Two efficient modifications of AZPRP conjugate gradient method with sufficient descent property

The conjugate gradient method can be applied in many fields, such as neural networks, image restoration, machine learning, deep learning, and many others. Polak–Ribiere–Polyak and Hestenses–Stiefel conjugate gradient methods are considered as the most efficient methods to solve nonlinear optimization problems. However, both methods cannot satisfy the descent property or global convergence property for general nonlinear functions. In this paper, we present two new modifications of the PRP method with restart conditions. The proposed conjugate gradient methods satisfy the global convergence property and descent property for general nonlinear functions. The numerical results show that the new modifications are more efficient than recent CG methods in terms of number of iterations, number of function evaluations, number of gradient evaluations, and CPU time.

Scrambled Linear Pseudorandom Number Generators

F 2 -linear pseudorandom number generators are very popular due to their high speed, to the ease with which generators with a sizable state space can be created, and to their provable theoretical properties. However, they suffer from linear artifacts that show as failures in linearity-related statistical tests such as the binary-rank and the linear-complexity test. In this article, we give two new contributions. First, we introduce two new F 2 -linear transformations that have been handcrafted to have good statistical properties and at the same time to be programmable very efficiently on superscalar processors, or even directly in hardware. Then, we describe some scramblers , that is, nonlinear functions applied to the state array that reduce or delete the linear artifacts, and propose combinations of linear transformations and scramblers that give extremely fast pseudorandom number generators of high quality. A novelty in our approach is that we use ideas from the theory of filtered linear-feedback shift registers to prove some properties of our scramblers, rather than relying purely on heuristics. In the end, we provide simple, extremely fast generators that use a few hundred bits of memory, have provable properties, and pass strong statistical tests.

Global weak solutions to fully cross-diffusive systems with nonlinear diffusion and saturated taxis sensitivity

Systems of the type u t = ∇ ⋅ ( D 1 ( u ) ∇ u − S 1 ( u ) ∇ v ) + f 1 ( u , v ) , v t = ∇ ⋅ ( D 2 ( v ) ∇ v + S 2 ( v ) ∇ u ) + f 2 ( u , v ) ( ⋆ ) can be used to model pursuit-evasion relationships between predators and prey. Apart from local kinetics given by f 1 and f 2, the key components in this system are the taxis terms −∇ ⋅ (S 1(u)∇v) and +∇ ⋅ (S 2(v)∇u); that is, the species are not only assumed to move around randomly in space but are also able to partially direct their movement depending on the nearby presence of the other species. In the present article, we construct global weak solutions of (⋆) for certain prototypical nonlinear functions D i , S i and f i , i ∈ {1, 2}. To that end, we first make use of a fourth-order regularisation to obtain global solutions to approximate systems and then rely on an entropy-like identity associated with (⋆) for obtaining various a priori estimates.

Total Harmonic Distortion of a Piezoelectric MEMS Loudspeaker in an IEC 60318-4 Coupler Estimation Using Static Measurements and a Nonlinear State Space Model

We propose a method to evaluate the Total Harmonic Distortion generated by a cantilever-based PZT loudspeaker inside an IEC 60318-4 coupler. The model is validated using experimental data of a commercial loudspeaker. Using the time domain equations of the equivalent electrical circuit of the loudspeaker inside the coupler and a state space formulation, the acoustic pressure response is calculated and compared to the measurement of the manufacturer. Next, the stiffness, transduction and capacitance nonlinear functions are evaluated with a Double-Beam Laser Interferometer (DBLI) and a nanoindenter on test devices and on the commercial loudspeaker. By introducing the nonlinear functions into the model as amplitude-dependent parameters, the THD generated by the loudspeaker is calculated and compared to the value provided by the manufacturer. The good agreement between the measurement and the simulation could allow for a rather quick simulation of the performance of similarly designed loudspeakers at the early stage of the design, by only estimating the static linearity of the main nonlinearity sources.

Nonlinear Friction and Resistance, Generating Sources of Optimal Points in the Energy Field of Agricultural Aggregates Working Process

The paper presents a point of view on the main sources that can generate some optimal points in the energy field of the agricultural machines working processes. It looks like a possible source of the existence of optimal points in the energetic field of work processes of agricultural machinery and equipment, are the coefficients of friction and specific resistance to deformation of soil. In the news models these coefficients became nonlinear functions. Similar forms are given for all three coefficients and is shown the existence of optimal points. They make some considerations about this method and include results obtained using it.

Rejection sampling for Bayesian uncertainty evaluation using the Monte Carlo techniques of GUM-S1

Supplement 1 to the GUM (GUM-S1) extends the GUM uncertainty framework to nonlinear functions and non-Gaussian distributions. For this purpose, it employs a Monte Carlo method that yields a probability density function for the measurand. This Monte Carlo method has been successfully applied in numerous applications throughout metrology. However, considerable criticism has been raised against the type A uncertainty evaluation of GUM-S1. Most of the criticism could be addressed by including prior information about the measurand which, however, is beyond the scope of GUM-S1. We propose an alternative Monte Carlo method that will allow prior information about the measurand to be included. The proposed method is based on a Bayesian uncertainty evaluation and applies a simple rejection sampling approach using the Monte Carlo techniques of GUM-S1. The range of applicability of the approach is explored theoretically and in terms of examples. The results are promising, leading us to conclude that many metrological applications could benefit from this approach. Software support is provided to ease its implementation.

Kinetics of epoxy resin optical characteristics during ultrasonic processing

In this paper, the ultrasonic processing of composite based on epoxy resin ED-20 filled by nanoparticle silicon–containing additives PDMS-5 and HDK during its preparation is studied. Changes in optical transmittance spectra of organosilicon gel (PDMS-5+HDK) and of composite ED-20+L-20+(PDMS-5+HDK) are reported. The observed optical transmission changes were modeled from the experimental results. New phenomenological model describing the kinetics of a change in transmittance with ultrasonic processing time of composite is proposed. The nonlinear differential equation of the process is formulated and solved. The solution of equation applies to description of the experimental data of monitoring of transmittance of composite ED-20+L-20+(PDMS-5+HDK) during ultrasonic processing. The nonlinear functions characterized by three plateaus are proposed to describe the experimental data of monitoring of optical properties of organosilicon gel (PDMS-5+HDK) during ultrasonic processing.

Investigation of the effectiveness of metric classification methods in identifying attacks in VANET

This paper discusses the problem of improving the efficiency of metric machine learning methods of identification attacks in vehicular adhoc networks (VANETs). The main idea of this research is to select the type of nonlinear functions for calculating the distances between the objects of the sample, describing the traffic of VANET using metric methods, such as the method of k-nearest neighbour with linearly decreasing weights and the Parzen window method. The analysis of the effectiveness of the methods considered was carried out on a synthetically generated sample with three different types of attacks on the network. Computational experiments have shown that the k-nearest neighbour method with decreasing weights based on an exponential function with base a < 1 is more efficient than the Parzen window method by about 0.3% and has an accuracy of 84.15%.