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PubMed2000

Phase diagram of an ising model with long-range frustrating interactions: A theoretical analysis

We present a theoretical study of the phase diagram of a frustrated Ising model with nearest-neighbor ferromagnetic interactions and long-range (Coulombic) antiferromagnetic interactions. For nonzero frustration, long-range ferromagnetic order is forbidden, and the ground state of the system consists of phases characterized by periodically modulated structures. At finite temperatures, the phase diagram is calculated within the mean-field approximation. Below the transition line that separates the disordered and the ordered phases, the frustration-temperature phase diagram displays an infinite number of "flowers," each flower being made by an infinite number of modulated phases generated by structure combination branching processes. The specificities introduced by the long-range nature of the frustrating interaction and the limitation of the mean-field approach are finally discussed.

Journal Article↗
PubMed2002

Continuously varying critical exponents in a sandpile model with internal disorder.

A sandpile model with an internal disorder is presented. The updating of critical sites is done according to a stochastic rule (with a probabilistic toppling q). Using a unified mean-field theory and numerical simulations, we have shown that the criticality is ensured for any value of q. The static critical exponents have been calculated and found to be the same as those obtained for the deterministic sandpile model, which is a particular case of the stochastic model. They have a universal q-independent behavior. In the limit of slow driving, we have developed a relation between our model and the branching process in order to compute the size exponent tau. It presents a continuous variation with the parameter of toppling q.

Journal Article↗
PubMed2002

Coevolutionary games on networks.

We study agents on a network playing an iterated Prisoner's dilemma against their neighbors. The resulting spatially extended coevolutionary game exhibits stationary states which are Nash equilibria. After perturbation of these equilibria, avalanches of mutations reestablish a stationary state. Scale-free avalanche distributions are observed that are in accordance with calculations from the Nash equilibria and a confined branching process. The transition from subcritical to critical avalanche dynamics can be traced to a change in the degeneracy of the cooperative macrostate and is observed for many variants of this game.

Journal Article↗
PubMed2005

Dynamics of book sales: endogenous versus exogenous shocks in complex networks.

We present an extensive study of the foreshock and aftershock signatures accompanying peaks of book sales. The time series of book sales are derived from the ranking system of Amazon.com. We present two independent ways of classifying peaks, one based on the acceleration pattern of sales and the other based on the exponent of the relaxation. They are found to be consistent and reveal the coexistence of two types of sales peaks: exogenous peaks occur abruptly and are followed by a power law relaxation, while endogenous sale peaks occur after a progressively accelerating power law growth followed by an approximately symmetrical power law relaxation which is slower than for exogenous peaks. We develop a simple epidemic model of buyers connected within a network of acquaintances which propagates rumors and opinions on books. The comparison between the predictions of the model and the empirical data confirms the validity of the model and suggests in addition that social networks have evolved to converge very close to criticality (here in the sense of critical branching processes of opinion spreading). We test in detail the evidence for a power law distribution of book sales and confirm a previous indirect study suggesting that the fraction of books (density distribution) P (S) of sales S is a power law P(S) approximately 1/ S(1+mu) with mu approximately equal to 2 .

Journal Article↗
PubMed2005

Universality class of one-dimensional directed sandpile models.

A general n-state directed "sandpile" model is introduced. The stationary properties of the n-state model are derived for n<infinity, and analytical arguments based on a central limit theorem show that the model belongs to the universality class of the totally asymmetric Oslo model, with a crossover to uncorrelated branching process behavior for small system sizes. Hence, the central limit theorem allows us to identify the existence of a large universality class of one-dimensional directed sandpile models.

Journal Article↗
PubMed2006

Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks.

