How the fittest compete for leadership: A tale of tails

We investigate how leaders emerge as a consequence of the competitive dynamics between coupled papers in a model citation network. Every paper is allocated an initial fitness depending on its intrinsic quality. Its fitness then involves dynamically as a consequence of the competition between itself and all the other papers in the field. It picks up citations as a result of this adaptive dynamics, becoming a leader if it has the highest citation count at a given time. Extensive analytical and numerical investigations of this model suggest the existence of a universal phase diagram, divided into regions of weak and strong coupling. In the former, we find an "extended" and rather structureless distribution of citation counts among many fit papers; leaders are not necessarily those with the maximal fitness at any given time. By contrast, the strong-coupling region is characterized by a strongly hierarchical distribution of citation counts, that are "localized" among only a few extremely fit papers, and exhibit strong history-to-history fluctuations, as a result of the complex dynamics among papers in the tail of the fitness distribution.

Universality in survivor distributions: Characterizing the winners of competitive dynamics

We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might not survive the predatory dynamics: all stochasticity is brought in by the initial state. Every such initial state leads to a unique and extended pattern of survivors and nonsurvivors, which is known as an attractor of the dynamics. We show that the number of such attractors grows exponentially with system size, so that their exact characterization is limited to only very small systems. Given this, we construct an analytical approach based on inhomogeneous mean-field theory to calculate survival probabilities for arbitrary networks. This powerful (albeit approximate) approach shows how universality arises in survivor distributions via a key concept-the dynamical fugacity. Remarkably, in the large-mass limit, the survivor probability of a node becomes independent of network geometry and assumes a simple form which depends only on its mass and degree.

Unusual electronic properties of clean and disordered zigzag graphene nanoribbons

We revisit the problem of electron transport in clean and disordered zigzag graphene nanoribbons, and expose numerous hitherto unknown peculiar properties of these systems at zero energy, where both sublattices decouple because of chiral symmetry. For clean ribbons, we give a quantitative description of the unusual power-law dispersion of the central energy bands and of its main consequences, including the strong divergence of the density of states near zero energy, and the vanishing of the transverse localization length of the corresponding edge states. In the presence of off-diagonal disorder, which respects the lattice chiral symmetry, all zero-energy localization properties are found to be anomalous. Recasting the problem in terms of coupled Brownian motions enables us to derive numerous asymptotic results by analytical means. In particular the typical conductance gN of a disordered sample of width N and length L is shown to decay as exp(-CNw√L), for arbitrary values of the disorder strength w, while the relative variance of ln gN approaches a non-trivial constant KN. The dependence of the constants CN and KN on the ribbon width N is predicted. From the mere viewpoint of the transfer-matrix formalism, zigzag ribbons provide a case study with many unusual features. The transfer matrix describing propagation through one unit cell of a clean ribbon is not diagonalizable at zero energy. In the disordered case, we encounter non-trivial random matrix products such that all Lyapunov exponents vanish identically.

Slow synaptic dynamics in a network: from exponential to power-law forgetting

We investigate a mean-field model of interacting synapses on a directed neural network. Our interest lies in the slow adaptive dynamics of synapses, which are driven by the fast dynamics of the neurons they connect. Cooperation is modeled from the usual Hebbian perspective, while competition is modeled by an original polarity-driven rule. The emergence of a critical manifold culminating in a tricritical point is crucially dependent on the presence of synaptic competition. This leads to a universal 1/t power-law relaxation of the mean synaptic strength along the critical manifold and an equally universal 1/√[t] relaxation at the tricritical point, to be contrasted with the exponential relaxation that is otherwise generic. In turn, this leads to the natural emergence of long- and short-term memory from different parts of parameter space in a synaptic network, which is the most original and important result of our present investigations.

