Generalised Clark-Ocone formulae for differential forms

We generalise the Clark-Ocone formula for functions to give analogous representations for differential forms on the classical Wiener space. Such formulae provide explicit expressions for closed and co-closed differential forms and, as a by-product, a new proof of the triviality of the L^2 de Rham cohomology groups on the Wiener space, alternative to Shigekawa's approach [16] and the chaos-theoretic version [18]. This new approach has the potential of carrying over to curved path spaces, as indicated by the vanishing result for harmonic one-forms in [6]. For the flat path group, the generalised Clark-Ocone formulae can be proved directly using the It\^o map

Characterization of LeCOP1 gene in Lycopersicon esculentum treated with various abiotic and oxidative stresses

A full-length cDNA of LeCOP1 was isolated from tomato (Lycopersicon esculentum). Phylogenetic analysis based on the deduced amino acid sequence of LeCOP1 cDNA revealed high sequence similarity to COP1 protein in Ipomoea nil (84% identity) and in Arabidopsis (77%). LeCOP1 shared high sequence identity with a hypothetical protein in Vitis vinifera and E3 ubiquitin-protein ligase COP1 in Pisum sativum (76%). LeCOP1 gene exists single copy in the tomato genome. Expression of LeCOP1 gene under abiotic and oxidative stresses was investigated, including exposure to 200 mM NaCl, 200 mM mannitol, cold (4°C), 100 ìM abscisic acid (ABA), 10 mM hydrogen peroxide (H2O2) and 50 ìM methyl vilogen (MV). LeCOP1 was significantly respectively induced at 1, 6, and 24 h after mannitol, NaCl and cold treatment. It was also induced after H2O2 treatment at 24 h. However, LeCOP1 was not induced by MV treatment. These observations suggest that LeCOP1 gene may be involved in abiotic and oxidative stresses.Key words: LeCOP1, Lycopersicon esculentum, abiotic stress, oxidative stress

The Application of Two-level Attention Models in Deep Convolutional Neural Network for Fine-grained Image Classification

Fine-grained classification is challenging because categories can only be discriminated by subtle and local differences. Variances in the pose, scale or rotation usually make the problem more difficult. Most fine-grained classification systems follow the pipeline of finding foreground object or object parts (where) to extract discriminative features (what). In this paper, we propose to apply visual attention to fine-grained classification task using deep neural network. Our pipeline integrates three types of attention: the bottom-up attention that propose candidate patches, the object-level top-down attention that selects relevant patches to a certain object, and the part-level top-down attention that localizes discriminative parts. We combine these attentions to train domain-specific deep nets, then use it to improve both the what and where aspects. Importantly, we avoid using expensive annotations like bounding box or part information from end-to-end. The weak supervision constraint makes our work easier to generalize. We have verified the effectiveness of the method on the subsets of ILSVRC2012 dataset and CUB200_2011 dataset. Our pipeline delivered significant improvements and achieved the best accuracy under the weakest supervision condition. The performance is competitive against other methods that rely on additional annotations

On stability of subelliptic harmonic maps with potential

In this paper, we investigate the stability problem of subelliptic harmonic maps with potential. First, we derive the first and second variation formulas for subelliptic harmonic maps with potential. As a result, it is proved that a subelliptic harmonic map with potential is stable if the target manifold has nonpositive curvature and the Hessian of the potential is nonpositive definite. We also give Leung type results which involve the instability of subelliptic harmonic maps with potential when the target manifold is a sphere of dimension $\geq 3$