Related papers: A dual watermaking scheme based on Sobolev type or…
In this work we propose a novel technique to quantify how distracting watermarks are on an image. We begin with watermark detection using a two-tower CNN model composed of a binary classification task and a semantic segmentation prediction.…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
The paper develops a second-order time-domain moment matching framework for the structure-preserving model reduction of second-order dynamical systems of high dimension, avoiding the first-order double-sized equivalent system. The moments…
This study aims to construct a stable, high-order compact finite difference method for solving Sobolev-type equations with Dirichlet boundary conditions in one-space dimension. Approximation of higher-order mixed derivatives in some…
Given a text, can we determine whether it was generated by a large language model (LLM) or by a human? A widely studied approach to this problem is watermarking. We propose an undetectable and elementary watermarking scheme in the closed…
We construct and analyze a strongly consistent second-order finite difference scheme for the steady two-dimensional Stokes flow. The pressure Poisson equation is explicitly incorporated into the scheme. Our approach suggested by the first…
We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected…
In this paper we introduce the data from mineral water probe with errors in both variables. For this case we apply our orthonormal polynomial expansion(OPEM) method to describe the data in the new error corridor. It receives the…
The rapid adoption of large language models (LLMs), such as GPT-4 and Claude 3.5, underscores the need to distinguish LLM-generated text from human-written content to mitigate the spread of misinformation and misuse in education. One…
The aim of this paper is to derive (by using two operators, representable by a Jacobi matrix) a family of q-orthogonal polynomials, which turn to be dual to alternative q-Charlier polynomials. A discrete orthogonality relation and a…
Zeilberger's algorithm provides a method to compute recurrence and differential equations from given hypergeometric series representations, and an adaption of Almquist and Zeilberger computes recurrence and differential equations for…
With the increasing popularity of large language models, concerns over content authenticity have led to the development of myriad watermarking schemes. These schemes can be used to detect a machine-generated text via an appropriate key,…
Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain $q$-analogues of Laguerre and Charlier polynomials. The moments of these orthogonal polynomials have combinatorial models in terms of crossings in permutations and set…
We develop a unified construction of matrix-valued orthogonal polynomials associated with discrete weights, yielding bispectral sequences as eigenfunctions of second-order difference operators. This general framework extends the discrete…
A new set of multiple orthogonal polynomials of both type I and type II with respect to two weight functions involving Gauss' hypergeometric function on the interval $(0,1)$ is studied. This type of polynomials have direct applications in…
This paper introduces a blind watermarking based on a convolutional neural network (CNN). We propose an iterative learning framework to secure robustness of watermarking. One loop of learning process consists of the following three stages:…
Watermarking technology is a method used to trace the usage of content generated by large language models. Sentence-level watermarking aids in preserving the semantic integrity within individual sentences while maintaining greater…
We construct new families of discrete vector orthogonal polynomials that have the property to be eigenfunctions of some difference operator. They are extensions of Charlier, Meixner and Kravchuk polynomial systems. The ideas behind our…
In this paper a blind, Secure, imperceptible and robust watermarking algorithm based on wavelet transform domain is proposed in which for more security, the watermark W is converted to a sequence and then a random binary sequence R of size…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…