On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems in R3\mathbb{R}^3

In this paper we use the blow up method of Dumortier and Roussarie \cite{dumortier_1991,dumortier_1993,dumortier_1996}, in the formulation due to Krupa and Szmolyan \cite{krupa_extending_2001}, to study the regularization of singularities of piecewise smooth dynamical systems \cite{filippov1988differential} in $\mathbb R^3$. Using the regularization method of Sotomayor and Teixeira \cite{Sotomayor96}, first we demonstrate the power of our approach by considering the case of a fold line. We quickly recover a main result of Bonet and Seara \cite{reves_regularization_2014} in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided a certain non-resonance condition holds. Finally, we provide numerical evidence for the existence of secondary canards near resonance.Comment: To appear in SIAM Journal of Applied Dynamical System

The rolling ball problem on the sphere

nuloBy a sequence of rolling motions without slipping or twisting along arcs of great circles outside the surface of a sphere of radius R, a spherical ball of unit radius has to be transferred from an initial state to an arbitrary final state taking into account the orientation of the ball. Assuming R > 1 we provide a new and shorter prove of the result of Frenkel and Garcia in [4] that with at most 4 moves we can go from a given initial state to an arbitrary final state. Important cases such as the so called elimination of the spin discrepancy are done with 3 moves only

The rolling ball problem on the sphere

nuloBy a sequence of rolling motions without slipping or twisting along arcs of great circles outside the surface of a sphere of radius R, a spherical ball of unit radius has to be transferred from an initial state to an arbitrary final state taking into account the orientation of the ball. Assuming R > 1 we provide a new and shorter prove of the result of Frenkel and Garcia in [4] that with at most 4 moves we can go from a given initial state to an arbitrary final state. Important cases such as the so called elimination of the spin discrepancy are done with 3 moves only

Global phase portraits of a predator-prey system

We classify the global dynamics of a family of Kolmogorov systems depending on three parameters which has ecological meaning as it modelizes a predator–prey system. We obtain all their topologically distinct global phase portraits in the positive quadrant of the Poincaré disc, so we provide all the possible distinct dynamics of these systems

The impact of COVID-19 on the well-being and cognition of older adults living in the United States and Latin America

BACKGROUND: In the COVID-19 pandemic, older adults from vulnerable ethnoracial groups are at high risk of infection, hospitalization, and death. We aimed to explore the pandemic\u27s impact on the well-being and cognition of older adults living in the United States (US), Argentina, Chile, Mexico, and Peru. METHODS: 1,608 (646 White, 852 Latino, 77 Black, 33 Asian; 72% female) individuals from the US and four Latin American countries aged ≥ 55 years completed an online survey regarding well-being and cognition during the pandemic between May and September 2020. Outcome variables (pandemic impact, discrimination, loneliness, purpose of life, subjective cognitive concerns) were compared across four US ethnoracial groups and older adults living in Argentina, Chile, Mexico, and Peru. FINDINGS: Mean age for all participants was 66.7 ( INTERPRETATION: The COVID-19 pandemic has differentially impacted the well-being of older ethnically diverse individuals in the US and Latin America. Future studies should examine how mediators like income and coping skills modify the pandemic\u27s impact. FUNDING: Massachusetts General Hospital Department of Psychiatry

Prevalence and Incidence of Parkinson\u27s Disease in Latin America: A Meta-Analysis

\ua9 2023 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society. Background: Parkinson\u27s disease (PD) is a rapidly growing neurodegenerative disorder, but up-to-date epidemiological data are lacking in Latin America. We sought to estimate the prevalence and incidence of PD and parkinsonism in Latin America. Methods: We searched Medline, Embase, Scopus, Web of Science, Scientific Electronic Library Online, and Literatura Latino-Americana e do Caribe em Ci\ueancias da Sa\ufade or the Latin American and Caribbean Health Science Literature databases for epidemiological studies reporting the prevalence or incidence of PD or parkinsonism in Latin America from their inception to 2022. Quality of studies was assessed using the Joanna Briggs Institute (JBI) Critical Appraisal Checklist. Data were pooled via random-effects meta-analysis and analyzed by data source (cohort studies or administrative databases), sex, and age group. Significant differences between groups were determined by meta-regression. Results: Eighteen studies from 13 Latin American countries were included in the review. Meta-analyses of 17 studies (nearly 4 million participants) found a prevalence of 472 (95% CI, 271–820) per 100,000 and three studies an incidence of 31 (95% CI, 23–40) per 100,000 person-years for PD; and seven studies found a prevalence of 4300 (95% CI, 1863–9613) per 100,000 for parkinsonism. The prevalence of PD differed by data source (cohort studies, 733 [95% CI, 427–1255] vs. administrative databases. 114 [95% CI, 63–209] per 100,000, P < 0.01), age group (P < 0.01), but not sex (P = 0.73). PD prevalence in ≥60 years also differed significantly by data source (cohort studies. 1229 [95% CI, 741–2032] vs. administrative databases, 593 [95% CI, 480–733] per 100,000, P < 0.01). Similar patterns were observed for parkinsonism. Conclusions: The overall prevalence and incidence of PD in Latin America were estimated. PD prevalence differed significantly by the data source and age, but not sex. \ua9 2023 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society

Exploring the natural history of intrinsic capacity impairments: longitudinal patterns in the 10/66 study

Backgroundintrinsic capacity (IC) is a construct encompassing people’s physical and mental abilities. There is an implicit link amongst IC domains: cognition, locomotion, nutrition, sensory and psychological. However, little is known about the integration of the domains.Objectivesto investigate patterns in the presentation and evolution of IC domain impairments in low-and-middle-income countries and if such patterns were associated with adverse outcomes.Methodssecondary analyses of the first two waves of the 10/66 study (population-based surveys conducted in eight urban and four rural catchment areas in Cuba, Dominican Republic, Puerto Rico, Venezuela, Peru, Mexico and China). We applied latent transition analysis on IC to find latent statuses (latent clusters) of IC domain impairments. We evaluated the longitudinal association of the latent statuses with the risk of frailty, disability and mortality, and tested concurrent and predictive validity.Resultsamongst 14,923 participants included, the four latent statuses were: high IC (43%), low deterioration with impaired locomotion (17%), high deterioration without cognitive impairment (22%), and high deterioration with cognitive impairment (18%). A total of 61% of the participants worsened over time, 35% were stable, and 3% improved to a healthier status.Participants with deteriorated IC had a significantly higher risk of frailty, disability and dementia than people with high IC. There was strong concurrent and predictive validity. (Mortality Hazard Ratio = 4.60, 95%CI 4.16; 5.09; Harrel’s C = 0.73 (95%CI 0.72;0.74)).Conclusionshalf of the study population had high IC at baseline, and most participants followed a worsening trend. Four qualitatively different IC statuses or statuses were characterised by low and high levels of deterioration associated with their risk of disability and frailty. Locomotion and cognition impairments showed other trends than psychological and nutrition domains across the latent statuses