Clustering in complex networks. I. General formalism

We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in that it involves the properties of two --and not just one-- vertices. The formalism is completed with the definition of a three-vertex correlation function, which is the fundamental quantity describing the properties of clustered networks. The formalism suggests new metrics that are able to thoroughly characterize transitive relations. A rigorous analysis of several real networks, which makes use of the new formalism and the new metrics, is also provided. It is also found that clustered networks can be classified into two main groups: the {\it weak} and the {\it strong transitivity} classes. In the first class, edge multiplicity is small, with triangles being disjoint. In the second class, edge multiplicity is high and so triangles share many edges. As we shall see in the following paper, the class a network belongs to has strong implications in its percolation properties

Covalently Binding the Photosystem I to Carbon Nanotubes

We present a chemical route to covalently couple the photosystem I (PS I) to carbon nanotubes (CNTs). Small linker molecules are used to connect the PS I to the CNTs. Hybrid systems, consisting of CNTs and the PS I, promise new photo-induced transport phenomena due to the outstanding optoelectronic properties of the robust cyanobacteria membrane protein PS I

Enhancement of quantum dot peak-spacing fluctuations in the fractional q uantum Hall regime

The fluctuations in the spacing of the tunneling resonances through a quantum dot have been studied in the quantum Hall regime. Using the fact that the ground-state of the system is described very well by the Laughlin wavefunction, we were able to determine accurately, via classical Monte Carlo calculations, the amplitude and distribution of the peak-spacing fluctuations. Our results clearly demonstrate a big enhancement of the fluctuations as the importance of the electronic correlations increases, namely as the density decreases and filling factor becomes smaller. We also find that the distribution of the fluctuations approaches a Gaussian with increasing density of random potentials.Comment: 6 pages, 3 figures all in gzipped tarred fil

Transmission through a n interacting quantum dot in the Coulomb blockade regime

The influence of electron-electron (e-e) interactions on the transmission through a quantum dot is investigated numerically for the Coulomb blockade regime. For vanishing magnetic fields, the conductance peak height statistics is found to be independent of the interactions strength. It is identical to the statistics predicted by constant interaction single electron random matrix theory and agrees well with recent experiments. However, in contrast to these random matrix theories, our calculations reproduces the reduced sensitivity to magnetic flux observed in many experiments. The relevant physics is traced to the short range Coulomb correlations providing thus a unified explanation for the transmission statistics as well as for the large conductance peak spacing fluctuations observed in other experiments.Comment: Final version as publishe

The Metropolis and Evangelical Life: Coherence and Fragmentation in the ‘Lost City of London’

This article examines the interplay of different processes of cultural and subjective fragmentation experienced by conservative evangelical Anglicans, based on an ethnographic study of a congregation in central London. The author focuses on the evangelistic speaking practices of members of this church to explore how individuals negotiate contradictory norms of interaction as they move through different city spaces, and considers their response to tensions created by the demands of their workplace and their religious lives. Drawing on Georg Simmel’s ‘The Metropolis and Mental Life’, the author argues that their faith provides a sense of coherence and unity that responds to experiences of cultural fragmentation characteristic of everyday life in the city, while simultaneously leading to a specific consciousness of moral fragmentation that is inherent to conservative evangelicalism

Understanding the social in a digital age

Datafication, algorithms, social media and their various assemblages enable massive connective processes, enriching personal interaction and amplifying the scope and scale of public networks. At the same time, surveillance capitalists and the social quantification sector are committed to monetizing every aspect of human communication, all of which threaten ideal social qualities, such as togetherness and connection. This Special Issue brings together a range of voices and provocations around ‘the social’, all of which aim to critically interrogate mediated human connection and their contingent socialities. Conventional methods may no longer be adequate, and we must rethink not only the fabric of the social but the very tools we use to make sense of our changing social formations. This Special Issue raises shared concerns with what the social means today, unpicking and rethinking the seams between digitization and social life that characterize today’s digital age

Size scaling of the addition spectra in silicon quantum dots

We investigate small artificial quantum dots obtained by geometrically controlled resistive confinement in low mobility silicon-on-insulator nanowires. Addition spectra were recorded at low temperature for various dot areas fixed by lithography. We compare the standard deviation of the addition spectra with theory in the high electron concentration regime. We find that the standard deviation scales as the inverse area of the dot and its absolute value is comparable to the energy spacing of the one particle spectrum.Comment: 4 pages, 5 figure

Addition Spectra of Chaotic Quantum Dots: Interplay between Interactions and Geometry

We investigate the influence of interactions and geometry on ground states of clean chaotic quantum dots using the self-consistent Hartree-Fock method. We find two distinct regimes of interaction strength: While capacitive energy fluctuations $\delta \chi$ follow approximately a random matrix prediction for weak interactions, there is a crossover to a regime where $\delta \chi$ is strongly enhanced and scales roughly with interaction strength. This enhancement is related to the rearrangement of charges into ordered states near the dot edge. This effect is non-universal depending on dot shape and size. It may provide additional insight into recent experiments on statistics of Coulomb blockade peak spacings.Comment: 4 pages, final version to appear in Phys. Rev. Let

Quantum and frustration effects on fluctuations of the inverse compressibility in two-dimensional Coulomb glasses

We consider interacting electrons in a two-dimensional quantum Coulomb glass and investigate by means of the Hartree-Fock approximation the combined effects of the electron-electron interaction and the transverse magnetic field on fluctuations of the inverse compressibility. Preceding systematic study of the system in the absence of the magnetic field identifies the source of the fluctuations, interplay of disorder and interaction, and effects of hopping. Revealed in sufficiently clean samples with strong interactions is an unusual right-biased distribution of the inverse compressibility, which is neither of the Gaussian nor of the Wigner-Dyson type. While in most cases weak magnetic fields tend to suppress fluctuations, in relatively clean samples with weak interactions fluctuations are found to grow with the magnetic field. This is attributed to the localization properties of the electron states, which may be measured by the participation ratio and the inverse participation number. It is also observed that at the frustration where the Fermi level is degenerate, localization or modulation of electrons is enhanced, raising fluctuations. Strong frustration in general suppresses effects of the interaction on the inverse compressibility and on the configuration of electrons.Comment: 15 pages, 18 figures, To appear in Phys. Rev.

Finite temperature effects in Coulomb blockade quantum dots and signatures of spectral scrambling

The conductance in Coulomb blockade quantum dots exhibits sharp peaks whose spacings fluctuate with the number of electrons. We derive the temperature-dependence of these fluctuations in the statistical regime and compare with recent experimental results. The scrambling due to Coulomb interactions of the single-particle spectrum with the addition of an electron to the dot is shown to affect the temperature-dependence of the peak spacing fluctuations. Spectral scrambling also leads to saturation in the temperature dependence of the peak-to-peak correlator, in agreement with recent experimental results. The signatures of scrambling are derived using discrete Gaussian processes, which generalize the Gaussian ensembles of random matrices to systems that depend on a discrete parameter -- in this case, the number of electrons in the dot.Comment: 14 pages, 4 eps figures included, RevTe