Optimal design of wireless sensor network for ionising radiation detection using Neyman–Pearson criteria

This paper deals with the optimal design of wireless sensor network (WSN) with parallel configuration using Neyman–Pearson methodology for monitoring and detecting the possible presence of ionising radiations in the vicinity of a nuclear power plant. We derive the design equations for the WSN with parallel configuration, focusing only on the signal processing task under certain assumptions. We present the detection performance of individual node and network of sensor nodes under two different operating options for different network parameters and sensor characteristics to understand the design trade-offs between sensor network parameters and performance measures. We also assess the robustness of the network designed against node failures.     

An efficient parallel solution for Caputo fractional reaction–diffusion equation

The computational complexity of Caputo fractional reaction–diffusion equation is \(O(MN^2)\) compared with \(O(MN)\) of traditional reaction–diffusion equation, where \(M\) , \(N\) are the number of time steps and grid points. A efficient parallel solution for Caputo fractional reaction–diffusion equation with explicit difference method is proposed. The parallel solution, which is implemented with MPI parallel programming model, consists of three procedures: preprocessing, parallel solver and postprocessing. The parallel solver involves the parallel tridiagonal matrix vector multiplication, vector vector addition and constant vector multiplication. The sum of constant vector multiplication is optimized. As to the authors’ knowledge, this is the first parallel solution for Caputo fractional reaction–diffusion equation. The experimental results show that the parallel solution compares well with the analytic solution. The parallel solution on single Intel Xeon X5540 CPU runs more than three times faster than the serial solution on single X5540 CPU core, and scales quite well on a distributed memory cluster system.     

An efficient adaptive three-term extension of the Hestenes–Stiefel conjugate gradient method

A new three-term Hestenes–Stiefel-type conjugate gradient method is proposed in which the search direction can satisfy the sufficient descent condition as well as an adaptive conjugacy condition. It is notable that search directions of the method are dynamically adjusted between that of the Newton method and the 3HS+ method, accelerating the convergence or reducing the condition number of iteration matrix. Under mild conditions, we show that the proposed method converges globally for general objective functions. Numerical experiments indicate that the method is practically promising.     

An extended basis inexact shift–invert Lanczos for the efficient solution of large-scale generalized eigenproblems

This paper proposes a technique, based on the Inexact Shift–Invert Lanczos (ISIL) method with Inexact Jacobi Orthogonal Component Correction (IJOCC) refinement, and a preconditioned conjugate-gradient (PCG) linear solver with multilevel preconditioner, for finding several eigenvalues for generalized symmetric eigenproblems. Several eigenvalues are found by constructing (with the ISIL process) an extended projection basis. Presented results of numerical experiments confirm the technique can be effectively applied to challenging, large-scale problems characterized by very dense spectra, such as resonant cavities with spatial dimensions which are large with respect to wavelengths of the resonating electromagnetic fields. It is also shown that the proposed scheme based on inexact linear solves delivers superior performance, as compared to methods which rely on exact linear solves, indicating tremendous potential of the ‘inexact solve’ concept. Finally, the scheme which generates an extended projection basis is found to provide a cost-efficient alternative to classical deflation schemes when several eigenvalues are computed.     

Stochastic resonance in binary composite hypothesis-testing problems in the Neyman–Pearson framework

Performance of some suboptimal detectors can be enhanced by adding independent noise to their inputs via the stochastic resonance (SR) effect. In this paper, the effects of SR are studied for binary composite hypothesis-testing problems. A Neyman–Pearson framework is considered, and the maximization of detection performance under a constraint on the maximum probability of false-alarm is studied. The detection performance is quantified in terms of the sum, the minimum, and the maximum of the detection probabilities corresponding to possible parameter values under the alternative hypothesis. Sufficient conditions under which detection performance can or cannot be improved are derived for each case. Also, statistical characterization of optimal additive noise is provided, and the resulting false-alarm probabilities and bounds on detection performance are investigated. In addition, optimization theoretic approaches to obtaining the probability distribution of optimal additive noise are discussed. Finally, a detection example is presented to investigate the theoretical results.     

