Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities

This paper is concerned with the problem of stochastic stability analysis of discrete-time two-dimensional (2-D) Markovian jump systems (MJSs) described by the Roesser model with interval time-varying delays. The transition probabilities of the jumping process/Markov chain are assumed to be uncertain, that is, they are not exactly known but can be estimated. A Lyapunov-like scheme is first extended to 2-D MJSs with delays. Based on some novel 2-D summation inequalities proposed in this paper, delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities (LMIs) which can be computationally solved by various convex optimization algorithms. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

Markov models and network analysis reveal sex-specific differences in the space-use of a coastal apex predator

Understanding the links between external variables such as habitat and interactions with conspecifics and animal space-use is fundamental to developing effective management measures. In the marine realm, automated acoustic tracking has become a widely used method for monitoring the movement of free-ranging animals, yet researchers generally lack robust methods for analysing the resulting spatial-usage data. In this study, acoustic tracking data from male and female broadnose sevengill sharks Notorynchus cepedianus, collected in a system of coastal embayments in southeast Tasmania were analyzed to examine sex-specific differences in the sharks' coastal space-use and test novel methods for the analysis of acoustic telemetry data. Sex-specific space-use of the broadnose sevengill shark from acoustic telemetry data was analysed in two ways: The recently proposed spatial network analysis of between-receiver movements was employed to identify sex-specific space-use patterns. To include the full breadth of temporal information held in the data, movements between receivers were furthermore considered as transitions between states of a Markov chain, with the resulting transition probability matrix allowing the ranking of the relative importance of different parts of the study area. Both spatial network and Markov chain analysis revealed sex-specific preferences of different sites within the study area. The identification of priority areas differed for the methods, due to the fact that in contrast to network analysis, our Markov chain approach preserves the chronological sequence of detections and accounts for both residency periods and movements. In addition to adding to our knowledge of the ecology of a globally distributed apex predator, this study presents a promising new step towards condensing the vast amounts of information collected with acoustic tracking technology into straightforward results which are directly applicable to the management and conservation of any species that meet the assumptions of our model.

A Markov switching unobserved component analysis of the CDX index term premium

Using a Markov switching unobserved component model we decompose the term premium of the North American CDX index into a permanent and a stationary component. We establish that the inversion of the CDX term premium is induced by sudden changes in the unobserved stationary component, which represents the evolution of the fundamentals underpinning the probability of default in the economy. We find evidence that the monetary policy response from the Fed during the crisis period was effective in reducing the volatility of the term premium. We also show that equity returns make a substantial contribution to the term premium over the entire sample period.

A field model for repairing 3D shapes

This paper proposes a field model for repairing 3D shapes constructed from multi-view RGB data. Specifically, we represent a 3D shape in a Markov random field (MRF) in which the geometric information is encoded by random binary variables and the appearance information is retrieved from a set of RGB images captured at multiple viewpoints. The local priors in the MRF model capture the local structures of object shapes and are learnt from 3D shape templates using a convolutional deep belief network. Repairing a 3D shape is formulated as the maximum a posteriori (MAP) estimation in the corresponding MRF. Variational mean field approximation technique is adopted for the MAP estimation. The proposed method was evaluated on both artificial data and real data obtained from reconstruction of practical scenes. Experimental results have shown the robustness and efficiency of the proposed method in repairing noisy and incomplete 3D shapes.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.