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We give new explicit formulas as well as new generating functions for the associated Meixner, Charlier, and Krawtchouk polynomials. The obtained results are then used to derive new generating functions and convolution-type formulas of the corresponding classical polynomials. Some consequences of our results are also mentioned. [ABSTRACT FROM AUTHOR]

In this paper, we consider Szász-Durrmeyer type operators based on Charlier polynomials associated with Srivastava-Gupta operators [17]. For the considered operators, we discuss error of estimation by using first and second order modulus of continuity, Lipchtiz-type space, Ditzian-Totik modulus of smoothness, Voronovskaya type asymptotic formula and weighted modulus of continuity. [ABSTRACT FROM AUTHOR]

Purpose: One of the well-known stylized facts of the distribution of asset returns is the pattern of skewness and kurtosis. Previous research has shown that financial crises and turbulences induce shocks that significantly affect the return distributions, which in addition to creating fat tails, also leads to an asymmetric reaction of the tails. Although skewness and kurtosis have a common impact on tail risk, their significance for risk forecasting has not been considered in empirical financial studies. Developing models for accurate risk forecasting is an important consideration that has always received considerable attention from policymakers, economists, financial market participants, and researchers. For this purpose, in this study, following Jimenez et al. (2022), to estimate the return density, a semi-nonparametric approach is adopted which is based on the asymptotic properties of Gram-Charlier extensions. This approach allows examining the significance of the inclusion of Hermit polynomials and their crossed products in the Gram-Charlier densities for risk forecasting. In fact, in the framework. Evaluating the risk measures in a semi-nonparametric framework allows for capturing all stylized facts of the return series for assessing skewness and kurtosis and their interactions by adding new parameters to the density function as a relevant source of information. Method: This research, for the first time, employs the modified Gram-Charlier density function (mGC), including the second and third moments (skewness and kurtosis) and their interactions for modeling the risk of distribution of the daily losses of the TEPIX. Moreover, the performance of alternative models based on different specifications of Gram-Charlier is evaluated in terms of the accuracy of risk forecasting measures using modern backtesting tests. For this purpose, the Value-at-Risk criteria and Median Shortfall measure, implied for the first time in the present study, are used. The sample includes the daily series of the TEPIX index covering the period from May 20, 2008, to August 22, 2023. Focusing on the right-tail of the TEPIX distribution, the loss series is calculated as a negative of log differences of prices. The models are estimated by R and MATLAB software. Modeling the losses is done through a two-step estimation process according to the following steps. Step 1: the ARMA(1,1)-GARCH(1,1) model is estimated using the quasi-maximum likelihood (QML) approach by assuming the Gaussian distribution for error terms. Step 2: the modified Gram-Charlier expansion and alternative specifications are estimated using standardized residuals extracted from the previous step. Different specifications of the Gram-Charlier density density fit using the maximum likelihood method. For in-sample fitting of the model, the estimation window size is chosen to be W=2656 observations and the step is chosen to be one new observation. The remaining 1000 observations are used for out-of-sample forecasts. Findings: The empirical findings from the in-sample fitting of the ARMA(1,1)-GARCH(1,1) model, under the Gram-Charlier densities for the innovations, indicate that skewness and kurtosis and their interactions are economically and financially significant. The results of the Backtesting for both 99%-VaR and 99%-MS confirm the out-of-sample forecasting performance of the Gram-Charlier density specification incorporating the skewness parameter, especially for the tails, compared to other specifications that have been taken into account in this research. Conclusion: Overall, the results show that the parameter related to the asymmetry of distribution alone can be a valuable source of information to the market participants by providing accurate risk measures. The empirical findings have practical implications for designing strategies for managing risk and decision-making in times of market instability. The novelity of this study is the application of a semi non-parametric approach to evaluate the risk forecasting of the TEPIX index. The previous studies have mainly modeled the return series based on parametric and non-parametric distributions. Therefore, the empirical findings of the present study provide a novel application for risk management in the Tehran Stock Exchange. The empirical findings can have useful implications for stabilizing the financial markets. [ABSTRACT FROM AUTHOR]

In this paper, the symbol-error rate (SER) performance of a coherent free-space optical (FSO) communication system in lognormal-Rician turbulence channel is analyzed using the generalized Gram-Charlier (GCC) series. We proposed the differential evolution (DE) algorithm to solve the parameters in GCC efficiently. It is shown that highly accurate closed-form SER expressions are obtained for M-ary phase-shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) schemes with maximum ratio combining (MRC) technique. The asymptotic error rate analysis is presented to reveal the performance behavior in the high signal-to-noise (SNR) regime. The effects of imperfect phase noise compensation on the error rate performance are also studied, and it is found that the impact of phase compensation error can be small enough with loop SNR ρc more than seven. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a new method of fast and stable calculation of the discrete orthogonal moments of Charlier and their inverses. This method is meant to accelerate the computation time and improve the quality of images reconstruction. In this method, we have combined two main concepts. The first concept is the digital filters based on the Z-transform to accelerate the calculation process of the discrete orthogonal moments of Charlier. The second concept is the partitioning of the image into a set of blocks of fixed sizes where each block is processed independently. The significant reduction in the image space during partitioning makes it possible to represent the minute details of the image with only low orders of Charlier’s discrete orthogonal moments, which ensures the digital stability during the processing of the image. In order to demonstrate the efficiency, stability, and precision of our method compared to other existing methods, some simulations have been performed on different types of binary images and gray images with and without noise. [ABSTRACT FROM AUTHOR]

