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In this paper, a combination of a time discrete technique on graded meshes with barycentric rational interpolation is employed to solve a class of one- and two-dimensional time-dependent partial integro-differential equations with weakly singular kernels. Equations of this type are also commonly called fractional evolution equations, whose solutions have some singular behaviours near the initial time. This makes that it's difficult to reach an expected convergence result for the numerical treatment concerning time variable on uniform meshes. In the temporal direction, a generalized Crank-Nicolson difference scheme and the product integration formula on graded meshes are used to discretize the differential term and the integral term, respectively. Moreover, it's proved that the time discrete scheme is unconditionally stable and quadratically convergent. Further, a fully discrete numerical approach is structured with spacial directional discretization in terms of barycentric rational interpolation. The results of numerical experiments display the efficiency of the method and confirm the theoretical analyses. In addition, the present scheme can reach second-order convergence in time both for smooth initial value and non-smooth initial value. [ABSTRACT FROM AUTHOR]

Although the herbicide linuron is banned for use in the EU due to its reproductive and developmental toxicity, it can still be found in randomly sampled foods grown in and outside the EU. It is not clear if metabolites of linuron can contribute to the endocrine disrupting effects following exposure to the parent compound. To address this gap, we analysed linuron and the metabolites 1-(3,4-dichlorophenyl) urea (DCU), 3,4-dichloroaniline (DCA) and 1-(3,4-dichlorophenyl)-3-methoxyurea (DCXU) for androgen receptor (AR) activities and effects on steroidogenesis. Generally, linuron and the metabolites showed qualitatively similar antiandrogenic profiles, but potencies varied. All compounds were AR antagonists, with linuron showing highest potency (IC 50 of 2.8 μM). The overall picture of effects on steroidogenesis showed that linuron and metabolites increased the levels of estrogens and corticosteroids, whereas the synthesis of androgens was inhibited. The metabolite DCU was by far the most potent inhibitor of testosterone synthesis (IC 50 of 6.7 μM compared to IC 50 of 51.1 μM for linuron). We suggest that it is likely that the metabolites contribute to the antiandrogenic effects of linuron in vivo , especially by inhibiting testosterone synthesis. [Display omitted] • Potency ranking for hAR antagonism: Linuron > DCXU > DCA > DCU. • Metabolite DCU is the most potent testosterone synthesis inhibitor in vitro. • The metabolites may contribute to linuron-induced male reproductive toxicity. [ABSTRACT FROM AUTHOR]

This paper proposes numerical quadrature rules for two-dimensional Cauchy principal-value integrals of the forms ∫ ∫ Ω f (x , y) (x − s) 2 + (y − t) 2 d y d x and ∫ ∫ Ω f (x , y) (x − s) (y − t) d y d x. The derivation of these quadrature rules is based on the Euler–Maclaurin error expansion of a modified trapezoidal rule for one-dimensional Cauchy singular integrals. The corresponding error estimations are investigated, and the convergence rates O (h m 2 μ + h n 2 μ) are obtained for the proposed quadrature rules, where h m and h n are partition sizes in x and y directions, μ is a positive integer determined by integrand. To further improve accuracy, a splitting extrapolation algorithm is developed based on the asymptotic error expansions. Several numerical tests are performed to verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Graphical abstract illustrating the approach used for identifying the chemical mixture risk drivers for male reproductive health. [Display omitted] Scientific evidence for underestimated toxicity from unintentional exposure to chemical mixtures is mounting. Yet, harmonized approaches on how to assess the actual risk of mixtures is lacking. As part of the European Joint programme 'Human Biomonitoring for Europe' we explored a novel methodology for mixture risk assessment of chemicals affecting male reproductive function. We explored a methodology for chemical mixture risk assessment based on human in vitro data combined with human exposure data, thereby circumventing the drawbacks of using hazard data from rodents and estimated exposure intake levels. Human androgen receptor (hAR) antagonism was selected as the most important molecular initiating event linked to adverse outcomes on male reproductive health. Our work identified 231 chemicals able to interfere with hAR activity. Among these were 61 finally identified as having both reliable hAR antagonist and human biomonitoring data. Calculation of risk quotients indicated that PCBs (118, 138, 157), phthalates (BBP, DBP, DIBP), benzophenone-3, PFOS, methylparaben, triclosan, some pesticides (i.e cypermethrin, β-endosulfan, methylparathion, p,p-DDE), and a PAH metabolite (1-hydroxypyrene) contributed to the mixture effect. The major chemical mixture drivers were PCB 118, BBP, PFOS, DBP, and the UV filter benzophenone-3, together contributing with 75% of the total mixture effect that was primarily driven by high exposure values. This viable way forward for mixture risk assessment of chemicals has the advantages of (1) being a more comprehensive mixture risk assessment also covering data-poor chemicals, and (2) including human data only. However, the approach is subjected to uncertainties in terms of in vitro to in vivo extrapolation, it is not ready for decision making, and needs further development. Still, the results indicate a concern for adverse effects on reproductive function in highly exposed boys, especially when considering additional exposure to data-poor chemicals and chemicals acting by other mechanisms of action. [ABSTRACT FROM AUTHOR]

