Showing papers on "Remainder published in 2018"
TL;DR: In this article, the Frechet derivatives of the principal square root matrix function at any order were described and a Taylor expansion with an integral remainder term was presented, yielding the first result for this class of matrix function.
36 citations
TL;DR: A novel reversible digital watermarking technique for medical images to achieve high level of secrecy, tamper detection, and blind recovery of the original image is proposed and ensures high security due to four keys used in chaotic map.
Abstract: A novel reversible digital watermarking technique for medical images to achieve high level of secrecy, tamper detection, and blind recovery of the original image is proposed. The technique selects some of the pixels from the host image using chaotic key for embedding a chaotically generated watermark. The rest of the pixels are converted to residues by using the Residue Number System (RNS). The chaotically selected pixels are represented by the polynomial. A primitive polynomial of degree four is chosen that divides the message polynomial and consequently the remainder is obtained. The obtained remainder is XORed with the watermark and appended along with the message. The decoder receives the appended message and divides it by the same primitive polynomial and calculates the remainder. The authenticity of watermark is done based on the remainder that is valid, if it is zero and invalid otherwise. On the other hand, residue is divided with a primitive polynomial of degree 3 and the obtained remainder is appended with residue. The secrecy of proposed system is considerably high. It will be almost impossible for the intruder to find out which pixels are watermarked and which are just residue. Moreover, the proposed system also ensures high security due to four keys used in chaotic map. Effectiveness of the scheme is validated through MATLAB simulations and comparison with a similar technique.
27 citations
TL;DR: The Mass-remainder analysis method was demonstrated by the analysis of various ethylene oxide/propylene oxide copolymers, and the intensities of the monoisotopes are increased to the value corresponding to the total intensity of their isotope peaks.
Abstract: A new data mining method is proposed for the determination of the copolymer composition from moderate/low resolution complex mass spectra. The Mass-remainder analysis (MARA) does not require a “Kendrick-like” transformation to a new mass scale, it is simply based on the calculation of the remainder after dividing by the exact mass of one of the repeat units of the copolymer (e.g., B of an A/B copolymer). Plotting the remainder of this division (MR) versus m/z the homologous series differing only by a number of base units (e.g., B unit) can be visualized. The number of A units (nA) and subsequently nB is assigned to the m/z peaks using the bijective nA, MR mapping. Simultaneously, our algorithm removes the isotopes from the peak list. However, the intensities of the monoisotopes are increased to the value corresponding, approximately, to the total intensity of their isotope peaks. The correction of the mass spectral peak intensities enables the accurate calculation of the usual polymer and copolymer quanti...
18 citations
TL;DR: In this article, the scaling limit of the spectral projector of the Laplacian onto frequency windows of constant size was shown to be a normalized Bessel function depending only on n.
Abstract: This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, we prove that near any non-self-focal point, the scaling limit of the spectral projector of the Laplacian onto frequency windows of constant size is a normalized Bessel function depending only on n.
18 citations
TL;DR: This paper proposes a pseudometric as a uniform framework to analyze the tradeoff between the error bound and the dynamic range for robust CRT, and presents the first robustCRT for multiple numbers to solve the problem raised by CRT-based undersampling frequency estimation in general.
Abstract: Chinese remainder theorem (CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory, and distributed data storage. Since traditional CRT is greatly sensitive to the errors in residues due to noises, the problem of robustly reconstructing integers via the erroneous residues has been intensively studied in the literature. In order to robustly reconstruct integers, there are basically two approaches: one is to introduce common divisors in the moduli and the other is to directly decrease the dynamic range. In this paper, we take further insight into the geometry property of the linear space associated with CRT. Echoing both ways to introduce redundancy, we propose a pseudometric as a uniform framework to analyze the tradeoff between the error bound and the dynamic range for robust CRT. Furthermore, we present the first robust CRT for multiple numbers to solve the problem raised by CRT-based undersampling frequency estimation in general. Based on symmetric polynomials proposed, we proved that in most cases, the problem can be solved efficiently in the polynomial time.
18 citations
TL;DR: In this article, the mean square of the remainder in the prime geodesic theorem for every co-finite Fuchsian group was shown to be upper bounded by the Selberg trace formula.
