Non-commutative symbolic coding

We give a non-commutative generalization of classical symbolic coding in the presence of a synchronizing word. This is done by a scattering theoretical approach. Classically, the existence of a synchronizing word turns out to be equivalent to asymptotic completeness of the corresponding Markov process. A criterion for asymptotic completeness in general is provided by the regularity of an associated extended transition operator. Commutative and non-commutative examples are analysed.

Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.

Rock art and social life - Revisiting the Neolithic transition in Mediterranean Iberia

This article revisits the Neolithic transition in Mediterranean Iberia taking into account an aspect usually neglected in the archaeological discourse: the rock art styles that emerged in this context. These distinct styles have been generally attributed to different populations, according to a historicist point of view that equates stylistic variability and ethnic identity. However, the recent recognition that they were developed by the same social group requires the formulation of an alternative explanation. My proposal is based on the exploration of the social context of production and consumption of the rock art, through the analysis of the patterns of location of the sites within the landscape and the definition of their archaeological context.