Репозиторий Университета

© 2021 Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an α-stable Lévy process is still lacking. Here, we propose an approach to infer all the uncertain non-Gaussian parameters and other system parameters by minimizing the Hellinger distance over the parameter space. The Hellinger distance measures the similarity between an empirical probability density of non-Gaussian observations and a solution (as a probability density) of the associated nonlocal Fokker-Planck equation. Numerical experiments verify that our method is feasible for estimating single and multiple parameters. Meanwhile, we find an optimal estimation interval of the estimated parameters. This method is beneficial for extracting governing dynamical system models under non-Gaussian fluctuations, as in the study of abrupt climate changes in the Dansgaard-Oeschger events.

© 2019, Pediatria Ltd. All rights reserved. Brain–lung–thyroid syndrome (BLTS) is a rare genetic disease associated with mutations in the NKX2.1 gene encoding thyroid transcription factor 1. The most common manifestations of this syndrome are benign hereditary chorea, hypothyroidism and respiratory distress syndrome, however, mutations in the NKX2.1 gene can also cause other pathologies of nervous, respiratory systems and thyroid gland. The article describes 4 patients with mutations in the NKX2.1 gene observed by authors. Based on the analysis of the observations of 168 patients with BLTS presented in the world literature from 1998 to 2019, current information on the genetics, pathogenesis, clinical X-ray manifestations, outcomes and treatment of the syndrome are summarized.