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In this paper, we present a method for the accurate estimation of the derivative (aka. sensitivity) of expectations of functions involving an indicator function by modifying a (stochastic) algorithmic differentiation, replacing the derivative of the indicator function with a suitable operator. We show that we can split this operator into a conditional expectation operator and the density. This allows using different or improved numerical approximation methods for these operators, e.g. regression. The method is an improvement of the approach presented in C.P. Fries [Automatic backward differentiation for American Monte-Carlo algorithms (conditional expectation). Risk, April, 2018; Stochastic automatic differentiation: Automatic differentiation for Monte-Carlo simulations, Quant. Finance 19(6) (2019), pp. 1043–1059]. The finite difference approximation of a partial derivative of a Monte-Carlo integral of a discontinuous function is known to exhibit a high Monte-Carlo error. The issue is evident since the Monte-Carlo approximation of a discontinuous function is just a finite sum of discontinuous functions and as such, not even differentiable. The algorithmic differentiation of a discontinuous function is problematic. A natural approach is to replace the discontinuity by continuous functions. This is equivalent to replacing a path-wise automatic differentiation by a (local) finite difference approximation. The decoupling of the integration of the Dirac delta and the remaining conditional expectation introduced here results in an improvement in terms of variance reduction and implementation design. [ABSTRACT FROM AUTHOR]

This paper presents an improved method for applying smoothed particle hydrodynamics within a nested Lagrangian domain of fluid particles. In our previous implementation, ghost particles, generated by Poisson-disk sampling to enclose the region occupied by fluid particles, transferred necessary physical quantities from the outer domain to the fluid. Using this technique, the local fluid motion agreed with results simulated by SPH over the entire domain. However, the cost of generating ghost particles was burdensome. We propose herein a much less expensive, patch-based sampling method to generate ghost particles. In this new approach, the ghost particles are generated locally around each fluid particle and corresponding physical quantities are determined using the local ghost particles. Furthermore, we introduce a new formulation that determines the physical quantities of ghost particles from the outer domain, and transfers them to the local fluid particles. [ABSTRACT FROM AUTHOR]

In this study, for two-dimensional Maxwell's equations, an efficient preconditioned generalized minimum residual method on the graphics processing unit (GPUPGMRES) is proposed to obtain numerical solutions of the equations that are discretized by a multisymplectic Preissmann scheme. In our proposed GPUPGMRES, a novel sparse matrix–vector multiplication (SpMV) kernel is suggested while keeping the compressed sparse row (CSR) intact. The proposed kernel dynamically assigns different number of rows to each thread block, and accesses the CSR arrays in a fully coalesced manner. This greatly alleviates the bottleneck of many existing CSR-based algorithms. Furthermore, the vector-operation and inner-product decision trees are automatically constructed. These kernels and their corresponding optimized compute unified device architecture parameter values can be automatically selected from the decision trees for vectors of any size. In addition, using the sparse approximate inverse technique, the preconditioner equation solving falls within the scope of SpMV. Numerical results show that our proposed kernels have high parallelism. GPUPGMRES outperforms a recently proposed preconditioned GMRES method, and a preconditioned GMRES implementation in the AmgX library. Moreover, GPUPGMRES is efficient in solving the two-dimensional Maxwell's equations. [ABSTRACT FROM AUTHOR]

In this paper, a three-dimensional (3D) multiscale model is proposed for the formation process of a primary thrombus. In the model, blood plasma is modelled by Navier–Stokes equations in macroscale because the blood plasma is seen as a continuous viscous fluid. The adhesion and aggregation of platelets are the main physiological processes of primary thrombus formation. As platelets and the primary thrombus are seen as rigid solids, these physiological processes are modelled in microscale according to the force related to the distance between the two solid bodies. We use level sets to represent the growth of the primary thrombus in 3D, and the multiscale model is applied to the 3D simulation of the primary thrombus formation. From numerical observations, the appearance of the formation process shows that it was affected by the change of blood-flow velocities. We can conclude that the appearance of the primary thrombus affects vascular blood flow. [ABSTRACT FROM PUBLISHER]

Two algorithms for generating random variables with a rational probability-generating function are presented. One of them implements the recently developed general range reduction method, and the other is an extension of the alias method designed for generating discrete finite-valued random variables to the case where the generated random variable is infinite-valued. An example of a random variable which was efficiently generated by random number generators implementing the presented algorithms is given. Possible ways of improving the complexity of the presented algorithms are discussed. [ABSTRACT FROM PUBLISHER]

