Positive bound states for nonlinear Schrödinger equations in exterior domains

Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2017.Estamos interessados na existência de uma solução positiva para duas classes de equaçãoes não lineares de Schrödinger em domínios exteriores: (veja a fórmula no resumo original) onde N ≥ 2; RN n é um domínio limitado regular, mas não há restrição sobre o seu tamanho, nem qualquer hipótese de simetria e também (veja a fórmula no resumo original) onde N≥3; RN n é um domínio limitado regular, e como acima não há restrição sobre o seu tamanho, nem qualquer hipótese de simetria. Nosso objetivo no primeiro capítulo é mostrar a existência de uma solução positiva do problema (PV ) onde o nível mínimo de energia não pode ser obtido. Usando uma nova abordagem desenvolvida recentemente por Évéquoz e Weth [31], Clapp e Maia [24] e Maia e Pellacci [37] uma solução positiva é encontrada, estendendo os resultados de existência obtidos nos artigos clássicos de Benci e Cerami [9] e Bahri e Lions [6], para não-linearidades gerais não homogêneas, superlineares ou assintoticamente lineares no infinito em um domínio exterior. O estudo de ondas solitárias de equações de Schrödinger não lineares ou equações não lineares de Klein-Gordon é modelado por (PV ) com = RN. Da mesma forma, problemas de fronteira de limite exterior podem estar associados a modelos de fluxos de estado estacionário na dinâmica de fluidos (ver [32]) e ao problema eletrostáatico de capacitores (veja [27], Volume 1, Capítulo II), por exemplo. Nossa contribuição principal no primeiro capítulo foi estender o resultado de Bahri e Lions [6] para f não homogêneas, sem hipótese de simetria em V ou . Além disso, permitimos que a função não linear f seja uma função menos suave, apenas em C1, melhorando as hipóteses em [24] e [37] onde esta foi considerada em C3 por razões técnicas (veja o Lemma 3.3 em [24]). O método que empregamos para resolver (PV ) tem muitas ideias em comum com [24, 37]. Do mesmo modo, o trabalho de [31] forneceu algumas ferramentas úteis e informações para estimativas, mesmo que seu problema seja para f super-linear em todo RN e usa a variedade de Nehari generalizada. Segundo o nosso conhecimento, os resultados que apresentamos aqui são novos e estendem os trabalhos anteriores encontrados na literatura para uma classe de problemas em domínios exteriores. Consideramos o problema elíptico -Δu + V (x)u = f(u) ; u 2 H1 0() (PV ) onde N ≥ 2, RN n _ BK(0) a bola do raio K e centro na origem em RN; de fato RN n é limitado, @ é regular e u 2 H1 0() e V é um potencial que satisfaça as condições: (V1) V 2 C0() , infx2 V (x) > 0 e lim jxj!+1 V (x) = V1; (V2) V (x) _ V1 + Cejxj, onde C > 0 e > 2 p V1. As condições que consideramos na não linearidade f são as seguintes: (veja a fórmula no resumo original) A função s 7! f(s)=s é crescente em s 2 (0;+1); Teorema A: Sob hipóteses (V1) (V2), (f1) (f5) e (U), o problema (PV ) tem uma solução positiva u em H1 0(). No segundo capítulo, procuramos uma solução positiva para o problema (P) onde um nível mínimo de energia não pode ser atingido. Aqui, estudamos não linearidades não homogêneas gerais, com condição de crescimento em f de potência dupla, que se comporta como uma potência subcrítica up no infinito e uma potência supercrítica uq perto da origem, onde p 0, u∨¿ϬΩ=0, ¿ where R N \ Ω is regular bounded domain and like as above there is no restriction on its size, nor any symmetry assumption. The nonlinear term f is general non- { −∆u+V (x )=F(u),∈Ω u H0 1 (Ω) homogeneous non-linearities with double-power growth condition. The existence of bound state solu- tion is established in situations where this problem does not have a ground state

The topology, stability, and instability of learning-induced brain network repertoires in schizophrenia

