Some Applications of the Extended Bendixson-Dulac Theorem

During the last years the authors have studied the number of limit cycles of several families of planar vector fields. The common tool has been the use of an extended version of the celebrated Bendixson-Dulac Theorem. The aim of this work is to present an unified approach of some of these results, together with their corresponding proofs. We also provide several applications.Comment: 19 pages, 3 figure

RTP801 regulates motor cortex synaptic transmission and learning.

BACKGROUND: RTP801/REDD1 is a stress-regulated protein whose upregulation is necessary and sufficient to trigger neuronal death in in vitro and in vivo models of Parkinson's and Huntington's diseases and is up regulated in compromised neurons in human postmortem brains of both neurodegenerative disorders. Indeed, in both Parkinson's and Huntington's disease mouse models, RTP801 knockdown alleviates motor-learning deficits. RESULTS: We investigated the physiological role of RTP801 in neuronal plasticity and we found RTP801 in rat, mouse and human synapses. The absence of RTP801 enhanced excitatory synaptic transmission in both neuronal cultures and brain slices from RTP801 knock-out (KO) mice. Indeed, RTP801 KO mice showed improved motor learning, which correlated with lower spine density but increased basal filopodia and mushroom spines in the motor cortex layer V. This paralleled with higher levels of synaptosomal GluA1 and TrkB receptors in homogenates derived from KO mice motor cortex, proteins that are associated with synaptic strengthening. CONCLUSIONS: Altogether, these results indicate that RTP801 has an important role modulating neuronal plasticity and motor learning. They will help to understand its role in neurodegenerative disorders where RTP801 levels are detrimentally upregulated

Darboux integrability and Algebraic limit cycles for a class of polynomial differential Systems

Agraïments: The first and third authors are partially supported by NNSF of China grant No. 10671123 and by a CICYT grant No. 2005SGR 00550. The third author is also partially supported by NCET of China grant No. 050391.This paper deals with the existence of Darboux first integrals for the planar polynomial differential systems ˙x = λx − y + Pn+1(x, y) + xF2n(x, y), ˙y = x + λy + Qn+1(x, y)+yF2n(x, y), where Pi(x, y), Qi(x, y) and Fi(x, y) are homogeneous polynomials of degree i. Inside this class we identify some new Darboux integrable systems having either a focus or a center at the origin. For such Darboux integrable systems having degrees 5 and 9 we give the explicit expressions of their algebraic limit cycles. For the systems having degrees 3, 5, 7 and 9 we present necessary and sufficient conditions for being Darboux integrable

Gene Expression Changes in the Prefrontal Cortex, Anterior Cingulate Cortex and Nucleus Accumbens of Mood Disorders Subjects That Committed Suicide

Suicidal behaviors are frequent in mood disorders patients but only a subset of them ever complete suicide. Understanding predisposing factors for suicidal behaviors in high risk populations is of major importance for the prevention and treatment of suicidal behaviors. The objective of this project was to investigate gene expression changes associated with suicide in brains of mood disorder patients by microarrays (Affymetrix HG-U133 Plus2.0) in the dorsolateral prefrontal cortex (DLPFC: 6 Non-suicides, 15 suicides), the anterior cingulate cortex (ACC: 6NS, 9S) and the nucleus accumbens (NAcc: 8NS, 13S). ANCOVA was used to control for age, gender, pH and RNA degradation, with P≤0.01 and fold change±1.25 as criteria for significance. Pathway analysis revealed serotonergic signaling alterations in the DLPFC and glucocorticoid signaling alterations in the ACC and NAcc. The gene with the lowest p-value in the DLPFC was the 5-HT2A gene, previously associated both with suicide and mood disorders. In the ACC 6 metallothionein genes were down-regulated in suicide (MT1E, MT1F, MT1G, MT1H, MT1X, MT2A) and three were down-regulated in the NAcc (MT1F, MT1G, MT1H). Differential expression of selected genes was confirmed by qPCR, we confirmed the 5-HT2A alterations and the global down-regulation of members of the metallothionein subfamilies MT 1 and 2 in suicide completers. MTs 1 and 2 are neuro-protective following stress and glucocorticoid stimulations, suggesting that in suicide victims neuroprotective response to stress and cortisol may be diminished. Our results thus suggest that suicide-specific expression changes in mood disorders involve both glucocorticoids regulated metallothioneins and serotonergic signaling in different regions of the brain

Worldwide trends in diabetes since 1980: a pooled analysis of 751 population-based studies with 4.4 million participants

