Semitoric integrable systems on symplectic 4-manifolds

Let M be a symplectic 4-manifold. A semitoric integrable system on M is a pair of real-valued smooth functions J, H on M for which J generates a Hamiltonian S^1-action and the Poisson brackets {J,H} vanish. We shall introduce new global symplectic invariants for these systems; some of these invariants encode topological or geometric aspects, while others encode analytical information about the singularities and how they stand with respect to the system. Our goal is to prove that a semitoric system is completely determined by the invariants we introduce

Scale-free memory model for multiagent reinforcement learning. Mean field approximation and rock-paper-scissors dynamics

A continuous time model for multiagent systems governed by reinforcement learning with scale-free memory is developed. The agents are assumed to act independently of one another in optimizing their choice of possible actions via trial-and-error search. To gain awareness about the action value the agents accumulate in their memory the rewards obtained from taking a specific action at each moment of time. The contribution of the rewards in the past to the agent current perception of action value is described by an integral operator with a power-law kernel. Finally a fractional differential equation governing the system dynamics is obtained. The agents are considered to interact with one another implicitly via the reward of one agent depending on the choice of the other agents. The pairwise interaction model is adopted to describe this effect. As a specific example of systems with non-transitive interactions, a two agent and three agent systems of the rock-paper-scissors type are analyzed in detail, including the stability analysis and numerical simulation. Scale-free memory is demonstrated to cause complex dynamics of the systems at hand. In particular, it is shown that there can be simultaneously two modes of the system instability undergoing subcritical and supercritical bifurcation, with the latter one exhibiting anomalous oscillations with the amplitude and period growing with time. Besides, the instability onset via this supercritical mode may be regarded as "altruism self-organization". For the three agent system the instability dynamics is found to be rather irregular and can be composed of alternate fragments of oscillations different in their properties.Comment: 17 pages, 7 figur

St. Joseph's Church Work Dispute

Five letters from J.P. Kirwan regarding a dispute over payment for the work done to St. Joseph's Church in San Jose

St. Joseph's Church Kirwan Receipts

Five receipts of payment by Fr. Nobili for work done at St. Joseph's Church in San Jose by J.P. Kirwan, 1853 to 1855

Increasing Whole Grain Intake as Part of Prevention and Treatment of Nonalcoholic Fatty Liver Disease

In conjunction with the rise in rates of obesity, there has been an increase in the rate of nonalcoholic fatty liver disease (NAFLD). While NAFLD at least partially originates from poor diet, there is a lack of nutritional recommendations for patients with suspected or confirmed diagnosis of NAFLD, beyond eating a healthy diet, increasing physical activity, and emphasising weight loss. The limited current literature suggests that there may be opportunities to provide more tailored dietary advice for people diagnosed with or at risk of NAFLD. Epidemiological studies consistently find associations between whole grain intake and a reduced risk of obesity and related diseases, yet no work has been done on the potential of whole grains to prevent and/or be a part of the treatment for fatty liver diseases. In this review, we examine the potential and the current evidence for whole grains having an impact on NAFLD. Due to their nutrient and phytochemical composition, switching from consuming mainly refined grains to whole grains should be considered as part of the nutritional guidelines for patients diagnosed with or at risk for fatty liver disease

Increasing Whole Grain Intake as Part of Prevention and Treatment of Nonalcoholic Fatty Liver Disease

In conjunction with the rise in rates of obesity, there has been an increase in the rate of nonalcoholic fatty liver disease (NAFLD). While NAFLD at least partially originates from poor diet, there is a lack of nutritional recommendations for patients with suspected or confirmed diagnosis of NAFLD, beyond eating a healthy diet, increasing physical activity, and emphasising weight loss. The limited current literature suggests that there may be opportunities to provide more tailored dietary advice for people diagnosed with or at risk of NAFLD. Epidemiological studies consistently find associations between whole grain intake and a reduced risk of obesity and related diseases, yet no work has been done on the potential of whole grains to prevent and/or be a part of the treatment for fatty liver diseases. In this review, we examine the potential and the current evidence for whole grains having an impact on NAFLD. Due to their nutrient and phytochemical composition, switching from consuming mainly refined grains to whole grains should be considered as part of the nutritional guidelines for patients diagnosed with or at risk for fatty liver disease

Exercise Training Rapidly Increases Hepatic Insulin Extraction in NAFLD

Purpose We aimed to determine the immediacy of exercise intervention on liver-specific metabolic processes in nonalcoholic fatty liver disease. Methods We undertook a short-term (7-d) exercise training study (60 min.d(-1) treadmill walking at 80%-85% of maximal heart rate) in obese adults (N= 13, 58 +/- 3 yr, 34.3 +/- 1.1 kg.m(-2), >5% hepatic lipid by(1)H-magnetic resonance spectroscopy). Insulin sensitivity index was estimated by oral glucose tolerance test using the Soonthorpun model. Hepatic insulin extraction (HIE) was calculated as the molar difference in area under the curve (AUC) for insulin and C-peptide (HIE = 1 - (AUC(Insulin)/AUC(C-Pep))). Results The increases in HIE, (V) over dotO(2max), and insulin sensitivity index after the intervention were 9.8%, 9.8%, and 34%, respectively (all,P< 0.05). Basal fat oxidation increased (pre: 47 +/- 6 mg.min(-1)vs post: 65 +/- 6 mg.min(-1),P< 0.05) and carbohydrate oxidation decreased (pre: 160 +/- 20 mg.min(-1)vs post: 112 +/- 15 mg.min(-1),P< 0.05) with exercise training. After the intervention, HIE correlated positively with adiponectin (r= 0.56,P< 0.05) and negatively with TNF-alpha (r= -0.78,P< 0.001). Conclusions By increasing HIE along with peripheral insulin sensitivity, aerobic exercise training rapidly reverses some of the underlying physiological mechanisms associated with nonalcoholic fatty liver disease, in a weight loss-independent manner. This reversal could potentially act through adipokine-related pathways