Rich-club connectivity dominates assortativity and transitivity of complex networks

Rich-club, assortativity and clustering coefficients are frequently-used measures to estimate topological properties of complex networks. Here we find that the connectivity among a very small portion of the richest nodes can dominate the assortativity and clustering coefficients of a large network, which reveals that the rich-club connectivity is leveraged throughout the network. Our study suggests that more attention should be payed to the organization pattern of rich nodes, for the structure of a complex system as a whole is determined by the associations between the most influential individuals. Moreover, by manipulating the connectivity pattern in a very small rich-club, it is sufficient to produce a network with desired assortativity or transitivity. Conversely, our findings offer a simple explanation for the observed assortativity and transitivity in many real world networks --- such biases can be explained by the connectivities among the richest nodes.Comment: 5 pages, 2 figures, accepted by Phys. Rev.

Assessing the critical material constraints on low carbon infrastructure transitions

We present an assessment method to analyze whether the disruption in supply of a group of materials endangers the transition to low-carbon infrastructure. We define criticality as the combination of the potential for supply disruption and the exposure of the system of interest to that disruption. Low-carbon energy depends on multiple technologies comprised of a multitude of materials of varying criticality. Our methodology allows us to assess the simultaneous potential for supply disruption of a range of materials. Generating a specific target level of low-carbon energy implies a dynamic roll-out of technology at a specific scale. Our approach is correspondingly dynamic, and monitors the change in criticality during the transition towards a low-carbon energy goal. It is thus not limited to the quantification of criticality of a particular material at a particular point in time. We apply our method to criticality in the proposed UK energy transition as a demonstration, with a focus on neodymium use in electric vehicles. Although we anticipate that the supply disruption of neodymium will decrease, our results show the criticality of low carbon energy generation increases, as a result of increasing exposure to neodymium-reliant technologies. We present a number of potential responses to reduce the criticality through a reduction in supply disruption potential of the exposure of the UK to that disruption

Selective ethylene trimerization by titanium complexes bearing phenoxy-imine ligands: NMR and EPR Spectroscopic studies of the reaction intermediates

The catalyst systems (FI)TiCl₃/MAO (FI = phenoxyimine ligand with an additional aryl–O–CH₃ donor) display exceptionally high activity in selective ethylene trimerization. By means of NMR and EPR spectroscopy, the nature of the Ti species formed in the catalyst systems (FI)TiCl₃/MAO, (FI)TiCl₃/MMAO, and (FI)TiCl₃/AlR₃/[Ph₃C]⁺[B(C₆F₅)₄]⁻ (R = Me, Et, ⁱBu) has been studied. It was shown that outer-sphere ion pairs of the type [(FI)TiIVMe₂]⁺[A]⁻ ([A]− = [MeMAO]⁻, [MeMMAO]⁻, [B(C₆F₅)₄]⁻) are formed at the initial stage of the reaction of (FI)TiCl₃ with MAO, MMAO, and AlMe₃/[Ph₃C]⁺[B(C₆F₅)₄]⁻. These ion pairs further partially convert into TiIII and TiII species. In the systems (FI)TiCl₃/MAO and (FI)TiCl₃/AlMe₃/[Ph₃C]⁺[B(C₆F5)₄]⁻, complexes with the proposed structures (FI)TiIIIMe₂, (FI)TiIICl, and [(FI)TiII(S)]⁺[A]⁻ ([A]− = [MeMAO]⁻, [B(C₆F₅)4)]⁻, S = solvent, vacancy) were observed (concentrations of TiIII species was lower than those of the TiII congeners). In contrast, in the system (FI)TiCl₃/MMAO, the concentrations of TiIII species (ion pairs of the type [(FI)TiIII(μ-H)(μ-Cl)AlⁱBu₂]⁺[MeMMAO]⁻) were higher than those of the TiII counterparts (ion pairs [(FI)TiII(S)]⁺[MeMMAO]⁻). The system (FI)TiCl₃/MMAO displays lower activity and selectivity in 1-hexene formation, in comparison to (FI)TiCl₃/MAO, due to undesirable PE generation. Probably, TiII and TiIV ion pairs are those participating in ethylene trimerization

Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinski-Moriya anisotropic antisymmetric interaction

Thermal entanglement of a two-qubit Heisenberg chain in presence of the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction and entanglement teleportation when using two independent Heisenberg chains as quantum channel are investigated. It is found that the DM interaction can excite the entanglement and teleportation fidelity. The output entanglement increases linearly with increasing value of input one, its dependences on the temperature, DM interaction and spin coupling constant are given in detail. Entanglement teleportation will be better realized via antiferromagnetic spin chain when the DM interaction is turned off and the temperature is low. However, the introduction of DM interaction can cause the ferromagnetic spin chain to be a better quantum channel for teleportation. A minimal entanglement of the thermal state in the model is needed to realize the entanglement teleportation regardless of antiferromagnetic or ferromagnetic spin chains.Comment: 1 tex;5eps. accepted by Physical Review