Alien Registration- Cyr, Yvonne C. (Madawaska, Aroostook County)

https://digitalmaine.com/alien_docs/35370/thumbnail.jp

Nivat's conjecture holds for sums of two periodic configurations

Nivat's conjecture is a long-standing open combinatorial problem. It concerns two-dimensional configurations, that is, maps $\mathbb Z^2 \rightarrow \mathcal A$ where $\mathcal A$ is a finite set of symbols. Such configurations are often understood as colorings of a two-dimensional square grid. Let $P_c(m,n)$ denote the number of distinct $m \times n$ block patterns occurring in a configuration $c$. Configurations satisfying $P_c(m,n) \leq mn$ for some $m,n \in \mathbb N$ are said to have low rectangular complexity. Nivat conjectured that such configurations are necessarily periodic. Recently, Kari and the author showed that low complexity configurations can be decomposed into a sum of periodic configurations. In this paper we show that if there are at most two components, Nivat's conjecture holds. As a corollary we obtain an alternative proof of a result of Cyr and Kra: If there exist $m,n \in \mathbb N$ such that $P_c(m,n) \leq mn/2$, then $c$ is periodic. The technique used in this paper combines the algebraic approach of Kari and the author with balanced sets of Cyr and Kra.Comment: Accepted for SOFSEM 2018. This version includes an appendix with proofs. 12 pages + references + appendi

Obesity Induces Hypothalamic Endoplasmic Reticulum Stress and Impairs Proopiomelanocortin (POMC) Post-translational Processing

It was shown previously that abnormal prohormone processing or inactive proconverting enzymes that are responsible for this processing cause profound obesity. Our laboratory demonstrated earlier that in the diet-induced obesity (DIO) state, the appetite-suppressing neuropeptide -melanocyte-stimulating hormone ( -MSH) is reduced, yet the mRNA of its precursor protein proopiomelanocortin (POMC) remained unaltered. It was also shown that the DIO condition promotes the development of endoplasmic reticulum (ER) stress and leptin resistance. In the current study, using an in vivo model combined with in vitro experiments, we demonstrate that obesity-induced ER stress obstructs the post-translational processing of POMC by decreasing proconverting enzyme 2, which catalyzes the conversion of adrenocorticotropin to -MSH, thereby decreasing -MSH peptide production. This novel mechanism of ER stress affecting POMC processing in DIO highlights the importance of ER stress in regulating central energy balance in obesity.Fil: Cakir, Isin. Brown University; Estados UnidosFil: Cyr, Nicole E.. Brown University; Estados UnidosFil: Perello, Mario. Brown University; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Litvinov, Bogdan Patedakis. Brown University; Estados UnidosFil: Romero, Amparo. Brown University; Estados UnidosFil: Stuart, Ronald C.. Brown University; Estados UnidosFil: Nillni, Eduardo A.. Brown University; Estados Unido