Cover times for sequences of reversible Markov chains on random graphs

We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (Type 1) is the class of cover times that are of the order of the maximal hitting times scaled by the logarithm of the size of vertex sets. The other type (Type 2) is the class of cover times that are of the order of the maximal hitting times. The conditions are described by some parameters determined by the underlying graphs: the volumes, the diameters with respect to the resistance metric, the coverings or packings by balls in the resistance metric. We apply the conditions to and classify a number of examples, such as supercritical Galton-Watson trees, the incipient infinite cluster of a critical Galton-Watson tree and the Sierpinski gasket graph.Comment: 28 pages, improved proposition 3.

Maximum and minimum of local times for two-dimensional random walk

We obtain the leading orders of the maximum and the minimum of local times for the simple random walk on the two-dimensional torus at time proportional to the cover time. We also estimate the number of points with large (or small) values of the local times. These are analogues of estimates on the two-dimensional Gaussian free fields by Bolthausen, Deuschel, and Giacomin [Ann. Probab., 29 (2001)] and Daviaud [Ann. Probab., 34 (2006)], but we have different exponents from the case of the Gaussian free field.Comment: 1 figur

Evaluation of Patient Positioning during Digital Tomosynthesis and Reconstruction Algorithms for Ilizarov Frames: A Phantom Study

Aim: Metallic components from circular external fixators, including the Ilizarov frame, cause artefacts on X-rays and obstruct clear visualisation of bone detail. We evaluated the ability of tomosynthesis to reduce interference on radiographs caused by metal artefacts and developed an optimal image acquisition method for such cases. Materials and methods: An Ilizarov frame phantom was constructed using rods placed on the bone for the purpose to evaluate the benefits of tomosynthesis. Distances between the rod and bone and the angle between the rod and X-ray tube orbit were set at three different levels. Filtered backprojection images were reconstructed using two different features of the reconstruction function: THICKNESS−− (CONTRAST4) and THICKNESS++ (METAL4); the first is suitable for improving contrast and the second is suitable for metal artefacts. The peak signal-to-noise ratio (PSNR) was used during image evaluation to determine the influence of the metallic rod on bone structure visibility. Results: The PSNR increased as the angle between the metal rod and the X-ray tube orbit and the distance between the metallic rod and bone increased. The PSNR was larger when using THICKNESS−− (CONTRAST4) than when using THICKNESS++ (METAL4). Conclusion: The optimal reconstruction function and image acquisition determined using the metallic rod in this study suggest that quality equal to that without the metallic rod can be obtained. Clinical significance: We describe an optimised method for image acquisition without unnecessary acquisition repetition and unreasonable posture changes when the bone cannot be adequately visualised

RNN Based Auto-tuning of PID Control Gains in Hot StripLooper Controller

In this study, auto tuning of PID control gains in hot strip looper controller is made based on RNN model. Neuro emulator is employed to model the characteristics of looper dynamics. Combining neuro emulator and RNN model, auto tuning system of PID control gains is constructed. As the inputs to RNN, plural evaluation functions which reflect individual preference of human experts. Further, Self learning mechamism is embeded to RNN model which enables adaptation to the change in rolling chracteristics. Through numerical experiments, the effect of the proposed method is ascertained