The matching problem often arises in image processing and involves finding a correspondence between similar objects. In particular, variational matching models optimize suitable energies that evaluate the dissimilarity between the current shape and the relative template. A penalty term often appears in the energy to constrain the regularity of the solution. To perform numerical computation, a discrete version of the energy is defined. Then, the question of consistency between the continuous and discrete solutions arises. This paper proves a Γ-convergence result for the discrete energy to the continuous one. In particular, we highlight some geometric properties that must be guaranteed in the discretization process to ensure the convergence of minimizers. We prove the result in the framework introduced in the 2017 paper of Charlier et al., which studies the matching problem between geometric structures carrying on a signal (fshapes). The matching energy is defined for L2 signals and evaluates the difference between fshapes in terms of the varifold norm. This paper maintains a dual attachment term, but we consider a BV penalty term in place of the original L2 norm. [ABSTRACT FROM AUTHOR]

This article explores the issue of anthelmintic resistance in Europe and the environmental concerns associated with its use. It suggests sustainable worm control practices, such as diagnostics, grazing management, and selective breeding, as alternatives to reduce the reliance on anthelmintics. The article emphasizes the need for a Community of Practice across Europe to promote sustainable worm control and involve all relevant stakeholders. It provides examples of different approaches to worm control in various European countries, including Ireland, Poland, the United Kingdom, and Greece. The article also discusses the need for improved deworming practices in the ruminant livestock population in Spain, highlighting the lack of registered anthelmintics for goats and the inefficient use of deworming due to the lack of diagnostics. It suggests the use of complementary control approaches and diagnostic tools for effective and sustainable control of helminths. The authors stress the importance of implementing sustainable worm control practices across Europe and propose the establishment of local and national networks, supported by an international stakeholder network, to ensure long-term sustainability. [Extracted from the article]

This paper introduces a new risk measure for portfolio choice and compares its performance with two related metrics, namely the behavioral variance and the modified variance by using a Taylor's expansion. The methodology for our proposal naturally incorporates investor attitudes to risk related to skewness and kurtosis by assuming a Gram-Charlier return distribution. The so-obtained risk measures represent a more reliable description of portfolio risk and encompass the cases where high-order moments are not relevant characteristics (i.e. under normality). Our results show the outperformance of our proposal for different risk tolerance parameters considering the minimum variance and Sharpe ratio criteria by employing random portfolio optimization technique for 11 sets of stocks. [ABSTRACT FROM AUTHOR]

All thermal vibrations of atoms are in fact anharmonic – this is the underlying reason for the manifestation of many physical properties of solids, primarily its thermal expansion. By now, over three decades have passed from the seminal works of Kuhs [Kuhs Statistical description of multimodal atomic probability densities. Acta Crystallogr A. 1983;39:148–158.Kuhs Lead Article Generalized Atomic Displacements in Crystallographic Structure Analysis. Acta Cryst. 1992;A48:80–98. Kuhs The Anharmonic Temperature Factor in Crystallographic Structure Analysis. Aust J Phys. 1988;41:369], and 'anharmonic' approaches are now widely used for the description of thermal displacements of the atoms. Experimental data for studies of this phenomenon can be acquired from targeted diffraction experiments, and in this mini review, we analyse the current state of this area, mostly for the inorganic structures. The modern crystallographic hardware and software permits to correct the description of anharmonicity for the objects whereof one or two decades ago this phenomenon was either neglected or beyond the power of data processing. In general, the asphericity of electron density distribution is not necessarily caused by anharmonic motions; another possible reason is the displacement of valence electrons due to the formation of chemical bonds. We analyse the hitherto reported examples of anharmonic description of thermal motions; this phenomenon is most pronounced for univalent cations (like alkalis, silver, copper and thallium) and anions (halides). We also present the new Anharmonicity program suite which permits to determine the maxima of distribution of probability density. [ABSTRACT FROM AUTHOR]

It has been known for over 70 years that there is an asymptotic transition of Charlier polynomials to Hermite polynomials. This transition, which is still presented in its classical form in modern reference works, is valid if and only if a certain parameter is integer. In this light, it is surprising that a much more powerful transition exists from Charlier polynomials to the Hermite function, valid for any real value of the parameter. This greatly strengthens the asymptotic connections between Charlier polynomials and special functions, with applications in queueing theory, where this transition is crucial for solving first-passage problems with moving boundaries. It is shown in this paper that the convergence is locally uniform, and a sharp rate bound is proved. In addition, it is shown that there is a transition of derivatives of Charlier polynomials to the derivative of the Hermite function, again with a sharp rate bound. Finally, it is proved that zeros of Charlier polynomials converge to zeros of the Hermite function. [ABSTRACT FROM AUTHOR]

