Duality theory for convex/quasiconvex functions and its application to optimization

In this paper an intuitive and geometric approach is presented explaining the basic ideas of convex/quasiconvex analysis and its relation to duality theory. As such, this paper does not contain new results but serves as a hopefully easy introduction to the most important results in duality theory for convex/quasiconvex functions on locally convex real topological vector spaces. Moreover, its connection to optimization is also discussed

Modulation of gut microbiota by antibiotics improves insulin signalling in high-fat fed mice

FAPESP – FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ – CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOA high-fat dietary intake induces obesity and subclinical inflammation, which play important roles in insulin resistance. Recent studies have suggested that increased concentrations of circulating lipopolysaccharide (LPS), promoted by changes in intestinal permeability, may have a pivotal role in insulin resistance. Thus, we investigated the effect of gut microbiota modulation on insulin resistance and macrophage infiltration. Swiss mice were submitted to a high-fat diet with antibiotics or pair-feeding for 8 weeks. Metagenome analyses were performed on DNA samples from mouse faeces. Blood was collected to determine levels of glucose, insulin, LPS, cytokines and acetate. Liver, muscle and adipose tissue proteins were analysed by western blotting. In addition, liver and adipose tissue were analysed, blinded, using histology and immunohistochemistry. Antibiotic treatment greatly modified the gut microbiota, reducing levels of Bacteroidetes and Firmicutes, overall bacterial count and circulating LPS levels. This modulation reduced levels of fasting glucose, insulin, TNF-alpha and IL-6; reduced activation of toll-like receptor 4 (TLR4), c-Jun N-terminal kinase (JNK), inhibitor of kappa light polypeptide gene enhancer in B cells, kinase beta (IKK beta) and phosphorylated IRS-1 Ser307; and consequently improved glucose tolerance and insulin tolerance and action in metabolically active tissues. In addition, there was an increase in portal levels of circulating acetate, which probably contributed to an increase in 5'-AMP-activated protein kinase (AMPK) phosphorylation in mice. We observed a striking reduction in crown-like structures (CLS) and F4/80(+) macrophage cells in the adipose tissue of antibiotic-treated mice. These results suggest that modulation of gut microbiota in obesity can improve insulin signalling and glucose tolerance by reducing circulating LPS levels and inflammatory signalling. Modulation also appears to increase levels of circulating acetate, which activates AMPK and finally leads to reduced macrophage infiltration551028232834FAPESP – FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ – CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP – FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ – CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGIC