Multiple IoT based Network Attacks Discrimination by Multilayer Feedforward Neural Networks

In this paper a new neural model for detection of multiple network IoT-based attacks, such as DDoS TCP, UDP, and HHTP flood, is presented. It consists of feedforward multilayer network with back propagation. A general algorithm for its optimization during training is proposed, leading to proper number of neurons in the hidden layers. The Scaled Gradient Descent algorithm and the Adam optimization are studied with better classification results, obtained by the developed classifiers, using the latter. Tangent hyperbolic function appears to be proper selection for the hidden neurons. Two sets of features, gathered from aggregated records of the network traffic, are tested, containing 8 and 10 components. While more accurate results are obtained for the 10-feature set, the 8-feature set offers twice lower training time and seems applicable for real-world applications. The detection rate for 7 of 10 different network attacks, primarily various types of floods, is higher than 90% and for 3 of them – mainly reconnaissance and keylogging activities with low intensity of the generated traffic, deviates between 57% and 68%. The classifier is considered applicable for industrial implementation.

Verification Analysis of the Relationship Between Soil Pressure and Displacement of Retaining Structure

Variation laws of earth pressure accounting for the displacement of are taining wall can be well described by mathmatical fitting in the study of the relationship between earth pressure and retaining wall displacement. The common mathematical function expressions of earth pressure displacement of retaining wall can be divided into sinusoidal function model, exponential like function model, hyperbolic function model, fitting function and semi-numerical and semi-analytical model function, etc. The characteristics and shortcomings of the current expression of earth pressure displacement function are summarized. Then combined with the field test and model test, the applicability and characteristics of various mathematical functions in predicting the displacement of earth pressure with retaining structures are analyzed. The results show that when the displacement is small, the sinusoidal function model and the quasi-exponential function model are close to the measured results. When the displacement of retaining structure is large, the fitting results of hyperbolic model and semi-numerical and semi-analytical model are better. For the prediction of earth pressure displacement relationship in passive area, the buried depth has a great influence. And the error between the theoretical value and the actual value has a great influence on the fitting result of the model.

Study on Date–Jimbo–Kashiwara–Miwa Equation with Conformable Derivative Dependent on Time Parameter to Find the Exact Dynamic Wave Solutions

In this article, we construct the exact dynamical wave solutions to the Date–Jimbo–Kashiwara–Miwa equation with conformable derivative by using an efficient and well-established approach, namely: the two-variable G’/G, 1/G-expansion method. The solutions of the Date–Jimbo–Kashiwara–Miwa equation with conformable derivative play a vital role in many scientific occurrences. The regular dynamical wave solutions of the abovementioned equation imply three different fundamental functions, which are the trigonometric function, the hyperbolic function, and the rational function. These solutions are classified graphically into three categories, such as singular periodic solitary, kink soliton, and anti-kink soliton wave solutions. Furthermore, the effect of the fractional parameter on these solutions is discussed through 2D plots.

Classification of All Single Traveling Wave Solutions of Fractional Coupled Boussinesq Equations via the Complete Discrimination System Method

In this paper, the complete discrimination system method is used to construct the exact traveling wave solutions for fractional coupled Boussinesq equations in the sense of conformable fractional derivatives. As a result, we get the exact traveling wave solutions of fractional coupled Boussinesq equations, which include rational function solutions, Jacobian elliptic function solutions, implicit solutions, hyperbolic function solutions, and trigonometric function solutions. Finally, the obtained solution is compared with the existing literature.

Deeper properties of the nonlinear Phi-four and Gross-Pitaevskii equations arising mathematical physics

In this paper, the rational sine–cosine and rational sinh–cosh methods are applied in extracting some properties of nonlinear Phi-four and Gross–Pitaevskii equations. The singular periodic wave solutions, dark soliton solutions and hyperbolic function solutions are reported. The solitary waves are observed from the traveling waves under the values of the parameters. Modulation instability analysis is also observed in various simulations. We also plot to observe the wave distributions of parameters of stability in 2D and 3D visuals via package program.