It often arises in practice that, although the first few moments of a distribution are known, the density of the distribution cannot be determined in closed form. In such cases, Gram-Charlier and Edgeworth series are commonly used to analytically approximate the unknown density in terms of the known moments. Although convenient, these series contain polynomial factors, and can hence lead to density approximations taking negative values or becoming multimodal in general. Consequently it is of interest to determine the set of moments for which the corresponding density approximations are positive definite and unimodal. In contrast to the existing literature that determines the boundaries of such sets numerically, explicit analytic expressions for the two boundaries are given in this paper for the Gram-Charlier series. Moreover, a method for projecting a given set of moments onto the boundaries of the two regions in order to minimizes the Kolmogorov-Smirnov statistic of corresponding density approximations is also provided. [ABSTRACT FROM AUTHOR]

In this paper, we propose a zero-watermarking scheme based on a new set of quaternion moments called Quaternion Radial Fractional Charlier Moments (QRFrCMs) for the copyright protection of color medical images. The proposed moments are developed from a new type of discrete orthogonal polynomials called Fractional Charlier Polynomials (FrCPs) and from quaternion theory. The robustness of the proposed scheme is ensured thanks to robustness of the proposed quaternion moments against image processing attacks and geometric attacks where the BCR is greater than 98%. In addition, the scheme uses the fractional order of QRFrCMs and a chaotic system based on two-dimensional CML (2DCML) using mixed linear-nonlinear coupling to provide a high level of security. Experimental results show the superiority of the proposed scheme over other recent schemes in terms of robustness against geometric attacks and common image processing attacks. The proposed scheme can be used for the secure transmission of color medical images over insecure networks. [ABSTRACT FROM AUTHOR]

This paper implements a procedure for dynamically selecting the Gram–Charlier approximation that best fits the empirical distribution of cryptocurrency returns at any point in time. The endogenous selection of the Gram–Charlier expansion length exploits its property for approximating frequency distributions through a flexible number of parameters that allows capturing changes at the tails provoked by new extreme events. The procedure is based on the differences between the cumulative distribution function of Gram–Charlier distributions with a particular focus on the fitting of the distribution left tail for risk assessment purposes. The method is tested through backtesting techniques for a group of major cryptocurrencies. The results show that the selection of the Gram–Charlier expansion order on the basis of cumulative distribution function dynamics, provides, in most cases, a significant improvement for conditional coverage compared to the use of fixed-order Gram–Charlier expansions. The method seems to be a useful tool for risk management purposes, especially for highly volatile assets such as cryptocurrencies. [ABSTRACT FROM AUTHOR]

In this paper, we propose efficient methods for the reconstruction, compression, compressive sensing (CS) and encryption of 1D signals. The proposed reconstruction method is based on the use of Charlier moments (CMs) and the Artificial Bee Colony (ABC) algorithm. The latter is used for optimizing the local parameter of Charlier polynomials during the computation of CMs. In addition, new methods are presented for 1D signal compression and CS using CMs and ABC algorithm that guarantees a high quality of the decompressed/reconstructed signal. Moreover, we suggest a new signal encryption/decryption scheme relying on fractional-order Charlier moments and ABC algorithm, which is used for providing a high quality of the decrypted signal and for improving the security of the proposed scheme. The results of the conducted simulations and comparisons clearly show the efficiency of the proposed 1D-signal analysis methods. [ABSTRACT FROM AUTHOR]

This paper is a sequel to Aschakulporn and Zhang (J Futures Mark 42(3):365–388, 2022). The errors of the Bakshi et al. (Rev Financ Stud 16(1):101–143, 2003) risk-neutral moment estimators is studied using the Gram–Charlier density—with the skewness and excess kurtosis specified. To obtain skewness with (absolute) errors less than 10 - 3 , the range of strikes ( K min , K max ) must contain at least 3/4 to 4/3 of the forward price and have a step size ( Δ K ) of no more than 0.1% of the forward price. The range of strikes and step size corresponds to truncation and discretization errors, respectively. This is consistent to Aschakulporn and Zhang (2022) for non-volatile market periods. [ABSTRACT FROM AUTHOR]

We derive uniform and non-uniform asymptotics of the Charlier polynomials by using difference equation methods alone. The Charlier polynomials are special in that they do not fit into the framework of the turning point theory, despite the fact that they are crucial in the Askey scheme. In this paper, asymptotic approximations are obtained, respectively, in the outside region, an intermediate region, and near the turning points. In particular, we obtain uniform asymptotic approximation at a pair of coalescing turning points with the aid of a local transformation. We also give a uniform approximation at the origin by applying the method of dominant balance and several matching techniques. [ABSTRACT FROM AUTHOR]

The aim of the paper is to study the characterization of delta operator associated with some Sheffer polynomials. In this paper, we consider Poisson-Charlier polynomials and investigate the characterization of delta operator via sequential representation of delta operator. From our investigation, we are able to prove an interesting propositions for the above mentioned. [ABSTRACT FROM AUTHOR]