AbstractThere is a paucity of graph theoretic methods applied to task-based data in schizophrenia (SCZ). Tasks are useful for modulating brain network dynamics, and topology. Understanding how changes in task conditions impact inter-group differences in topology can elucidate unstable network characteristics in SCZ. Here, in a group of patients and healthy controls (n = 59 total, 32 SCZ), we used an associative learning task with four distinct conditions (Memory Formation, Post-Encoding Consolidation, Memory Retrieval, and Post-Retrieval Consolidation) to induce network dynamics. From the acquired fMRI time series data, betweenness centrality (BC), a metric of a node’s integrative value was used to summarize network topology in each condition. Patients showed (a) differences in BC across multiple nodes and conditions; (b) decreased BC in more integrative nodes, but increased BC in less integrative nodes; (c) discordant node ranks in each of the conditions; and (d) complex patterns of stability and instability of node ranks across conditions. These analyses reveal that task conditions induce highly variegated patterns of network dys-organization in SCZ. We suggest that the dys-connection syndrome that is schizophrenia, is a contextually evoked process, and that the tools of network neuroscience should be oriented toward elucidating the limits of this dys-connection

Burden of injury along the development spectrum: associations between the Socio-demographic Index and disability-adjusted life year estimates from the Global Burden of Disease Study 2017

Background The epidemiological transition of non-communicable diseases replacing infectious diseases as the main contributors to disease burden has been well documented in global health literature. Less focus, however, has been given to the relationship between sociodemographic changes and injury. The aim of this study was to examine the association between disability-adjusted life years (DALYs) from injury for 195 countries and territories at different levels along the development spectrum between 1990 and 2017 based on the Global Burden of Disease (GBD) 2017 estimates. Methods Injury mortality was estimated using the GBD mortality database, corrections for garbage coding and CODEm-the cause of death ensemble modelling tool. Morbidity estimation was based on surveys and inpatient and outpatient data sets for 30 cause-of-injury with 47 nature-of-injury categories each. The Socio-demographic Index (SDI) is a composite indicator that includes lagged income per capita, average educational attainment over age 15 years and total fertility rate. results For many causes of injury, age-standardised DALY rates declined with increasing SDI, although road injury, interpersonal violence and self-harm did not follow this pattern. Particularly for self-harm opposing patterns were observed in regions with similar SDI levels. For road injuries, this effect was less pronounced. Conclusions The overall global pattern is that of declining injury burden with increasing SDI. However, not all injuries follow this pattern, which suggests multiple underlying mechanisms influencing injury DALYs. There is a need for a detailed understanding of these patterns to help to inform national and global efforts to address injury-related health outcomes across the development spectrum

Global, regional, and national burden of traumatic brain injury and spinal cord injury, 1990-2016: a systematic analysis for the Global Burden of Disease Study 2016.

Traumatic brain injury (TBI) and spinal cord injury (SCI) are increasingly recognised as global health priorities in view of the preventability of most injuries and the complex and expensive medical care they necessitate. We aimed to measure the incidence, prevalence, and years of life lived with disability (YLDs) for TBI and SCI from all causes of injury in every country, to describe how these measures have changed between 1990 and 2016, and to estimate the proportion of TBI and SCI cases caused by different types of injury. METHODS: We used results from the Global Burden of Diseases, Injuries, and Risk Factors (GBD) Study 2016 to measure the global, regional, and national burden of TBI and SCI by age and sex. We measured the incidence and prevalence of all causes of injury requiring medical care in inpatient and outpatient records, literature studies, and survey data. By use of clinical record data, we estimated the proportion of each cause of injury that required medical care that would result in TBI or SCI being considered as the nature of injury. We used literature studies to establish standardised mortality ratios and applied differential equations to convert incidence to prevalence of long-term disability. Finally, we applied GBD disability weights to calculate YLDs. We used a Bayesian meta-regression tool for epidemiological modelling, used cause-specific mortality rates for non-fatal estimation, and adjusted our results for disability experienced with comorbid conditions. We also analysed results on the basis of the Socio-demographic Index, a compound measure of income per capita, education, and fertility. FINDINGS: In 2016, there were 27·08 million (95% uncertainty interval [UI] 24·30-30·30 million) new cases of TBI and 0·93 million (0·78-1·16 million) new cases of SCI, with age-standardised incidence rates of 369 (331-412) per 100 000 population for TBI and 13 (11-16) per 100 000 for SCI. In 2016, the number of prevalent cases of TBI was 55·50 million (53·40-57·62 million) and of SCI was 27·04 million (24·98-30·15 million). From 1990 to 2016, the age-standardised prevalence of TBI increased by 8·4% (95% UI 7·7 to 9·2), whereas that of SCI did not change significantly (-0·2% [-2·1 to 2·7]). Age-standardised incidence rates increased by 3·6% (1·8 to 5·5) for TBI, but did not change significantly for SCI (-3·6% [-7·4 to 4·0]). TBI caused 8·1 million (95% UI 6·0-10·4 million) YLDs and SCI caused 9·5 million (6·7-12·4 million) YLDs in 2016, corresponding to age-standardised rates of 111 (82-141) per 100 000 for TBI and 130 (90-170) per 100 000 for SCI. Falls and road injuries were the leading causes of new cases of TBI and SCI in most regions. INTERPRETATION: TBI and SCI constitute a considerable portion of the global injury burden and are caused primarily by falls and road injuries. The increase in incidence of TBI over time might continue in view of increases in population density, population ageing, and increasing use of motor vehicles, motorcycles, and bicycles. The number of individuals living with SCI is expected to increase in view of population growth, which is concerning because of the specialised care that people with SCI can require. Our study was limited by data sparsity in some regions, and it will be important to invest greater resources in collection of data for TBI and SCI to improve the accuracy of future assessments