Abstract: We prove upper bounds for the mean square of the remainder in the prime geodesic theorem, for every cofinite Fuchsian group, which improve on average on the best known pointwise bounds. The proof relies on the Selberg trace formula. For the modular group we prove a refined upper bound by using the Kuznetsov trace formula.
18 citations
01 Jan 2018
TL;DR: In this article, an asymptotic expansion at spatial infinity of a weak time-periodic solution to the Navier-Stokes equations with a non-zero drift term in the three-dimensional whole space is carried out.
Abstract: An asymptotic expansion at spatial infinity of a weak time-periodic solution to the Navier-Stokes equations with a non-zero drift term in the three-dimensional whole-space is carried out. The asymptotic profile is explicitly identified and expressed in terms of the well-known Oseen fundamental solution. A pointwise estimate is given for the remainder term.
16 citations
TL;DR: This paper proposes a tighter set-membership filter for some nonlinear dynamic systems by using an analytic method and a boundary sampling technique to obtain a tighter bounding ellipsoid to cover the remainder.
Abstract: In this paper, we propose a tighter set-membership filter for some nonlinear dynamic systems by using an analytic method and a boundary sampling technique. The nonlinear dynamic systems can be linearized about the current estimate, then the remainder term is bounded in real time by an optimization ellipsoid, other than a priori remainder bound. For a 2-D radar system and a quadratic system, some regular properties can be derived for the remainder term, which helps us obtain a tighter bounding ellipsoid to cover the remainder. Moreover, the prediction step and the measurement update step are derived based on the recent optimization method and the on-line bounding ellipsoid of the remainder, so that a tighter set-membership filter can be achieved. The numerical examples demonstrate the effectiveness of the proposed filter.
16 citations
01 Aug 2018
TL;DR: In this article, the authors studied the asymptotic behavior of pick functions, analytic functions which take the upper half plane to itself, and showed that a two-variable Pick function has real residues to order 2N − 1 at infinity and the imaginary part of the remainder between f and this expansion is of order 2 n + 1, if and only if the 2N + 1-th derivative is given by a polynomial.
Abstract: We study the asymptotic behavior of Pick functions, analytic functions which take the upper half plane to itself. We show that if a two variable Pick function f has real residues to order 2N − 1 at infinity and the imaginary part of the remainder between f and this expansion is of order 2N + 1, then f has real residues to order 2N and directional residues to order 2N + 1. Furthermore, f has real residues to order 2N + 1 if and only if the 2N + 1-th derivative is given by a polynomial, thus obtaining a two variable analogue of a higher order Julia-Caratheodory type theorem.
15 citations
TL;DR: In this article, a connection between bounded remainder sets and cut-and-project sets in R d was made, together with the fact that each one-dimensional Pisot substitution sequence is bounded distance equivalent to some lattice.
13 citations
07 Nov 2018
TL;DR: In this paper, a survey concerning representations for the remainder term of Bernstein-Schurer-Stancu and respectively Stancu (based on factorial powers) bivariate approximation formulas, using bivariate divided differences is presented.
Abstract: The paper is a survey concerning representations for the remainder term of Bernstein-Schurer-Stancu and respectively Stancu (based on factorial powers) bivariate approximation formulas, using bivariate divided differences. As particular cases the remainder terms of bivariate Bernstein-Stancu, Schurer and classical Bernstein bivariate approximation formulas are obtained. Finally, one presents some mean value properties, similar to those of the remainder term of classical Bernstein univariate approximation formula.
TL;DR: This paper has derived the exact probability of detection for both methods applied in a pulsed Doppler radar and has shown excellent agreement.
Abstract: In pulsed Doppler radars, subsampling causes incorrect estimates of the radial velocity of the detected targets whenever its related Doppler frequency is greater than the pulse repetition frequency of the radar. The classic Chinese remainder theorem is a well-known method to overcome this problem. On the other hand, the robust Chinese remainder theorem is a search-based algorithm that, under some conditions, can guarantee the correct estimation of the Doppler frequency. In this paper, we have derived the exact probability of detection for both methods applied in a pulsed Doppler radar. Simulations have been compared to the analytical results and have shown an excellent agreement.
TL;DR: In this article, the finite-difference solution of singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay was studied.