Relatively fresh volcanic rocks have been sampled by a remotely operated vehicle in situ from the NE caldera wall of Brothers submarine volcano, associated with Seafloor Massive Sulfide‐SMS deposits. Here, we present the first complete stratigraphic column of the NE caldera wall, comprising at least 12 massive dacitic lava flows, up to 80 m‐thick intercalated with multiple volcaniclastic layers associated with tuffaceous sediment layers. Detailed petrographic and geochemical analyses from hand specimen to crystal to silicate melt scale show chemical variability with depth, correlating partly with an increase in pervasive alteration due to volatile degassing. Moreover, while sulfide saturation occurred prior to volatile exsolution—which sequestrated most chalcophile elements as confirmed by the low metal contents of melt inclusions (e.g., Cu ≤ 1.3 μg/g and Au ≤ 7.0 μg/g)—silicate glass records a Cu enrichment and Au loss with differentiation, with interstitial glass accounting for Cu = 4.2 μg/g and Au = 6.6 μg/g and matrix glass for Cu = 6.0 μg/g and Au = 2.8 μg/g, respectively. Our findings suggest multiple sources for metals compensating for the low initial metal contents: (a) from hydrothermal fluids and volatile percolation ensuing interaction with the host rock and thus also replacement and/or dissolution of pre‐existing magmatic sulfides, (b) directly from the magma, consistent with metal release during magma degassing of metal‐ and Cl‐, and S‐ rich volatiles, and (c) from fluid circulation within unusually metal‐rich andesitic volcaniclastic layers (Cu = 40 μg/g, Au = 1.5 ng/g, and Pt = 0.99 ng/g). Our results elucidate the capacity of such hybrid mineralizing submarine volcanic systems to effectively scavenge, transport, and concentrate metals. Plain Language Summary: Based on a set of samples collected by a remotely operated vehicle, we composed the first stratigraphic column of the NE Caldera wall of the Brothers active submarine volcano. In order to understand the source and transport mechanism of metals in the volcanic system, we performed petrographic observations and chemical analyses of glass inclusions (representing the source of the magma), minerals and their host rocks. Our findings show a chemical variability with depth, down the caldera wall, correlating with alteration caused by degassing. Moreover, our results indicate that although the magma at depth was not unusually high in metals, likely because of early sulfide saturation (sequestrating most metals at depth), multiple other processes compensated for the metal loss and contributed to the metal enrichment of the system, including: (a) dissolution of pre‐existing magmatic sulfides, (b) magma degassing of metal‐ and Cl‐, and S‐rich volatiles, and (c) from fluid circulation within metal‐rich lithologies. Key Points: Underwater high‐resolution imagery and in situ rock sampling allow the reconstruction of a 375 m stratigraphic column of the caldera wallPetrography and geochemistry from hand specimen to crystal to silicate melt scale indicate weak to moderate chemical variability depending on depth and/or lithologyMultiple metal inputs from the magma, from magmatic sulfide dissolution, and from fluid circulation within metal‐rich volcaniclastics [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for image classification by the content in heterogeneous databases. This approach is based on the use of new series of separable discrete orthogonal moments as shape descriptors and the Support Vector Machine as classifier. In fact, the proposed descriptors moments are defined from the bivariate discrete orthogonal polynomials of Charlier-Meixner which are invariant to translation, scaling and rotation of the image. We also propose a new algorithm to accelerate the image classification process. This algorithm is based on two steps: the first step is the fast computation of the values of Charlier-Meixner polynomials by using a new recurrence relationship between the values of polynomials Charlier-Meixner. The second one is the new image representation and slice blocks. The proposed method is tested on three different sets of standard data which are well known to computer vision: COIL-100, 256-CALTECH and Corel. The simulation results show the invariance of the discrete orthogonal separable moments of Charlier-Meixner against the various geometric transformations and the ability for the classification of heterogeneous images. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new fast way to compute both the image Charlier moments and its inverses using Clenshaw's recurrence formula. Firstly, we present recursive polynomials of Charlier with respect to the order n and with respect to the variable x and then we define Clenshaw's recurrence formula to improve the consuming time of the proposed algorithm. So, to show the robustness of the proposed method, a comparative study with the classical method is carried out. In fact, the results of the simulations carried out on binary and gray-scale images show the effectiveness of the proposed method in terms of the calculation time of Charlier moments and in terms of image reconstruction capacity with respect to Krawtchouk moments. [ABSTRACT FROM AUTHOR]

The Gram–Charlier expansion of a target probability density, f (x) , is an L 2 -convergent series f (x) = ∑ 0 ∞ c n p n (x) f ∗ (x) in terms of a reference density f ∗ (x) and its orthonormal polynomials p n (x). We implement this for the density of a regime-switching Lévy process at a given time horizon T. The main step is the evaluation of moments of all orders of f (x) in terms of model primitives, for which we give a matrix-exponential representation. A number of numerical examples, in part involving pricing of European options, are presented. The traditional choice of f ∗ (x) as normal with the same mean and variance as f (x) only works for the regime-switching Black–Scholes model. Outside the scope of Black–Scholes, f ∗ (x) is typically taken as a normal inverse Gaussian. A similar analysis is given for time-changed Lévy processes modelling stochastic volatility. [ABSTRACT FROM AUTHOR]

