Related papers: $\alpha$-Parameterized Differential Transform Meth…
Differential privacy is becoming one gold standard for protecting the privacy of publicly shared data. It has been widely used in social science, data science, public health, information technology, and the U.S. decennial census.…
We propose the time-delayed transformer (TD-TF), a simplified transformer architecture for data-driven modeling of unsteady spatio-temporal dynamics. TD-TF bridges linear operator-based methods and deep sequence models by showing that a…
The theme of symbolic computation in algebraic categories has become of utmost importance in the last decade since it enables the automatic modeling of modern algebra theories. On this theoretical background, the present paper reveals the…
In this paper, we have proposed a new method for solving the Gaussian integral. Introducing a parameter that depends on a $n$ index, we have found a general solution for this type of integral inspired by Taylor series of a simple function.…
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of…
In this preliminary work, we present nonstandard time-stepping strategies to solve differential equations based on the algebraic estimation method applied to the estimation of time-derivative, which provides interesting properties of…
Designing privacy-preserving machine learning algorithms has received great attention in recent years, especially in the setting when the data contains sensitive information. Differential privacy (DP) is a widely used mechanism for data…
In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
The purpose of this paper is to develop a mathematical analysis theory to solve differential privacy problems. The heart of our approaches is to use analytic tools to characterize the correlations among the outputs of different datasets,…
The classical Fourier transform is, in essence, a way to take data and extract components (in the form of complex exponentials) which are invariant under cyclic shifts. We consider a case in which the components must instead be invariant…
In this paper, we tackle the parametric complete multiplicity problem for a univariate polynomial. Our approach to the parametric complete multiplicity problem has a significant difference from the classical method, which relies on repeated…
This paper introduces a meta-learning approach for parameterized pseudo-differential operators with deep neural networks. With the help of the nonstandard wavelet form, the pseudo-differential operators can be approximated in a compressed…
We propose a new sequential monitoring scheme for changes in the parameters of a multivariate time series. In contrast to procedures proposed in the literature which compare an estimator from the training sample with an estimator calculated…
We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…
We present a variational method for recovering the phase term from the information obtained from phase-shifting methods. First we introduce the new method based on a variational approach and then describe the numerical solution of the…
A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rules is introduced.
The theory of Touchard polynomials is generalized using a method based on the definition of exponential operators, which extend the notion of the shift operator. The proposed technique, along with the use of the relevant operational…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…