Roles of modified Chaplygin–Jacobi and Chaplygin–Abel gases in FRW universe

In this paper, we have considered flat Friedmann–Robertson–Walker (FRW) model of the universe and reviewed the modified Chaplygin gas as the fluid source. Associated with the scalar field model, we have determined the Hubble parameter as a generating function in terms of the scalar field. Instead of hyperbolic function, we have taken Jacobi elliptic function and Abel function in the generating function and obtained modified Chaplygin–Jacobi gas (MCJG) and modified Chaplygin–Abel gas (MCAG) equation of states, respectively. Next, we have assumed that the universe is filled in dark matter, radiation, and dark energy. The sources of dark energy candidates are assumed as MCJG and MCAG. We have constrained the model parameters by recent observational data analysis. Using [Formula: see text] minimum test (maximum likelihood estimation), we have determined the best-fit values of the model parameters by OHD[Formula: see text]CMB[Formula: see text]BAO[Formula: see text]SNIa joint data analysis. To examine the viability of the MCJG and MCAG models, we have determined the values of the deviations of information criteria like △AIC, △BIC and △DIC. The evolutions of cosmological and cosmographical parameters (like equation of state, deceleration, jerk, snap, lerk, statefinder, Om diagnostic) have been studied for our best-fit values of model parameters. To check the classical stability of the models, we have examined the values of square speed of sound [Formula: see text] in the interval [Formula: see text] for expansion of the universe.

On Soliton Solutions of Perturbed Boussinesq and KdV-Caudery-Dodd-Gibbon Equations

Nonlinear science is a fundamental science frontier that includes research in the common properties of nonlinear phenomena. This article is devoted for the study of new extended hyperbolic function method (EHFM) to attain the exact soliton solutions of the perturbed Boussinesq equation (PBE) and KdV–Caudery–Dodd–Gibbon (KdV-CDG) equation. We can claim that these solutions are new and are not previously presented in the literature. In addition, 2d and 3d graphics are drawn to exhibit the physical behavior of obtained new exact solutions.

Coordinate-free exponentials of general multivector in Cl(p,q) algebras for p+q=3

Closed form expressions in real Clifford geometric algebras Cl(0,3), Cl(3,0), Cl(1,2), and Cl(2,1) are presented in a coordinate-free form for exponential function when the exponent is a general multivector. The main difficulty in solving the problem is connected with an entanglement (or mixing) of vector and bivector components a and a in a form (a-a), i≠ j≠ k . After disentanglement, the obtained formulas simplify to the well-known Moivre-type trigonometric/hyperbolic function for vector or bivector exponentials. The presented formulas may find wide application in solving GA differential equations, in signal processing, automatic control and robotics.

Elliptic- and hyperbolic-function solutions of the nonlocal reverse-time and reverse-space-time nonlinear Schrödinger equations

In this paper, we obtain the stationary elliptic- and hyperbolic-function solutions of the nonlocal reverse-time and reverse-space-time nonlinear Schrödinger (NLS) equations based on their connection with the standard Weierstrass elliptic equation. The reverse-time NLS equation possesses the bounded dn-, cn-, sn-, sech-, and tanh-function solutions. Of special interest, the tanh-function solution can display both the dark- and antidark-soliton profiles. The reverse-space-time NLS equation admits the general Jacobian elliptic-function solutions (which are exponentially growing at one infinity or display the periodical oscillation in x), the bounded dn- and cn-function solutions, as well as the K-shifted dn- and sn-function solutions. At the degeneration, the hyperbolic-function solutions may exhibit an exponential growth behavior at one infinity, or show the gray- and bright-soliton profiles.

2-step reaction kinetics for hydrogen absorption into bulk material via dissociative adsorption on the surface

We have demonstrated that the process of hydrogen absorption into a solid experimentally follows a Langmuir-type (hyperbolic) function instead of Sieverts law. This can be explained by independent two theories. One is the well-known solubility theory which is the basis of Sieverts law. It explains that the amount of hydrogen absorption can be expressed as a Langmuir-type (hyperbolic) function of the square root of the hydrogen pressure. We have succeeded in drawing the same conclusion from the other theory. It is a 2-step reaction kinetics (2sRK) model that expresses absorption into the bulk via adsorption on the surface. The 2sRK model has an advantage to the solubility theory: Since it can describe the dynamic process, it can be used to discuss both the amount of hydrogen absorption and the absorption rate. Some phenomena with absorption via adsorption can be understood in a unified manner by the 2sRK model.