Flow Motifs Reveal Limitations of the Static Framework to Represent Human interactions

Networks are commonly used to define underlying interaction structures where infections, information, or other quantities may spread. Although the standard approach has been to aggregate all links into a static structure, some studies suggest that the time order in which the links are established may alter the dynamics of spreading. In this paper, we study the impact of the time ordering in the limits of flow on various empirical temporal networks. By using a random walk dynamics, we estimate the flow on links and convert the original undirected network (temporal and static) into a directed flow network. We then introduce the concept of flow motifs and quantify the divergence in the representativity of motifs when using the temporal and static frameworks. We find that the regularity of contacts and persistence of vertices (common in email communication and face-to-face interactions) result on little differences in the limits of flow for both frameworks. On the other hand, in the case of communication within a dating site (and of a sexual network), the flow between vertices changes significantly in the temporal framework such that the static approximation poorly represents the structure of contacts. We have also observed that cliques with 3 and 4 vertices con- taining only low-flow links are more represented than the same cliques with all high-flow links. The representativity of these low-flow cliques is higher in the temporal framework. Our results suggest that the flow between vertices connected in cliques depend on the topological context in which they are placed and in the time sequence in which the links are established. The structure of the clique alone does not completely characterize the potential of flow between the vertices

On Clifford Subalgebras, Spacetime Splittings and Applications

Z2-gradings of Clifford algebras are reviewed and we shall be concerned with an alpha-grading based on the structure of inner automorphisms, which is closely related to the spacetime splitting, if we consider the standard conjugation map automorphism by an arbitrary, but fixed, splitting vector. After briefly sketching the orthogonal and parallel components of products of differential forms, where we introduce the parallel [orthogonal] part as the space [time] component, we provide a detailed exposition of the Dirac operator splitting and we show how the differential operator parallel and orthogonal components are related to the Lie derivative along the splitting vector and the angular momentum splitting bivector. We also introduce multivectorial-induced alpha-gradings and present the Dirac equation in terms of the spacetime splitting, where the Dirac spinor field is shown to be a direct sum of two quaternions. We point out some possible physical applications of the formalism developed.Comment: 22 pages, accepted for publication in International Journal of Geometric Methods in Modern Physics 3 (8) (2006

Quantum critical superconductors in string theory and M-theory

We construct zero-temperature solutions of supergravity theories in five and four dimensions which interpolate between two copies of anti-de Sitter space, one of which preserves an abelian gauge symmetry while the other breaks it. These domain wall solutions can be lifted to solutions of type IIB string theory and eleven-dimensional supergravity. They describe quantum critical behavior and emergent relativistic conformal symmetry in a superfluid or superconducting state of a strongly coupled dual gauge theory. We include computations of frequency-dependent conductivities which exhibit power law scaling in the infrared, with exponents determined by irrelevant perturbations to the symmetry-breaking anti-de Sitter background.Comment: 5 pages, 3 figures. v2: References slightly improved, mentioned F^F constrain

Bulk viscosity of strongly coupled plasmas with holographic duals

We explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field. Whereas earlier investigations required the computation of the leading dissipative term in the dispersion relation for sound waves, our method requires only the leading frequency dependence of an appropriate Green's function in the low-frequency limit. With a scalar potential chosen to mimic the equation of state of QCD, we observe a slight violation of the lower bound on the ratio of the bulk and shear viscosities conjectured in arXiv:0708.3459.Comment: 33 pages, 3 figure

Study of models of the sine-Gordon type in flat and curved spacetime

We study a new family of models of the sine-Gordon type, starting from the sine-Gordon model, including the double sine-Gordon, the triple one, and so on. The models appears as deformations of the starting model, with the deformation controlled by two parameters, one very small, used to control a linear expansion on it, and the other, which specifies the particular model in the family of models. We investigate the presence of topological defects, showing how the solutions can be constructed explicitly from the topological defects of the sine-Gordon model itself. In particular, we delve into the double sine-Gordon model in a braneworld scenario with a single extra dimension of infinite extent, showing that a stable gravity scenario is admissible. Also, we briefly show that the deformation procedure can be used iteratively, leading to a diversity of possibilities to construct families of models of the sine-Gordon type.Comment: 8 pages, 7 figures; Title changed, author and new results included; version to appear in EPJ