Global, regional, and national burden of neurological disorders, 1990–2016 : a systematic analysis for the Global Burden of Disease Study 2016

Background: Neurological disorders are increasingly recognised as major causes of death and disability worldwide. The aim of this analysis from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2016 is to provide the most comprehensive and up-to-date estimates of the global, regional, and national burden from neurological disorders. Methods: We estimated prevalence, incidence, deaths, and disability-adjusted life-years (DALYs; the sum of years of life lost [YLLs] and years lived with disability [YLDs]) by age and sex for 15 neurological disorder categories (tetanus, meningitis, encephalitis, stroke, brain and other CNS cancers, traumatic brain injury, spinal cord injury, Alzheimer's disease and other dementias, Parkinson's disease, multiple sclerosis, motor neuron diseases, idiopathic epilepsy, migraine, tension-type headache, and a residual category for other less common neurological disorders) in 195 countries from 1990 to 2016. DisMod-MR 2.1, a Bayesian meta-regression tool, was the main method of estimation of prevalence and incidence, and the Cause of Death Ensemble model (CODEm) was used for mortality estimation. We quantified the contribution of 84 risks and combinations of risk to the disease estimates for the 15 neurological disorder categories using the GBD comparative risk assessment approach. Findings: Globally, in 2016, neurological disorders were the leading cause of DALYs (276 million [95% UI 247–308]) and second leading cause of deaths (9·0 million [8·8–9·4]). The absolute number of deaths and DALYs from all neurological disorders combined increased (deaths by 39% [34–44] and DALYs by 15% [9–21]) whereas their age-standardised rates decreased (deaths by 28% [26–30] and DALYs by 27% [24–31]) between 1990 and 2016. The only neurological disorders that had a decrease in rates and absolute numbers of deaths and DALYs were tetanus, meningitis, and encephalitis. The four largest contributors of neurological DALYs were stroke (42·2% [38·6–46·1]), migraine (16·3% [11·7–20·8]), Alzheimer's and other dementias (10·4% [9·0–12·1]), and meningitis (7·9% [6·6–10·4]). For the combined neurological disorders, age-standardised DALY rates were significantly higher in males than in females (male-to-female ratio 1·12 [1·05–1·20]), but migraine, multiple sclerosis, and tension-type headache were more common and caused more burden in females, with male-to-female ratios of less than 0·7. The 84 risks quantified in GBD explain less than 10% of neurological disorder DALY burdens, except stroke, for which 88·8% (86·5–90·9) of DALYs are attributable to risk factors, and to a lesser extent Alzheimer's disease and other dementias (22·3% [11·8–35·1] of DALYs are risk attributable) and idiopathic epilepsy (14·1% [10·8–17·5] of DALYs are risk attributable). Interpretation: Globally, the burden of neurological disorders, as measured by the absolute number of DALYs, continues to increase. As populations are growing and ageing, and the prevalence of major disabling neurological disorders steeply increases with age, governments will face increasing demand for treatment, rehabilitation, and support services for neurological disorders. The scarcity of established modifiable risks for most of the neurological burden demonstrates that new knowledge is required to develop effective prevention and treatment strategies. Funding: Bill & Melinda Gates Foundation

