Shape anisotropy of polymers in disordered environment

We study the influence of structural obstacles in a disordered environment on the size and shape characteristics of long flexible polymer macromolecules. We use the model of self-avoiding random walks on diluted regular lattices at the percolation threshold in space dimensions d=2, 3. Applying the Pruned-Enriched Rosenbluth Method (PERM), we numerically estimate rotationally invariant universal quantities such as the averaged asphericity A_d and prolateness S of polymer chain configurations. Our results quantitatively reveal the extent of anisotropy of macromolecules due to the presence of structural defects.Comment: 8 page

The Effect of Disease-induced Mortality on Structural Network Properties

As the understanding of the importance of social contact networks in the spread of infectious diseases has increased, so has the interest in understanding the feedback process of the disease altering the social network. While many studies have explored the influence of individual epidemiological parameters and/or underlying network topologies on the resulting disease dynamics, we here provide a systematic overview of the interactions between these two influences on population-level disease outcomes. We show that the sensitivity of the population-level disease outcomes to the combination of epidemiological parameters that describe the disease are critically dependent on the topological structure of the population's contact network. We introduce a new metric for assessing disease-driven structural damage to a network as a population-level outcome. Lastly, we discuss how the expected individual-level disease burden is influenced by the complete suite of epidemiological characteristics for the circulating disease and the ongoing process of network compromise. Our results have broad implications for prediction and mitigation of outbreaks in both natural and human populations.Comment: 23 pages, 6 figure

From brain to earth and climate systems: Small-world interaction networks or not?

We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with commonly used time series analysis based approaches to network characterization

Kinetic-growth self-avoiding walks on small-world networks

Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz small-world networks, rewired from a two-dimensional square lattice. The maximum length L of this kind of walks is limited in regular lattices by an attrition effect, which gives finite values for its mean value . For random networks, this mean attrition length scales as a power of the network size, and diverges in the thermodynamic limit (large system size N). For small-world networks, we find a behavior that interpolates between those corresponding to regular lattices and randon networks, for rewiring probability p ranging from 0 to 1. For p < 1, the mean self-intersection and attrition length of kinetically-grown walks are finite. For p = 1, grows with system size as N^{1/2}, diverging in the thermodynamic limit. In this limit and close to p = 1, the mean attrition length diverges as (1-p)^{-4}. Results of approximate probabilistic calculations agree well with those derived from numerical simulations.Comment: 10 pages, 7 figure

Kinetic growth walks on complex networks

Kinetically grown self-avoiding walks on various types of generalized random networks have been studied. Networks with short- and long-tailed degree distributions $P(k)$ were considered ($k$, degree or connectivity), including scale-free networks with $P(k) \sim k^{-\gamma}$. The long-range behaviour of self-avoiding walks on random networks is found to be determined by finite-size effects. The mean self-intersection length of non-reversal random walks, , scales as a power of the system size $N$: $ \sim N^{\beta}$, with an exponent $\beta = 0.5$ for short-tailed degree distributions and $\beta < 0.5$ for scale-free networks with $\gamma < 3$. The mean attrition length of kinetic growth walks, , scales as $\sim N^{\alpha}$, with an exponent $\alpha$ which depends on the lowest degree in the network. Results of approximate probabilistic calculations are supported by those derived from simulations of various kinds of networks. The efficiency of kinetic growth walks to explore networks is largely reduced by inhomogeneity in the degree distribution, as happens for scale-free networks.Comment: 10 pages, 8 figure

Self-avoiding walks on scale-free networks

Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAWs) are expected to be more suitable than unrestricted random walks to explore various kinds of real-life networks. Here we study long-range properties of random SAWs on scale-free networks, characterized by a degree distribution $P(k) \sim k^{-\gamma}$. In the limit of large networks (system size $N \to \infty$), the average number $s_n$ of SAWs starting from a generic site increases as $\mu^n$, with $\mu = / - 1$. For finite $N$, $s_n$ is reduced due to the presence of loops in the network, which causes the emergence of attrition of the paths. For kinetic growth walks, the average maximum length, $$, increases as a power of the system size: $\sim N^{\alpha}$, with an exponent $\alpha$ increasing as the parameter $\gamma$ is raised. We discuss the dependence of $\alpha$ on the minimum allowed degree in the network. A similar power-law dependence is found for the mean self-intersection length of non-reversal random walks. Simulation results support our approximate analytical calculations.Comment: 9 pages, 7 figure

A Quality and Cost Approach for Comparison of Small-World Networks

We propose an approach based on analysis of cost-quality tradeoffs for comparison of efficiency of various algorithms for small-world network construction. A number of both known in the literature and original algorithms for complex small-world networks construction are shortly reviewed and compared. The networks constructed on the basis of these algorithms have basic structure of 1D regular lattice with additional shortcuts providing the small-world properties. It is shown that networks proposed in this work have the best cost-quality ratio in the considered class.Comment: 27 pages, 16 figures, 1 tabl

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com

Access to recorded interviews: A research agenda

Recorded interviews form a rich basis for scholarly inquiry. Examples include oral histories, community memory projects, and interviews conducted for broadcast media. Emerging technologies offer the potential to radically transform the way in which recorded interviews are made accessible, but this vision will demand substantial investments from a broad range of research communities. This article reviews the present state of practice for making recorded interviews available and the state-of-the-art for key component technologies. A large number of important research issues are identified, and from that set of issues, a coherent research agenda is proposed

Heusler 4.0: Tunable Materials

Heusler compounds are a large family of binary, ternary and quaternary compounds that exhibit a wide range of properties of both fundamental and potential technological interest. The extensive tunability of the Heusler compounds through chemical substitutions and structural motifs makes the family especially interesting. In this article we highlight recent major developments in the field of Heusler compounds and put these in the historical context. The evolution of the Heusler compounds can be described by four major periods of research. In the latest period, Heusler 4.0 has led to the observation of a variety of properties derived from topology that includes: topological metals with Weyl and Dirac points; a variety of non-collinear spin textures including the very recent observation of skyrmions at room temperature; and giant anomalous Hall effects in antiferromagnetic Heuslers with triangular magnetic structures. Here we give a comprehensive overview of these major achievements and set research into Heusler materials within the context of recent emerging trends in condensed matter physics