Representer Theorem for Learning Koopman Operators

In this work, the problem of learning Koopman operator of a discrete-time autonomous system is considered. The learning problem is formulated as a constrained regularized empirical loss minimization in the infinite-dimensional space of linear operators. We show that under certain but general conditions, a representer theorem holds for the learning problem. This allows reformulating the problem in a finite-dimensional space without any approximation and loss of precision. Following this, we consider various cases of regularization and constraints in the learning problem, including the operator norm, the Frobenius norm, rank, nuclear norm, and stability. Subsequently, we derive the corresponding finite-dimensional problem. Furthermore, we discuss the connection between the proposed formulation and the extended dynamic mode decomposition. Finally, we provide an illustrative numerical example

Operating Task Redistribution in Hyperconverged Networks

In this article, a searching method for the rational task distribution through the nodes of a hyperconverged network is presented in which it provides the rational distribution of task sets towards a better performance. With using new subsettings related to distribution of nodes in the network based on distributed processing, we can minimize average packet delay. The distribution quality is provided with using a special objective function considering the penalties in the case of having delays. This process is considered in order to create the balanced delivery systems. The initial redistribution is determined based on the minimum penalty. After performing a cycle (iteration) of redistribution in order to have the appropriate task distribution, a potential system is formed for functional optimization. In each cycle of the redistribution, a rule for optimizing contour search is used. Thus, the obtained task distribution, including the appeared failure and success, will be rational and can decrease the average packet delay in the hyperconverged networks. The effectiveness of our proposed method is evaluated by using the model of hyperconverged support system of the university E-learning provided by V.N. Karazin Kharkiv National University. The simulation results based on the model clearly confirm the acceptable and better performance of our approach in comparison to the classical approach of task distribution

Neonatal Respiratory Distress Syndrome: Things to Consider and Ways to Manage

Involving more commonly the premature (less than 37 weeks of gestational age) infants, neonatal respiratory distress syndrome is an important clinical syndrome responsible for a high rate of mortality and morbidity. The main progress in respiratory distress syndrome (RDS) management is attributable to prescription of surfactant for fastening pulmonary maturation. Respiratory protection, such as mechanical ventilation and nasal continuous positive airway pressure, and surfactant are building blocks of disease treatment. In this chapter, we are going to have a rapid review on epidemiology, diagnosis and treatments of RDS

Kernel-based Impulse Response Identification with Side-Information on Steady-State Gain

In this paper, we consider the problem of system identification when side-information is available on the steady-state (or DC) gain of the system. We formulate a general nonparametric identification method as an infinite-dimensional constrained convex program over the reproducing kernel Hilbert space (RKHS) of stable impulse responses. The objective function of this optimization problem is the empirical loss regularized with the norm of RKHS, and the constraint is considered for enforcing the integration of the steady-state gain side-information. The proposed formulation addresses both the discrete-time and continuous-time cases. We show that this program has a unique solution obtained by solving an equivalent finite-dimensional convex optimization. This solution has a closed-form when the empirical loss and regularization functions are quadratic and exact side-information is considered. We perform extensive numerical comparisons to verify the efficiency of the proposed identification methodology