BACKGROUND: One of the global targets for non-communicable diseases is to halt, by 2025, the rise in the age-standardised adult prevalence of diabetes at its 2010 levels. We aimed to estimate worldwide trends in diabetes, how likely it is for countries to achieve the global target, and how changes in prevalence, together with population growth and ageing, are affecting the number of adults with diabetes. METHODS: We pooled data from population-based studies that had collected data on diabetes through measurement of its biomarkers. We used a Bayesian hierarchical model to estimate trends in diabetes prevalence—defined as fasting plasma glucose of 7·0 mmol/L or higher, or history of diagnosis with diabetes, or use of insulin or oral hypoglycaemic drugs—in 200 countries and territories in 21 regions, by sex and from 1980 to 2014. We also calculated the posterior probability of meeting the global diabetes target if post-2000 trends continue. FINDINGS: We used data from 751 studies including 4 372 000 adults from 146 of the 200 countries we make estimates for. Global age-standardised diabetes prevalence increased from 4·3% (95% credible interval 2·4–7·0) in 1980 to 9·0% (7·2–11·1) in 2014 in men, and from 5·0% (2·9–7·9) to 7·9% (6·4–9·7) in women. The number of adults with diabetes in the world increased from 108 million in 1980 to 422 million in 2014 (28·5% due to the rise in prevalence, 39·7% due to population growth and ageing, and 31·8% due to interaction of these two factors). Age-standardised adult diabetes prevalence in 2014 was lowest in northwestern Europe, and highest in Polynesia and Micronesia, at nearly 25%, followed by Melanesia and the Middle East and north Africa. Between 1980 and 2014 there was little change in age-standardised diabetes prevalence in adult women in continental western Europe, although crude prevalence rose because of ageing of the population. By contrast, age-standardised adult prevalence rose by 15 percentage points in men and women in Polynesia and Micronesia. In 2014, American Samoa had the highest national prevalence of diabetes (>30% in both sexes), with age-standardised adult prevalence also higher than 25% in some other islands in Polynesia and Micronesia. If post-2000 trends continue, the probability of meeting the global target of halting the rise in the prevalence of diabetes by 2025 at the 2010 level worldwide is lower than 1% for men and is 1% for women. Only nine countries for men and 29 countries for women, mostly in western Europe, have a 50% or higher probability of meeting the global target. INTERPRETATION: Since 1980, age-standardised diabetes prevalence in adults has increased, or at best remained unchanged, in every country. Together with population growth and ageing, this rise has led to a near quadrupling of the number of adults with diabetes worldwide. The burden of diabetes, both in terms of prevalence and number of adults affected, has increased faster in low-income and middle-income countries than in high-income countries. FUNDING: Wellcome Trust

Worldwide trends in body-mass index, underweight, overweight, and obesity from 1975 to 2016: a pooled analysis of 2416 population-based measurement studies in 128·9 million children, adolescents, and adults.

BACKGROUND: Underweight, overweight, and obesity in childhood and adolescence are associated with adverse health consequences throughout the life-course. Our aim was to estimate worldwide trends in mean body-mass index (BMI) and a comprehensive set of BMI categories that cover underweight to obesity in children and adolescents, and to compare trends with those of adults. METHODS: We pooled 2416 population-based studies with measurements of height and weight on 128·9 million participants aged 5 years and older, including 31·5 million aged 5-19 years. We used a Bayesian hierarchical model to estimate trends from 1975 to 2016 in 200 countries for mean BMI and for prevalence of BMI in the following categories for children and adolescents aged 5-19 years: more than 2 SD below the median of the WHO growth reference for children and adolescents (referred to as moderate and severe underweight hereafter), 2 SD to more than 1 SD below the median (mild underweight), 1 SD below the median to 1 SD above the median (healthy weight), more than 1 SD to 2 SD above the median (overweight but not obese), and more than 2 SD above the median (obesity). FINDINGS: Regional change in age-standardised mean BMI in girls from 1975 to 2016 ranged from virtually no change (-0·01 kg/m2 per decade; 95% credible interval -0·42 to 0·39, posterior probability [PP] of the observed decrease being a true decrease=0·5098) in eastern Europe to an increase of 1·00 kg/m2 per decade (0·69-1·35, PP>0·9999) in central Latin America and an increase of 0·95 kg/m2 per decade (0·64-1·25, PP>0·9999) in Polynesia and Micronesia. The range for boys was from a non-significant increase of 0·09 kg/m2 per decade (-0·33 to 0·49, PP=0·6926) in eastern Europe to an increase of 0·77 kg/m2 per decade (0·50-1·06, PP>0·9999) in Polynesia and Micronesia. Trends in mean BMI have recently flattened in northwestern Europe and the high-income English-speaking and Asia-Pacific regions for both sexes, southwestern Europe for boys, and central and Andean Latin America for girls. By contrast, the rise in BMI has accelerated in east and south Asia for both sexes, and southeast Asia for boys. Global age-standardised prevalence of obesity increased from 0·7% (0·4-1·2) in 1975 to 5·6% (4·8-6·5) in 2016 in girls, and from 0·9% (0·5-1·3) in 1975 to 7·8% (6·7-9·1) in 2016 in boys; the prevalence of moderate and severe underweight decreased from 9·2% (6·0-12·9) in 1975 to 8·4% (6·8-10·1) in 2016 in girls and from 14·8% (10·4-19·5) in 1975 to 12·4% (10·3-14·5) in 2016 in boys. Prevalence of moderate and severe underweight was highest in India, at 22·7% (16·7-29·6) among girls and 30·7% (23·5-38·0) among boys. Prevalence of obesity was more than 30% in girls in Nauru, the Cook Islands, and Palau; and boys in the Cook Islands, Nauru, Palau, Niue, and American Samoa in 2016. Prevalence of obesity was about 20% or more in several countries in Polynesia and Micronesia, the Middle East and north Africa, the Caribbean, and the USA. In 2016, 75 (44-117) million girls and 117 (70-178) million boys worldwide were moderately or severely underweight. In the same year, 50 (24-89) million girls and 74 (39-125) million boys worldwide were obese. INTERPRETATION: The rising trends in children's and adolescents' BMI have plateaued in many high-income countries, albeit at high levels, but have accelerated in parts of Asia, with trends no longer correlated with those of adults. FUNDING: Wellcome Trust, AstraZeneca Young Health Programme

