Synchronization reveals topological scales in complex networks

We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well-defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology, and spectral graph analysis.

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

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 different metrics that are able to thoroughly characterize transitive relations. A rigorous analysis of several real networks, which makes use of this formalism and the metrics, is also provided. It is also found that clustered networks can be classified into two main groups: the weak and the 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.

Simple model for nonexponential relaxation in complex fluids

The nonexponential relaxation occurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in any time scale becomes apparent in an effective temperature field, which leads to a hierarchy of relaxation times responsible for the slow relaxation phenomena.

Clustering in complex networks. II. Percolation properties

The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows us to find the critical threshold and the size of the giant component. Numerical simulations confirm the accuracy of our results. In more general terms, we show that weak clustering hinders the onset of the giant component whereas strong clustering favors its appearance. This is a direct consequence of the differences in the k-core structure of the networks, which are found to be totally different depending on the level of clustering. An empirical analysis of a real social network confirms our predictions.

Protein-protein interactions between adenovirus DNA polymerase and nuclear factor I mediate formation of the DNA replication preinitiation complex.

The in vitro adenovirus (Ad) DNA replication system provides an assay to study the interaction of viral and host replication proteins with the DNA template in the formation of the preinitiation complex. This initiation system requires in addition to the origin DNA sequences 1) Ad DNA polymerase (Pol), 2) Ad preterminal protein (pTP), the covalent acceptor for protein-primed DNA replication, and 3) nuclear factor I (NFI), a host cell protein identical to the CCAAT box-binding transcription factor. The interactions of these proteins were studied by coimmunoprecipitation and Ad origin DNA binding assays. The Ad Pol can bind to origin sequences only in the presence of another protein which can be either pTP or NFI. While NFI alone can bind to its origin recognition sequence, pTP does not specifically recognize DNA unless Ad Pol is present. Thus, protein-protein interactions are necessary for the targetting of either Ad Pol or pTP to the preinitiation complex. DNA footprinting demonstrated that the Ad DNA site recognized by the pTP.Pol complex was within the first 18 bases at the end of the template which constitutes the minimal origin of replication. Mutagenesis studies have defined the Ad Pol interaction site on NFI between amino acids 68-150, which overlaps the DNA binding and replication activation domain of this factor. A putative zinc finger on the Ad Pol has been mutated to a product that fails to bind the Ad origin sequences but still interacts with pTP. These results indicate that both protein-protein and protein-DNA interactions mediate specific recognition of the replication origin by Ad DNA polymerase.

Evolution of the Pelagonian carbonate platform complex and the adjacent oceanic realm in response to plate tectonic forcing (Late Triassic and Jurassic), Evvoia, Greece

The Late Triassic and Jurassic platform and the oceanic complexes in Evvoia, Greece, share a complementary plate-tectonic evolution. Shallow marine carbonate deposition responded to changing rates of subsidence and uplift, whilst the adjacent ocean underwent spreading, and then convergence, collision and finally obduction over the platform complex. Late Triassic ocean spreading correlated with platform subsidence and the formation of a long-persisting peritidal passive-margin platform. Incipient drowning occurred from the Sinemurian to the late Middle Jurassic. This subsidence correlated with intra-oceanic subduction and plate convergence that led to supra-subduction calc-alkaline magmatism and the formation of a primitive volcanic arc. During the Middle Jurassic, plate collision caused arc uplift above the carbonate compensation depth (CCD) in the oceanic realm, and related thrust-faulting, on the platform, led to sub-aerial exposures. Patch-reefs developed there during the Late Oxfordian to Kimmeridgian. Advanced oceanic nappe-loading caused platform drowning below the CCD during the Tithonian, which is documented by intercalations of reefal turbidites with non-carbonate radiolarites. Radiolarites and bypass-turbidites, consisting of siliciclastic greywacke, terminate the platform succession beneath the emplaced oceanic nappe during late Tithonian to Valanginian time.

A review of the Tripterygion tripteronotus (Risso, 1810) complex, with a description of a new species from the Mediterranean Sea (Teleostei: Tripterygiidae)

We compared specimens of Tripterygion tripteronotus from 52 localities of the Mediterranean Sea and adjacent waters, using four gene sequences (12S rRNA, tRNA-valine, 16S rRNA and COI) and morphological characters. Two well-differentiated clades with a mean genetic divergence of 6.89±0.73% were found with molecular data, indicating the existence of two different species. These two species have disjunctive geographic distribution areas without any molecular hybrid populations. Subtle but diagnostic morphological differences were also present between the two species. T. tripteronotus is restricted to the northern Mediterranean basin, from the NE coast of Spain to Greece and Turkey, including the islands of Malta and Cyprus. T. tartessicum n. sp. is geographically distributed along the southern coast of Spain, from Cape of La Nao to the Gulf of Cadiz, the Balearic Islands and northern Africa, from Morocco to Tunisia. According to molecular data, these two species could have diverged during the Pliocene glaciations 2.7-3.6 Mya.

Connections between signal processing and complex analysis

We describe one of the research lines of the Grup de Teoria de Funcions de la UAB UB, which deals with sampling and interpolation problems in signal analysis and their connections with complex function theory.

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Geochemical and H-O-Sr-Nd isotope evidence for magmatic processes and meteoric-water interactions in the basal complex of La Gomera, Canary Islands

The plutonic rocks of the Basal Complex of La Gomera, Canary Islands, Spain, were studied by means of major and trace element contents and by H-O-Sr-Nd isotope compositions in order to distinguish primary magmatic characteristics and late-stage alteration products. Deciphering the effects of alteration allowed us to determine primary, plume-related compositions that indicated D- and (18)O-depletion relative to normal upper mantle, supporting the conclusions of earlier studies on the plutonic rocks of Fuerteventura and La Palma. Late-stage alteration took place during the formation of the intrusive series induced by interaction with meteoric water. Inferred isotopic compositions of the meteoric water indicate that the water infiltrated into the rock edifice at a height of about 1500 m above sea level, suggesting the existence of a subaerial volcano which was active during the intrusive activity and that it has been either distroyed or remain buried by later volcanic and landslide events.