A Group-Based Yule Model for Bipartite Author-Paper Networks

This paper presents a novel model for author-paper networks, which is based on the assumption that authors are organized into groups and that, for each research topic, the number of papers published by a group is based on a success-breeds-success model. Collaboration between groups is modeled as random invitations from a group to an outside member. To analyze the model, a number of different metrics that can be obtained in author-paper networks were extracted. A simulation example shows that this model can effectively mimic the behavior of a real-world author-paper network, extracted from a collection of 900 journal papers in the field of complex networks.Comment: 13 pages (preprint format), 7 figure

Power-law distributions from additive preferential redistributions

We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary random interactions with a simple additive preferential rule, while the sum of quantities is conserved. The situation described by this model is similar to those of closed $N$-particle systems when conservative two-body collisions are only allowed. We obtain stationary distributions of these quantities both analytically and numerically while varying parameters of the model, and find that the model exhibits the scaling behavior for some parameter ranges. Unlike well-known growth models, this alternative mechanism generates the power-law distribution when the growth is not expected and the dynamics of the system is based on interactions between elements. This model can be applied to some examples such as personal wealths, city sizes, and the generation of scale-free networks when only rewiring is allowed.Comment: 12 pages, 4 figures; Changed some expressions and notations; Added more explanations and changed the order of presentation in Sec.III while results are the sam

Critical and Near-Critical Branching Processes

Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what happens to these power laws when such conditions are violated. From a branching process model, we predict the behavior of two systems which seem to exhibit near scale-free behavior--rank-frequency distributions of number of subtaxa in biology, and abundance distributions of genotypes in an artificial life system. In the light of these, we discuss distributions of avalanche sizes in the Bak-Tang-Wiesenfeld sandpile model.Comment: 9 pages LaTex with 10 PS figures. v.1 of this paper contains results from non-critical sandpile simulations that were excised from the published versio

Rank Statistics in Biological Evolution

We present a statistical analysis of biological evolution processes. Specifically, we study the stochastic replication-mutation-death model where the population of a species may grow or shrink by birth or death, respectively, and additionally, mutations lead to the creation of new species. We rank the various species by the chronological order by which they originate. The average population N_k of the kth species decays algebraically with rank, N_k ~ M^{mu} k^{-mu}, where M is the average total population. The characteristic exponent mu=(alpha-gamma)/(alpha+beta-gamma)$ depends on alpha, beta, and gamma, the replication, mutation, and death rates. Furthermore, the average population P_k of all descendants of the kth species has a universal algebraic behavior, P_k ~ M/k.Comment: 4 pages, 3 figure

Nanoscale electrochemical visualization of grain-dependent anodic iron dissolution from low carbon steel

The properties of steels and other alloys are often tailored to suit specific applications through the manipulation of microstructure (e.g., grain structure). Such microscopic heterogeneities are also known to modulate corrosion susceptibility/resistance, but the exact dependency remains unclear, largely due to the challenge of probing and correlating local electrochemistry and structure at complex (alloy) surfaces. Herein, high-resolution scanning electrochemical cell microscopy (SECCM) is employed to perform spatially-resolved potentiodynamic polarisation measurements, which, when correlated to co-located structural information from electron backscatter diffraction (EBSD), analytical scanning electron microscopy (SEM) and scanning transmission electron microscopy (STEM), reveal the relationship between anodic metal (iron) dissolution and the crystallographic orientation of low carbon steel in aqueous sulfuric acid (pH 2.3). Considering hundreds of individual measurements made on each of the low-index planes of body-centred cubic (bcc) low carbon steel, the rate of iron dissolution, and thus overall corrosion susceptibility, increases in the order (101) < (111) < (100). These results are rationalized by complementary density functional theory (DFT) calculations, where the experimental rate of iron dissolution correlates with the energy required to remove (and ionise) one iron atom at the surface of a lattice, calculated for each low index orientation. Overall, this study further demonstrates how nanometre-resolved electrochemical techniques such as SECCM can be effectively utilised to vastly improve the understanding of structure-function in corrosion science, particularly when combined with complementary, co-located structural characterisation (EBSD, STEM etc.) and computational analysis (DFT)

Virus-induced gene complementation reveals a transcription factor network in modulation of tomato fruit ripening

Plant virus technology, in particular virus-induced gene silencing, is a widely used reverse- and forward-genetics tool in plant functional genomics. However the potential of virus technology to express genes to induce phenotypes or to complement mutants in order to understand the function of plant genes is not well documented. Here we exploit Potato virus X as a tool for virus-induced gene complementation (VIGC). Using VIGC in tomato, we demonstrated that ectopic viral expression of LeMADS-RIN, which encodes a MADS-box transcription factor (TF), resulted in functional complementation of the non-ripening rin mutant phenotype and caused fruits to ripen. Comparative gene expression analysis indicated that LeMADS-RIN up-regulated expression of the SBP-box (SQUAMOSA promoter binding protein-like) gene LeSPL-CNR, but down-regulated the expression of LeHB-1, an HD-Zip homeobox TF gene. Our data support the hypothesis that a transcriptional network may exist among key TFs in the modulation of fruit ripening in tomato

A Yule-Simon process with memory

The Yule-Simon model has been used as a tool to describe the growth of diverse systems, acquiring a paradigmatic character in many fields of research. Here we study a modified Yule-Simon model that takes into account the full history of the system by means of an hyperbolic memory kernel. We show how the memory kernel changes the properties of preferential attachment and provide an approximate analytical solution for the frequency distribution density as well as for the frequency-rank distribution.Comment: 7 pages, 5 figures; accepted for publication in Europhysics Letter

Power Law Distribution of Wealth in a Money-Based Model

A money-based model for the power law distribution (PLD) of wealth in an economically interacting population is introduced. The basic feature of our model is concentrating on the capital movements and avoiding the complexity of micro behaviors of individuals. It is proposed as an extension of the Equiluz and Zimmermann's (EZ) model for crowding and information transmission in financial markets. Still, we must emphasize that in EZ model the PLD without exponential correction is obtained only for a particular parameter, while our pattern will give it within a wide range. The Zipf exponent depends on the parameters in a nontrivial way and is exactly calculated in this paper.Comment: 5 pages and 4 figure

Dimension reduction for systems with slow relaxation

We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal' model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof