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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]

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]

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]

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]

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]

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]

We present exact analytical expressions of moments of all orders for neuronal membrane potentials in the multiplicative nonstationary Poisson shot noise model. As an application, we derive closed-form Gram–Charlier density expansions that show how the probability density functions of potentials in such models differ from their Gaussian diffusion approximations. This approach extends the results of Brigham and Destexhe (Preprint, 2015a; Phys Rev E 91:062102, 2015b) by the use of exact combinatorial expressions for the moments of multiplicative nonstationary filtered shot noise processes. Our results are confirmed by stochastic simulations and apply to single- and multiple-noise-source models. [ABSTRACT FROM AUTHOR]

In this paper, we give some direct approximation results by modified Kantorovich–Szász type operators involving Charlier polynomials. Further, approximation results are also developed in polynomial weighted spaces. Moreover, for the functions of bounded variation, approximation results are proved. Finally, some graphical examples are provided to show comparisons of convergence between old and modified operators towards a function under different parameters and conditions. [ABSTRACT FROM AUTHOR]

In this contribution, we consider the sequence { Q n λ } n ≥ 0 of monic polynomials orthogonal with respect to the following inner product involving differences 〈 p , q 〉 λ = ∫ 0 ∞ p x q x d ψ (a) (x) + λ Δp (c) Δq (c) , where λ ∈ ℝ + , Δ denotes the forward difference operator defined by Δf (x) = f (x + 1) − f (x), ψ(a) with a > 0 is the well-known Poisson distribution of probability theory d ψ (a) (x) = e − a a x x ! at x = 0 , 1 , 2 , ... , and c ∈ ℝ is such that ψ(a) has no points of increase in the interval (c,c + 1). We derive its corresponding hypergeometric representation. The ladder operators and two different versions of the linear difference equation of second-order corresponding to these polynomials are given. Recurrence formulas of five and three terms, the latter with rational coefficients, are presented. Moreover, for real values of c such that c + 1 < 0, we obtain some results on the distribution of its zeros as decreasing functions of λ, when this parameter goes from zero to infinity. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a bivariate Kantorovich variant of combination of Szász and Chlodowsky operators based on Charlier polynomials. Then, we study local approximation properties for these operators. Also, we estimate the approximation order in terms of Peetre's K-functional and partial moduli of continuity. Furthermore, we introduce the associated GBS-case (Generalized Boolean Sum) of these operators and study the degree of approximation by means of the Lipschitz class of Bögel continuous functions. Finally, we present some graphical examples to illustrate the rate of convergence of the operators under consideration. [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]

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 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]

A simple discrete model of the two-dimensional isotropic harmonic oscillator is presented. It is superintegrable with su(2) as its symmetry algebra. It is constructed with the help of the algebraic properties of the bivariate Charlier polynomials. This adds to the other discrete superintegrable models of the oscillator based on Krawtchouk and Meixner orthogonal polynomials in several variables. [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]

Berberan-Santos relates one probability distribution to another wherein one distribution is expressed in terms of the derivatives of the other Berberan-Santos (J Math Chem 42:585, ). We derive the result in a straightforward manner based on a generalization of the Edgeworth/Gram Charlier. [ABSTRACT FROM AUTHOR]

We continue studying the generalized coherent states for oscillator-like systems associated with a given family of orthogonal polynomials. We consider the case of generalized oscillators generated by the Charlier q-polynomials. [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]

Given a sequence of polynomials $$(p_n)_n$$ , an algebra of operators $${\mathcal A}$$ acting in the linear space of polynomials, and an operator $$D_p\in {\mathcal A}$$ with $$D_p(p_n)=np_n$$ , we form a new sequence of polynomials $$(q_n)_n$$ by considering a linear combination of $$m+1$$ consecutive $$p_n$$ : $$q_n=p_n+\sum _{j=1}^m\beta _{n,j}p_{n-j}$$ . Using the concept of $$\mathcal {D}$$ -operator, we determine the structure of the sequences $$\beta _{n,j}, j=1,\ldots ,m,$$ so that the polynomials $$(q_n)_n$$ are eigenfunctions of an operator in the algebra $${\mathcal A}$$ . As an application, from the classical discrete families of Charlier, Meixner, and Krawtchouk, we construct orthogonal polynomials $$(q_n)_n$$ which are also eigenfunctions of higher-order difference operators. [ABSTRACT FROM AUTHOR]

In this paper we introduce a notion of duality for matrix valued orthogonal polynomials with respect to a measure supported on the nonnegative integers. We show that the dual families are closely related to certain difference operators acting on the matrix orthogonal polynomials. These operators belong to the so called Fourier algebras, which play a key role in the construction of the families. In order to illustrate duality, we describe a family of Charlier type matrix orthogonal polynomials with explicit shift operators which allow us to find explicit formulas for three term recurrences, difference operators and squared norms. These are the essential ingredients for the construction of different dual families. [ABSTRACT FROM AUTHOR]

