ABSTRACT
SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton, Proctor, and Kutz, Proc. Natl. Acad. Sci. USA 113, 3932 (2016)PNASA60027-842410.1073/pnas.1517384113]. In this article, we propose an extension of the SINDy method that learns systems of differential equations in cases where some of the variables are not observed. Our extension is based on regressing a higher order time derivative of a target variable onto a dictionary of functions that includes lower order time derivatives of the target variable. We evaluate our method by measuring the prediction accuracy of the learned dynamical systems on synthetic data and on a real data set of temperature time series provided by the Réseau de Transport d'Électricité. Our method provides high quality short-term forecasts and it is orders of magnitude faster than competing methods for learning differential equations with latent variables.
ABSTRACT
Objectives: Early life represents a sensitive and critical period for an individual. Nutrition plays a crucial role in the maturation and functional development of the central nervous system. Inadequate nutrition before birth and during the postnatal life can seriously interfere with brain development and lead to behavioral and neurological disorders such as learning disabilities and psychiatric diseases. In addition, the quality of mother-infant interactions represents an important adaptive pathway that prepares offspring for the conditions of life. In this work, we asked if protein malnutrition alters maternal care and offspring development and if these phenotypes can be transmitted to next generation.Methods: Female mice were fed with a normal or hypoproteic diet during pregnancy and lactation. Nurturing behaviors, i.e. arched, blanket and passive nursing, and liking and grooming of the pups, were evaluated from postnatal day 1 (PD1) to postnatal day 7 (PD7). The same protocol was employed to evaluate maternal behavior for filial generation 1 (F1) and filial generation 2 (F2) dams. Offspring development was evaluated for F1, F2, and F3 generations. Developmental landmarks and neurological reflexes were assessed from PD8 until complete development of the landmark or acquisition of the reflex.Results: Our results show that malnourished dams provide a lesser and more fragmented maternal care than their normally fed counterparts. This altered maternal behavior as well as the delay in the physical and neurological development observed in the offspring from malnourished mothers was transmitted up to two generations at least.Conclusion: These results highlight the harmful effects of protein malnutrition even for generations that are not directly exposed to this environmental adversity.