Mapping child growth failure across low- and middle-income countries

Child growth failure (CGF), manifested as stunting, wasting, and underweight, is associated with high 5 mortality and increased risks of cognitive, physical, and metabolic impairments. Children in low- and middle-income countries (LMICs) face the highest levels of CGF globally. Here we illustrate national and subnational variation of under-5 CGF indicators across LMICs, providing 2000–2017 annual estimates mapped at a high spatial resolution and aggregated to policy-relevant administrative units and national levels. Despite remarkable declines over the study period, many LMICs remain far from the World Health 10 Organization’s ambitious Global Nutrition Targets to reduce stunting by 40% and wasting to less than 5% by 2025. Large disparities in prevalence and rates of progress exist across regions, countries, and within countries; our maps identify areas where high prevalence persists even within nations otherwise succeeding in reducing overall CGF prevalence. By highlighting where subnational disparities exist and the highest-need populations reside, these geospatial estimates can support policy-makers in planning locally 15 tailored interventions and efficient directing of resources to accelerate progress in reducing CGF and its health implications

Mapping 123 million neonatal, infant and child deaths between 2000 and 2017

Since 2000, many countries have achieved considerable success in improving child survival, but localized progress remains unclear. To inform efforts towards United Nations Sustainable Development Goal 3.2—to end preventable child deaths by 2030—we need consistently estimated data at the subnational level regarding child mortality rates and trends. Here we quantified, for the period 2000–2017, the subnational variation in mortality rates and number of deaths of neonates, infants and children under 5 years of age within 99 low- and middle-income countries using a geostatistical survival model. We estimated that 32% of children under 5 in these countries lived in districts that had attained rates of 25 or fewer child deaths per 1,000 live births by 2017, and that 58% of child deaths between 2000 and 2017 in these countries could have been averted in the absence of geographical inequality. This study enables the identification of high-mortality clusters, patterns of progress and geographical inequalities to inform appropriate investments and implementations that will help to improve the health of all populations

Global estimates on the number of people blind or visually impaired by cataract: a meta-analysis from 2000 to 2020

Background: To estimate global and regional trends from 2000 to 2020 of the number of persons visually impaired by cataract and their proportion of the total number of vision-impaired individuals. Methods: A systematic review and meta-analysis of published population studies and gray literature from 2000 to 2020 was carried out to estimate global and regional trends. We developed prevalence estimates based on modeled distance visual impairment and blindness due to cataract, producing location-, year-, age-, and sex-specific estimates of moderate to severe vision impairment (MSVI presenting visual acuity &lt;6/18, ≥3/60) and blindness (presenting visual acuity &lt;3/60). Estimates are age-standardized using the GBD standard population. Results: In 2020, among overall (all ages) 43.3 million blind and 295 million with MSVI, 17.0 million (39.6%) people were blind and 83.5 million (28.3%) had MSVI due to cataract blind 60% female, MSVI 59% female. From 1990 to 2020, the count of persons blind (MSVI) due to cataract increased by 29.7%(93.1%) whereas the age-standardized global prevalence of cataract-related blindness improved by −27.5% and MSVI increased by 7.2%. The contribution of cataract to the age-standardized prevalence of blindness exceeded the global figure only in South Asia (62.9%) and Southeast Asia and Oceania (47.9%). Conclusions: The number of people blind and with MSVI due to cataract has risen over the past 30 years, despite a decrease in the age-standardized prevalence of cataract. This indicates that cataract treatment programs have been beneficial, but population growth and aging have outpaced their impact. Growing numbers of cataract blind indicate that more, better-directed, resources are needed to increase global capacity for cataract surgery.</p

Burden of injury along the development spectrum : associations between the Socio-demographic Index and disability-adjusted life year estimates from the Global Burden of Disease Study 2017

Background The epidemiological transition of non-communicable diseases replacing infectious diseases as the main contributors to disease burden has been well documented in global health literature. Less focus, however, has been given to the relationship between sociodemographic changes and injury. The aim of this study was to examine the association between disability-adjusted life years (DALYs) from injury for 195 countries and territories at different levels along the development spectrum between 1990 and 2017 based on the Global Burden of Disease (GBD) 2017 estimates. Methods Injury mortality was estimated using the GBD mortality database, corrections for garbage coding and CODEm-the cause of death ensemble modelling tool. Morbidity estimation was based on surveys and inpatient and outpatient data sets for 30 cause-of-injury with 47 nature-of-injury categories each. The Socio-demographic Index (SDI) is a composite indicator that includes lagged income per capita, average educational attainment over age 15 years and total fertility rate. Results For many causes of injury, age-standardised DALY rates declined with increasing SDI, although road injury, interpersonal violence and self-harm did not follow this pattern. Particularly for self-harm opposing patterns were observed in regions with similar SDI levels. For road injuries, this effect was less pronounced. Conclusions The overall global pattern is that of declining injury burden with increasing SDI. However, not all injuries follow this pattern, which suggests multiple underlying mechanisms influencing injury DALYs. There is a need for a detailed understanding of these patterns to help to inform national and global efforts to address injury-related health outcomes across the development spectrum.Peer reviewe

