Interacting Particles on the Line and Dunkl Intertwining Operator of Type A: Application to the Freezing Regime

We consider a one-dimensional system of Brownian particles that repel each other through a logarithmic potential. We study two formulations for the system and the relation between them. The first, Dyson's Brownian motion model, has an interaction coupling constant determined by the parameter beta > 0. When beta = 1,2 and 4, this model can be regarded as a stochastic realization of the eigenvalue statistics of Gaussian random matrices. The second system comes from Dunkl processes, which are defined using differential-difference operators (Dunkl operators) associated with finite abstract vector sets called root systems. When the type-A root system is specified, Dunkl processes constitute a one-parameter system similar to Dyson's model, with the difference that its particles interchange positions spontaneously. We prove that the type-A Dunkl processes with parameter k > 0 starting from any symmetric initial configuration are equivalent to Dyson's model with the parameter beta = 2k. We focus on the intertwining operators, since they play a central role in the mathematical theory of Dunkl operators, but their general closed form is not yet known. Using the equivalence between symmetric Dunkl processes and Dyson's model, we extract the effect of the intertwining operator of type A on symmetric polynomials from these processes' transition probability densities. In the strong coupling limit, the intertwining operator maps all symmetric polynomials onto a function of the sum of their variables. In this limit, Dyson's model freezes, and it becomes a deterministic process with a final configuration proportional to the roots of the Hermite polynomials multiplied by the square root of the process time, while being independent of the initial configuration.Comment: LaTeX, 30 pages, 1 figure, 1 table. Corrected for submission to Journal of Physics

Impact of the COVID-19 pandemic on people with epilepsy: Findings from the US arm of the COV-E study

Objectives: As part of the COVID-19 and Epilepsy (COV-E) global study, we aimed to understand the impact of COVID-19 on the medical care and well-being of people with epilepsy (PWE) in the United States, based on their perspectives and those of their caregivers. Methods: Separate surveys designed for PWE and their caregivers were circulated from April 2020 to July 2021; modifications in March 2021 included a question about COVID-19 vaccination status. Results: We received 788 responses, 71% from PWE (n = 559) and 29% (n = 229) from caregivers of persons with epilepsy. A third (n = 308) of respondents reported a change in their health or in the health of the person they care for. Twenty-seven percent (n = 210) reported issues related to worsening mental health. Of respondents taking ASMs (n = 769), 10% (n = 78) reported difficulty taking medications on time, mostly due to stress causing forgetfulness. Less than half of respondents received counseling on mental health and stress. Less than half of the PWE reported having discussions with their healthcare providers about sleep, ASMs, and potential side effects, while a larger proportion of caregivers (81%) reported having had discussions with their healthcare providers on the same topics. More PWE and caregivers reported that COVID-19-related measures caused adverse impact on their health in the post-vaccine period than during the pre-vaccine period, citing mental health issues as the primary reason. Significance: Our findings indicate that the impact of the COVID-19 pandemic in the US on PWE is multifaceted. Apart from the increased risk of poor COVID-19 outcomes, the pandemic has also had negative effects on mental health and self-management. Healthcare providers must be vigilant for increased emotional distress in PWE during the pandemic and consider the importance of effective counseling to diminish risks related to exacerbated treatment gaps

Adoção de sistemas de integração lavoura-pecuária-floresta (ILPF) em São Paulo.

Este estudo objetivou caracterizar a adoção dos sistemas de integração no Estado de São Paulo e identificar demandas. Uma amostra de 175 propriedades rurais, sendo 66 adotantes de sistemas de Integração Lavoura-Pecuária (ILP), 24 adotantes de sistemas de Integração PecuáriaFloresta (IPF) e 85 não adotantes de sistemas integrados, compôs a base de dados analisados por meio de estatística descritiva e teste qui-quadrado (x2) de Pearson. Os resultados indicam que os adotantes de sistemas ILP possuem maior experiência com atividades agrícolas, participação mais frequente em cooperativas agrícolas, palestras e dias de campo, bem como recebem mais orientação técnica. O acesso ao crédito rural e o uso mais frequente de mecanismos para gestão do risco climático e econômico estão associados ao componente agrícola do ILP. O fator escala de produção explica propriedades rurais mais extensas e estrutura mais robusta de máquinas agrícolas. A adoção dos sistemas IPF encontra-se em fase experimental nas propriedades rurais. Esses adotantes contam com outra fonte de renda, o que os confere maior flexibilidade para testar o sistema, em sua maioria, implantado de forma escalonada na área de pastagem e com recursos próprios. Predominam propriedades rurais menores, com relevo mais ondulado, solos arenosos, rebanhos menores e concentrados nas fases de cria/recria, além de maior diversificação da produção.bitstream/item/214315/1/AdocaoSistemasIntegracao.pd

Impact of the COVID-19 pandemic on people with epilepsy: findings from the Brazilian arm of the COV-E study

The COVID-19 pandemic has had an unprecedented impact on people and healthcare services. The disruption to chronic illnesses, such as epilepsy, may relate to several factors ranging from direct infection to secondary effects from healthcare reorganization and social distancing measures. Objectives: As part of the COVID-19 and Epilepsy (COV-E) global study, we ascertained the effects of COVID-19 on people with epilepsy in Brazil, based on their perspectives and their perspectives those of those of their caregivers. We also evaluated the impact of COVID-19 on the care delivered to people with epilepsy by healthcare workers. Methods: We designed separate online surveys for people with epilepsy and their caregivers. A further survey for healthcare workers contained additional assessments of changes to working patterns, productivity, and concerns for those with epilepsy under their care. The Brazilian arm of COV-E initially collected data from April to November 2020 during the country's first wave. We also examined national data to identify the Brazilian states with the highest COVID-19 incidence and related mortality. Lastly, we applied this geographic grouping to our data to explore whether local disease burden played a direct role in difficulties faced by people with epilepsy. Results: Two hundred and forty-one people returned the survey, 20% were individuals with epilepsy (n = 48); 22% were caregivers (n = 53) and 58% were healthcare workers (n = 140). Just under half (43%) of people with epilepsy reported health changes during the pandemic, including worsening seizure control, with specific issues related to stress and impaired mental health. Of respondents prescribed antiseizure medication, 11% reported difficulty taking medication on time due to problems acquiring prescriptions and delayed or cancelled medical appointments. Only a small proportion of respondents reported discussing significant epilepsy-related risks in the previous 12 months. Analysis of national COVID-19 data showed a higher disease burden in the states of Sao Paulo and Rio de Janeiro compared to Brazil as a whole. There were, however, no geographic differences observed in survey responses despite variability in the incidence of COVID-19. Conclusion: Our findings suggest that Brazilians with epilepsy have been adversely affected by COVID-19 by factors beyond infection or mortality. Mental health issues and the importance of optimal communication are critical during these difficult times. Healthcare services need to find nuanced approaches and learn from shared international experiences to provide optimal care for people with epilepsy as the direct burden of COVID-19 improves in some countries. In contrast, others face resurgent waves of the pandemic