It has been shown in Ferreira et al. (Adv. Appl. Math 31:61–85, []), López and Temme (Methods Appl. Anal. 6:131–196, []; J. Cpmput. Appl. Math. 133:623–633, []) that the three lower levels of the Askey table of hypergeometric orthogonal polynomials are connected by means of asymptotic expansions. In this paper we continue with that investigation and establish asymptotic connections between the fourth level and the two lower levels: we derive twelve asymptotic expansions of the Hahn, dual Hahn, continuous Hahn and continuous dual Hahn polynomials in terms of Hermite, Charlier and Laguerre polynomials. From these expansions, several limits between polynomials are derived. Some numerical experiments give an idea about the accuracy of the approximations and, in particular, about the accuracy in the approximation of the zeros of the Hahn, dual Hahn, continuous Hahn and continuous dual Hahn polynomials in terms of the zeros of the Hermite, Charlier and Laguerre polynomials. [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]

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]

The Charlier polynomials are used for constructing oscillator-like systems. We introduce coherent states of the system are defined and study the main properties (in particular, the (over)completeness property). We show that the coherent states on the associated uncertainty relation take the minimum value. In the case under consideration, the Mandel parameter vanishes, which corresponds to the Poisson statistics of quasiexcitation spectrum for the considered oscillator. Bibliography: 30 titles. [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]

We study pair correlation functions for planar Coulomb systems in the pushed phase, near a ring-shaped impenetrable wall. We assume coupling constant Γ = 2 and that the number n of particles is large. We find that the correlation functions decay slowly along the edges of the wall, in a narrow interface stretching a distance of order 1/n from the hard edge. At distances much larger than 1 / n , the effect of the hard wall is negligible and pair correlation functions decay very quickly, and in between sits an interpolating interface that we call the “semi-hard edge”. More precisely, we provide asymptotics for the correlation kernel K n (z , w) as n → ∞ in two microscopic regimes (with either | z - w | = O (1 / n) or | z - w | = O (1 / n) ), as well as in three macroscopic regimes (with | z - w | ≍ 1 ). For some of these regimes, the asymptotics involve oscillatory theta functions and weighted Szegő kernels. [ABSTRACT FROM AUTHOR]

The capabilities and limitations of the simulation of the probability density of rough sea surface elevations using the Gram-Charlier series are analyzed. The data of direct wave measurements at an oceanographic platform in the Black Sea are used in the analysis. The skewness of the sea surface elevation's distribution depends on the mean slope formed by the dominating waves and on the degree of the wave field development. A weak trend in the variations of the peakedness during the measurements of these parameters is also observed. The estimates of the errors in the peakedness measurements during the construction of the probability density of the sea surface elevations using the first five terms of the Gram-Charlier series are presented. [ABSTRACT FROM AUTHOR]

In the present paper, we study modified Szász–Durrmeyer positive linear operators involving Charlier polynomials, one of the discrete orthogonal polynomials which are generalization of Szász Durrmeyer operators. Also, King type modification of these operators is given. We obtain uniform convergence of our operators with the help of Korovkin theorem, asymptotic formula and the order of approximation by using classical modulus of continuity. [ABSTRACT FROM AUTHOR]

An explicit formula relating the probability density function with its cumulants is derived and discussed. A generalization of the Gram-Charlier expansion is presented, allowing to express one PDF in terms of another. The coefficients of this general expansion are explicitly obtained. [ABSTRACT FROM AUTHOR]

By using two operators representable by Jacobi matrices, we introduce a family of q-orthogonal polynomials, which turn out to be dual with respect to alternative q-Charlier polynomials. A discrete orthogonality relation and the completeness property for these polynomials are established. [ABSTRACT FROM AUTHOR]

Disordered protein sequences can exhibit different binding modes, ranging from well-ordered folding-upon-binding to highly dynamic fuzzy binding. The primary function of the intrinsically disordered region of the antitoxin HigA2 from Vibrio cholerae is to neutralize HigB2 toxin through ultra-high-affinity folding-upon-binding interaction. Here, we show that the same intrinsically disordered region can also mediate fuzzy interactions with its operator DNA and, through interplay with the folded helix-turn-helix domain, regulates transcription from the higBA2 operon. NMR, SAXS, ITC and in vivo experiments converge towards a consistent picture where a specific set of residues in the intrinsically disordered region mediate electrostatic and hydrophobic interactions while “hovering” over the DNA operator. Sensitivity of the intrinsically disordered region to scrambling the sequence, position-specific contacts and absence of redundant, multivalent interactions, point towards a more specific type of fuzzy binding. Our work demonstrates how a bacterial regulator achieves dual functionality by utilizing two distinct interaction modes within the same disordered sequence.Here, the authors dissect the fuzzy interaction between the prokaryote transcription factor HigA2 and its DNA target and show that specific, transient interactions drive specificity despite HigA2 remaining mostly disordered. [ABSTRACT FROM AUTHOR]

