A DEEP DIVE INTO THE BASICS OF DEEP LEARNING

Deep learning is a type of machine learning (ML) that is growing in importance in the medical field. It can often perform better than traditional ML models on different metrics, and it can handle non-linear problems due to activation functions. Activation functions are different non-linear functions that are used to restrict the values propagated to an interval. In deep learning, information propagates forward, passing through different layers of weights and activation functions, before reaching the final layer. Then a cost function is evaluated and propagated back through the network to adjust weights. A convolutional neural network (CNN) is a form of deep learning that is used primarily in imaging. CNNs perform significantly well with grid-like inputs because they learn shapes well. CNNs compute dot products between layers and kernels in a convolutional layer, prior to pooling, which outputs summary statistics. CNNs are better than trivial neural networks for imaging due to a number of reasons, like sparse interaction and equivariance of translation

Numerical Spline Method for Simulation of Stochastic Differential Equations systems: طريقة شرائحية عددية لمحاكاة حل نظم من المعادلات التفاضلية العشوائية

In this paper, numerical spline method is presented with collocation two parameters for solving systems of multi-dimensional stochastic differential equations (SDEs). Multi-Wiener's time-continuous process is simulated as a discrete process, and then the mean-square stability of proposed method when applied to a system of two-dimensional linear SDEs is studied. The study shows that the method is mean-square stability and third-order convergent when applied to a system of linear and nonlinear SDEs. Moreover, the effectiveness of our method was tested by solving two test linear and non-linear problems. The numerical results show that the accuracy and applicability of the proposed method are worthy of attention.

VISCOSITY IN SEAKEEPING

Application of strip theory for the prediction of ship motions in waves relies on sectional hydrodynamic coefficients; i.e. the added mass and damping coefficients. These coefficients apply to linearised problems and are normally computed for inviscid fluids. It is possible to account for viscosity but this cannot be done by the RANS equations, as in linear problems there is no room for turbulence. The hydrodynamic coefficients can include the effect of viscosity but this can be done rightly through the classic Navier–Stokes equations for laminar (non-turbulent) flows. For solving these equations commercial RANS software can be used, assuming no Reynolds stresses.

The Simulation of One-Step Algorithms for Treating Higher Order Initial Value Problems

The simulation of one-step methods using interpolation and collocation for the treatment of higher order initial value problems is proposed in this paper. The new approach is derived using interpolation and collocation as a basic function through power series polynomial, where the basic properties are also analyzed. The derived method is used to treat some highly stiff linear problems. The new approach compute clearly showed that the method is reliable, efficient and gives faster convergence when compared with those in literature.

Dynamic Characteristic Analysis of Vibration Screen Based on Joint Face Analysis

Vibrating screens play an important role in industrial production. While the cross beam fracture is the main reason for the shutdown of the screen. In order to solve the problem of fatigue fracture of the beam of the large-scale vibrating screen, the 3.6x7.3 m banana vibrating screen was taken as the research object, and the joint surface analysis was introduced at the joint surface of each part of the beam to simulate the stiffness and stress concentration of the joint surface, so that the nonlinear problems will be transformed into linear problems, and the stress and deformation of the connection area are correctly simulated, thereby this project has given an accurate basis for further optimization and optimizing the structure.

Extended Fully Fuzzy Linear Regression to Analyze a Solid Cantilever Beam Moment

There are several procedures such as possibilistic and least-square methods to estimate regression models. In this study, first, a fully fuzzy regression equation is converted into a fully fuzzy linear framework. By considering a least-square approach, a model is suggested based on matrix equations for solving fully fuzzy regression models. The main advantage of this method over existing ones is that this method considered values based on their specification, and all linear problems can be easily solved. Moreover, a case study for solid mechanics about the quantity of beam momentum is considered. In this example, the inner data are force values, and the output is momentum values.

The Direct Simulation of Third Order Linear Problems on Single Step Block Method

In this article, the direct simulation of third order linear problems on single step block method has been proposed. In order to overcoming the setbacks in reduction method, direct method has been proposed using power series to reduce computational burden that occur in the reduction method. Numerical properties for the block method are established and the method developed is consistent, convergent and zero-stable. To validate the accuracy of the block method, certain numerical test problems were considered, the results shown that the accuracy of our method are more accurate over the existing method in literature.

Emergency of Tsallis statistics in fractal networks

Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy collisions, or from the number of contacts one person has, on average, to the flux of vehicles in the streets of urban centres, all these complex, non-linear problems are better understood under the light of the scale-free network’s properties. A few mechanisms have been found to explain the emergence of scale invariance in complex networks, and here we discuss a mechanism based on the way information is locally spread among agents in a scale-free network. We show that the correct description of the information dynamics is given in terms of the q-exponential function, with the power-law behaviour arising in the asymptotic limit. This result shows that the best statistical approach to the information dynamics is given by Tsallis Statistics. We discuss the main properties of the information spreading process in the network and analyse the role and behaviour of some of the parameters as the number of agents increases. The different mechanisms for optimization of the information spread are discussed.