Rosario. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Química Rosario; ArgentinaFil: Marsili, Lucía A.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Química Rosario. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Química Rosario; ArgentinaFil: Mischne, Mirta Paulina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Química Rosario. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Química Rosario; Argentin

Theory of Self-organized Criticality for Problems with Extremal Dynamics

We introduce a general theoretical scheme for a class of phenomena characterized by an extremal dynamics and quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochastic one with cognitive memory and on other concepts which permit a mathematical characterization of the self-organized nature of the avalanche type dynamics. In addition it is possible to compute the relevant critical exponents directly from the microscopic model. A specific application to Invasion Percolation is presented but the approach can be easily extended to various other problems.Comment: 11 pages Latex (revtex), 3 postscript figures included. Submitted to Europhys. Let

Generalized Dielectric Breakdown Model

We propose a generalized version of the Dielectric Breakdown Model (DBM) for generic breakdown processes. It interpolates between the standard DBM and its analog with quenched disorder, as a temperature like parameter is varied. The physics of other well known fractal growth phenomena as Invasion Percolation and the Eden model are also recovered for some particular parameter values. The competition between different growing mechanisms leads to new non-trivial effects and allows us to better describe real growth phenomena. Detailed numerical and theoretical analysis are performed to study the interplay between the elementary mechanisms. In particular, we observe a continuously changing fractal dimension as temperature is varied, and report an evidence of a novel phase transition at zero temperature in absence of an external driving field; the temperature acts as a relevant parameter for the ``self-organized'' invasion percolation fixed point. This permits us to obtain new insight into the connections between self-organization and standard phase transitions.Comment: Submitted to PR

On the rise and fall of networked societies

We review recent results on the dynamics of social networks which suggest that the interplay between the network formation process and volatility may lead to the occurrence of discontinuous phase transitions and phase coexistence in a large class of models. We then investigate the effects of negative links -- links inhibiting local growth of the network -- and of a geographical distribution of the agents in such models. We show, by extensive numerical simulations, that both effects enhance this phenomenology, i.e. it increases the size of the coexistence region.Comment: 6 pages, 4 figures, Proceedings of Granada Workshop 200