Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Learning Shape Segmentation Using Constrained Spectral Clustering and Probabilistic Label Transfer

International audienceWe propose a spectral learning approach to shape segmentation. The method is composed of a constrained spectral clustering algorithm that is used to supervise the segmentation of a shape from a training data set, followed by a probabilistic label transfer algorithm that is used to match two shapes and to transfer cluster labels from a training-shape to a test-shape. The novelty resides both in the use of the Laplacian embedding to propagate must-link and cannot-link constraints, and in the segmentation algorithm which is based on a learn, align, transfer, and classify paradigm. We compare the results obtained with our method with other constrained spectral clustering methods and we assess its performance based on ground-truth data

Anitigen recognition pathways in allograft rejection

SIGLEAvailable from British Library Document Supply Centre- DSC:DX96130 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Markov modelling and parameterisation of genetic evolutionary test generations

Genetic algorithm, Parameter selection, Markov model, Hardware design verification,