Dictionary-based Tensor Canonical Polyadic Decomposition

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images

Spectral Unmixing with Multiple Dictionaries

Spectral unmixing aims at recovering the spectral signatures of materials, called endmembers, mixed in a hyperspectral or multispectral image, along with their abundances. A typical assumption is that the image contains one pure pixel per endmember, in which case spectral unmixing reduces to identifying these pixels. Many fully automated methods have been proposed in recent years, but little work has been done to allow users to select areas where pure pixels are present manually or using a segmentation algorithm. Additionally, in a non-blind approach, several spectral libraries may be available rather than a single one, with a fixed number (or an upper or lower bound) of endmembers to chose from each. In this paper, we propose a multiple-dictionary constrained low-rank matrix approximation model that address these two problems. We propose an algorithm to compute this model, dubbed M2PALS, and its performance is discussed on both synthetic and real hyperspectral images

Antagonistic Effect of Intestinal Bacteria from the Microflora of Holoxenic (Conventional) Piglets, Against Clostridium Perfringens in the Digestive Tract of Gnotoxenic Mice and Gnotoxenic Piglets

Antagonistic effect of piglet microflora against Clostridium perfringens was studied in germfree mice, to isolate bacterial strains responsible for this colonization resistance. The 1:100 dilution of the feces of a 2 day-old conventional piglet, given per os to germfree mice already harboring C. perfringens, led to the elimination of C. perfringens. From this piglet flora, 8 bacterial strains were selected, belonging to the genera Bacteroides, Clostridium, Eubacterium, Bifidobacterium, Lactobacillus and a strain belonging to the class of Mollicutes. When the 8 strains were given to germfree mice 3 days after C. perfringens inoculation, they led to rapid elimination of C. perfringens from feces. Sixteen other mixtures of 2 to 7 strains were similarly tested, but none was able to fully antagonize C. perfringens. When the 8 strains were given per os to germfree piglets after C. perfringens inoculation, they led to the rapid elimination of C. perfringens from pig feces, and to a quick recovery from diarrhea. This study led to the identification of a simplified fraction of gut microflora, able to exert a barrier effect against C. perfringens comparable to the entire flora of the piglet. This study suggests that gnotoxenic mice can be a suitable model for simplifying the flora responsible for a given effect in another host, animal or human

Non-abelian cubic vertices for higher-spin fields in anti-de Sitter space

We use the Fradkin-Vasiliev procedure to construct the full set of non-abelian cubic vertices for totally symmetric higher spin gauge fields in anti-de Sitter space. The number of such vertices is given by a certain tensor-product multiplicity. We discuss the one-to-one relation between our result and the list of non-abelian gauge deformations in flat space obtained elsewhere via the cohomological approach. We comment about the uniqueness of Vasiliev's simplest higher-spin algebra in relation with the (non)associativity properties of the gauge algebras that we classified. The gravitational interactions for (partially)-massless (mixed)-symmetry fields are also discussed. We also argue that those mixed-symmetry and/or partially-massless fields that are described by one-form connections within the frame-like approach can have nonabelian interactions among themselves and again the number of nonabelian vertices should be given by tensor product multiplicities.Comment: 30 pages, v2: minor corrections, reference adde