Neumann and Bargmann systems associated with an extension of the coupled KdV hierarchy

An eigenvalue problem with a reference function and the corresponding hierarchy of nonlinear evolution equations are proposed. The bi-Hamiltonian structure of the hierarchy is established by using the trace identity. The isospectral problem is nonlinearized as to be finite-dimensional completely integrable systems in Liouville sense under Neumann and Bargmann constraints

Dependency Grammar Induction with Neural Lexicalization and Big Training Data

We study the impact of big models (in terms of the degree of lexicalization) and big data (in terms of the training corpus size) on dependency grammar induction. We experimented with L-DMV, a lexicalized version of Dependency Model with Valence and L-NDMV, our lexicalized extension of the Neural Dependency Model with Valence. We find that L-DMV only benefits from very small degrees of lexicalization and moderate sizes of training corpora. L-NDMV can benefit from big training data and lexicalization of greater degrees, especially when enhanced with good model initialization, and it achieves a result that is competitive with the current state-of-the-art.Comment: EMNLP 201

Active Methylene-based Multicomponent Reactions under Microwave Heating

The use of emerging multicomponent reactions (MCRs) in conjunction with microwave (MW)-assisted chemistry techniques is dramatically reducing chemical waste and reaction times in several organic syntheses and chemical transformations. MW-assisted active methylene-based multicomponent reactions serve as a rapid and efficient tool for the synthesis of versatile heterocycles, particularly those containing structural diversity and complexity via a one-pot operation. This minireview covers our recent advances on multicomponent reactions involving active methylene compounds for the construction of bioactive molecule skeletons. In many cases, MW-assisted MCRs offer considerable improvements in selectivity, chemical yield and purity and constitutes a very simple and extremely rapid method to access a diverse range of heterocyclic motifs

The Coexistence of a Community of Species with Limited Competition

AbstractThis paper is a study of a system modeling a biological community of species with limited competition. The community consists of two competing subcommunities, all species of which cooperate, and some species of one subcommunity can invade the steady state of another subcommunity, whereas others cannot. Sufficient conditions are given that all species can coexist. For Lotka–Volterra systems we can improve this result by showing that there is a unique, globally asymptotically stable steady state

Disruption of Vitamin D and Calcium Signaling in Keratinocytes Predisposes to Skin Cancer.

1,25 dihydroxyvitamin D (1,25(OH)2D), the active metabolite of vitamin D, and calcium regulate epidermal differentiation. 1,25(OH)2D exerts its effects through the vitamin D receptor (VDR), a transcription factor in the nuclear hormone receptor family, whereas calcium acts through the calcium sensing receptor (Casr), a membrane bound member of the G protein coupled receptor family. We have developed mouse models in which the Vdr and Casr have been deleted in the epidermis ((epid) Vdr (-∕-) and (epid) Casr (-∕-)). Both genotypes show abnormalities in calcium induced epidermal differentiation in vivo and in vitro, associated with altered hedgehog (HH) and β-catenin signaling that when abnormally expressed lead to basal cell carcinomas (BCC) and trichofolliculomas, respectively. The Vdr (-∕-) mice are susceptible to tumor formation following UVB or chemical carcinogen exposure. More recently we found that the keratinocytes from these mice over express long non-coding RNA (lncRNA) oncogenes such as H19 and under express lncRNA tumor suppressors such as lincRNA-21. Spontaneous tumors have not been observed in either the (epid) Vdr (-∕-) or (epid) Casr (-∕-). But in mice with epidermal specific deletion of both Vdr and Casr ((epid) Vdr (-∕-)/(epid) Casr (-∕-) [DKO]) tumor formation occurs spontaneously when the DKO mice are placed on a low calcium diet. These results demonstrate important interactions between vitamin D and calcium signaling through their respective receptors that lead to cancer when these signals are disrupted. The roles of the β-catenin, hedgehog, and lncRNA pathways in predisposing the epidermis to tumor formation when vitamin D and calcium signaling are disrupted will be discussed