Five to ten percent of mammalian genomes is occupied by multiple clades of endogenous retroviruses (ERVs), that may count thousands of members. New ERV clades arise by retroviral infection of the germline followed by expansion by reinfection and/or retrotransposition. ERV mobilization is a source of deleterious variation, driving the emergence of ERV silencing mechanisms, leaving "DNA fossils". Here we show that the ERVK[2-1-LTR] clade is still active in the bovine and a source of disease-causing alleles. We develop a method to measure the rate of ERVK[2-1-LTR] mobilization, finding an average of 1 per ~150 sperm cells, with >10-fold difference between animals. We perform a genome-wide association study and identify eight loci affecting ERVK[2-1-LTR] mobilization. We provide evidence that polymorphic ERVK[2-1-LTR] elements in four of these loci cause the association. We generate a catalogue of full length ERVK[2-1-LTR] elements, and show that it comprises 15% of C-type autonomous elements, and 85% of D-type non-autonomous elements lacking functional genes. We show that >25% of the variance of mobilization rate is determined by the number of C-type elements, yet that de novo insertions are dominated by D-type elements. We propose that D-type elements act as parasite-of-parasite gene drives that may contribute to the observed demise of ERV elements. Endogenous retroviruses constitute 5–10% of mammalian genome space. This study characterize the bovine ERVK[2-1- LTR] clade showing that its activity varies between individuals as a function of the number of inherited autonomous elements, yet that most de novo insertions are non-autonomous elements lacking functional genes. [ABSTRACT FROM AUTHOR]

The Eiffel Tower (Paris, France) has been attracting many candidates for suicide over the years. The aim of this study was to determine the patterns of people who committed suicide by jumping. Permission to access the unpublished records of the Paris Police Prefecture made it possible to compile press articles related to suicides from April 1950 to March 1989. 155 articles corresponding to 79 cases were kept for analysis. There were significantly more males (66%), as compared with an expected theoretical distribution of 1/2 for each sex (p = 0.002). Median age was 38.0 years old. Suicide peak was reached during the months of August and October (13% for each), while February was poor in suicides (3%). Tuesdays and Saturdays were the more impacted days. Hourly suicide rates were 8% (morning), 11% (noon), 7% (afternoon), and 5% (evening-night). Moon phases did not correlate with suicide occurrence. The main context described was that of a psychiatric pathology (49%). Death occurred in 92% of the reported cases. Sex ratio, ages, decrease during the cold season, no association with moon phases, and underlying psychiatric pathologies were consistent with trends for either all-cause suicides or suicide jumps from a platform. Conversely, unusual trough in suicides on Mondays and noon peak in suicide rate have been, respectively, attributed to small sample size and closure at night. As jumping corresponds to both ease and proximity, we believe the implementation of protective measures in the early 1960s succeeded in reducing the number of suicides overall. [ABSTRACT FROM AUTHOR]

Objectives: King Henri IV of France (reign from 1589 to 1610) was one of the most important kings of France. Embalmed and buried in Saint-Denis, his remains were beheaded in 1793. His head (including his larynx) survived in successive private collections until its definitive identification in 2010. The purpose of the study was to provide a morphologic study of the larynx with a 3D reconstitution. Methods: A flexible endoscopy was performed via the mouth and via the trachea. Measures of the larynx (vocal folds lengths, thickness, width, larynx height) were collected from the CT-scan by a panel of experts blind each other. The segmentation of the laryngeal anatomical components (vocal folds, cartilages) was performed using 3DSlicer®. Mesh smoothing and 3D reconstitution were performed using Fusion 360®. Reconstitution was discussed between the experts. Decision was made by consensus after discussion. Results: Cricoid, thyroid, arytenoid cartilages, vocal folds and hyoid bone were identified and a computed 3D reconstitution of the larynx was made. The laryngeal 3D model appeared morphologically similar to a living subject. Measures were similar but smaller than those of a modern subject. Conclusions: The 3D reconstitution of the larynx of Henri IV of France was conducted from the CT-scan of his mummified head. This work constitutes a first valuable morphologic analysis of a larynx from an embalmed individual. This anatomical work is the first step towards the reconstruction of the voice of this historical character, which we hope to concretize with computer modeling tools in a second step. Level of evidence: V based on experiential and non-research evidence. [ABSTRACT FROM AUTHOR]

We derive an asymptotic approximation of Plancherel-Rotach type for the Charlier polynomials on the positive real line. [ABSTRACT FROM AUTHOR]

