A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.

A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

Wavefront reconstruction by adding modulation capabilities of two liquid crystal devices

We analyze the behavior of complex information in the Fresnel domain, taking into account the limited capability to display complex values of liquid crystal devices when they are used as holographic displays. To do this analysis we study the reconstruction of Fresnel holograms at several distances using the different parts of the complex distribution. We also use the information adjusted with a method that combines two configurations of the devices in an adding architecture. The results of the error analysis show different behavior for the reconstructions when using the different methods. Simulated and experimental results are presented.

Effect of cocoa powder on the modulation of inflammatory biomarkers in patients at high risk of cardiovascular disease

Background: Epidemiologic studies have suggested that flavonoid intake plays a critical role in the prevention of coronary heart disease. Because atherosclerosis is considered a low-grade inflammatory disease, some feeding trials have analyzed the effects of cocoa (an important source of flavonoids) on inflammatory biomarkers, but the results have been controversial. Objective: The objective was to evaluate the effects of chronic cocoa consumption on cellular and serum biomarkers related to atherosclerosis in high-risk patients. Design: Forty-two high-risk volunteers (19 men and 23 women; mean 6 SD age: 69.7 6 11.5 y) were included in a randomized crossover feeding trial. All subjects received 40 g cocoa powder with 500 mL skim milk/d (C+M) or only 500 mL skim milk/d (M) for 4 wk. Before and after each intervention period, cellular and serum inflammatory biomarkers related to atherosclerosis were evaluated. Results: Adherence to the dietary protocol was excellent. No significant changes in the expression of adhesion molecules on T lymphocyte surfaces were found between the C+M and M groups. However, in monocytes, the expression of VLA-4, CD40, and CD36 was significantly lower (P = 0.005, 0.028, and 0.001, respectively) after C+M intake than after M intake. In addition, serum concentrations of the soluble endothelium-derived adhesion molecules P-selectin and intercellular adhesion molecule-1 were significantly lower (both P = 0.007) after C+M intake than after M intake. Conclusions: These results suggest that the intake of cocoa polyphenols may modulate inflammatory mediators in patients at high risk of cardiovascular disease. These antiinflammatory effects may contribute to the overall benefits of cocoa consumption against atherosclerosis. This trial was registered in the Current Controlled Trials at London, International Standard Randomized Controlled Trial Number, at controlled-trials.com as ISRCTN75176807.

Epigenetic alterations in hippocampus of SAMP8 senescent mice and modulation by voluntary physical exercise.

The senescence-accelerated SAMP8 mouse model displays features of cognitive decline and Alzheimer's disease. With the purpose of identifying potential epigenetic markers involved in aging and neurodegeneration, here we analyzed the expression of 84 mature miRNAs, the expression of histone-acetylation regulatory genes and the global histone acetylation in the hippocampus of 8-month-old SAMP8 mice, using SAMR1 mice as control. We also examined the modulation of these parameters by 8 weeks of voluntary exercise. Twenty-one miRNAs were differentially expressed between sedentary SAMP8 and SAMR1 mice and seven miRNAs were responsive to exercise in both strains. SAMP8 mice showed alterations in genes involved in protein acetylation homeostasis such as Sirt1 and Hdac6 and modulation of Hdac3 and Hdac5 gene expression by exercise. Global histone H3 acetylation levels were reduced in SAMP8 compared with SAMR1 mice and reached control levels in response to exercise. In sum, data presented here provide new candidate epigenetic markers for aging and neurodegeneration and suggest that exercise training may prevent or delay some epigenetic alterations associated with accelerated aging.

Epigenetic alterations in hippocampus of SAMP8 senescent mice and modulation by voluntary physical exercise.

The senescence-accelerated SAMP8 mouse model displays features of cognitive decline and Alzheimer's disease. With the purpose of identifying potential epigenetic markers involved in aging and neurodegeneration, here we analyzed the expression of 84 mature miRNAs, the expression of histone-acetylation regulatory genes and the global histone acetylation in the hippocampus of 8-month-old SAMP8 mice, using SAMR1 mice as control. We also examined the modulation of these parameters by 8 weeks of voluntary exercise. Twenty-one miRNAs were differentially expressed between sedentary SAMP8 and SAMR1 mice and seven miRNAs were responsive to exercise in both strains. SAMP8 mice showed alterations in genes involved in protein acetylation homeostasis such as Sirt1 and Hdac6 and modulation of Hdac3 and Hdac5 gene expression by exercise. Global histone H3 acetylation levels were reduced in SAMP8 compared with SAMR1 mice and reached control levels in response to exercise. In sum, data presented here provide new candidate epigenetic markers for aging and neurodegeneration and suggest that exercise training may prevent or delay some epigenetic alterations associated with accelerated aging.

