Information transmittal, Newton’s law of gravitation, and tensor approach to general relativity

The special relativity considered in [A. Einstein, Zur Elektrodynamik der bewegte Körper. Ann. Physik, 17 (1905) 891-921] is based on the concept of finite speed of information transmittal by the available signals (rays of light). It is demonstrated that the same concept applies to Newton’s law of universal gravitation since the magnitude of distances between attracting masses can be physically defined (carried, accounted in acting forces of gravity) only by signals (physical processes) propagating at finite velocities. It follows that the speed of propagation of gravity is finite. The linear transformations of special relativity are applied to Newton’s law of gravitation to take into account the relativistic effects of information transmittal in a field of central forces of attraction. Relativistic representations of Newton’s law are obtained with respect to the center of gravity exposing illusory effects that appear at high velocities. It is verified that in atomic physics the effect of Newtonian gravitation on the motion of elementary particles at high velocities is negligible also in relativistic consideration. Computational methods are developed to measure the intensity of gravitation at a distant space-time location using a body that travels in space, emitting uniform pulses of light that are received by the observer at a different space-time location. It is demonstrated that the tensor approach to the general relativity and the united theory of space, time and gravitation in which the geometrical properties (metric) of the four-dimensional space-time continuum depend on the distribution of gravitating masses in space and their motion represent a transformed Lorentz invariant with a new type of inertia in the field of forces changing in space and time. Real physical processes evolve according to the forces represented in the tensor form by this invariant which is equivalent to the coordinate-free local invariant of relativistic dynamics that defines the field and the motion of a body whose velocities and accelerations can be measured by relativistic identification methods at a point, time and direction of interest. The results open new avenues for research in the general relativity and can be used for software development, field measurements and experimental studies in application to distant or fast moving systems.     

An inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities

In this paper, we investigate an inexact hybrid projection-proximal method for solving a class of generalized mixed variational inequalities in Hilbert spaces. We construct a general inexact hybrid projection-proximal point algorithm, in which an inexact relaxed proximal point step is followed by a suitable orthogonal projection onto a hyperplane. Under some suitable conditions concerned with the pseudomonotone set-valued mapping T, the nonsmooth convex function f and the step size λ_k, we prove the convergence of the inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities in Hilbert spaces.     

Two-way D algorithm for path planning and replanning

Inspired by the Witkowski’s algorithm, we introduce a novel path planning and replanning algorithm — the two-way D^∗ (TWD^∗) algorithm — based on a two-dimensional occupancy grid map of the environment. Unlike the Witkowski’s algorithm, which finds optimal paths only in binary occupancy grid maps, the TWD^∗ algorithm can find optimal paths in weighted occupancy grid maps. The optimal path found by the TWD^∗ algorithm is the shortest possible path for a given occupancy grid map of the environment. This path is more natural than the path found by the standard D^∗ algorithm as it consists of straight line segments with continuous headings. The TWD^∗ algorithm is tested and compared to the D^∗ and Witkowski’s algorithms by extensive simulations and experimentally on a Pioneer 3DX mobile robot equipped with a laser range finder.     

The automatic model selection and variable kernel width for RBF neural networks

The Orthogonal Least Squares (OLS) algorithm has been extensively used in basis selection for RBF networks, but it is unable to perform model selection automatically because the tolerance ρ must be specified manually. This introduces noise and it is difficult to implement in the parametric complexity of real-time system. Therefore, a generic criterion that detects the optimum number of its basis functions is proposed. In this paper, not only the Bayesian Information Criterion (BIC) method, used for fitness calculation, is incorporated into the basis function selection process of the OLS algorithm for assigning its appropriate number, but also a new method is developed to optimize the widths of the Gaussian functions in order to improve the generalization performance. The augmented algorithm is employed to the Radial Basis Function Neural Networks (RBFNN) for known and unknown noise nonlinear dynamic systems and its performance is compared with the standard OLS; experimental results show that both the efficacy of BIC for fitness calculation and the importance of proper choice of basis function widths are significant.     

Growing fuzzy topology adaptive resonance theory models with a push-pull learning algorithm

A new incrementally growing neural network model, called the growing fuzzy topology ART (GFTART) model, is proposed based on integrating the conventional fuzzy ART model with the incremental topology-preserving mechanism of the growing cell structure (GCS) model. This is in addition, to a new training algorithm, called the push-pull learning algorithm. The proposed GFTART model has two purposes: First, to reduce the proliferation of incrementally generated nodes in the F2 layer by the conventional fuzzy ART model based on replacing each F2 node with a GCS. Second, to enhance the class-dependent clustering representation ability of the GCS model by including the categorization property of the conventional fuzzy ART model. In addition, the proposed push-pull training algorithm enhances the cluster discriminating property and partially improves the forgetting problem of the training algorithm in the GCS model.     

