Gaussian Belief with dynamic data and in dynamic network

In this paper we analyse Belief Propagation over a Gaussian model in a dynamic environment. Recently, this has been proposed as a method to average local measurement values by a distributed protocol ("Consensus Propagation", Moallemi & Van Roy, 2006), where the average is available for read-out at every single node. In the case that the underlying network is constant but the values to be averaged fluctuate ("dynamic data"), convergence and accuracy are determined by the spectral properties of an associated Ruelle-Perron-Frobenius operator. For Gaussian models on Erdos-Renyi graphs, numerical computation points to a spectral gap remaining in the large-size limit, implying exceptionally good scalability. In a model where the underlying network also fluctuates ("dynamic network"), averaging is more effective than in the dynamic data case. Altogether, this implies very good performance of these methods in very large systems, and opens a new field of statistical physics of large (and dynamic) information systems.Comment: 5 pages, 7 figure

Transgressive coastal systems (1st part): barrier migration processes and geometric principles

Coastal processes during transgression have been explored through morpho-kinematic simulations using the Shoreface Translation Model (STM). Our STM experiments show that the landward migration of coastal system is controlled by the rate of sea level rise (SLR), the rate of sediment supply (Vs), the shelf slope (?), and the morphology of the coastal profile (M). Additionally, the geometric relationships between shoreface and plane of translation govern three kinematic modes of coastal barrier migration: (1) roll-over, (2) hybrid, (3) encroachment. Each mode exhibits differences along the coastal profile in relation to zones of erosion (cut) and redeposition (fill) and to the consequent sediment exchanges across the profile (from the cut to the fill). Each mode produces distinctive facies architectures and specific stratigraphic position of the shoreface-ravinement surface. Environmental conditions (rates of sea-level rise, sediment supply (±), barrier morphology) and kinematic modes both control stratal preservation. Transgressive roll-over, in particular, occurs on gently sloping shelves and involves erosion along the entire shoreface and landward sediment redeposition (by overwash and tidal inlet processes). Three different types of roll-over are possible depending on the conditions of sediment supply (Vs) to the coastal cell: neutral roll-over (Vs=0 m3), which produces no effect on the shelf; depositional roll-over (Vs >0) and erosional (Vs<0) roll-over, which modify the shelf through stratal preservation and erosion, respectively. These differences are quantified in simulations by tracking parameters that principally relate to the trajectory of a ‘neutral point’ (maximum depth of shoreface erosion). The shoreface-ravinement defines the trajectory in all the transgressions and in principle is preserved in the rock record, making it a much more useful tracking point than the shoreline trajectory analysed in other studies. Coastal migration in all kinematic modes includes state-dependent inertial effects, experimentally well evident when, after a perturbation, the drivers (SLR, Vs, ?, M) are maintained constant for a long interval of time. Kinematic inertia appears as progressive geometric self-adjustments of the barrier until it acquires a shape that is stable under prevailing conditions (constant drivers). At this stage (kinematic equilibrium), which is unlikely ever to be attained in nature, simulated transgressions finally evolve with processes and geological products that remain invariant. Kinematic inertia is likely to be an additional factor that governs the real transgressions under most circumstances

Transgressive coastal systems (2nd part): geometric principles of stratal preservation on gently sloping continental shelves

This study focuses on the causes and mechanisms of coastal-lithosome preservation during transgressions driven by roll-over processes of barrier migration. Using the Shoreface Translation Model, a large range of idealised coastal settings was simulated to identify the environmental conditions of stratal preservation. Preservation occurs within two broad categories of experimental conditions. The first category relates to transgressive phases evolving under relatively constant conditions in which stratal preservation takes place only if the coastal barrier experiences positive net sediment supplies. The resulting deposits show tabular geometries, have poorly differentiated internal architectures and tend to extend continuously with quite uniform thickness upslope across plain regions of the shelf. In the second category, by comparison, deposits are thicker and stratal preservation is more localised. Moreover preservation occurs as an adaptive morpho-kinematic response to environmental perturbations due to variations in: (1) the ratio of sediment supply (Vs) to accommodation generated by sea-level rise (SLR); (2) the substrate topography; (3) the morphology of the barrier profile. More specifically, changes of the ratio Vs /SLR, where SLR is an approximate surrogate for added accommodation space, directly promotes growth of the barrier (Vs /SLR >> 0) and its subsequent drowning (Vs /SLR?0). The topographic variations of the substrate may include minor irregularities as well as sudden changes in gradient that afford other types of preservation, such as local fills and residual littoral packages. Finally, barrier-profile changes inducing stratal preservation may include the reduction in barrier width and depth of surf base as well as the increment in shoreface concavity and shoreface length. Simplified methods are given for relating the geometry of preserved deposits to rates of sea-level rise and sediment supply over different shelf slopes, and for identifying the position of the shoreline at specific times. Holocene evolution of some coastal deposits from the Tuscan shelf (Italy) is presented in a morpho kinematic reconstruction to illustrate the geometric relationships for stratal preservation

Resonances in a spring-pendulum: algorithms for equivariant singularity theory

A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.