Firefly algorithm is a bio-inspired optimization algorithm which has been empirically demonstrated to perform well on many optimization problems. However, it can easily get trapped in the local optima and causes low precision. Therefore, improvement of this disadvantage is the very important. In this paper, we propose a wise strategy for step setting, which considers the information of firefly's personal and the global best positions. The results show that the modified algorithm enhances the performance of the basic firefly algorithm. [ABSTRACT FROM PUBLISHER]

In the multi-focus image fusion problem, the source images are obtained from the same scene. They are fused to get an image that contains all well-focussed objects. Previously, individual machine-learning models are proposed for image fusion. The performance of individual models is limited to fuse the useful information extracted from the blurred images. To address this problem, we developed a novel ensemble scheme for multi-focus image fusion using support vector machines (SVMs). In the proposed scheme, first, SVM models are constructed using different kernel functions of linear, polynomial, radial basis, and sigmoid. The predictions of individual SVM models are then combined using majority voting. In this way, the combined decision space becomes more informative and discriminant. A comparative analysis of the proposed scheme is carried out with previous techniques. It is found that our scheme is more accurate for synthesized-blurred and real defocussed images. [ABSTRACT FROM AUTHOR]

If we are observing very small objects in the microscope the information appears somehow distorted. This distortion is called point spread function (PSF) and it can be measured and simulated as we show in this article. Many experiments and simulations were done in the field of confocal or deconvolution microscopy, but we want to present 3D reconstruction and measurement of PSF in the bright field (or phase contrast) microscopy. Our goal is to use this knowledge about PSF to estimate objective focus. We want to use this method for automatic focusing of the microscope. We measured the PSF on our microscope in bright field using a 100×objective. We used 15 nm gold and 200 nm latex particles as point sources. We used two different simulations; first one was Airy disc simulation; the second one was Extended Nijboer–Zernike theory. Both approaches were used for description of PSF and finding the position of the focus. [ABSTRACT FROM PUBLISHER]

In this paper, a novel semi-fragile watermarking scheme for authenticating an audio signal based on dual-tree complex wavelet transform (DT-CWT) and discrete cosine transform (DCT) is proposed. Specifically, the watermark data are efficiently inserted into the coefficients of the low-frequency sub-band of DT-CWT taking advantages of both DCT and quantization index modulation (QIM). First, the original digital audio signal is segmented and then performed with DT-CWT. Second, based on the energy compression property, the low-frequency sub-band coefficients of the DT-CWT domain are performed with DCT, and the DC component is utilized to embed one distorted watermark bit by the QIM technique. Finally, inverse DCT and DT-CWT are orderly implemented on the watermarked coefficients of each audio segment to get a watermarked audio signal. Simulation results show that the hybrid embedding domain constructed by DT-CWT and DCT is effective, and the proposed watermarking scheme is not only inaudible, but also robust against content persistent non-malicious audio signal processing operations, such as MP3 compression, noise addition, re-sampling, re-quantization, etc. Furthermore, the proposed scheme can effectively authenticate the veracity and integrity of audio content and greatly expands the applicability of the audio watermarking scheme. [ABSTRACT FROM AUTHOR]

In this paper, the sufficient conditions that guarantee the convergence of the variational iteration method when applied to solve a coupled system of nonlinear partial differential equations are presented. Especial attention is given to the error bound of the nth term of the resultant sequence. Numerical examples to show the efficiency of the method are presented. [ABSTRACT FROM AUTHOR]

This work is carried out within a research collaboration with the Astronomical Observatory of Arcetri (Florence, Italy) aimed at the development of a parallel version of the adaptive optics simulation software named CAOS (Code for Adaptive Optics System). CAOS is currently used at the Arcetri Observatory to simulate the behaviour of an adaptive optic system, from the atmospheric turbulence corruption to the subsequent adaptive correction made on the wavefronts coming from the astronomical objects onto the pupils of the ground-based telescopes. We describe the computational efforts towards the integration of the CAOS package into a high-performance computing architecture, implementing three different parallelization approaches of a fast fourier transform (FFT)-based CAOS module and discuss the performance using standard performance metrics. [ABSTRACT FROM AUTHOR]

In the context of finite population survey sampling, we propose a new model-based mean estimator, when the function that links the variables is discontinuous. The available estimators of the mean based on nonparametric regression are derived under the assumption that the regression function is continuous. We propose a new approach to adjust for the effect of discontinuity on regression estimation of the mean. The performance of the proposed estimator is analysed through a simulation study because the theoretic study of asymptotics is not possible. In the literature, the new estimator requires more computational cost than others, but the simulation experiments indicate that the proposed method has higher efficiency than other traditional parametric and nonparametric regression methods. [ABSTRACT FROM AUTHOR]