The paper deals with the approximation of first order derivative of a function by the first order derivative of Szász-type operators based on Charlier polynomials introduced by Varma and Taşdelen [ 20 ]. The uniform convergence theorem, Voronovskaja type asymptotic theorem and an estimate of error in terms of the second order modulus of continuity of the derivative of the function are investigated. Further, it is shown that linear combinations of the derivative of the above operators converge to the derivative of function at a faster rate. Finally, an estimate of error in the approximation is obtained in terms of the (2 k + 2) t h (2 k + 2) t h order modulus of continuity using Steklov mean. [ABSTRACT FROM AUTHOR]

Strong stability preserving (SSP) coefficients govern the maximally allowable step-size at which positivity or contractivity preservation of integration methods for initial value problems is guaranteed. In this paper, we show that the task of computing optimal linear SSP coefficients of explicit one-step methods is, to a certain extent, equivalent to the problem of characterizing positive quadratures with integer nodes with respect to Poisson–Charlier measures. Using this equivalence, we provide sharp upper and lower bounds for the optimal linear SSP coefficients in terms of the zeros of generalized Laguerre orthogonal polynomials. This in particular provides us with a sharp upper bound for the optimal SSP coefficients of explicit Runge–Kutta methods. Also based on this equivalence, we propose a highly efficient and stable algorithm for computing these coefficients, and their associated optimal linear SSP methods, based on adaptive spectral transformations of Poisson–Charlier measures. The algorithm possesses the remarkable property that its complexity depends only on the order of the method and thus is independent of the number of stages. Our results are achieved by adapting and extending an ingenious technique by Bernstein (Acta Math 52:1–66, 1928) in his seminal work on absolutely monotonic functions. Moreover, the techniques introduced in this work can be adapted to solve the integer quadrature problem for any positive discrete multi-parametric measure supported on N under some mild conditions on the zeros of the associated orthogonal polynomials. [ABSTRACT FROM AUTHOR]

Charlier polynomials (CHPs) and their moments are commonly used in image processing due to their salient performance in the analysis of signals and their capability in signal representation. The major issue of CHPs is the numerical instability of coefficients for high-order polynomials. In this study, a new recurrence algorithm is proposed to generate CHPs for high-order polynomials. First, sufficient initial values are obtained mathematically. Second, the reduced form of the recurrence algorithm is determined. Finally, a new symmetry relation for CHPs is realized to reduce the number of recurrence times. The symmetry relation is applied to calculate ∼ 50% of the polynomial coefficients. The performance of the proposed recurrence algorithm is evaluated in terms of computational cost and reconstruction error. The evaluation involves a comparison with existing recurrence algorithms. Moreover, the maximum size that can be generated using the proposed recurrence algorithm is investigated and compared with those of existing recurrence algorithms. Comparison results; indicate that the proposed algorithm exhibits better performance because it can generate a polynomial 44 times faster than existing recurrence algorithms. In addition, the improvement of the proposed algorithm over the traditional recurrence algorithms in terms of maximum-generated size is between 19.25 and 42.85. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to define and investigate more general multiple Charlier polynomials on the linear lattice ω N = { 0 , ω , 2 ω , ... } , ω ∈ R . We call these polynomials ω-multiple Charlier polynomials. Some of their properties, such as the raising operator, the Rodrigues formula, an explicit representation and a generating function are obtained. Also an (r + 1) th order difference equation is given. As an example we consider the case ω = 3 2 and define 3 2 -multiple Charlier polynomials. It is also mentioned that, in the case ω = 1 , the obtained results coincide with the existing results of multiple Charlier polynomials. [ABSTRACT FROM AUTHOR]

This paper analyses risk quantification for three main stock market index exchange‐traded funds in world financial markets. We compare the relative performance of a set of parametric and semi‐nonparametric models in terms of both value‐at‐risk and expected shortfall backtesting techniques. To this end, we explore the result of the jointly elicitability of these two risk measures. We provide a new mixture of Gram–Charlier distributions that have been used in this framework for the first time and derive a close formula for directly computing expected shortfall. This model is compared to the Gaussian (benchmark model), Student's t, generalized Pareto (a case of the extreme value theory) and mixtures of Gram–Charlier distributions. The results show that peaks‐over‐threshold (extreme value theory) and flexible Gram–Charlier approximations are suitable to quantify market risk and mitigate concerns about possible financial instabilities generated by misuse of exchange‐traded funds trading. [ABSTRACT FROM AUTHOR]

The problem of 3D digital object invariability is encountered in image processing, especially in pattern classification/recognition. The 3D object should be correctly recognized regardless of its particular position and orientation in the scene. This paper proposes a new method to extract 3D Charlier moment invariants to translation and scaling (3DCMITS). These descriptors are extracted directly from discrete orthogonal Charlier polynomials without using 3D geometric moment invariants. This method is fast and does not require any numerical approximation compared to the indirect method based on 3D geometric moment invariants. The results show the proposed method's effectiveness in terms of speed with an improvement exceeding 99,97%. For validation purposes and as an illustration of the interest of 3DCMITS, this paper offers a classification system for 3D objects based on the proposed 3DCMITS and Support Vector Machine (SVM) classifier. The obtained results are verified with K-Nearest Neighbor (KNN) classifier and other existing works in the literature. [ABSTRACT FROM AUTHOR]