Diminishing benefits of urban living for children and adolescents’ growth and development

Optimal growth and development in childhood and adolescence is crucial for lifelong health and well-being1–6. Here we used data from 2,325 population-based studies, with measurements of height and weight from 71 million participants, to report the height and body-mass index (BMI) of children and adolescents aged 5–19 years on the basis of rural and urban place of residence in 200 countries and territories from 1990 to 2020. In 1990, children and adolescents residing in cities were taller than their rural counterparts in all but a few high-income countries. By 2020, the urban height advantage became smaller in most countries, and in many high-income western countries it reversed into a small urban-based disadvantage. The exception was for boys in most countries in sub-Saharan Africa and in some countries in Oceania, south Asia and the region of central Asia, Middle East and north Africa. In these countries, successive cohorts of boys from rural places either did not gain height or possibly became shorter, and hence fell further behind their urban peers. The difference between the age-standardized mean BMI of children in urban and rural areas was <1.1 kg m–2 in the vast majority of countries. Within this small range, BMI increased slightly more in cities than in rural areas, except in south Asia, sub-Saharan Africa and some countries in central and eastern Europe. Our results show that in much of the world, the growth and developmental advantages of living in cities have diminished in the twenty-first century, whereas in much of sub-Saharan Africa they have amplified

Repositioning of the global epicentre of non-optimal cholesterol

High blood cholesterol is typically considered a feature of wealthy western countries1,2. However, dietary and behavioural determinants of blood cholesterol are changing rapidly throughout the world3 and countries are using lipid-lowering medications at varying rates. These changes can have distinct effects on the levels of high-density lipoprotein (HDL) cholesterol and non-HDL cholesterol, which have different effects on human health4,5. However, the trends of HDL and non-HDL cholesterol levels over time have not been previously reported in a global analysis. Here we pooled 1,127 population-based studies that measured blood lipids in 102.6 million individuals aged 18 years and older to estimate trends from 1980 to 2018 in mean total, non-HDL and HDL cholesterol levels for 200 countries. Globally, there was little change in total or non-HDL cholesterol from 1980 to 2018. This was a net effect of increases in low- and middle-income countries, especially in east and southeast Asia, and decreases in high-income western countries, especially those in northwestern Europe, and in central and eastern Europe. As a result, countries with the highest level of non-HDL cholesterol—which is a marker of cardiovascular risk—changed from those in western Europe such as Belgium, Finland, Greenland, Iceland, Norway, Sweden, Switzerland and Malta in 1980 to those in Asia and the Pacific, such as Tokelau, Malaysia, The Philippines and Thailand. In 2017, high non-HDL cholesterol was responsible for an estimated 3.9 million (95% credible interval 3.7 million–4.2 million) worldwide deaths, half of which occurred in east, southeast and south Asia. The global repositioning of lipid-related risk, with non-optimal cholesterol shifting from a distinct feature of high-income countries in northwestern Europe, north America and Australasia to one that affects countries in east and southeast Asia and Oceania should motivate the use of population-based policies and personal interventions to improve nutrition and enhance access to treatment throughout the world