122 research outputs found
Bayesian analysis of spectral mixture data using Markov Chain Monte Carlo Methods
This paper presents an original method for the analysis of multicomponent spectral data sets. The proposed algorithm is based on Bayesian estimation theory and Markov Chain Monte Carlo (MCMC) methods. Resolving spectral mixture analysis aims at recovering the unknown component spectra and at assessing the concentrations of the underlying species in the mixtures. In addition to non-negativity constraint, further assumptions are generally needed to get a unique resolution. The proposed statistical approach assumes mutually independent spectra and accounts for the non-negativity and the sparsity of both the pure component spectra and the concentration profiles. Gamma distribution priors are used to translate all these information in a probabilistic framework. The estimation is performed using MCMC methods which lead to an unsupervised algorithm, whose performances are assessed in a simulation study with a synthetic data set
Chow Rings of Matroids as Permutation Representations
Given a matroid and a group of its matroid automorphisms, we study the
induced group action on the Chow ring of the matroid. This turns out to always
be a permutation action. Work of Adiprasito, Huh and Katz showed that the Chow
ring satisfies Poincar\'e duality and the Hard Lefschetz theorem. We lift these
to statements about this permutation action, and suggest further conjectures in
this vein.Comment: 21 pages, 3 figure
Chow Rings of Vector Space Matroids
The Chow ring of a matroid (or more generally, atomic latice) is an invariant
whose importance was demonstrated by Adiprasito, Huh and Katz, who used it to
resolve the long-standing Heron-Rota-Welsh conjecture. Here, we make a detailed
study of the Chow rings of uniform matroids and of matroids of finite vector
spaces. In particular, we express the Hilbert series of such matroids in terms
of permutation statistics; in the full rank case, our formula yields the
maj-exc -Eulerian polynomials of Shareshian and Wachs. We also provide a
formula for the Charney-Davis quantities of such matroids, which can be
expressed in terms of either determinants or -secant numbers
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