We propose a new algorithm for accelerating the computation time of Charlier discrete orthogonal moments for three-dimensional (3D) images, based on two fundamental notions: The first is a new representation of 3D images called image cuboid representation (ICR) in which the 3D image is decomposed into a set of cuboids of the same gray level instead of voxels, enabling a considerable reduction in both the amount of treated voxels and the computation time of Charlier moments. The second is a matrix calculation of the Charlier moments instead of direct or recursive calculations. The significant reduction in the computation time for Charlier moments, in combination with the ICR method, motivated the development of this new method for 3D image reconstruction. Simulation results confirm the effectiveness of the proposed method in terms of the calculation time of 3D Charlier moments as well as the speed and quality of image reconstruction. [ABSTRACT FROM AUTHOR]

This paper presents two new sets of nonseparable discrete orthogonal Charlier and Meixner moments describing the images with noise and that are noise-free. The basis functions used by the proposed nonseparable moments are bivariate Charlier or Meixner polynomials introduced by Tratnik et al. This study discusses the computational aspects of discrete orthogonal Charlier and Meixner polynomials, including the recurrence relations with respect to variable x and order n. The purpose is to avoid large variation in the dynamic range of polynomial values for higher order moments. The implementation of nonseparable Charlier and Meixner moments does not involve any numerical approximation, since the basis function of the proposed moments is orthogonal in the image coordinate space. The performances of Charlier and Meixner moments in describing images were investigated in terms of the image reconstruction error, and the results of the experiments on the noise sensitivity are given. [ABSTRACT FROM AUTHOR]

In this paper, we present a new set of bivariate discrete orthogonal polynomials defined from the product of Charlier and Hahn discrete orthogonal polynomials with one variable. This bivriate polynomial is used to define other set of separable two-dimensional discrete orthogonal moments called Charlier-Hahn's moments. We also propose the use of the image slice representation methodology for fast computation of Charlier-Hahn's moments. In this approach the image is decomposed into series of non-overlapped binary slices and each slice is described by a number of homogenous rectangular blocks. Thus, the moments of Charlier-Hahn can be computed fast and easily from the blocks of each slice. A novel set of Charlier-Hahn invariant moments is also presented. These invariant moments are derived algebraically from the geometric invariant moments and their computation is accelerated using an image representation scheme. The presented approaches are tested in several well known computer vision datasets including computational time, image reconstruction, the moment's invariability and the classification of objects. The performance of these invariant moments used as pattern features for a pattern classification is compared with Charlier, Hahn, Tchebichef-Krawtchouk, Tchebichef-Hahn and Krawtchouk-Hahn invariant moments. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to develop a loan insurance pricing model allowing for the skewness and kurtosis existing in underlying asset returns.Design/methodology/approach Using the theory of Gram-Charlier option, the authors first derive a closed-form solution of the Gram-Charlier pricing model. To address the difficulties in implementing the pricing model, the authors subsequently propose an iterative method to estimate skewness and kurtosis in practical application, which shows a relatively fast convergence rate in the empirical test.Findings Not only the theoretical analysis but also the empirical evidence shows that the effects of skewness and kurtosis on loan insurance premium tend to be negative and positive, respectively. Furthermore, the actual values of skewness and kurtosis are usually negative and positive, respectively, which leads to the empirical result that the pricing model ignoring skewness and kurtosis substantially underestimates loan insurance premium.Originality/value This paper proposes a loan insurance pricing model considering the skewness and kurtosis of asset returns, in which the authors use the theory of Gram-Charlier option. More importantly, the authors further propose a novel iterative method to estimate skewness and kurtosis in practical application. The empirical evidence suggests that the Gram-Charlier pricing model captures the information content of skewness and kurtosis. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new kind of Kantorovich-Sz'asz type operators based on Charlier polynomials and study its various approximation properties. We establish some local direct theorems, e.g., Voronovskaja type asymptotic theorem and an estimate of error by means of the Lipschitz type maximal function and the Peetre's K-functional. We also discuss the weighted approximation properties. Next, we construct a bivariate case of the above operators and study the degree of approximation with the aid of the complete and partial moduli of continuity. A Voronovskaja type asymptotic theorem and the order of convergence by considering the second order modulus of continuity are also proved. We define the associated Generalized Boolean Sum (GBS) operators and discuss the degree of approximation by using mixed modulus of smoothness for Bögel continuous and Bögel differentiable functions. Furthermore, by means of a numerical example it is shown that the proposed operators provide us a better approximation than the operators corresponding to the particular case - = 1. We also illustrate the convergence of the bivariate operators and the associated GBS operators to a certain function and show that the GBS operators enable us a better error estimation than the bivariate operators using Matlab algorithm. [ABSTRACT FROM AUTHOR]

