Absence of kinetic effects in reaction-diffusion processes in scale-free networks

We show that the chemical reactions of the model systems of A+A->0 and A+B->0 when performed on scale-free networks exhibit drastically different behavior as compared to the same reactions in normal spaces. The exponents characterizing the density evolution as a function of time are considerably higher than 1, implying that both reactions occur at a much faster rate. This is due to the fact that the discerning effects of the generation of a depletion zone (A+A) and the segregation of the reactants (A+B) do not occur at all as in normal spaces. Instead we observe the formation of clusters of A (A+A reaction) and of mixed A and B (A+B reaction) around the hubs of the network. Only at the limit of very sparse networks is the usual behavior recovered.Comment: 4 pages, 4 figures, to be published in Physical Review Letter

Stability and topology of scale-free networks under attack and defense strategies

We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an intentional attack with insufficient knowledge on the network. We determine, for all strategies, the critical fraction p_c of nodes that must be removed for disintegrating the network. We find that for an intentional attack, little knowledge of the well-connected sites is sufficient to strongly reduce p_c. At criticality, the topology of the network depends on the removal strategy, implying that different strategies may lead to different kinds of percolation transitions.Comment: Accepted in PR

Avoiding catastrophic failure in correlated networks of networks

Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in abrupt failures. This theoretical finding bares an intrinsic paradox: If natural systems organize in interconnected networks, how can they be so stable? Here we provide a solution to this conundrum, showing that the stability of a system of networks relies on the relation between the internal structure of a network and its pattern of connections to other networks. Specifically, we demonstrate that if network inter-connections are provided by hubs of the network and if there is a moderate degree of convergence of inter-network connection the systems of network are stable and robust to failure. We test this theoretical prediction in two independent experiments of functional brain networks (in task- and resting states) which show that brain networks are connected with a topology that maximizes stability according to the theory.Comment: 40 pages, 7 figure

Modularity map of the network of human cell differentiation

Cell differentiation in multicellular organisms is a complex process whose mechanism can be understood by a reductionist approach, in which the individual processes that control the generation of different cell types are identified. Alternatively, a large scale approach in search of different organizational features of the growth stages promises to reveal its modular global structure with the goal of discovering previously unknown relations between cell types. Here we sort and analyze a large set of scattered data to construct the network of human cell differentiation (NHCD) based on cell types (nodes) and differentiation steps (links) from the fertilized egg to a crying baby. We discover a dynamical law of critical branching, which reveals a fractal regularity in the modular organization of the network, and allows us to observe the network at different scales. The emerging picture clearly identifies clusters of cell types following a hierarchical organization, ranging from sub-modules to super-modules of specialized tissues and organs on varying scales. This discovery will allow one to treat the development of a particular cell function in the context of the complex network of human development as a whole. Our results point to an integrated large-scale view of the network of cell types systematically revealing ties between previously unrelated domains in organ functions.Comment: 32 pages, 7 figure

Universality of ac-conduction in anisotropic disordered systems: An effective medium approximation study

Anisotropic disordered system are studied in this work within the random barrier model. In such systems the transition probabilities in different directions have different probability density functions. The frequency-dependent conductivity at low temperatures is obtained using an effective medium approximation. It is shown that the isotropic universal ac-conduction law, $\sigma \ln \sigma=u$, is recovered if properly scaled conductivity ($\sigma$) and frequency ($u$) variables are used.Comment: 5 pages, no figures, final form (with corrected equations

Beating of hemp bast fibres: an examination of a hydro-mechanical treatment on chemical, structural, and nanomechanical property evolutions

