Kauffman Boolean model in undirected scale free networks

We investigate analytically and numerically the critical line in undirected random Boolean networks with arbitrary degree distributions, including scale-free topology of connections $P(k)\sim k^{-\gamma}$. We show that in infinite scale-free networks the transition between frozen and chaotic phase occurs for $3<\gamma < 3.5$. The observation is interesting for two reasons. First, since most of critical phenomena in scale-free networks reveal their non-trivial character for $\gamma<3$, the position of the critical line in Kauffman model seems to be an important exception from the rule. Second, since gene regulatory networks are characterized by scale-free topology with $\gamma<3$, the observation that in finite-size networks the mentioned transition moves towards smaller $\gamma$ is an argument for Kauffman model as a good starting point to model real systems. We also explain that the unattainability of the critical line in numerical simulations of classical random graphs is due to percolation phenomena

Interplay between network structure and self-organized criticality

We investigate, by numerical simulations, how the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model can induce emergence of scale-free (SF) networks and how this emerging structure affects dynamics of the system. We also discuss how the observed phenomenon can be used to explain evolution of scientific collaboration.Comment: 4 pages, 4 figure

Power densities for two-step gamma-ray transitions from isomeric states

We have calculated the incident photon power density P_2 for which the two-step induced emission rate from an isomeric nucleus becomes equal to the natural isomeric decay rate. We have analyzed two-step transitions for isomeric nuclei with a half-life greater than 10 min, for which there is an intermediate state of known energy, spin and half-life, for which the intermediate state is connected by a known gamma-ray transition to the isomeric state and to at least another intermediate state, and for which the relative intensities of the transitions to lower states are known. For the isomeric nucleus 166m-Ho, which has a 1200 y isomeric state at 5.98 keV, we have found a value of P_2=6.3 x 10^7 W cm^{-2}, the intermediate state being the 263.8 keV level. We have found power densities P_2 of the order of 10^{10} W cm^{-2} for several other isomeric nuclei.Comment: 9 pages, 1 eps figure, 1 tabl

Supremacy distribution in evolving networks

We study a supremacy distribution in evolving Barabasi-Albert networks. The supremacy $s_i$ of a node $i$ is defined as a total number of all nodes that are younger than $i$ and can be connected to it by a directed path. For a network with a characteristic parameter $m=1,2,3,...$ the supremacy of an individual node increases with the network age as $t^{(1+m)/2}$ in an appropriate scaling region. It follows that there is a relation $s(k) \sim k^{m+1}$ between a node degree $k$ and its supremacy $s$ and the supremacy distribution $P(s)$ scales as $s^{-1-2/(1+m)}$. Analytic calculations basing on a continuum theory of supremacy evolution and on a corresponding rate equation have been confirmed by numerical simulations.Comment: 4 pages, 4 figure

Leiken, R. S. Europe’s Angry Muslims: The Revolt of the Second Generation. Oxford and New York: Oxford University Press, 2016.

Book review

Thermodynamic forces, flows, and Onsager coefficients in complex networks

We present Onsager formalism applied to random networks with arbitrary degree distribution. Using the well-known methods of non-equilibrium thermodynamics we identify thermodynamic forces and their conjugated flows induced in networks as a result of single node degree perturbation. The forces and the flows can be understood as a response of the system to events, such as random removal of nodes or intentional attacks on them. Finally, we show that cross effects (such as thermodiffusion, or thermoelectric phenomena), in which one force may not only give rise to its own corresponding flow, but to many other flows, can be observed also in complex networks.Comment: 4 pages, 2 figure

Biased random walks on complex networks: the role of local navigation rules

We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to study efficiency of different routing protocols in communication networks. We derive exact expressions for the stationary occupation probability, and for the mean transit time between two nodes. The effect of the cyclic search on transit times is also explored. Results presented in this paper give the basis for theoretical treatment of the transport-related problems on complex networks, including quantitative estimation of the critical value of the packet generation rate.Comment: 5 pages (Phys. Rev style), 3 Figure

Universal scaling of distances in complex networks

Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k_i and k_j equals to =A-B log(k_i k_j). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree _nn calculated for the nearest neighbors and on network clustering coefficients.Comment: 4 pages, 3 figures, 1 tabl

Investigation of the chemocatalytic and biocatalytic valorization of a range of different lignin preparations: The importance of β-O-4 content

A set of seven different lignin preparations was generated from a range of organosolv (acidic, alkaline, ammonia-treated, and dioxane-based), ionic liquid, autohydrolysis, and Kraft pretreatments of lignocelluloses. Each lignin was characterized by 2D HSQC NMR spectroscopy, showing significant variability in the β-O-4 content of the different lignin samples. Each lignin was then valorised using three biocatalytic methods (microbial biotransformation with Rhodococcus jostii RHA045, treatment with Pseudomonas fluorescens Dyp1B or Sphingobacterium sp. T2 manganese superoxide dismutase) and two chemocatalytic methods (catalytic hydrogenation using Pt/alumina catalyst, DDQ benzylic oxidation/Zn reduction). Highest product yields for DDQ/Zn valorization were observed from poplar ammonia percolation-organosolv lignin, which had the highest β-O-4 content of the investigated lignins and also gave the highest yield of syringaldehyde (243 mg L -1 ) when using R. jostii RHA045 and the most enzymatic products using P. fluorescens Dyp1B. The highest product yield from the Pt/alumina hydrogenation was observed using oak dioxasolv lignin, which also had a high β-O-4 content. In general, highest product yields for both chemocatalytic and biocatalytic valorization methods were obtained from preparations that showed highest β-O-4 content, while variable yields were obtained with preparations containing intermediate β-O-4 content, and little or no product was obtained with preparations containing low β-O-4 content