Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry

The box-ball system is an integrable cellular automaton on one dimensional lattice. It arises from either quantum or classical integrable systems by the procedures called crystallization and ultradiscretization, respectively. The double origin of the integrability has endowed the box-ball system with a variety of aspects related to Yang-Baxter integrable models in statistical mechanics, crystal base theory in quantum groups, combinatorial Bethe ansatz, geometric crystals, classical theory of solitons, tau functions, inverse scattering method, action-angle variables and invariant tori in completely integrable systems, spectral curves, tropical geometry and so forth. In this review article, we demonstrate these integrable structures of the box-ball system and its generalizations based on the developments in the last two decades.Comment: 73 page

Adipocytes promote malignant growth of breast tumours with monocarboxylate transporter 2 expression via β-hydroxybutyrate

Adipocytes are the most abundant stromal partners in breast tissue. However, the crosstalk between breast cancer cells and adipocytes has been given less attention compared to cancer-associated fibroblasts. Here we find, through systematic screening, that primary mammary gland-derived adipocytes (MGDAs) promote growth of breast cancer cells that express monocarboxylate transporter 2 (MCT2) both in vitro and in vivo. We show that β-hydroxybutyrate is secreted by MGDAs and is required to enhance breast cancer cells malignancy in vitro. Consistently, β-hydroxybutyrate is sufficient to promote tumorigenesis of a mouse xenograft model of MCT2-expressing breast cancer cells. Mechanistically we observe that upon co-culturing with MGDAs or treatment with β-hydroxybutyrate, breast cancer cells expressing MCT2 increase the global histone H3K9 acetylation and upregulate several tumour-promoting genes. These results suggest that adipocytes promote malignancy of MCT2-expressing breast cancer via β-hydroxybutyrate potentially by inducing the epigenetic upregulation of tumour-promoting genes