Adaptive RTRL based neurocontroller for damping subsynchronous oscillations using TCSC

Modern interconnected electrical power systems are complex and require perfect planning, design and operation. Hence the recent trends towards restructuring and deregulation of electric power supply has put great emphasis on the system operation and control. Flexible AC transmission system (FACTS) devices such as thyristor controlled series capacitor (TCSC) are capable of controlling power flow, improving transient stability and mitigating subsynchronous resonance (SSR). In this paper an adaptive neurocontroller is designed for controlling the firing angle of TCSC to damp subsynchronous oscillations. This control scheme is suitable for non-linear system control, where the exact linearised mathematical model of the system is not required. The proposed controller design is based on real time recurrent learning (RTRL) algorithm in which the neural network (NN) is trained in real time. This control scheme requires two sets of neural networks. The first set is a recurrent neural network (RNN) which is a fully connected dynamic neural network with all the system outputs fed back to the input through a delay. This neural network acts as a neuroidentifier to provide a dynamic model of the system to evaluate and update the weights connected to the neurons. The second set of neural network is the neurocontroller which is used to generate the required control signals to the thyristors in TCSC. This is a single layer neural network. Performance of the system with proposed neurocontroller is compared with two linearised controllers, a conventional controller and with a discrete linear quadratic Gaussian (DLQG) compensator which is an optimal controller. The linear controllers are designed based on a linearised model of the IEEE first benchmark system for SSR studies in which a modular high bandwidth (six-samples per cycle) linear time-invariant discrete model of TCSC is interfaced with the rest of the system. In the proposed controller, since the response time is highly dependent on the number of states of the system, it is often desirable to approximate the system by its reduced model. By using standard Hankels norm approximation technique, the system order is reduced from 27 to 11th order by retaining the dominant dynamic characteristics of the system. To validate the proposed controller, computer simulation using MATLAB is performed and the simulation studies show that this controller can provide simultaneous damping of swing mode as well as torsional mode oscillations, which is difficult with a conventional controller. Moreover the fast response of the system can be used for real-time applications. The performance of the controller is tested for different operating conditions.     

An elitist non-dominated sorting genetic algorithm enhanced with a neural network applied to the multi-objective optimization of a polysiloxane synthesis process

This paper presents an original software implementation of the elitist non-dominated sorting genetic algorithm (NSGA-II) applied and adapted to the multi-objective optimization of a polysiloxane synthesis process. An optimized feed-forward neural network, modeling the variation in time of the main parameters of the process, was used to calculate the vectorial objective function of NSGA-II, as an enhancement to the multi-objective optimization procedure. An original technique was utilized in order to find the most appropriate parameters for maximizing the performance of NSGA-II. The algorithm provided the optimum reaction conditions (reaction temperature, reaction time, amount of catalyst, and amount of co-catalyst), which maximize the reaction conversion and minimize the difference between the obtained viscometric molecular weight and the desired molecular weight. The algorithm has proven to be able to find the entire non-dominated Pareto front and to quickly evolve optimal solutions as an acceptable compromise between objectives competing with each other. The use of the neural network makes it also suitable to the multi-objective optimization of processes for which the amount of knowledge is limited.     

一种求解Ramsey数的DNA计算机算法

Ramsey理论是组合数学中一个庞大而又丰富的领域,在集合论、逻辑学、分析以及代数学上具有极重要的应用.Ramsey数的求解是非常困难的,迄今为止只求出9个Ramsey数的准确值.探讨了DNA生物分子超级计算在求解这一困难数学问题的可能性.将Adleman-Lipton模型生物操作与粘贴模型解空间相结合的DNA计算模型...     

基于免疫算法和反向传播神经元网络的无线网络入侵检测研究

为了能够检测到无线网络系统中已知和未知类型的入侵者,提高无线网络系统的安全性,在对网络数据分析和研究的基础上,提出一种基于免疫算法和反向传播神经元网络的入侵检测方法。首先利用免疫算法对网络数据进行预处理,再运用反向传播神经元网络对处理后的数据(程序)进行识别。实验表明用该方法检测无线网络系统中的新型入侵者是可行、有效的,检测入侵者的准确率可达到97%。