Boundedness in a taxis-consumption system involving signal-dependent motilities and concurrent enhancement of density-determined diffusion and cross-diffusion

This paper is concerned with the migration-consumption taxis system involving signal-dependent motilities $$\left\{ \begin{array}{l} u_t = \Delta \big(u^m\phi(v)\big), \\[1mm] v_t = \Delta v-uv, \end{array} \right. \qquad \qquad (\star)$$ in smoothly bounded domains $\Omega\subset\mathbb{R}^n$, where $m>1$ and $n\ge2$. It is shown that if $\phi\in C^3([0,\infty))$ is strictly positive on $[0,\infty)$, for all suitably regular initial data an associated no-flux type initial-boundary value problem possesses a globally defined bounded weak solution, provided $m>\frac{n}{2}$, which is consistent with the restriction imposed on $m$ in corresponding signal production counterparts of $(\star)$ so as to establish the similar result.Comment: 19 pages, 0 figure

L0L_0-Sampler: An L0L_{0} Model Guided Volume Sampling for NeRF

Since being proposed, Neural Radiance Fields (NeRF) have achieved great success in related tasks, mainly adopting the hierarchical volume sampling (HVS) strategy for volume rendering. However, the HVS of NeRF approximates distributions using piecewise constant functions, which provides a relatively rough estimation. Based on the observation that a well-trained weight function $w(t)$ and the $L_0$ distance between points and the surface have very high similarity, we propose $L_0$-Sampler by incorporating the $L_0$ model into $w(t)$ to guide the sampling process. Specifically, we propose to use piecewise exponential functions rather than piecewise constant functions for interpolation, which can not only approximate quasi-$L_0$ weight distributions along rays quite well but also can be easily implemented with few lines of code without additional computational burden. Stable performance improvements can be achieved by applying $L_0$-Sampler to NeRF and its related tasks like 3D reconstruction. Code is available at https://ustc3dv.github.io/L0-Sampler/ .Comment: Project page: https://ustc3dv.github.io/L0-Sampler

Mittag–Leffler synchronization for impulsive fractional-order bidirectional associative memory neural networks via optimal linear feedback control

In this paper, we are concerned with the synchronization scheme for fractional-order bidirectional associative memory (BAM) neural networks, where both synaptic transmission delay and impulsive effect are considered. By constructing Lyapunov functional, sufficient conditions are established to ensure the Mittag–Leffler synchronization. Based on Pontryagin’s maximum principle with delay, time-dependent control gains are obtained, which minimize the accumulative errors within the limitation of actuator saturation during the Mittag–Leffler synchronization. Numerical simulations are carried out to illustrate the feasibility and effectiveness of theoretical results with the help of the modified predictor-corrector algorithm and the forward-backward sweep method

A switching control for finite-time synchronization of memristor-based BAM neural networks with stochastic disturbances

This paper deals with the finite-time stochastic synchronization for a class of memristorbased bidirectional associative memory neural networks (MBAMNNs) with time-varying delays and stochastic disturbances. Firstly, based on the physical property of memristor and the circuit of MBAMNNs, a MBAMNNs model with more reasonable switching conditions is established. Then, based on the theory of Filippov’s solution, by using Lyapunov–Krasovskii functionals and stochastic analysis technique, a sufficient condition is given to ensure the finite-time stochastic synchronization of MBAMNNs with a certain controller. Next, by a further discussion, an errordependent switching controller is given to shorten the stochastic settling time. Finally, numerical simulations are carried out to illustrate the effectiveness of theoretical results

Isolation of AhDHNs from Arachis hypogaea L. and evaluation of AhDHNs expression under exogenous abscisic acid (ABA) and water stress

The peanut (Arachis hypogaea L.) is an important oil and cash crop all over the world. It is mostly planted in arid and semi-arid regions. To determine the mechanism by which dehydrins (DHNs) are regulated by abscisic acid (ABA) in peanuts, three Arachis hypogaea L. dehydrins (AhDHNs) were isolated from peanut plants and sequenced. By blasting the protein sequences of these AhDHNs, AhDHN1 was found belonging to the YnSKn subfamily. AhDHN2 and AhDHN3 were found belonging to the SKn and YnKn types, respectively. 100 μM ABA enhanced AhDHNs expression in peanut leaves. When peanut plants were treated with ABA and then with the ABA synthesis inhibitor sodium tungstate 12 h later, AhDHN expression was suppressed. However, AhDHN2 was inhibited by sodium tungstate at 2 h, though other AhDHNs were not. AhDHNs expressions increased greatly in peanut leaves treated with 30% polyethylene glycol (PEG). Sodium tungstate along with PEG inhibited the expression of AhDHNs. This study found that exogenous and endogenous ABA can both affect the expression of AhDHN independently. The differential expression of AhDHNs to exogenous ABA may be because of differences in the structure of different AhDHNs.Keywords: Arachis hypogaea L. dehydrins (AhDHNs), peanut, abscisic acid (ABA), expression, sodium tungstate, water stres

Balance, Imbalance, and Rebalance: Understanding Robust Overfitting from a Minimax Game Perspective

Adversarial Training (AT) has become arguably the state-of-the-art algorithm for extracting robust features. However, researchers recently notice that AT suffers from severe robust overfitting problems, particularly after learning rate (LR) decay. In this paper, we explain this phenomenon by viewing adversarial training as a dynamic minimax game between the model trainer and the attacker. Specifically, we analyze how LR decay breaks the balance between the minimax game by empowering the trainer with a stronger memorization ability, and show such imbalance induces robust overfitting as a result of memorizing non-robust features. We validate this understanding with extensive experiments, and provide a holistic view of robust overfitting from the dynamics of both the two game players. This understanding further inspires us to alleviate robust overfitting by rebalancing the two players by either regularizing the trainer's capacity or improving the attack strength. Experiments show that the proposed ReBalanced Adversarial Training (ReBAT) can attain good robustness and does not suffer from robust overfitting even after very long training. Code is available at https://github.com/PKU-ML/ReBAT.Comment: Accepted by NeurIPS 202