A Novel Noise-Enhanced Back-Propagation Technique for Weak Signal Detection in Neyman–Pearson Framework

Neural Processing Letters - In this paper, we propose a noise enhanced neural network based detector. The proposed method can detect the known weak signal in additive non-Gaussian noise. Carefully...     

Noise enhanced hypothesis-testing according to restricted Neyman–Pearson criterion

Noise enhanced hypothesis-testing is studied according to the restricted Neyman–Pearson (NP) criterion. First, a problem formulation is presented for obtaining the optimal probability distribution of additive noise in the restricted NP framework. Then, sufficient conditions for improvability and nonimprovability are derived in order to specify if additive noise can or cannot improve detection performance over scenarios in which no additive noise is employed. Also, for the special case of a finite number of possible parameter values under each hypothesis, it is shown that the optimal additive noise can be represented by a discrete random variable with a certain number of point masses. In addition, particular improvability conditions are derived for that special case. Finally, theoretical results are provided for a numerical example and improvements via additive noise are illustrated.     

An efficient solution of the resource allotment problem with the Groves–Ledyard mechanism under transferable utility

This paper designs an allotment mechanism for a limited amount of an infinitely divisible good (resource) among a finite number of agents under transferable utility. The mechanism is efficient in the sense of total agents’ utility maximization. As a solution, we introduce an adaptation of the Groves–Ledyard “quadratic government” that was initially suggested for the problem of public good.     

Comments on the applicability of “An improved weighted recursive PCA algorithm for adaptive fault detection”

This paper discusses some limitations of the weighted recursive PCA algorithm (WARP) proposed by Portnoy, Melendez, Pinzon, and Sanjuan (2016) which is used for fault detection (FD) by arguing that it can reduce false alarms. The motivation of these comments is the lack of a clear criterion in the WARP algorithm to distinguish between process deviations and faults' scenarios, and as a consequence, the applicability of this algorithm is questionable from the FD point of view. Moreover, we address the absence of a formal justification why the computational complexity achieved by using the WARP algorithm is reduced in comparison with methods discussed in the paper.     

An adaptive approach for the reduction of quantization errors†

This paper presents an adaptive quantization scheme for the reduction of the percentage error in the output of the quantizer. The improvement in the system performance is illustrated by simulating a uniform step and an adaptive quantizer on a digital computer and comparing their outputs. A significant improvement in the output is achieved by using the suggested scheme.     

An efficient split-step compact finite difference method for the coupled Gross–Pitaevskii equations

ABSTRACT

In this study, we propose an efficient split-step compact finite difference (SSCFD) method for computing the coupled Gross–Pitaevskii (CGP) equations. The coupled equations are divided into two parts, nonlinear subproblems and linear ones. Commonly, the nonlinear subproblems could be integrated directly and accurately, but it fails when the time-dependent potential cannot be integrated exactly. In this case, the midpoint and trapezoidal rules are applied approximately. At the same time, the split order is not reduced. For the linear ones, compact finite difference cannot be designed directly. To circumvent this problem, a linear transformation is introduced to decouple the system, which can make the split-step method be used again. Additionally, the proposed SSCFD method also holds for the coupled nonlinear Schrödinger (CNLS) system with time-dependent potential. Finally, numerical experiments for CGP equations and CNLS equations are well simulated, conservative properties and convergence rates are demonstrated as well. It is shown from the numerical tests that the present method is efficient and reliable.     

A closed-form expression for the quantile function of the Gompertz–Makeham distribution

In this note, we give a closed-form expression in terms of the Lambert W function for the quantile function of the Gompertz–Makeham distribution. This probability distribution has frequently been used to describe human mortality and to establish actuarial tables. The analytical expression provided for the quantile function is helpful to generate random samples drawn from the Gompertz–Makeham distribution by means of the inverse transform method.     

