Errors of linear multistep methods and Runge-Kutta methods for singular perturbation problems with delays

AbstractThis paper is concerned with the error analysis of linear multistep methods and Runge-Kutta methods applied to some classes of one-parameter stiff singularly perturbed problems with delays. We derive the global error estimates of A(α)-stable linear multistep methods and algebraically and diagonally stable Runge-Kutta methods with Lagrange interpolation procedure. Numerical experiments confirm our theoretical analysis

Detection of low-dimensional chaos in drill bit torsional vibration time series

The near-bit strap-down measurement-while-drilling (MWD) system has been developed in this paper. By means of triaxial magnetometers, calculation method for bit rotational velocity was developed to monitor the drill bit torsional vibration. A number of techniques were applied to perform a nonlinear analysis of the experimental data of torsional vibration. Estimate delay time with mutual information and calculated the embedding dimension through Cao’s method, after reconstruct the phase space, the chaotic characteristics of the system were analyzed by calculating the correlation dimension and the largest Lyapunov exponent. We show that the largest Lyapunov exponent is positive and the correlation dimension is more than two, which is a strong indicator for the chaotic behaviour of the system. We also found that chaotic characteristics of the drill bit torsional vibration even existed in the whole drilling process, and thus the techniques based on phase space dynamics can be used to analyze and to predict drill bit torsional vibration. The results of this paper are of interest to applied and theoretical mechanics and petroleum engineering

Parameter Selection and Uncertainty Measurement for Variable Precision Probabilistic Rough Set

In this paper, we consider the problem of parameter selection and uncertainty measurement for a variable precision probabilistic rough set. Firstly, within the framework of the variable precision probabilistic rough set model, the relative discernibility of a variable precision rough set in probabilistic approximation space is discussed, and the conditions that make precision parameters α discernible in a variable precision probabilistic rough set are put forward. Concurrently, we consider the lack of predictability of precision parameters in a variable precision probabilistic rough set, and we propose a systematic threshold selection method based on relative discernibility of sets, using the concept of relative discernibility in probabilistic approximation space. Furthermore, a numerical example is applied to test the validity of the proposed method in this paper. Secondly, we discuss the problem of uncertainty measurement for the variable precision probabilistic rough set. The concept of classical fuzzy entropy is introduced into probabilistic approximation space, and the uncertain information that comes from approximation space and the approximated objects is fully considered. Then, an axiomatic approach is established for uncertainty measurement in a variable precision probabilistic rough set, and several related interesting properties are also discussed. Thirdly, we study the attribute reduction for the variable precision probabilistic rough set. The definition of reduction and its characteristic theorems are given for the variable precision probabilistic rough set. The main contribution of this paper is twofold. One is to propose a method of parameter selection for a variable precision probabilistic rough set. Another is to present a new approach to measurement uncertainty and the method of attribute reduction for a variable precision probabilistic rough set

Instruct-NeuralTalker: Editing Audio-Driven Talking Radiance Fields with Instructions

Recent neural talking radiance field methods have shown great success in photorealistic audio-driven talking face synthesis. In this paper, we propose a novel interactive framework that utilizes human instructions to edit such implicit neural representations to achieve real-time personalized talking face generation. Given a short speech video, we first build an efficient talking radiance field, and then apply the latest conditional diffusion model for image editing based on the given instructions and guiding implicit representation optimization towards the editing target. To ensure audio-lip synchronization during the editing process, we propose an iterative dataset updating strategy and utilize a lip-edge loss to constrain changes in the lip region. We also introduce a lightweight refinement network for complementing image details and achieving controllable detail generation in the final rendered image. Our method also enables real-time rendering at up to 30FPS on consumer hardware. Multiple metrics and user verification show that our approach provides a significant improvement in rendering quality compared to state-of-the-art methods.Comment: 11 pages, 8 figure

Photonic crystal fiber half-taper probe based refractometer

A compact singlemode - photonic crystal fiber - singlemode fiber tip (SPST) refractive index sensor is demonstrated in this paper. A CO2 laser cleaving technique is utilised to provide a clean-cut fiber tip which is then coated by a layer of gold to increase reflection. An average sensitivity of 39.1 nm/RIU and a resolvable index change of 2.56 x 10-4 are obtained experimentally with a ~3.2 µm diameter SPST. The temperature dependence of this fiber optic sensor probe is presented. The proposed SPST refractometer is also significantly less sensitive to temperature and an experimental demonstration of this reduced sensitivity is presented in the paper. Because of its compactness, ease of fabrication, linear response, low temperature dependency, easy connectivity to other fiberized optical components and low cost, this refractometer could find various applications in chemical and biological sensing