The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real-world webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with weights) for weighted networks based on the concept of percolating k-cliques with high enough intensity. The algorithm allows overlaps between the modules. First, we give detailed analytical and numerical results about the critical point of weighted k-clique percolation on (weighted) Erdős-Rényi graphs. Then, for a scientist collaboration web and a stock correlation graph we compute three-link weight correlations and with the CPMw the weighted modules. After reshuffling link weights in both networks and computing the same quantities for the randomised control graphs as well, we show that groups of 3 or more strong links prefer to cluster together in both original graphs.

Abstract.-In this paper we introduce a non-fuzzy measure which has been designed to rank the partitions of a network's nodes into overlapping communities. Such a measure can be useful for both quantifying clusters detected by various methods and during finding the overlapping community-structure by optimization methods. The theoretical problem referring to the separation of overlapping modules is discussed, and an example for possible applications is given as well.Introduction. -Networks -in the sense they are used throughout the present paper -are basically graphs describing real-life complex systems taken from the most different scientific areas, but primarily from biology, economy and sociology. According to recent discoveries, reallife networks tend to have some interesting and rather unexpected common properties, such as scale-free degree distribution, strong disposition to form clusters (also called as communities or modules) or having the so called "smallworld" property [1][2][3].

Selective area growth is a promising technique to realize semiconductorsuperconductor hybrid nanowire networks potentially hosting topologically protected Majorana-based qubits. In some cases, however, such as molecular beam epitaxy of InSb on InP or GaAs substrates, nucleation and selective growth conditions do not necessarily overlap. To overcome this challenge we propose Metal-Sown Selective Area Growth (MS SAG) technique which allows decoupling selective deposition and nucleation growth conditions by temporarily isolating these stages. It consists of three steps: (i) selective deposition of In droplets only inside the mask openings at relatively high temperatures favoring selectivity, (ii) nucleation of InSb under Sb flux from In droplets which act as a reservoir of group III adatoms, done at relatively low temperatures favoring nucleation of InSb, (iii) homoepitaxy of InSb on top of formed nucleation Page 3 of 43 ACS Paragon Plus Environment Nano Letters layer under simultaneous supply of In and Sb fluxes at conditions favoring selectivity and high crystal quality. We demonstrate that complex InSb nanowire networks of high crystal and electrical quality can be achieved this way. We extract mobility values of 10,000-25,000 cm V-1 s-1 consistently from field-effect and Hall mobility measurements across single nanowire segments as well as wires with junctions. Moreover, we demonstrate ballistic transport in a 440 nm long channel in a single nanowire under magnetic field below 1 T. We also extract a phase-coherent length of ~8 µm at 50 mK in mesoscopic rings. Semiconductor-superconductor hybrid nanowire (NW) networks are promising candidates for hosting topologically protected Majorana-based qubits, which have a potential to revolutionize the emerging field of quantum computing. 1 The III-V semiconductor InSb is of particular interest in this regard owing to its large g-factor, which enables a relatively small magnetic field to drive a hybrid semiconductor-superconductor NW into the topological regime. Moreover the small effective mass favorably leads to a large subband spacing. 2 So far, mostly single 3 or small-scale networks 4 of InSb NWs were used in Majorana-related transport experiments. To support further progress in the field,

We have developed an experimental setup of very simple self-propelled robots to observe collective motion emerging as a result of inelastic collisions only. A circular pool and commercial RC boats were the basis of our first setup, where we demonstrated that jamming, clustering, disordered and ordered motion are all present in such a simple experiment and showed that the noise level has a fundamental role in the generation of collective dynamics. Critical noise ranges and the transition characteristics between the different collective patterns were also examined. In our second experiment we used a real-time tracking system and a few steerable model boats to introduce intelligent leaders into the flock. We demonstrated that even a very small portion of guiding members can determine group direction and enhance ordering through inelastic collisions. We also showed that noise can facilitate and speed up ordering with leaders. Our work was extended with an agent-based simulation model, too, and high similarity between real and simulation results were observed. The simulation results show clear statistical evidence of three states and negative correlation between density and ordered motion due to the onset of jamming. Our experiments confirm the different theoretical studies and simulation results in the literature about collision-based, noise-dependent and leader-driven self-propelled particle systems. PACS: 05.70.Fh, 05.65.+b, 89.75.Fb Simulation resultsSimilarly to the experiments, the simulations reveal ordered motion in one (with leaders) or in both directions (without leaders) for low noise levels (figure 14).

No abstract