An iterative Langevin solution for contaminant dispersion simulation using the Gram–Charlier PDF

An alternative numerical method to solve the three-dimensional stochastic Langevin equation applied to the air pollution dispersion is proposed and tested. We obtain a first-order differential equation whose solution is known and determined by an integrating factor. A Langevin model for inhomogeneous turbulence is obtained, considering the Gram–Charlier Probability Density Function (PDF) of turbulent velocity. The calculus process is based on an iterative scheme through the Picard Iterative Method. Numerical simulations and comparisons with measured data from two different tracer experiments are realized, showing a good agreement between predicted and observed values. Furthermore, the results obtained with the new approach are compared with the ones obtained by three different models.     

An efficient split-step quasi-compact finite difference method for the nonlinear fractional Ginzburg–Landau equations

In this paper, we propose a split-step quasi-compact finite difference method to solve the nonlinear fractional Ginzburg–Landau equations both in one and two dimensions. The original equations are split into linear and nonlinear subproblems. The Riesz space fractional derivative is approximated by a fourth-order fractional quasi-compact method. Furthermore, an alternating direction implicit scheme is constructed for the two dimensional linear subproblem. The unconditional stability and convergence of the schemes are proved rigorously in the linear case. Numerical experiments are performed to confirm our theoretical findings and the efficiency of the proposed method.     

An analytic solution for the space–time fractional advection–dispersion equation using the optimal homotopy asymptotic method

We present an analytic algorithm to solve the space–time fractional advection–dispersion equation (FADE) based on the optimal homotopy asymptotic method (OHAM), which has the advantage of controlling the region and rate of convergence of the solution series via several auxiliary parameters over the traditional homotopy analysis method (HAM) having only one auxiliary parameter. Furthermore, our proposed algorithm gives better results compared to the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM) in the sense that fewer iterations are required to get a sufficiently accurate solution and the solution has a greater radius of convergence. We find that the iterations obtained by the proposed method converge to the numerical/exact solution of the ADE as the fractional orders $\alpha ,\beta ,\gamma$ tend to their integral values. Numerical examples are given to illustrate the proposed algorithm. The figures and tables show the superiority of the OHAM over the HAM.     

EFFORT: A new host–network cooperated framework for efficient and effective bot malware detection

Bots are still a serious threat to Internet security. Although a lot of approaches have been proposed to detect bots at host or network level, they still have shortcomings. Host-level approaches can detect bots with high accuracy. However they usually pose too much overhead on the host. While network-level approaches can detect bots with less overhead, they have problems in detecting bots with encrypted, evasive communication C&C channels. In this paper, we propose EFFORT, a new host–network cooperated detection framework attempting to overcome shortcomings of both approaches while still keeping both advantages, i.e., effectiveness and efficiency. Based on intrinsic characteristics of bots, we propose a multi-module approach to correlate information from different host- and network-level aspects and design a multi-layered architecture to efficiently coordinate modules to perform heavy monitoring only when necessary. We have implemented our proposed system and evaluated on real-world benign and malicious programs running on several diverse real-life office and home machines for several days. The final results show that our system can detect all 17 real-world bots (e.g., Waledac, Storm) with low false positives (0.68%) and with minimal overhead. We believe EFFORT raises a higher bar and this host–network cooperated design represents a timely effort and a right direction in the malware battle.     

An hp finite element adaptive scheme to solve the Laplace model for fluid–solid vibrations

In this paper we introduce an hp finite element method to solve a two-dimensional fluid–structure spectral problem. This problem arises from the computation of the vibration modes of a bundle of parallel tubes immersed in an incompressible fluid. We prove the convergence of the method and a priori error estimates for the eigenfunctions and the eigenvalues. We define an a posteriori error estimator of the residual type which can be computed locally from the approximate eigenpair. We show its reliability and efficiency by proving that the estimator is equivalent to the energy norm of the error up to higher order terms, the equivalence constant of the efficiency estimate being suboptimal in that it depends on the polynomial degree. We present an hp adaptive algorithm and several numerical tests which show the performance of the scheme, including some numerical evidence of exponential convergence.