Lithium-ion batteries have become the main power source of many electronic devices. Accurate capacity estimation and cycle life prediction of lithium-ion batteries are of great significance to ensure the reliability of electronic devices. Extreme learning machine(ELM) is a kind of single hidden layer feedforward neural network with fast learning speed and good generalization performance. Considering the shortcomings of deep learning and the increasing size of battery datasets, this paper introduces the idea of Broad Learning(BL) and develops a new ELM model: Broad Learning-Extreme Learning Machine(BL-ELM). First, an ELM network is constructed, and the feature nodes are produced by feature mapping of the input data. Second, the enhancement operation is performed on the mapped features to produce the enhancement nodes. Next, all these two kinds of nodes are merged to become the new input layer of the network, so that the model can quickly and fully obtain effective feature information from the input data. Finally, experiments are performed with different battery datasets. The results show that BL-ELM method can not only ensure the accuracy of estimation and prediction but also save time greatly. Further comparisons with other algorithms show that this novel model is more effective and competitive. Image 1 • A new method of battery capacity estimation and cycle life prediction is developed. • The hybrid neural network of extreme learning machine and broad learning is applied. • This model overcomes the complexity of deep learning and is easy to implement. • NASA, CALCE and multi-dimensional MIT&Stanford battery datasets are considered. • The developed method is more competitive in time and precision. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a quadrature method based on multi-variate Bernstein polynomials. The method is used to solve multidimensional Volterra integral equations with weakly singular kernels. Firstly, we use multi-variate Bernstein polynomials to approximate the unknown function of an equation, then a discrete function equation can be obtained by substituting the approximate solution into the equation. Secondly, the discrete function system is transformed into an algebra equation system by using some discrete points. We can perform the integral operations without discrete kernel function, and the weakly singular integrals can be calculated directly by using quadrature method, so the method is easy to implement. Thirdly, we prove the existence and uniqueness of the solution of the approximate equation, as well as the error analysis of the proposed method. Six numerical examples are given to illustrate the efficiency of this method. [ABSTRACT FROM AUTHOR]

The interface flux plays an important role in designing numerical methods for scalar conservation laws with discontinuous flux function in space. Based on the (A , B) -type entropy solutions defined by Bürger et al. (2009), we introduce a new modified Local Lax–Friedrichs interface flux to approximate this system. The interface flux is Lipschitz continuous and monotone with respect to its two variables. Moreover, we present some numerical experiments to demonstrate the efficiency of our method. [ABSTRACT FROM AUTHOR]

Highlights • An improved Lagrange polynomial are provided for solving multi dimensional systems of Fredholm integral equations. • The technique can improve the common disadvantages of the Lagrange interpolation, which is stable with special nodal distribution. • Theoretical analysis and convincible numerical examples are provided. • The method can easily extend to solve multi dimensional integro-differential problems. Abstract A highly accurate meshfree approach based on the barycentric Lagrange basis functions is reported for solving the linear and nonlinear multi-dimensional systems of Fredholm integral equations (FIEs) of the second kind. The method is an improved Lagrange interpolation technique which possesses high precision and inexpensive procedure. The systems of FIEs are handled with the barycentric formula and transformed into the corresponding linear and nonlinear systems of algebraic equations. The stability of the solved integral equation systems is guaranteed by the numerical stability of the barycentric Lagrange formula, which is dominated by barycentric weights. The convergence analysis and error estimation are included. Some computational results indicate that the method is simple and efficient. [ABSTRACT FROM AUTHOR]