Background: Psoroptic mange, caused by Psoroptes ovis mites, is affecting Belgian Blue cattle's welfare and production potential. The Belgian Blue cattle—known for its high degree of muscling, low feed conversion ratio and high beef quality—is highly susceptible for this disease. Results: In this study, we phenotyped 1975 Belgian Blue cattle from more than 100 different groups on commercial beef farms for their psoroptic mange susceptibility. Substantial individual differences were observed within these management groups, with lesion extent differences up to ± 15%. Animal models showed that estimated heritabilities were low for lesion extent and severe lesion extent (0.07 and 0.09, respectively) and 0.12 for the number of mites. A genome wide association study for mange susceptibility revealed signals on BTA6, BTA11, BTA15 and BTA24. In these regions, candidate genes GBA3, RAG2, and TRAF6 were identified. Conclusions: Despite the challenges in phenotyping for psoroptic mange due to the timing of screening, the continuous evolution of lesions and different management conditions, we successfully conducted a study on the genetic susceptibility to psoroptic mange in Belgian Blue cattle. Our results clearly indicate that psoroptic mange is under polygenic control and the underlying candidate genes should be studied more thoroughly. This is the first study providing candidate genes for this complex disease. These results are already valuable for Belgian Blue breeding, however, further research is needed to unravel the architecture of this disease and to identify causal mutations. [ABSTRACT FROM AUTHOR]

Abundant carbon was identified on Mercury by MESSENGER, which is interpreted as the remnant of a primordial graphite flotation crust, suggesting that the magma ocean and core were saturated in carbon. We re-evaluate carbon speciation in Mercury's interior in light of the high pressure-temperature experiments, thermodynamic models and the most recent geophysical models of the internal structure of the planet. Although a sulfur-free melt would have been in the stability field of graphite, sulfur dissolution in the melt under the unique reduced conditions depressed the sulfur-rich liquidus to temperatures spanning the graphite-diamond transition. Here we show it is possible, though statistically unlikely, that diamond was stable in the magma ocean. However, the formation of a solid inner core caused diamond to crystallize from the cooling molten core and formation of a diamond layer becoming thicker with time. A diamond layer that becomes thicker with time is generated from carbon exsolution at the core-mantle boundary of Mercury, owing to cooling of its metallic core and potentially the silicate magma ocean. [ABSTRACT FROM AUTHOR]

Let T be an n × n truncation of an (n + α) × (n + α) Haar distributed unitary matrix. We consider the disk counting statistics of the eigenvalues of T. We prove that as n → + ∞ with α fixed, the associated moment generating function enjoys asymptotics of the form exp (C 1 n + C 2 + o (1)) , where the constants C 1 and C 2 are given in terms of the incomplete Gamma function. Our proof uses the uniform asymptotics of the incomplete Beta function. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive investigation of the swelling behaviour of a compacted bentonite–sand mixture subjected to hydration under constant volume conditions. Contrary to previous studies, the tested sample was isotropically compacted before being hydrated under constant volume conditions until full saturation was reached. The total axial pressure, total radial pressures at four different heights of the sample, and injected water volume were recorded over time. The experimental data reveal a complex and non-uniform evolution of the axial and radial stresses over time, as well as anisotropy of the total stresses, which persist at the saturated equilibrated state. To gain further insights, a numerical analysis was performed using an advanced hydromechanical framework for partially saturated porous media, accounting for the evolving microstructure of the material. The complex evolution of the total axial and radial pressures with time is attributed to the advancing hydration and swelling front in the sample, along with the development of irreversible strains. The good agreement between the numerical results and the experimental data enables validation of the developed framework. Implications for engineered barriers in deep geological disposal of radioactive waste are discussed. Highlights: The swelling behaviour of an isotropically compacted bentonite-based material under constant-volume conditions is investigated. Hydration of the sample generates stress heterogeneity and anisotropy, which persist at the saturated equilibrated state. Numerical modelling shows that the complex evolution of the total axial and radial pressures can be attributed to the advancing hydration and swelling front in the sample, along with the development of irreversible strains. The relationship between the local dry density and the radial stress seems to follow the global dry density-swelling pressure trend determined on small-scale samples. [ABSTRACT FROM AUTHOR]

We consider the Boussinesq equation on the line for a broad class of Schwartz initial data for which (i) no solitons are present, (ii) the spectral functions have generic behavior near ± 1, and (iii) the solution exists globally. In a recent work, we identified 10 main sectors describing the asymptotic behavior of the solution, and for each of these sectors we gave an exact expression for the leading asymptotic term. In this paper, we give a proof for the formula corresponding to the sector ... . [ABSTRACT FROM AUTHOR]

Given a finite set of positive integers G and polynomials , , with degree of equal to g, we associate to them a sequence of Charlier type polynomials defined from the Charlier polynomials by using certain Casoratian determinants (whose entries are the polynomials). Charlier type polynomials are eigenfunctions of higher order difference operators. When , the polynomials are also orthogonal, and then satisfy a three term recurrente relation. In this paper, we prove that whatever the polynomials 's are, the Charlier type polynomials always satisfy higher order recurrence relations. We also introduce and characterize the algebra of difference operators associated to the recurrence relations satisfied by the sequence. Our characterization is constructive and surprisingly simple. As a consequence, we prove that is, essentially, the unique choice such that the polynomials are orthogonal with respect to a measure. [ABSTRACT FROM AUTHOR]

