SINDy-SA framework: enhancing nonlinear system identification with sensitivity analysis.

Machine learning methods have revolutionized studies in several areas of knowledge, helping to understand and extract information from experimental data. Recently, these data-driven methods have also been used to discover structures of mathematical models. The sparse identification of nonlinear dynamics (SINDy) method has been proposed with the aim of identifying nonlinear dynamical systems, assuming that the equations have only a few important terms that govern the dynamics. By defining a library of possible terms, the SINDy approach solves a sparse regression problem by eliminating terms whose coefficients are smaller than a threshold. However, the choice of this threshold is decisive for the correct identification of the model structure. In this work, we build on the SINDy method by integrating it with a global sensitivity analysis (SA) technique that allows to hierarchize terms according to their importance in relation to the desired quantity of interest, thus circumventing the need to define the SINDy threshold. The proposed SINDy-SA framework also includes the formulation of different experimental settings, recalibration of each identified model, and the use of model selection techniques to select the best and most parsimonious model. We investigate the use of the proposed SINDy-SA framework in a variety of applications. We also compare the results against the original SINDy method. The results demonstrate that the SINDy-SA framework is a promising methodology to accurately identify interpretable data-driven models. Supplementary Information: The online version contains supplementary material available at 10.1007/s11071-022-07755-2.

Framework for enhancing the estimation of model parameters for data with a high level of uncertainty.

Reliable data are essential to obtain adequate simulations for forecasting the dynamics of epidemics. In this context, several political, economic, and social factors may cause inconsistencies in the reported data, which reflect the capacity for realistic simulations and predictions. In the case of COVID-19, for example, such uncertainties are mainly motivated by large-scale underreporting of cases due to reduced testing capacity in some locations. In order to mitigate the effects of noise in the data used to estimate parameters of models, we propose strategies capable of improving the ability to predict the spread of the diseases. Using a compartmental model in a COVID-19 study case, we show that the regularization of data by means of Gaussian process regression can reduce the variability of successive forecasts, improving predictive ability. We also present the advantages of adopting parameters of compartmental models that vary over time, in detriment to the usual approach with constant values.

Physical Exercise and Neuroinflammation in Major Depressive Disorder.

Major depressive disorder (MDD) is a prevalent psychiatric disorder associated with varied prognosis, chronic course, and duration of illness with reduced quality of life. One factor that significantly contributes to the relevant disease burden of MDD is the heterogeneous treatment response patients experience with current treatment options. A variety of experimental protocols in humans and animals have highlighted that inflammation and neuroinflammation are relevant biological factors that interact with external stimuli and neurophysiological mechanisms, and can trigger MDD. It is well established that exercise is efficacious in treating mild to moderate depression with response rates comparable to mainstream therapies such as antidepressant medication and cognitive behavioral therapy. Several studies have shown that physical exercise is beneficial for a range of chronic diseases. Indeed, physical exercise can promote molecular changes that swerve a chronic pro-inflammatory state to an anti-inflammatory state in both periphery and central nervous system. The changes caused by physical exercise include an increase in PGC1α gene expression, a transcriptional co-activator involved in reducing the synthesis and releasing of pro-inflammatory cytokines, and an increase in anti-inflammatory cytokines. PGC1α changes the metabolism of kynurenine towards, and, in turn, it reduces glutamatergic neurotoxicity. Moreover, some studies have shown that physical exercise promotes alterations in the circuitry of monoaminergic neurotransmission, at least in some aspects, through the effects on the release of proinflammatory cytokines. This review will highlight the effects of physical exercise as therapy and its relation with the biological mechanisms involved in the pathophysiology of MDD, with particular emphasis in the interactions among physical exercise, hypothalamic-pituitary-adrenal (HPA) axis, neuroinflammation, and with the neurotransmitters underlying the main brain circuits involved in the MDD.

Performance and parameterization of the algorithm Simplified Generalized Simulated Annealing

The main goal of this study is to find the most effective set of parameters for the Simplified Generalized Simulated Annealing algorithm, SGSA, when applied to distinct cost function as well as to find a possible correlation between the values of these parameters sets and some topological characteristics of the hypersurface of the respective cost function. The SGSA algorithm is an extended and simplified derivative of the GSA algorithm, a Markovian stochastic process based on Tsallis statistics that has been used in many classes of problems, in particular, in biological molecular systems optimization. In all but one of the studied cost functions, the global minimum was found in 100 percent of the 50 runs. For these functions the best visiting parameter, qV, belongs to the interval [1.2, 1.7]. Also, the temperature decaying parameter, qT, should be increased when better precision is required. Moreover, the similarity in the locus of optimal parameter sets observed in some functions indicates that possibly one could extract topological information about the cost functions from these sets.