Abstract: This study is concerned with the finite-difference solution of singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay. The method is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. The emphasis is on the convergence of numerical method. It is shown that the method displays uniform convergence in respect to the perturbation parameter. Numerical results are also given.
TL;DR: The results imply that a zero of the derivative of the distortion for these densities, which has been previously conjectured optimal, is indeed the optimal step size, because the distortion is convex either globally or locally over a sufficiently wide interval to ensure a global minimizer.
Abstract: This paper investigates the convexity of the mean squared-error distortion of symmetric uniform scalar quantization with respect to step size. The principal results include proofs for odd numbers of levels that distortion is not convex for any symmetric density and that it is convex for even numbers of levels for densities, such as Gaussian, Laplacian, and gamma, but is not, in general for two-sided Rayleigh. For the latter case, an interval is derived that includes the optimal step size and over which the distortion is convex. The proofs of convexity use the Euler–Maclaurin formula applied to the second derivative of distortion, with upper bounds on the remainder term. These results imply that a zero of the derivative of the distortion for these densities, which has been previously conjectured optimal, is indeed the optimal step size, because the distortion is convex either globally or locally over a sufficiently wide interval to ensure a global minimizer.
TL;DR: The experimental results show the evidence that the proposed mixed technique combining PVD and LSB does not show the step effects, so will not be vulnerable to PDH analysis and the recorded hiding capacity value is larger than the existing techniques without decreasing the PSNR.
Abstract: Pixel difference range mismatch at sender and receiver is a main problem with pixel value differencing (PVD) steganography techniques. This paper proposes a mixed technique combining PVD and LSB to address the above problems. The PVD uses modulus function (MF) and multi-directional edges. It uses 2×3 size pixel blocks to exploit the edges in five directions. The first two LSBs of every pixel forms the lower bit plane (also called as remainder plane) and the remaining six MSBs form the higher bit plane (also called as quotient plane). LSB substitution is applied at remainder plane and PVD is applied at quotient plane. From the 2×3 size pixel block, a 2×3 quotient block is formulated. A quotient is obtained after dividing the pixel values by 4. Thus from the pixel block a quotient block is obtained. The central quotient in the quotient block is considered as reference value and five difference values with five neighboring quotients are calculated. Based on the average of these five difference values, the hiding capacity in all the five directions is decided. The remainder plane of central pixel acts like indicator, so that extraction can be done successfully from the five neighboring pixels at the time of extraction. The experimental results show the evidence that the proposed technique does not show the step effects, so will not be vulnerable to PDH analysis. Furthermore, it is also observed that the recorded hiding capacity value is larger than the existing techniques without decreasing the PSNR. DOI: http://dx.doi.org/10.5755/j01.itc.47.4.19593
TL;DR: In this article, the authors derived the first exact, rigorous but practical, globally valid remainder terms for asymptotic expansions about saddle and contour endpoints of arbitrary order degeneracy derived from the method of steepest descents.
Abstract: We derive the first exact, rigorous but practical, globally valid remainder terms for asymptotic expansions about saddles and contour endpoints of arbitrary order degeneracy derived from the method of steepest descents. The exact remainder terms lead naturally to sharper novel asymptotic bounds for truncated expansions that are a significant improvement over the previous best existing bounds for quadratic saddles derived two decades ago. We also develop a comprehensive hyperasymptotic theory, whereby the remainder terms are iteratively reexpanded about adjacent saddle points to achieve better-than-exponential accuracy. By necessity of the degeneracy, the form of the hyperasymptotic expansions is more complicated than in the case of quadratic endpoints and saddles and requires generalizations of the hyperterminants derived in those cases. However, we provide efficient methods to evaluate them, and we remove all possible ambiguities in their definition. We illustrate this approach for three different exampl...
TL;DR: In this article, the authors considered the Hardy inequality on RN, the critical Hardy inequalities on a ball and the Rellich inequalities on RN, and refined them by adding remainder terms.
Abstract: We consider the Hardy inequality on RN , the critical Hardy inequality on a ball, and the Rellich inequality on RN . These three Hardy type inequalities can be refined by adding remainder terms. Our remainder terms are expressed by a distance from the families of “virtual” extremals. A key ingredient is the critical Hardy inequality on RN which was proved by Machihara, Ozawa and Wadade [21]. Mathematics subject classification (2010): 35A23, 26D10.