The space-time epidemic-type aftershock sequence model is a stochastic branching process in which earthquake activity is classified into background and clustering components and each earthquake triggers other earthquakes independently according to certain rules. This paper gives the probability distributions associated with the largest event in a cluster and their properties for all three cases when the process is subcritical, critical, and supercritical. One of the direct uses of these probability distributions is to evaluate the probability of an earthquake to be a foreshock, and magnitude distributions of foreshocks and nonforeshock earthquakes. To verify these theoretical results, the Japan Meteorological Agency earthquake catalog is analyzed. The proportion of events that have 1 or more larger descendants in total events is found to be as high as about 15%. When the differences between background events and triggered event in the behavior of triggering children are considered, a background event has a probability about 8% to be a foreshock. This probability decreases when the magnitude of the background event increases. These results, obtained from a complicated clustering model, where the characteristics of background events and triggered events are different, are consistent with the results obtained in [Ogata, Geophys. J. Int. 127, 17 (1996)] by using the conventional single-linked cluster declustering method.

Journal Article↗
PubMed2000

dc = 4 is the upper critical dimension for the Bak-Sneppen model.

Numerical results are presented indicating d(c) = 4 as the upper critical dimension for the Bak-Sneppen evolution model. This finding agrees with previous theoretical arguments, but contradicts a recent Letter [Phys. Rev. Lett. 80, 5746 (1998)] that placed d(c) as high as d = 8. In particular, we find that avalanches are compact for all dimensions d< or =4 and are fractal for d>4. Under those conditions, scaling arguments predict a d(c) = 4, where hyperscaling relations hold for d< or =4. Other properties of avalanches, studied for 1< or =d< or =6, corroborate this result. To this end, an improved numerical algorithm is presented that is based on the equivalent branching process.

Algorithms↗
PubMed2001

Autocatalytic polymerization generates persistent random walk of crawling cells.

The autocatalytic polymerization kinetics of the cytoskeletal actin network provides the basic mechanism for a persistent random walk of a crawling cell. It is shown that network remodeling by branching processes near the cell membrane is essential for the bimodal spatial stability of the network which induces a spontaneous breaking of isotropic cell motion. Details of the phenomena are analyzed using a simple polymerization model studied by analytical and simulation methods.

Actins↗
PubMed2002

Tip splittings and phase transitions in the dielectric breakdown model: mapping to the diffusion-limited aggregation model.

We show that the fractal growth described by the dielectric breakdown model exhibits a phase transition in the multifractal spectrum of the growth measure. The transition takes place because the tip splitting of branches forms a fixed angle. This angle is eta dependent but it can be rescaled onto an "effectively" universal angle of the diffusion-limited aggregation branching process. We derive an analytic rescaling relation which is in agreement with numerical simulations. The dimension of the clusters decreases linearly with the angle and the growth becomes non-ractal at an angle close to 74 degrees (which corresponds to eta = 4.0+/-0.3).

Journal Article↗
PubMed2003

Sandpile on scale-free networks.

We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on scale-free (SF) networks, where the threshold height of each node is distributed heterogeneously, given as its own degree. We find that the avalanche size distribution follows a power law with an exponent tau. Applying the theory of the multiplicative branching process, we obtain the exponent tau and the dynamic exponent z as a function of the degree exponent gamma of SF networks as tau=gamma divided by (gamma-1) and z=(gamma-1) divided by (gamma-2) in the range 2 3, with a logarithmic correction at gamma=3. The analytic solution supports our numerical simulation results. We also consider the case of a uniform threshold, finding that the two exponents reduce to the mean-field ones.

Journal Article↗
PubMed2002

Modeling and real-time prediction of classical swine fever epidemics.

We propose a new method to analyze outbreak data of an infectious disease such as classical swine fever. The underlying model is a two-type branching process. It is used to deduce information concerning the epidemic from detected cases. In particular, the method leads to prediction of the future course of the epidemic and hence can be used as a basis for control policy decisions. We test the model with data from the large 1997-1998 classical swine fever epidemic in The Netherlands. It turns out that our results are in good agreement with the data.

Animals↗
PubMed2003

Nonstochastic variation of species-level diversification rates within angiosperms.