This article derives the generalized Gram-Charlier (GGC) series in multivariate that expands an unknown joint probability density function (pdf) of a random vector in terms of the differentiations of joint pdf of a known reference random vector. Conventionally, the higher order differentiations of a multivariate pdf and corresponding to it the multivariate GGC series use multi-element array or tensor representations. Instead, the current article derives them in vector notations. The required higher order differentiations of a multivariate pdf are achieved in vector notations through application of a specific Kronecker product based differentiation operator. The resultant multivariate GGC series expression is more compact and more elementary compare to the coordinatewise tensor notations as using vector notations. It is also more comprehensive as apparently more nearer to its counterpart for univariate. Same notations and advantages are shared by other expressions obtained in the article, such as the mutual relations between cumulants and moments of a random vector, integral form of a multivariate pdf, integral form of the multivariate Hermite polynomials, the multivariate Gram-Charlier A series and others. Overall, the article uses only elementary calculus of several variables instead of tensor calculus to achieve the extension of a specific derivation for the GGC series in univariate (Berberan-Santos in J Math Chem 42(3):585-594, 2007) to multivariate. [ABSTRACT FROM AUTHOR]

We consider Toeplitz determinants whose symbol has: (i) a one-cut regular potential $V$ , (ii) Fisher–Hartwig singularities and (iii) a smooth function in the background. The potential $V$ is associated with an equilibrium measure that is assumed to be supported on the whole unit circle. For constant potentials $V$ , the equilibrium measure is the uniform measure on the unit circle and our formulas reduce to well-known results for Toeplitz determinants with Fisher–Hartwig singularities. For non-constant $V$ , our results appear to be new even in the case of no Fisher–Hartwig singularities. As applications of our results, we derive various statistical properties of a determinantal point process which generalizes the circular unitary ensemble. [ABSTRACT FROM AUTHOR]

Objective: Storytelling engages audiences, passes down traditions and history, educates, and helps people understand and interpret their environment. Many of those who work in agriculture have been part of the storytelling tradition since childhood. Research has demonstrated the emotional impact of personal stories and how prevention information is conveyed effectively "farmer to farmer" through this method of communication. Methods: Since 2016, the Telling the Story Project has provided a space for those directly or indirectly involved in an agricultural incident to share their story and unique perspectives on how similar incidents can be avoided. Results: This collaborative project, developed between the National Institute for Occupational Safety and Health (NIOSH) Agriculture Safety Centers, has resulted in 11 stories on a dedicated website, safety and health resources, and educational guides. The stories and educational guidelines have been marketed extensively through traditional and social media sources, employed in safety training, and embraced by educators in agricultural programs. The website has provided a national and international reach with more than 35,000 visits. Conclusion: Qualitative thematic analysis of the stories provided data on the circumstances leading up to each incident, valuable information on how the storytellers interpreted the aftermath, and a novel perspective on how safety professionals can create messaging that will resonate with the farming community. [ABSTRACT FROM AUTHOR]

Bentonite-based materials have emerged as a highly promising choice for engineered barriers in nuclear waste deep geological disposal. These materials are characterised by low permeability, high swelling capacity and effective radionuclide retardation, making them suitable for sealing underground galleries and canisters containing nuclear waste. However, the presence of technological gaps within the bentonite or the host rock can significantly influence their hydromechanical behaviour, potentially creating preferential pathways for radionuclide migration, thus affecting the overall performance of the engineered barrier. In this study, two different modelling strategies (namely, "gap" and "no-gap") to reproduce technological gaps and their effect on the hydromechanical behaviour of bentonite-based materials during intermediate saturation stages are proposed. The numerical model is used to simulate laboratory tests, and the numerical results are compared with experimental data coming from hydration test conducted under overall constant volume (isochoric) conditions. It is noteworthy that the specimen used in the experimental study is characterised by a localised gap between its side and the cell wall. The paper highlights the benefits of the "gap" numerical model, which employs interface elements to reproduce technological gaps at the side of the cell and exhibits satisfactory capabilities in reproducing the experimental swelling pressure evolution during bentonite hydration, especially during the transient wetting stages. Significant implications are expected for predicting site performance of engineered barrier systems in nuclear waste disposal applications. Highlights: The effect of technological gaps on the hydro-mechanical behaviour of bentonite-based materials for nuclear waste disposal is investigated. Two different modelling strategies, "gap" and "no-gap", are proposed to simulate the presence of technological gaps in the bentonite. The numerical results are compared with experimental data from a hydration test under constant volume conditions. The advantages of the "gap" numerical model, which can reproduce the experimental swelling pressure evolution more accurately, are demonstrated and its implications are discussed for the performance of engineered barrier systems. [ABSTRACT FROM AUTHOR]