TL;DR: Density functional theory within the Kohn–Sham density functional theory (KS-DFT) ansatz has been implemented into bubbles and cube real-space molecular electronic structure framework, where functions containing steep cusps in the vicinity of the nuclei are expanded in atom-centered one-dimensional numerical grids multiplied with spherical harmonics (bubbles).
Abstract: Density functional theory within the Kohn–Sham density functional theory (KS-DFT) ansatz has been implemented into our bubbles and cube real-space molecular electronic structure framework, where functions containing steep cusps in the vicinity of the nuclei are expanded in atom-centered one-dimensional (1D) numerical grids multiplied with spherical harmonics (bubbles). The remainder, i.e., the cube, which is the cusp-free and smooth difference between the atomic one-center contributions and the exact molecular function, is represented on a three-dimensional (3D) equidistant grid by using a tractable number of grid points. The implementation of the methods is demonstrated by performing 3D numerical KS-DFT calculations on light atoms and small molecules. The accuracy is assessed by comparing the obtained energies with the best available reference energies.
10 Jan 2018
TL;DR: In this paper, it was shown that it is impossible to get a better remainder than the classical one in the Wiener-Ikehara theorem even if one assumes analytic continuation of the Mellin transform after subtraction of the pole to a halfplane.
Abstract: We show that it is impossible to get a better remainder than the classical one in the Wiener-Ikehara theorem even if one assumes analytic continuation of the Mellin transform after subtraction of the pole to a half-plane. We also prove a similar result for the Ingham-Karamata theorem.
Journal Article•
TL;DR: In this paper, a weighted version of the Hardy inequality, which is a special case of the more general Caffarelli- Kohn-Nirenberg inequalities, is improved on the whole space or on a bounded domain by adding various remainder terms.
Abstract: In this paper, we concern a weighted version of the Hardy inequality, which is a special case of the more general Caffarelli- Kohn-Nirenberg inequalities. We improve the inequality on the whole space or on a bounded domain by adding various remainder terms. On the whole space, we show the existence of a remain- der term which has the form of ratio of two weighted integrals. Also we give a simple derivation of the remainder term involving a distance from the manifold of the \virtual extremals". Finally on a bounded domain, we prove the existence of remainder terms involving the gradient of functions.
TL;DR: In this paper, the speed of convergence to zero of the remainder for a function f in terms of its distance from a space of Mellin band-limited functions was studied and the resulting estimates turn out to be of best possible order.
Abstract: The general Poisson summation formula of Mellin analysis can be considered as a quadrature formula for the positive real axis with remainder. For Mellin bandlimited functions it becomes an exact quadrature formula. Our main aim is to study the speed of convergence to zero of the remainder for a function f in terms of its distance from a space of Mellin bandlimited functions. The resulting estimates turn out to be of best possible order. Moreover, we characterize certain rates of convergence in terms of Mellin–Sobolev and Mellin–Hardy type spaces that contain f. Some numerical experiments illustrate and confirm these results.
TL;DR: In this paper, the authors analyzed the topological properties of the remainder partial derivative M := beta(s) of the semialgebraic Stone-Cech compactification of a set M subset of R-m.
TL;DR: In this article, the authors studied the Cauchy problem for the 3D incompressible hyperdissipative Navier-Stokes equations and considered the well-posedness and illposedness in critical Fourier-Herz spaces.
Abstract: We study the Cauchy problem for the 3D incompressible hyperdissipative Navier–Stokes equations and consider the well-posedness and ill-posedness in critical Fourier-Herz spaces . We prove that if and , the system is locally well-posed for large initial data as well as globally well-posed for small initial data. Also, we obtain the same result for and . More importantly, we show that the system is ill-posed in the sense of norm inflation for and q > 2. The proof relies heavily on particular structure of initial data u 0 that we construct, which makes the first iteration of solution inflate. Specifically, the special structure of u 0 transforms an infinite sum into a finite sum in 'remainder term', which permits us to control the remainder.
TL;DR: In this article, the symbol of the coefficient of the remainder function in planar N=4 Super Yang-Mills in multi-regge kinematics region was extracted from the symbol in full kinematic.