Variations in the origination and extinction rates of species over geological time often are linked with a range of factors, including the evolution of key innovations, changes in ecosystem structure, and environmental factors such as shifts in climate and physical geography. Before hypothesizing causality of a single factor, it is critical to demonstrate that the observed variation in diversification is significantly greater than one would expect due to natural stochasticity in the evolutionary branching process. Here, we use a likelihood-ratio test to compare taxonomic rate heterogeneity to a neutral birth-death model, using data on well-supported sister pairs of taxa and their species richness. We test the likelihood that the distribution of extant species among angiosperm genera and families could be the result of constant diversification rates. Results strongly support the conclusion that there is significantly more heterogeneity in diversity at the species level within angiosperms than would be expected due to stochastic processes. This result is consistent in datasets of genus pairs and family pairs and is not affected significantly by degrading pairs to simulate inaccuracy in the assumption of simultaneous origin of sister taxa. When we parse taxon pairs among higher groups of angiosperms, results indicate that a constant rates model is not rejected by rosid and basal eudicot pairs but is rejected by asterid and eumagnoliid pairs. These results provide strong support for the hypothesis that species-level rates of origination and/or extinction have varied nonrandomly within angiosperms and that the magnitude of heterogeneity varies among major groups within angiosperms.

Biological Evolution↗
PubMed1995

An analysis of the growth of the retinal cell population in embryonic chicks yielding proliferative ratios, numbers of proliferative and non-proliferative cells and cell-cycle times for successive generations of cell cycles.

Growth curves of the retinal cell population of embryonic chicks were fitted by a branching-process model of cell population growth, thereby estimating the proliferative ratios and mean cell-cycle times of the generations of cell cycles that underlie retinal growth. The proliferative ratio determines the proportion of cells that divides in the next generation, so the numbers of proliferative and non-proliferative cells in each generation of cell cycles were obtained. The mean cell-cycle times determine the times over which the generations are extant. Assuming growth starts from one cell in generation 0, the proliferative cells reach 3.6 x 10(6) and the non-proliferative cells reach 1.1 x 10(6) by generation 23. The next four generations increase the proliferative cell numbers to 13.9 x 10(6) and produce 20.1 x 10(6) non-proliferative cells. In the next five generations in the end phase of growth, non-proliferative cells are produced in large numbers at an average of 13.9 x 10(6) cells per generation as the retinal lineages are completed. The retinal cell population reaches a maximum estimated here at 98.2 x 10(6) cells. The mean cell-cycle time estimates range between 6.8 and 10.1 h in generations before the end phase of growth and between 10.6 and 17.2 h in generations in the end phase. The retinal cell population growth is limited by the depletion of the proliferative cell population that the production of non-proliferative cells entails. The proliferative ratios and the cell-cycle-time distribution parameters are the likely determinants of retinal growth rates. The results are discussed in relation to other results of spatial and temporal patterns of the cessation of cell cycling in the embryonic chick retina.

Animals↗
PubMed1981

Demonstration of Ia antigens on certain dendritic cells and on a novel elongate cell found in human synovial tissue.

Adherent cells from dissociated human synovial tissue obtained at surgery contain two types of distinctive cells with one or more elongated branching processes that strongly express Ia antigens. One type of cell with Ia antigens is non-phagocytic and resembles the murine dendritic cell. It is primarily found in patients with rheumatoid arthritis and accounts for a considerable proportion of the identifiable cells with a stellate or dendritic morphology. The expression of Ia antigens progressively diminished in culture. The second type of novel cell with Ia antigens was highly elongate and fibroblastoid. It was readily obtained from patients with osteoarthritis. The cell was frequently characterized by a blunt-ended filopodium-like process at one pole of the cell, one or two tapering processes, and zones of microvilli. Evidence was obtained suggesting that this cell, which might otherwise be considered fibroblast-like, is in the mononuclear phagocyte lineage.

Arthritis, Rheumatoid↗
PubMed1976

Growth of deleterious mutant genes in a large population.

Formulae for the arrival probability and first arrival time for a single mutant gene to reach a certain number have been obtained by using a continuous branching process. If the mean of the progeny number of heterozygotes is less than one the arrival probability increases with increasing variance of the progeny distribution whereas if the mean is greater than one the contrary is true. Since most human populations are growing at fairly high rates, the result indicates that the probability for a single mutation to grow to a large number is quite high. Numerical computations show that the mean first arrival time decreases with increasing variance of the progeny distribution of the mutant carriers. The results have been applied to investigate the case of the acheiropodia gene in Brazil. The hypothesis that all acheiropodia genes in Brazil were derived from a single mutation seems to be tenable.

