Some properties of solutions for a class of metaparabolic equations

In this paper, we study the initial boundary value problem for a class of metaparabolic equations. We establish the existence of solutions by the energy techniques. Some results on the regularity, blow-up and existence of global attractor are obtained

Finite-time control for uncertain systems and application to flight control

In this paper, the finite-time control design problem for a class of nonlinear systems with matched and mismatched uncertainty is addressed. The finite-time control scheme is designed by integrating multi power reaching (MPR) law and finite-time disturbance observer (FTDO) into integral sliding mode control, where a novel sliding surface is designed, and the FTDO is applied to estimate the uncertainty. Then the fixed-time reachability of the MPR law is analyzed, and the finite-time stability of the closed-loop system is proven in the framework of Lyapunov stability theory. Finally, numerical simulation and the application to the flight control of hypersonic vehicle (HSV) are provided to show the effectiveness of the designed controller

On Computing Multiple Solutions of Nonlinear PDEs Without Variational Structure

Variational structure plays an important role in critical point theory and methods. However many differential problems are non-variational i.e. they are not the Euler- Lagrange equations of any variational functionals, which makes traditional critical point approach not applicable. In this thesis, two types of non-variational problems, a nonlinear eigen solution problem and a non-variational semi-linear elliptic system, are studied. By considering nonlinear eigen problems on their variational energy profiles and using the implicit function theorem, an implicit minimax method is developed for numerically finding eigen solutions of focusing nonlinear Schrodinger equations subject to zero Dirichlet/Neumann boundary condition in the order of their eigenvalues. Its mathematical justification and some related properties, such as solution intensity preserving, bifurcation identification, etc., are established, which show some significant advantages of the new method over the usual ones in the literature. A new orthogonal subspace minimization method is also developed for finding multiple (eigen) solutions to defocusing nonlinear Schrodinger equations with certain symmetries. Numerical results are presented to illustrate these methods. A new joint local min orthogonal method is developed for finding multiple solutions of a non-variational semi-linear elliptic system. Mathematical justification and convergence of the method are discussed. A modified non-variational Gross-Pitaevskii system is used in numerical experiment to test the method

Conjugated linoleic acid attenuates neuropathic pain induced by sciatic nerve in mice

Purpose: Conjugated linoleic acid (CLA) has been suggested to be necessary for human health, but there is limited research regarding its effect on neuropathic pain (NP). Here, we aim to investigate the potential effect of CLA administration on NP development and nerve recovery. Methods: Forty mice were divided into four equal groups randomly. The mice in control group underwent a sham operation to achieve a unilateral sciatic nerve cut. Other groups were subjected to partial sciatic nerve ligation (PSNL) surgery followed by 4 weeks of CLA treatment. Behavioral tests were performed shortly before mice were sacrificed. Blood, sciatic nerve and spinal cord tissues were collected after sacrifice. Electron microscopy was performed to determine myelin thickness and calculate myelin thickness/axon diameter ratio. Results: Mice that received daily oral CLA treatment for 4 weeks after PSNL surgery showed less mechanical and thermal allodynia than mice in PSNL surgery alone group. Behavioral tests showed that CLA treatment was associated with marked increases in both nerve conduction velocity (NCV) and force of gastrocnemius contraction. In addition, CLA reduced the levels of interleukin-1β (IL-1β) and tumor necrosis factor-α (TNF-α), sciatic myeloperoxidase (MPO) activity, and activating transcription factor-3 (ATF-3) expression. CLA also restored mitochondrial manganese superoxide dismutase (MnSOD) activity which was decreased in the sciatic nerves and spinal cords of the PSNL surgery group. Regeneration of myelins and axons in nerve fibers in CLA group was faster and more complete than that in the vehicle group. Conclusion: The current study demonstrates that CLA effectively attenuates NP and significantly inhibits neuro-inflammation and oxidative stress. This treatment improves sciatic nerve form and function after injury, suggesting that it can attenuate NP

SSL-Auth: An Authentication Framework by Fragile Watermarking for Pre-trained Encoders in Self-supervised Learning

Self-supervised learning (SSL), utilizing unlabeled datasets for training powerful encoders, has achieved significant success recently. These encoders serve as feature extractors for downstream tasks, requiring substantial resources. However, the challenge of protecting the intellectual property of encoder trainers and ensuring the trustworthiness of deployed encoders remains a significant gap in SSL. Moreover, recent researches highlight threats to pre-trained encoders, such as backdoor and adversarial attacks. To address these gaps, we propose SSL-Auth, the first authentication framework designed specifically for pre-trained encoders. In particular, SSL-Auth utilizes selected key samples as watermark information and trains a verification network to reconstruct the watermark information, thereby verifying the integrity of the encoder without compromising model performance. By comparing the reconstruction results of the key samples, malicious alterations can be detected, as modified encoders won't mimic the original reconstruction. Comprehensive evaluations on various encoders and diverse downstream tasks demonstrate the effectiveness and fragility of our proposed SSL-Auth.Comment: Submitted to AAAI2024. 9 pages, 7 figure