Estimation of continental Os/Os values by using Os/Os and Nd/Nd ratios in marine manganese nodules

The relationship between (187)Os/(186)Os and (143)Nd/(144)Nd in different manganese nodule fields is used to determine the (187)Os/(186)Os ratio of the continental terrains bounding the major ocean basins. The Atlantic Ocean drainages yield (187)Os/(186)Os of about 11; the Pacific Ocean, between 25 and 36; and the western Indian Ocean, 20. By assuming a two-component continental crust composed of "ultramafic rocks" (high Os concentration, low (187)Os/(186)Os) and "granite" with only radiogenic (187)Os produced in accessory Re-bearing molybdenite, the ultramafic contribution to weathering is about 0.2%. Some or most of this may come from the alteration of oceanic ultramafics.

THE ACTION OF X-RAYS ON EUPLOTES TAYLORI AND ASSOCIATED BACTERIA

1. The minimum lethal dose of x-rays for Euplotes taylori was determined. Under the conditions of this investigation a 220 second exposure (2110 Roentgen units per second) was required to kill the protozoon. Much less exposure was sufficient to kill the associated bacteria. This difference in resistance permits the sterilization of protozoa with comparative ease. 2. Irradiation of Euplotes for 100 to 220 seconds caused a complete but temporary cessation of ciliary activity in many of the organisms, the percentage so affected increasing with the length of irradiation. 3. Pure cultures of Pseudomonas fluorescens and Bacillus coli, K(13), separately irradiated, were found to be killed much more readily than protozoa,-the former in 15 seconds exposure (2530 Roentgen units per second) and the latter in 45 seconds. 4. The death of these organisms by irradiation was not due to the action of toxic products in the medium since separately irradiated media were not found to be toxic. 5. Irradiated bacteria were found unsatisfactory for the nutrition of Euplotes, previously sterilized either by irradiation or washing.

Localization of the maximal entropy random walk

We define a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic random walk if it takes place on a regular lattice, but it is not if the underlying lattice is irregular. In particular, we consider a lattice with weak dilution. We show that the stationary probability of finding a particle performing maximal entropy random walk localizes in the largest nearly spherical region of the lattice which is free of defects. This localization phenomenon, which is purely classical in nature, is explained in terms of the Lifshitz states of a certain random operator.

Random symmetric matrices with a constraint: the spectral density of random impedance networks

We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found recently for the average density of resonances in random impedance networks [Y.V. Fyodorov, J. Phys. A 32, 7429 (1999)]. In the case of banded matrices, the analytical results are compared with those extracted from the numerical solution of Kirchhoff equations for quasi-one-dimensional random impedance networks.

Aging, phase ordering, and conformal invariance

In a variety of systems which exhibit aging, the two-time response function scales as R(t,s) approximately s(-1-a)f(t/s). We argue that dynamical scaling can be extended towards conformal invariance, thus obtaining the explicit form of the scaling function f. This quantitative prediction is confirmed in several spin systems, both for T<T(c) (phase ordering) and T = T(c) (nonequilibrium critical dynamics). The 2D and 3D Ising models with Glauber dynamics are studied numerically, while exact results are available for the spherical model with a nonconserved order parameter, both for short-ranged and long-ranged interactions, as well as for the mean-field spherical spin glass.

Full angular profile of the coherent polarization opposition effect

We use the rigorous vector theory of weak photon localization for a semi-infinite medium composed of nonabsorbing Rayleigh scatterers to compute the full angular profile of the polarization opposition effect. The effect is caused by coherent backscattering of unpolarized incident light and accompanies the well-known backscattering intensity peak.

Models of competitive learning: complex dynamics, intermittent conversions, and oscillatory coarsening

We present two models of competitive learning, which are respectively interfacial (i.e., where the interiors of domains are unaffected by the rules of the model) and cooperative (i.e., where the bulk as well as the interface of an individual domain is governed by the rules of the model) learning. This learning is outcome related, so that spatially and temporally local environments influence the conversion of a given site between one of two different types. We focus here on the behavior of the models at coexistence, which yields critical behavior and the existence of a phase involving a type of coarsening which is oscillatory in nature. In the discussion we speculate on, among other issues, the likely behavior of the models away from coexistence.