Abstract: We introduce a method to extract the symbol of the coefficient of $(2\pi i)^2$ of MHV remainder functions in planar N=4 Super Yang-Mills in multi-Regge kinematics region directly from the symbol in full kinematics. At two loops this symbol can be uplifted to the full function in a unique way, without any beyond-the-symbol ambiguities. We can therefore determine all two-loop MHV amplitudes at function level in all kinematic regions with different energy signs in multi-Regge kinematics. We analyse our results and we observe that they are consistent with the hypothesis of a contribution from the exchange of a three-Reggeon composite state starting from two loops and eight points in certain kinematic regions.
Posted Content•
TL;DR: In this paper, the speed of convergence to zero of the remainder for a function $f$ in terms of its distance from a space of Mellin band-limited functions was studied, and the resulting estimates turn out to be of best possible order.
Abstract: The general Poisson summation formula of Mellin analysis can be considered as a quadrature formula for the positive real axis with remainder For Mellin bandlimited functions it becomes an exact quadrature formula Our main aim is to study the speed of convergence to zero of the remainder for a function $f$ in terms of its distance from a space of Mellin bandlimited functions The resulting estimates turn out to be of best possible order Moreover, we characterize certain rates of convergence in terms of Mellin--Sobolev and Mellin--Hardy type spaces that contain $f$ Some numerical experiments illustrate and confirm these results
Posted Content•
TL;DR: In this paper, the steady Navier-Stokes-Fourier system with non-slip boundary conditions was derived for 2D convex domains with diffusive boundary condition.
Abstract: Consider the stationary Boltzmann equation in 2D convex domains with diffusive boundary condition. In this paper, we establish the hydrodynamic limits while the boundary layers are present, and derive the steady Navier-Stokes-Fourier system with non-slip boundary conditions. Our contribution focuses on novel weighted $W^{1,\infty}$ estimates for the Milne problem with geometric correction. Also, we develop stronger remainder estimates based on an $L^{2m}-L^{\infty}$ framework.
Posted Content•
TL;DR: A \v{S}ura-Bura Lemma for $G^*$, showing that components of the remainder of the 1-complex of a graph $G$ can be separated pairwise by finite order separations of $G$.
Abstract: We show that the tangle space of a graph, which compactifies it, is a quotient of its Stone-Cech remainder obtained by contracting the connected components.
17 Sep 2018
TL;DR: This work is motivated by the computations of normal forms and pseudo-remainders with respect to regular chains and reports on the implementation of those algorithms with the BPAS library.
Abstract: We discuss algorithms for pseudo-division and division with remainder of multivariate polynomials with sparse representation. This work is motivated by the computations of normal forms and pseudo-remainders with respect to regular chains. We report on the implementation of those algorithms with the BPAS library.
TL;DR: In this article, the Edgeworth expansion of general orders with an explicitly expressed remainder was used to find upper and lower bounds of the Kolmogorov distance in the case of an arbitrary sequence { F n }.
Patent•
18 Sep 2018
TL;DR: In this paper, a photovoltaic power prediction method based on a deep convolution nerve network is proposed, which comprises the following steps: using a variation modal decomposition algorithm to carry out modality decomposition for an obtained history photovolastic power sequence, and decomposing the sequence into a plurality of frequency components and a remainder component; respectively arranging the components into data of a two dimensional format; using the frequency components of the two dimensions as the input of a multichannel DNN model, predicting and outputting a frequency component predicted value sum; using
Abstract: The invention discloses a photovoltaic power prediction method based on a deep convolution nerve network; the method comprises the following steps: using a variation modal decomposition algorithm to carry out modal decomposition for an obtained history photovoltaic power sequence, and decomposing the sequence into a plurality of frequency components and a remainder component; respectively arranging the components into data of a two dimensional format; using the frequency components of the two dimensional format as the input of a multichannel deep convolution nerve network model, predicting andoutputting a frequency component predicted value sum; using a single-channel deep convolution nerve network model to extract high order features of the remainder component in the two dimensional format, using the extracted high order features and meteorology data as the input of a support vector machine model, and predicting and outputting a remainder component predicted value; adding the frequency component predicted value sum with the remainder component predicted value, thus obtaining a photovoltaic power prediction result at a to-be-predicted moment. The method can obviously improve the photovoltaic power prediction precision, and can effectively guide the power grid in scheduling, thus ensuring the power system to stably and safely operate.