Deep learning-based models appropriately perform in modeling complex problems in computer vision and natural language processing (NLP). With this in mind, nonlinear system identification methods can benefit from tools developed in deep learning, leading to enriched frameworks to choose from. For this purpose, we are going to review some potential structures and methods of deep learning that can be used in nonlinear system identification. Although we comprehensively review the applicable tools of deep learning to system identification, this paper mainly focuses on using latent variable models (LVM) for identifying nonlinear state space models. LVMs are powerful tools for extending generative models primarily developed for only generating static data, yet by a combination of recurrent neural network (RNN) and variational auto-encoders (VAE), they can also generate sequential data. A structured version of introduced models compatible with control systems will also be given. The study shows that the deep learning models have a comparative performance to traditional and classic ones.

Introduction and Objective: The growth models own a very great importance in biological systems. For example, by analyzing the growth curve of ruminant animals and poultries, it is possible to fastener and to manage their rearing, nutritional and behavioral requirements, based on their growth routines and principles. On the other hand, the growth pattern of animals might be used in evaluating their genetic potential for breeding purposes. Thus, to evaluate and describe the growth pattern of Japanese quail, this study aimed to evaluate the capabilities and advantages of non-linear and nonlinear mixed models to describe and evaluate the growth pattern of Japanese quail. Material and Methods: In order to assess and designate the growth pattern of Japanese quail, we used the growth data of three groups,high weight (HW), low weight (LW) and the control lines of Japanese quail. Different models, including logistic, Gompertz and Richard's both nonlinear and nonlinear mixed models were fitted to the data. For evaluation of models three criteria including coefficient of determination (R2), mean square error (MSE) and Akaike's information criterion (AIC) were employed as criteria to compare the mentioned six different models. Results: Values of the coefficient of determination (R2), for logistic, Gompertz and Richard's nonlinear models were 0. 954, 0. 957 and 0. 951, mean square error (MSE) for three models were 74. 034, 72. 560 and 72. 730, and Akaike's information criterion (AIC) for the models were 65829, 65307 and 65349, respectively. The results for non-linear mixed models, in the same order mentioned above and for R2, MSE and AIC, were 0. 976, 0. 978 and 0. 978,33. 400, 31. 658 and 31. 849,61449, 60641 and 60591 respectively. Conclusion: The results showed that nonlinear mixed models had higher accuracy and less mean square error, compared to nonlinear models and Richard’, s model is more capable (better) to the predict growth pattern of Japanese quail. Also among non-linear models Gompertz model had a better fit to the purpose. In general, it can be said that the parameters determined by the functions inspected in this study, are not much different.

In this work we investigate the thermal entanglement between two-level atoms and photons in a nonlinear cavity. We consider intensity-dependent couplings and calculate the negativity, as a measure of atom-photon entanglement. The cavity is assumed to be at a temperature T, so that all number of photons, and at the same time, both atomic states, with definite probabilities, are present. We then demonstrate a condition under which the intensity-dependent coupling leads to entanglement. It is also shown that, as in the case of linear Jaynes- Cummings model, the thermal states of atoms and photons are never separable.

In this paper, the nonlinear regression models when the model errors follow a slash skew-elliptical distribution, are considered. In the special case of nonlinear regression models under slash skew-t distribution, we present some distributional properties, and to estimate their parameters, we use an EM-type algorithm. Also, to find the estimation errors, we derive the observed information matrix analytically. To describe the influence of the observations on the ML estimates, we use a sensitivity analysis. Finally, we conduct some simulation studies and a real data analysis to show the performance of the proposed model.