Global, regional, and national burden of stroke and its risk factors, 1990–2019: a systematic analysis for the Global Burden of Disease Study 2019

Background Regularly updated data on stroke and its pathological types, including data on their incidence, prevalence, mortality, disability, risk factors, and epidemiological trends, are important for evidence-based stroke care planning and resource allocation. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) aims to provide a standardised and comprehensive measurement of these metrics at global, regional, and national levels. Methods We applied GBD 2019 analytical tools to calculate stroke incidence, prevalence, mortality, disability-adjusted life-years (DALYs), and the population attributable fraction (PAF) of DALYs (with corresponding 95% uncertainty intervals [UIs]) associated with 19 risk factors, for 204 countries and territories from 1990 to 2019. These estimates were provided for ischaemic stroke, intracerebral haemorrhage, subarachnoid haemorrhage, and all strokes combined, and stratified by sex, age group, and World Bank country income level. Findings In 2019, there were 12·2 million (95% UI 11·0–13·6) incident cases of stroke, 101 million (93·2–111) prevalent cases of stroke, 143 million (133–153) DALYs due to stroke, and 6·55 million (6·00–7·02) deaths from stroke. Globally, stroke remained the second-leading cause of death (11·6% [10·8–12·2] of total deaths) and the third-leading cause of death and disability combined (5·7% [5·1–6·2] of total DALYs) in 2019. From 1990 to 2019, the absolute number of incident strokes increased by 70·0% (67·0–73·0), prevalent strokes increased by 85·0% (83·0–88·0), deaths from stroke increased by 43·0% (31·0–55·0), and DALYs due to stroke increased by 32·0% (22·0–42·0). During the same period, age-standardised rates of stroke incidence decreased by 17·0% (15·0–18·0), mortality decreased by 36·0% (31·0–42·0), prevalence decreased by 6·0% (5·0–7·0), and DALYs decreased by 36·0% (31·0–42·0). However, among people younger than 70 years, prevalence rates increased by 22·0% (21·0–24·0) and incidence rates increased by 15·0% (12·0–18·0). In 2019, the age-standardised stroke-related mortality rate was 3·6 (3·5–3·8) times higher in the World Bank low-income group than in the World Bank high-income group, and the age-standardised stroke-related DALY rate was 3·7 (3·5–3·9) times higher in the low-income group than the high-income group. Ischaemic stroke constituted 62·4% of all incident strokes in 2019 (7·63 million [6·57–8·96]), while intracerebral haemorrhage constituted 27·9% (3·41 million [2·97–3·91]) and subarachnoid haemorrhage constituted 9·7% (1·18 million [1·01–1·39]). In 2019, the five leading risk factors for stroke were high systolic blood pressure (contributing to 79·6 million [67·7–90·8] DALYs or 55·5% [48·2–62·0] of total stroke DALYs), high body-mass index (34·9 million [22·3–48·6] DALYs or 24·3% [15·7–33·2]), high fasting plasma glucose (28·9 million [19·8–41·5] DALYs or 20·2% [13·8–29·1]), ambient particulate matter pollution (28·7 million [23·4–33·4] DALYs or 20·1% [16·6–23·0]), and smoking (25·3 million [22·6–28·2] DALYs or 17·6% [16·4–19·0]). Interpretation The annual number of strokes and deaths due to stroke increased substantially from 1990 to 2019, despite substantial reductions in age-standardised rates, particularly among people older than 70 years. The highest age-standardised stroke-related mortality and DALY rates were in the World Bank low-income group. The fastest-growing risk factor for stroke between 1990 and 2019 was high body-mass index. Without urgent implementation of effective primary prevention strategies, the stroke burden will probably continue to grow across the world, particularly in low-income countries.publishedVersio