In this study, a gradually increased hydro-mechanical treatments duration were applied to native hemp bast fibres with a traditional pulp and paper beating device (laboratory Valley beater). There is often a trade-off between the treatment applied to the fibres and the effect on their integrity. The multimodal analysis provided an understanding of the beating impact on the fibres at multiple scales and the experimental design made it possible to distinguish the effects of hydro- and hydro-mechanical treatment. Porosity analyses showed that beating treatment doubled the macroporosity and possibly reduced nanoporosity between the cellulose microfibrils. The beating irregularly extracted the amorphous components known to be preferentially located in the middle lamellae and the primary cell walls rather than in the secondary walls, the overall increasing the crystallinity of cellulose from 49.3 % to 59.1 %, but a non-significant change in the indentation moduli of the cell wall was observed. In addition, beating treatments with two distinct mechanical severities showed a disorganization of the cellulose conformation, which significant dropped the indention moduli by 11.2 GPa and 8.4 GPa for 10 and 20 minutes of Valley beater hydro-mechanical treatment, respectively, compared to hydro-treated hemp fibres (16.6 GPa). Pearson’s correlation coefficients between physicochemical features and the final indentation moduli were calculated. Strong positive correlations were highlighted between the cellulose crystallinity and rhamnose, galactose and mannose as non-cellulosic polysaccharide components of the cell wall

Explosive Percolation in the Human Protein Homology Network

We study the explosive character of the percolation transition in a real-world network. We show that the emergence of a spanning cluster in the Human Protein Homology Network (H-PHN) exhibits similar features to an Achlioptas-type process and is markedly different from regular random percolation. The underlying mechanism of this transition can be described by slow-growing clusters that remain isolated until the later stages of the process, when the addition of a small number of links leads to the rapid interconnection of these modules into a giant cluster. Our results indicate that the evolutionary-based process that shapes the topology of the H-PHN through duplication-divergence events may occur in sudden steps, similarly to what is seen in first-order phase transitions.Comment: 13 pages, 6 figure

Walks on Apollonian networks

We carry out comparative studies of random walks on deterministic Apollonian networks (DANs) and random Apollonian networks (RANs). We perform computer simulations for the mean first passage time, the average return time, the mean-square displacement, and the network coverage for unrestricted random walk. The diffusions both on DANs and RANs are proved to be sublinear. The search efficiency for walks with various strategies and the influence of the topology of underlying networks on the dynamics of walks are discussed. Contrary to one's intuition, it is shown that the self-avoiding random walk, which has been verified as an optimal strategy for searching on scale-free and small-world networks, is not the best strategy for the DAN in the thermodynamic limit.Comment: 5 pages, 4 figure

Diffusion with random distribution of static traps

The random walk problem is studied in two and three dimensions in the presence of a random distribution of static traps. An efficient Monte Carlo method, based on a mapping onto a polymer model, is used to measure the survival probability P(c,t) as a function of the trap concentration c and the time t. Theoretical arguments are presented, based on earlier work of Donsker and Varadhan and of Rosenstock, why in two dimensions one expects a data collapse if -ln[P(c,t)]/ln(t) is plotted as a function of (lambda t)^{1/2}/ln(t) (with lambda=-ln(1-c)), whereas in three dimensions one expects a data collapse if -t^{-1/3}ln[P(c,t)] is plotted as a function of t^{2/3}lambda. These arguments are supported by the Monte Carlo results. Both data collapses show a clear crossover from the early-time Rosenstock behavior to Donsker-Varadhan behavior at long times.Comment: 4 pages, 6 figure

Temperature dependence of the charge carrier mobility in gated quasi-one-dimensional systems

The many-body Monte Carlo method is used to evaluate the frequency dependent conductivity and the average mobility of a system of hopping charges, electronic or ionic on a one-dimensional chain or channel of finite length. Two cases are considered: the chain is connected to electrodes and in the other case the chain is confined giving zero dc conduction. The concentration of charge is varied using a gate electrode. At low temperatures and with the presence of an injection barrier, the mobility is an oscillatory function of density. This is due to the phenomenon of charge density pinning. Mobility changes occur due to the co-operative pinning and unpinning of the distribution. At high temperatures, we find that the electron-electron interaction reduces the mobility monotonically with density, but perhaps not as much as one might intuitively expect because the path summation favour the in-phase contributions to the mobility, i.e. the sequential paths in which the carriers have to wait for the one in front to exit and so on. The carrier interactions produce a frequency dependent mobility which is of the same order as the change in the dc mobility with density, i.e. it is a comparably weak effect. However, when combined with an injection barrier or intrinsic disorder, the interactions reduce the free volume and amplify disorder by making it non-local and this can explain the too early onset of frequency dependence in the conductivity of some high mobility quasi-one-dimensional organic materials.Comment: 9 pages, 8 figures, to be published in Physical Review