Flavonoids affect host-microbiota crosstalk through TLR modulation

Interaction between host cells and microbes is known as crosstalk. Among other mechanisms, this takes place when certain molecules of the micro-organisms are recognized by the toll-like receptors (TLRs) in the body cells, mainly in the intestinal epithelial cells and in the immune cells. TLRs belong to the pattern-recognition receptors and represent the first line of defense against pathogens, playing a pivotal role in both innate and adaptive immunity. Dysregulation in the activity of such receptors can lead to the development of chronic and severe inflammation as well as immunological disorders. Among components present in the diet, flavonoids have been suggested as antioxidant dietary factors able to modulate TLR-mediated signaling pathways. This review focuses on the molecular targets involved in the modulatory action of flavonoids on TLR-mediated signaling pathways, providing an overview of the mechanisms involved in such action. Particular flavonoids have been able to modify the composition of the microbiota, to modulate TLR gene and protein expression, and to regulate the downstream signaling molecules involved in the TLR pathway. These synergistic mechanisms suggest the role of some flavonoids in the preventive effect on certain chronic diseases.

Flavonoids affect host-microbiota crosstalk through TLR modulation

Interaction between host cells and microbes is known as crosstalk. Among other mechanisms, this takes place when certain molecules of the micro-organisms are recognized by the toll-like receptors (TLRs) in the body cells, mainly in the intestinal epithelial cells and in the immune cells. TLRs belong to the pattern-recognition receptors and represent the first line of defense against pathogens, playing a pivotal role in both innate and adaptive immunity. Dysregulation in the activity of such receptors can lead to the development of chronic and severe inflammation as well as immunological disorders. Among components present in the diet, flavonoids have been suggested as antioxidant dietary factors able to modulate TLR-mediated signaling pathways. This review focuses on the molecular targets involved in the modulatory action of flavonoids on TLR-mediated signaling pathways, providing an overview of the mechanisms involved in such action. Particular flavonoids have been able to modify the composition of the microbiota, to modulate TLR gene and protein expression, and to regulate the downstream signaling molecules involved in the TLR pathway. These synergistic mechanisms suggest the role of some flavonoids in the preventive effect on certain chronic diseases.

Families of periodic horseshoe orbits in the restricted three-body problem

We compute families of symmetric periodic horseshoe orbits in the restricted three-body problem. Both the planar and three-dimensional cases are considered and several families are found.We describe how these families are organized as well as the behavior along and among the families of parameters such as the Jacobi constant or the eccentricity. We also determine the stability properties of individual orbits along the families. Interestingly, we find stable horseshoe-shaped orbit up to the quite high inclination of 17◦

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Pancreatic Cancer Cell Glycosylation Regulates Cell Adhesion and Invasion through the Modulation of a2b1 Integrin and E-Cadherin Function

In our previous studies we have described that ST3Gal III transfected pancreatic adenocarcinoma Capan-1 and MDAPanc-28 cells show increased membrane expression levels of sialyl-Lewis x (SLex) along with a concomitant decrease in α2,6-sialic acid compared to control cells. Here we have addressed the role of this glycosylation pattern in the functional properties of two glycoproteins involved in the processes of cancer cell invasion and migration, α2β1 integrin, the main receptor for type 1 collagen, and E-cadherin, responsible for cell-cell contacts and whose deregulation determines cell invasive capabilities. Our results demonstrate that ST3Gal III transfectants showed reduced cell-cell aggregation and increased invasive capacities. ST3Gal III transfected Capan-1 cells exhibited higher SLex and lower α2,6-sialic acid content on the glycans of their α2β1 integrin molecules. As a consequence, higher phosphorylation of focal adhesion kinase tyrosine 397, which is recognized as one of the first steps of integrin-derived signaling pathways, was observed in these cells upon adhesion to type 1 collagen. This molecular mechanism underlies the increased migration through collagen of these cells. In addition, the pancreatic adenocarcinoma cell lines as well as human pancreatic tumor tissues showed colocalization of SLex and E-cadherin, which was higher in the ST3Gal III transfectants. In conclusion, changes in the sialylation pattern of α2β1 integrin and E-cadherin appear to influence the functional role of these two glycoproteins supporting the role of these glycans as an underlying mechanism regulating pancreatic cancer cell adhesion and invasion