Parameter estimation of fractional uncertain differential equations via Adams method

Parameter estimation of uncertain differential equations becomes popular very recently. This paper suggests a new method based on fractional uncertain differential equations for the first time, which hold more parameter freedom degrees. The Adams numerical method and Adam algorithm are adopted for the optimization problems. The estimation results are compared to show a better forecast. Finally, the predictor–corrector method is adopted to solve the fractional uncertain differential equations. Numerical solutions are demonstrated with varied α-paths

Five-dimensional generalized f(R)f(R) gravity with curvature-matter coupling

The generalized $f(R)$ gravity with curvature-matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal spacelike Killing vector field of 5D spacetime, and it can be reduced to the 4D formulism of FRW universe. This theory is quite general and can give the corresponding results to the Einstein gravity, $f(R)$ gravity with both no-coupling and non-minimal coupling in 5D spacetime as special cases, that is, we would give the some new results besides previous ones given by Ref.\cite{60}. Furthermore, in order to get some insight into the effects of this theory on the 4D spacetime, by considering a specific type of models with $f_{1}(R)=f_{2}(R)=\alpha R^{m}$ and $B(L_{m})=L_{m}=-\rho$, we not only discuss the constraints on the model parameters $m$, $n$, but also illustrate the evolutionary trajectories of the scale factor $a(t)$, the deceleration parameter $q(t)$ and the scalar field $\epsilon(t)$, $\phi(t)$ in the reduced 4D spacetime. The research results show that this type of $f(R)$ gravity models given by us could explain the current accelerated expansion of our universe without introducing dark energy.Comment: arXiv admin note: text overlap with arXiv:0912.4581, arXiv:gr-qc/0411066 by other author

IMAGE-BASED MEASUREMENT AND BIOMECHANICAL ANALYSIS OF THE KNEE JOINT DURING FUNCTIONAL ACTIVITIES

A new approach based on the integration of medical image-based measurement techniques, infrared stereophotogrammetry and finite element modelling (FEM) was developed for comprehensive subject-specific biomechanical analyses of the knee joint during weight-bearing functional activities including cycling. The medical image-based methods include digitally reconstructed radiograph (DRR) based 3D fluoroscopy methods, and a new slice-to-volume registration method using FLASH MRI for the real-time measurement of the 3D kinematics of the knee in vivo. With the new approach, the soft tissue artefacts associated with skin marker-based stereophotogrammetry and their effects on the calculated biomechanical variables were also investigated

Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow

We prove several differential Harnack inequalities for positive solutions to nonlinear backward heat equations with different potentials coupled with the Ricci flow. We also derive an interpolated Harnack inequality for the nonlinear heat equation under the $\varepsilon$-Ricci flow on a closed surface. These new Harnack inequalities extend the previous differential Harnack inequalities for linear heat equations with potentials under the Ricci flow.Comment: 17 pages. New explanations added; Final versio

Improved Noisy Student Training for Automatic Speech Recognition

Recently, a semi-supervised learning method known as "noisy student training" has been shown to improve image classification performance of deep networks significantly. Noisy student training is an iterative self-training method that leverages augmentation to improve network performance. In this work, we adapt and improve noisy student training for automatic speech recognition, employing (adaptive) SpecAugment as the augmentation method. We find effective methods to filter, balance and augment the data generated in between self-training iterations. By doing so, we are able to obtain word error rates (WERs) 4.2%/8.6% on the clean/noisy LibriSpeech test sets by only using the clean 100h subset of LibriSpeech as the supervised set and the rest (860h) as the unlabeled set. Furthermore, we are able to achieve WERs 1.7%/3.4% on the clean/noisy LibriSpeech test sets by using the unlab-60k subset of LibriLight as the unlabeled set for LibriSpeech 960h. We are thus able to improve upon the previous state-of-the-art clean/noisy test WERs achieved on LibriSpeech 100h (4.74%/12.20%) and LibriSpeech (1.9%/4.1%).Comment: 5 pages, 5 figures, 4 tables; v2: minor revisions, reference adde