This paper proposes an image encryption algorithm based on a chaotic map and information entropy. Unlike Fridrich’s structure, the proposed method contains permutation, modulation, diffusion (PMD) operations. avoids shortcoming in traditional schemes of strictly shuffling pixel positions before encryption. Information entropy is employed to influence generation keystream. The initial keys used permutation stages interact with each other. As result, acts as indivisible entity enhance...

Uplift modeling is an emerging machine learning approach for estimating the treatment effect at individual or subgroup level. It can be used optimizing performance of interventions such as marketing campaigns and product designs. to estimate which users are likely benefit from a then prioritize delivering promoting preferred experience those users. An important but so far neglected use case uplift experiment with multiple groups that have different costs, example when communication channels...

In this article, a backward heat conduction problem is considered. A modified Tikhonov regularization method presented and error estimates are obtained with an priori strategy posteriori choice rule to find the parameter. Numerical tests show that proposed effective stable.

A numerical differentiation problem for a given function with noisy data is discussed in this paper. truncated spectral method has been introduced to deal the ill-posedness of problem. The theoretical analysis shows that smoother genuine solution, higher convergence rate solution by our method. Numerical examples are also show efficiency

Based on the idea of Fourier extension, we develop a new method for numerical differentiation two-dimensional functions an arbitrary domain. The function will be extended to periodic larger Tikhonov regularization in Hilbert scales is presented deal with ill-posedness problem. Sobolev norm defined domain used as stabilizer. An error analysis provided parameter chosen by discrepancy principle. Numerical experiments are also illustrate effectiveness proposed method.

We develop a multi-dimensional numerical differentiation method in this paper. To obtain stable derivatives, the Tikhonov regularization Hilbert scales is proposed to deal with illposedness of problem. The penalty term functional more general so that we can choose parameter without smoothness and priori bound exact solution. Numerical examples are also presented check effectiveness method.

The numerical analytic continuation of a function f(z) = f(x + iy) on strip is discussed in this paper. Data are only given approximately the real axis. A mollification method based expanded Hermite functions has been introduced to deal with ill-posedness problem. We have shown that parameter can be chosen by discrepancy principle and corresponding error estimate also obtained. Numerical tests show effectiveness method.

In this paper, we consider the problem for determining an unknown source in heat equation. The Tikhonov regularization method Hilbert scales is presented to deal with ill-posedness of and error estimates are obtained a posteriori choice rule find parameter. smoothness parameter priori bound exact solution not needed rule. Numerical tests show that proposed effective stable.

In this article we consider the numerical differentiation of periodic functions specified by noisy data. A new method, which is based on truncated singular value decomposition (TSVD) regularization technique a suitable compact operator, presented and analysed. It turns out method coincides with some type Fourier series approach. Numerical examples are also given to show efficiency method.

In this paper we consider the problem for identifying an unknown steady source in a space fractional diffusion equation. A truncation method based on Hermite function expansion is proposed, and regularization parameter chosen by discrepancy principle. An error estimate between exact solution its approximation given. numerical implementation discussed corresponding results are presented to verify effectiveness of method.

This paper develops a new method to deal with the problem of identifying unknown source in Poisson equation. We obtain regularization solution by Tikhonov super-order penalty term. The order optimal error bounds can be obtained for various smooth conditions when we choose parameter discrepancy principle and process is uniform. Numerical examples show that proposed effective stable.

Uplift modeling is an emerging machine learning approach for estimating the treatment effect at individual or subgroup level. It can be used optimizing performance of interventions such as marketing campaigns and product designs. to estimate which users are likely benefit from a then prioritize delivering promoting preferred experience those users. An important but so far neglected use case uplift experiment with multiple groups that have different costs, example when communication channels...

In this paper, an inverse problem of determining a source in time-fractional diffusion equation is investigated. A Fourier extension scheme used to approximate the solution avoid impact on smoothness caused by directly using singular system eigenfunctions for approximation. modified implicit iteration method proposed as regularization technique stabilize process. The convergence rates are derived when discrepancy principle serves choosing parameters. Numerical tests provided further verify...

In this paper, we consider the solution of linear ill-posed problems when right-hand side include some noise. A super order regularization scheme in Hilbert scales is proposed, and a theoretical framework under general smoothness conditions established. The process new uniform for various solution, it can adaptively obtain order-optimal error bounds parameter chosen either priori or posteriori by discrepancy principle. We use two model to verify relevant results show details method specific problems.

In this paper, we present a Newton-type method with double regularization parameters for nonlinear ill-pose problems. The key step in the process that reasonable choice rule to determine these two is presented. And convergence and stability of are discussed. Numerical experiment shows effectiveness method.

In this paper, we present a new method for numerical differentiation of bivariate periodic functions when set noisy data is given. TSVD chosen as the needed regularization technique. It turns out coincides with some type truncated Fourier series approach. A example also given to show efficiency method.