Brazil↗
PubMed1988

Neurite extension and increased expression of RI cyclic AMP-binding protein in ouabain-resistant neuroblastoma mutants.

Morphological and biochemical parameters of neuroblastoma differentiation were assessed in 12 clonal derivatives of the N-18 mouse neuroblastoma cell line selected for their ouabain-resistant (ouar) property. When cultured in a normal growth medium, nine of the 12 ouar cell lines exhibited a more complex pattern of neurite outgrowth than the parental N-18 cells. The morphological pattern most frequently observed with the ouar cells was the extension of several branched processes per cell. This pattern of spontaneous neurite outgrowth in the ouar cell lines can be correlated with an increase in expression of the 47,000-dalton RI cyclic AMP (cAMP)-binding protein. The growth rate, intracellular level of cAMP, and acetylcholinesterase activity of the ouar cell lines were not significantly different from those of the parental N-18 neuroblastoma cells. Treatment of the parental and ouar neuroblastoma cell lines with 1 mM N6, O2-dibutyryl cAMP promoted an elaborate pattern of neurite outgrowth and marked increases in acetylcholinesterase and RI cAMP-binding activities. The distinctive pattern of differentiation phenotype exhibited by the ouar cells and the dibutyryl cAMP-induced differentiated neuroblastoma cell suggests that these two protocols yielded different degrees of differentiation. Furthermore, our results suggest a linkage of the biochemical events underlying ouabain resistance and expression of differentiation phenotypes in the mouse neuroblastoma cells.

Animals↗
PubMed2006

New approximations to the Malthusian parameter.

Approximations to the Malthusian parameter of an age-dependent branching process are obtained in terms of the moments of the lifetime distribution, by exploiting a link with renewal theory. In several examples, the new approximations are more accurate than those currently in use, even when based on only the first two moments. The new approximations are extended to include a form of asymmetric cell division that occurs in some species of yeast. When used for inference, the new approximations are shown to have high efficiency.

Biometry↗
PubMed1987

Electrophysiological properties of ependymal cells (radial glia) in dorsal cortex of the turtle, Pseudemys scripta.

1. We have investigated the electrophysiological properties of ependymal cells in the isolated dorsal cortex of the turtle, Pseudemys scripta. The cell bodies of these radial glia form an epithelium at the ventricular surface, and each cell sends one or more branching processes through the cortex to the pial surface. Very few non-ependymal glia exist in the dorsal cortex. 2. Ependymal cells had high resting membrane potentials (-90 mV), very fast time constants and a lack of intrinsic excitability or synaptic potentials. 3. Changes in the K+ concentration ([K+]) of the bathing solution caused near-Nernstian changes of ependymal membrane potentials. When local neuronal pathways were activated, ependymal cells slowly depolarized while extracellular voltage shifted negatively. Simultaneous measurements of extracellular [K+] ([K+]o) near the impaled ependymal cell body showed that these slow depolarizations were fully accounted for by activity-dependent increases in [K+]o. Similar measurements during focal pressure applications of solutions with high [K+] suggested that intrasomatic recordings reflect predominantly the [K+]o adjacent to the cell body, and not the intracortical process. 4. Intracellular injections of the fluorescent dye Lucifer Yellow CH, and simultaneous recordings from neighbouring cells, indicated that ependymal cells are chemically and electrically coupled to one another. Increasing the ambient CO2 level from 5 to 40% depolarized cells, increased their input resistance, and abolished interglial dye coupling. 5. The physiological properties of ependymal cells are very similar to those of a variety of glial cell types in a range of vertebrate and invertebrate species. In the absence of other types of glia, radial glia may function as the sole cellular mediators of K+ redistribution (i.e. K+ spatial buffering) following neural activity, as well as the generators of slow extracellular potentials.

Action Potentials↗