We introduce a new sequence of linear positive operators by combining the Charlier polynomials and the Szász type operators defined by Jain (in J Aust Math Soc 13(3):271–276, 1972). We obtain the degree of approximation of these operators by means of the weighted modulus of continuity and for functions in a Lipschitz type space. We also study the approximation of functions having a derivative equivalent with a function of bounded variation. [ABSTRACT FROM AUTHOR]

The superlattice obtained by aligning a monolayer graphene and boron nitride (BN) inherits from the hexagonal lattice a sixty degrees periodicity with the layer alignment. It implies that, in principle, the properties of the heterostructure must be identical for 0° and 60° of layer alignment. Here, we demonstrate, using dynamically rotatable van der Waals heterostructures, that the moiré superlattice formed in a bilayer graphene/BN has different electronic properties at 0° and 60° of alignment. Although the existence of these non-identical moiré twins is explained by different relaxation of the atomic structures for each alignment, the origin of the observed valley Hall effect remains to be explained. A simple Berry curvature argument is not sufficient to explain the 120° periodicity of this observation. Our results highlight the complexity of the interplay between mechanical and electronic properties in moiré structures and the importance of taking into account atomic structure relaxation to understand their electronic properties. Here, the authors report the unexpected observation of different electronic properties of bilayer graphene/boron nitride heterostructures at 0° and 60° twist angles, showing the complex interplay between lattice relaxation and the electronic properties of moiré structures. [ABSTRACT FROM AUTHOR]

We consider a combination of Chlodowsky polynomials with generalized Szasz operators involving Charlier polynomials. We give the degree of approximation for these bivariate operators by means of the complete and partial modulus of continuity, and also by using weighted modulus of continuity. Furthermore, we construct a GBS (Generalized Boolean Sum) operator of bivariate Chlodowsky-Szasz-Charlier type and estimate the order of approximation in terms of mixed modulus of continuity. [ABSTRACT FROM AUTHOR]

We derive Mehler-Heine type asymptotic formulas for Charlier and Meixner polynomials, and also for their associated families. These formulas provide good approximations for the polynomials in the neighborhood of $$x=0$$ and determine the asymptotic limit of their zeros as the degree $$n$$ goes to infinity. [ABSTRACT FROM AUTHOR]

We analyze the Charlier polynomials C n ( χ) and their zeros asymptotically as n → ∞. We obtain asymptotic approximations, using the limit relation between the Krawtchouk and Charlier polynomials, involving some special functions. We give numerical examples showing the accuracy of our formulas. [ABSTRACT FROM AUTHOR]

Remote Healthcare Monitoring Systems (RHMs) that employ fetal phonocardiography (fPCG) signals are highly efficient technologies for monitoring continuous and long-term fetal heart rate. Wearable devices used in RHMs still face a challenge that decreases their efficacy in terms of energy consumption because these devices have limited storage and are powered by batteries. This paper proposes an effective fPCG compression algorithm to reduce RHM energy consumption. In the proposed algorithm, the Discrete Orthogonal Charlier Moment (DOCMs) is used to extract features of the signal. The householder orthonormalization method (HOM) is used with the Charlier Moment to overcome the propagation of numerical errors that occur when computing high-order Charlier polynomials. The proposed algorithm's performance is evaluated in terms of CR, PRD, SNR, PSNR, and QS and provides the average values 18.33, 0.21, 48.85, 68.86, and 90.88, respectively. The results of the comparison demonstrate the proposed compression algorithm's superiority over other algorithms. It also tested in terms of compression speed and computational efficiency. The results indicate that the proposed algorithm has a high Compression speed (218.672 bps) and high computational efficiency (21.33). Additionally, the results reveal that the proposed algorithm decreases the energy consumption of a wearable device due to the transmission time decreasing for data by 3.68 s. [ABSTRACT FROM AUTHOR]

Digital watermarking of images is an essential method for copyright protection and image security. This paper presents an innovative, robust watermarking system for color images based on moment and wavelet transformations, algebraic decompositions, and chaotic systems. First, we extended classical Charlier moments to quaternary Charlier moments (QCM) using quaternion algebra. This approach eliminates the need to decompose color images before applying the discrete wavelet transform (DWT), reducing the computational load. Next, we decompose the resulting DWT matrix using QR and singular value decomposition (SVD). To enhance the system's security and robustness, we introduce a modified version of Henon's 2D chaotic map. Finally, we integrate the arithmetic optimization algorithm to ensure dynamic and adaptive watermark insertion. Our experimental results demonstrate that our approach outperforms current color image watermarking methods in security, storage capacity, and resistance to various attacks, while maintaining a high level of invisibility. [ABSTRACT FROM AUTHOR]