Numerical assessment of the percolation threshold using complement networks

Models of percolation processes on networks currently assume locally tree-like structures at low densities, and are derived exactly only in the thermodynamic limit. Finite size effects and the presence of short loops in real systems however cause a deviation between the empirical percolation threshold $p_c$ and its model-predicted value $\pi_c$. Here we show the existence of an empirical linear relation between $p_c$ and $\pi_c$ across a large number of real and model networks. Such a putatively universal relation can then be used to correct the estimated value of $\pi_c$. We further show how to obtain a more precise relation using the concept of the complement graph, by investigating on the connection between the percolation threshold of a network, $p_c$, and that of its complement, $\bar{p}_c$

Multiple structural transitions in interacting networks

Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected networks as inter-network interactions are established. We reveal multiple structural transitions for the algebraic connectivity of such systems, between regimes in which each network layer keeps its independent identity or drives diffusive processes over the whole system, thus generalizing previous results reporting a single transition point. Furthermore we show that, at first order in perturbation theory, the growth of the algebraic connectivity of each layer depends only on the degree configuration of the interaction network (projected on the respective Fiedler vector), and not on the actual interaction topology. Our findings can have important implications in the design of robust interconnected networked system, particularly in the presence of network layers whose integrity is more crucial for the functioning of the entire system. We finally show results of perturbation theory applied to the adjacency matrix of the interconnected network, which can be useful to characterize percolation processes on such systems

Fragility and anomalous susceptibility of weakly interacting networks

Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less interlinks than the connections within each layer. For these kinds of structures, both continuous and abrupt phase transition are observed in the size of the giant component. The continuous (second-order) transition corresponds to the formation of a giant cluster inside one layer, and has a well defined percolation threshold. The abrupt transition instead corresponds to the merger of coexisting giant clusters among different layers, and is characterised by a remarkable uncertainty in the percolation threshold, which in turns causes an anomalous trend in the observed susceptibility. We develop a simple mathematical model able to describe this phenomenon and to estimate the critical threshold for which the abrupt transition is more likely to occur. Remarkably, finite-size scaling analysis in the abrupt region supports the hypothesis of a genuine first-order phase transition

Structural changes in the interbank market across the financial crisis from multiple core-periphery analysis

Interbank markets are often characterised in terms of a core-periphery network structure, with a highly interconnected core of banks holding the market together, and a periphery of banks connected mostly to the core but not internally. This paradigm has recently been challenged for short time scales, where interbank markets seem better characterised by a bipartite structure with more core-periphery connections than inside the core. Using a novel core-periphery detection method on the eMID interbank market, we enrich this picture by showing that the network is actually characterised by multiple core-periphery pairs. Moreover, a transition from core-periphery to bipartite structures occurs by shortening the temporal scale of data aggregation. We further show how the global financial crisis transformed the market, in terms of composition, multiplicity and internal organisation of core-periphery pairs. By unveiling such a fine-grained organisation and transformation of the interbank market, our method can find important applications in the understanding of how distress can propagate over financial networks.Comment: 17 pages, 9 figures, 1 tabl

Spacecraft dynamics under the action of Y-dot magnetic control law

The paper investigates the dynamic behavior of a spacecraft when a single magnetic torque-rod is used for achieving a pure spin condition by means of the so-called Y-dot control law. Global asymptotic convergence to a pure spin condition is proven on analytical grounds when the dipole moment is proportional to the rate of variation of the component of the magnetic field along the desired spin axis. Convergence of the spin axis towards the orbit normal is then explained by estimating the average magnetic control torque over one orbit. The validity of the analytical results, based on some simplifying assumptions and approximations, is finally investigated by means of numerical simulation for a fully non-linear attitude dynamic model, featuring a tilted dipole model for Earth׳s magnetic field. The analysis aims to support, in the framework of a sound mathematical basis, the development of effective control laws in realistic mission scenarios. Results are presented and discussed for relevant test cases

Dimensional reduction of solvency contagion dynamics on financial networks

Study of the application of dimensional reduction methods to the propagation of credit shocks within an interbank network, modeled according to the DebtRank dynamics

True scale-free networks hidden by finite size effects

We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned on the basis of statistical testing of the validity of power law distributions of network degrees by contrasting real data. Specifically, we analyze by finite-size scaling analysis the datasets of real networks to check whether purported departures from the power law behavior are due to the finiteness of the sample size. In this case, power laws would be recovered in the case of progressively larger cutoffs induced by the size of the sample. We find that a large number of the networks studied follow a finite size scaling hypothesis without any self-tuning. This is the case of biological protein interaction networks, technological computer and hyperlink networks, and informational networks in general. Marked deviations appear in other cases, especially infrastructure and transportation but also social networks. We conclude that underlying scale invariance properties of many naturally occurring networks are extant features often clouded by finite-size effects due to the nature of the sample data

Conductance crossovers in coherent surface transport on y nanojunctions

Conductance characteristics of a nonplanar two-dimensional electron gas (2DEG) can expose the role of its bending on the 2DEG electronic states. In particular, the presence of an effective geometric potential can be revealed. Here, we present a numerical study of the coherent electron transport on Y nanojunctions of three cylindrical 2DEGs, including a proposal for the experimental detection of the geometric potential. We describe the analytical approach leading to the reduction of the problem dimensionality from 3D to 2D and sketch our simulation scheme. © 2009 IOP Publishing Ltd

Carbon???Carbon Bond Coupling of Vinyl Molecules with an Allenyl Ligand at a Diruthenium Complex

The room-temperature reactions of the diruthenium μ-allenyl complex [Ru2Cp2(CO)2(NCMe){μ-η1:η2-CH═C═CMe2}]BF4, 3-NCMe, with a series of alkenes, RCH═CH2, afforded the complexes [Ru2Cp2(CO)2{μ-η3:η2-CH(R)CHC(Me)C(Me)CH2}]BF4(R═Ph, 4; 4-C6H4Me, 5; Me, 6; nBu, 7; CO2Me, 8; and H, 9), containing an uncommon pentacarbon alkenyl-allyl ligand. Cross experiments with deuterated reagents, i.e., [Ru2Cp2(CO)2(NCMe){μ-η1:η2-CD═C═CMe2}]BF4(3b-NCMe) and CD2═CD(C6H5) (styrene-d3), revealed that the formation of 4-9 is initiated by an attack of the alkene to the central carbon of the allenyl moiety, triggering two distinct C-H activation processes. Compounds 4-9 were characterized by analytical and spectroscopic methods and by single-crystal X-ray diffraction in the cases of 4, 7, and 8. Reported here is the clean coupling on a metallic scaffold between two C2and C3functions invoked in Fischer-Tropsch mechanistic models