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The paper presents some properties and. related simulation results of optimal control strategies in problems arising from cancer chemotherapy. Two bilinear models of a proliferation cycle are considered. A numerical gradient method is applied to solve the problems.

We first present a method to mathematically build a learning rule for closed-loop neural networks. This rule is then applied to climbing fibers in the cerebellar cortex. Our analytical study is based on previous experimental non-analytical studies, which suggests that climbing fibers carry out an error signal to the brain. Thus, our goal is to find the class of functions for the activity propagated by climbing fibers, allowing the output of the Purkinje cell to converge towards a desired output. These functions must tend towards zero when the objective is reached. Our techniques are generalized to other network models.

This paper presents an improved version of the traction method that was proposed as a solution to shape optimization problems of domain boundaries in which boundary value problems of partial differential equations are defined. The principle of the traction method is presented based on the theory of the gradient method in Hilbert space. Based on this principle, a new method is proposed by selecting another bounded coercive bilinear form from the previous method. The proposed method obtains domain variation with a solution to a boundary value problem with the Robin condition by using the shape gradient.

A three-dimensional AB off-lattice protein model, which involves two species of residues interacting through simplified backbone and modified Lennard-Jones potentials, is studied. Incorporating an extra energy contribution into the original potential energy function, we develop and study a simple gradient algorithm for finding the lowest energy states of this protein model. The performance of our algorithm is tested on the Fibonacci sequences of lengths ranging from 13 to 55 residues previously studied by Hsu et al. Computational performance and behavior of our algorithm are also discussed.

An interference alignment (IA) algorithm that doesn't require channel reciprocity in multiple input multiple output (MIMO) cognitive radio network (CRN) is proposed. Multiple primary users (PUs) and multiple secondary users (SUs) are considered in the network. In the primary network, the PUs perform an IA algorithm to eliminate the interference between the PUs. In the secondary network, firstly, we encode the SUs and set up to the equivalent mode after eliminate the interference between the PUs and SUs. Secondly, we establish the cost function of maximizing the total capacity and apply the gradient method on Grassmann manifold to design the optimal precoding matrices. Finally, the receiver postprocessing matrices are designed by the criterion of maximizing signal-to-interference-plus-noise. Simulation results show that the same results are provided by the proposed algorithm and the existing typical algorithms at low SNRs, but the best results are provided by the proposed algorithm at high SNRs.

A problem of parameter estimation for Markov-Additive Processes of arrivals is considered. It is supposed that empirical data are aggregated: only overall numbers of arrivals of various classes are observed in a long time interval. Maximum likelihood method is used for estimation: score function is derived and the gradient method is used for the optimization. Numerical example is considered.