Dispersion spreading of polarization-entangled states of light and two-photon interference

We study the interference structure of the second-order intensity correlation function for polarization-entangled two-photon light obtained from type-II collinear frequency-degenerate spontaneous parametric down-conversion (SPDC). The structure is visualised due to the spreading of the two-photon amplitude as two-photon light propagates through optical fibre with group-velocity dispersion (GVD). Because of the spreading, polarization-entangled Bell states can be obtained without any birefringence compensation at the output of the nonlinear crystal; instead, proper time selection of the intensity correlation function is required. A birefringent material inserted at the output of the nonlinear crystal (either reducing the initial o-e delay between the oppositely polarized twin photons or increasing this delay) leads to a more complicated interference structure of the correlation function.Comment: Extended version of our recent PRL paper. Submitted to PR

Elite opinion and foreign policy in post-communist Russia

Russian elite opinion on matters of foreign policy may be classified as ‘Liberal Westerniser’, ‘Pragmatic Nationalist’ and ‘Fundamentalist Nationalist’, terms that reflect longstanding debates about the country’s relationship with the outside world. An analysis of press statements and election manifestoes together with a programme of elite interviews between 2004 and 2006 suggests a clustering of opinion on a series of strategic issues. Liberal Westernisers seek the closest possible relationship with Europe, and favour eventual membership of the EU and NATO. Pragmatic Nationalists are more inclined to favour practical co-operation, and do not assume an identity of values or interests with the Western countries. Fundamentalist Nationalists place more emphasis on the other former Soviet republics, and on Asia as much as Europe, and see the West as a threat to Russian values as well as to its state interests. Each of these positions, in turn, draws on an identifiable set of domestic constituencies: Liberal Westernisers on the promarket political parties, Pragmatic Nationalists on the presidential administration and defence and security ministries, and Fundamentalist Nationalists on the Orthodox Church and Communists

The interplay of microscopic and mesoscopic structure in complex networks

Not all nodes in a network are created equal. Differences and similarities exist at both individual node and group levels. Disentangling single node from group properties is crucial for network modeling and structural inference. Based on unbiased generative probabilistic exponential random graph models and employing distributive message passing techniques, we present an efficient algorithm that allows one to separate the contributions of individual nodes and groups of nodes to the network structure. This leads to improved detection accuracy of latent class structure in real world data sets compared to models that focus on group structure alone. Furthermore, the inclusion of hitherto neglected group specific effects in models used to assess the statistical significance of small subgraph (motif) distributions in networks may be sufficient to explain most of the observed statistics. We show the predictive power of such generative models in forecasting putative gene-disease associations in the Online Mendelian Inheritance in Man (OMIM) database. The approach is suitable for both directed and undirected uni-partite as well as for bipartite networks

Efficient ultrafast all-optical modulation in a nonlinear crystalline gallium phosphide nanodisk at the anapole excitation

High–refractive index nanostructured dielectrics have the ability to locally enhance electromagnetic fields with low losses while presenting high third-order nonlinearities. In this work, we exploit these characteristics to achieve efficient ultrafast all-optical modulation in a crystalline gallium phosphide (GaP) nanoantenna through the optical Kerr effect (OKE) and two-photon absorption (TPA) in the visible/near-infrared range. We show that an individual GaP nanodisk can yield differential reflectivity modulations of up to ~40%, with characteristic modulation times between 14 and 66 fs, when probed at the anapole excitation (AE). Numerical simulations reveal that the AE represents a unique condition where both the OKE and TPA contribute with the same modulation sign, maximizing the response. These findings highly outperform previous reports on sub–100-fs all-optical switching from resonant nanoscale dielectrics, which have demonstrated modulation depths no larger than 0.5%, placing GaP nanoantennas as a promising choice for ultrafast all-optical modulation at the nanometer scale

Statistical Inference for Valued-Edge Networks: Generalized Exponential Random Graph Models

Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a ubiquitous means of analysis. However, they are limited by an inability to model networks with valued edges. We solve this problem by introducing a class of generalized exponential random graph models capable of modeling networks whose edges are valued, thus greatly expanding the scope of networks applied researchers can subject to statistical analysis

Joint Cosmological Formation of QSOs and Bulge-dominated Galaxies

Older and more recent pieces of observational evidence suggest a strong connection between QSOs and galaxies; in particular, the recently discovered correlation between black hole and galactic bulge masses suggests that QSO activity is directly connected to the formation of galactic bulges. The cosmological problem of QSO formation is analyzed in the framework of an analytical model for galaxy formation; for the first time a joint comparison with galaxy and QSO observables is performed. In this model it is assumed that the same physical variable which determines galaxy morphology is able to modulate the mass of the black hole responsible for QSO activity. Both halo spin and the occurence of a major merger are considered as candidates to this role. The predictions of the model are compared to available data for the type-dependent galaxy mass functions, the star-formation history of elliptical galaxies, the QSO luminosity function and its evolution (including the obscured objects contributing to the hard-X-ray background), the mass function of dormant black holes and the distribution of black-hole -- bulge mass ratios. A good agreement with observations is obtained if the halo spin modulates the efficiency of black-hole formation, and if the galactic halos at $z=0$ have shone in an inverted order with respect to the hierarchical one (i.e., stars and black holes in bigger galactic halos have formed before those in smaller ones). This inversion of hierarchical order for galaxy formation, which reconciles galaxy formation with QSO evolution, is consistent with many pieces of observational evidence.Comment: 20 pages, figures included, mn.sty, in press on MNRAS, fig 6 changed (new data added at z=4.4

Modern temporal network theory: A colloquium

The power of any kind of network approach lies in the ability to simplify a complex system so that one can better understand its function as a whole. Sometimes it is beneficial, however, to include more information than in a simple graph of only nodes and links. Adding information about times of interactions can make predictions and mechanistic understanding more accurate. The drawback, however, is that there are not so many methods available, partly because temporal networks is a relatively young field, partly because it more difficult to develop such methods compared to for static networks. In this colloquium, we review the methods to analyze and model temporal networks and processes taking place on them, focusing mainly on the last three years. This includes the spreading of infectious disease, opinions, rumors, in social networks; information packets in computer networks; various types of signaling in biology, and more. We also discuss future directions.Comment: Final accepted versio