Reduced projection method for quasiperiodic Schr\"{o}dinger eigenvalue problems

This paper presents a reduced algorithm to the classical projection method for the solution of $d$-dimensional quasiperiodic problems, particularly Schr\"{o}dinger eigenvalue problems. Using the properties of the Schr\"{o}dinger operator in higher-dimensional space via a projection matrix of size $d\times n$, we rigorously prove that the generalized Fourier coefficients of the eigenfunctions decay exponentially along a fixed direction associated with the projection matrix. An efficient reduction strategy of the basis space is then proposed to reduce the degrees of freedom from $O(N^{n})$ to $O(N^{n-d}D^d)$, where $N$ is the number of Fourier grids in one dimension and the truncation coefficient $D$ is much less than $N$. Correspondingly, the computational complexity of the proposed algorithm for solving the first $k$ eigenpairs using the Krylov subspace method decreases from $O(kN^{2n})$ to $O(kN^{2(n-d)}D^{2d})$. Rigorous error estimates of the proposed reduced projection method are provided, indicating that a small $D$ is sufficient to achieve the same level of accuracy as the classical projection method. We present numerical examples of quasiperiodic Schr\"{o}dinger eigenvalue problems in one and two dimensions to demonstrate the accuracy and efficiency of our proposed method.Comment: 20 pages, 9 figure

Pythagoras Superposition Principle for Localized Eigenstates of 2D Moir\'e Lattices

Moir\'e lattices are aperiodic systems formed by a superposition of two periodic lattices with a relative rotational angle. In optics, the photonic moir\'e lattice has many promising mysteries such as its ability to localize light, thus attracting much attention to exploring features of such a structure. One fundamental research area for photonic moir\'e lattices is the properties of eigenstates, particularly the existence of localized eigenstates and the localization-to-delocalization transition in the energy band structure. Here we propose an accurate algorithm for the eigenproblems of aperiodic systems by combining plane wave discretization and spectral indicator validation under the higher-dimensional projection, allowing us to explore energy bands of fully aperiodic systems. A localization-delocalization transition regarding the intensity of the aperiodic potential is observed and a novel Pythagoras superposition principle for localized eigenstates of 2D moir\'e lattices is revealed by analyzing the relationship between the aperiodic and its corresponding periodic eigenstates. This principle sheds light on exploring the physics of localizations for moir\'e lattice.Comment: 7 pages, 3 figure

CasIL: Cognizing and Imitating Skills via a Dual Cognition-Action Architecture

Enabling robots to effectively imitate expert skills in longhorizon tasks such as locomotion, manipulation, and more, poses a long-standing challenge. Existing imitation learning (IL) approaches for robots still grapple with sub-optimal performance in complex tasks. In this paper, we consider how this challenge can be addressed within the human cognitive priors. Heuristically, we extend the usual notion of action to a dual Cognition (high-level)-Action (low-level) architecture by introducing intuitive human cognitive priors, and propose a novel skill IL framework through human-robot interaction, called Cognition-Action-based Skill Imitation Learning (CasIL), for the robotic agent to effectively cognize and imitate the critical skills from raw visual demonstrations. CasIL enables both cognition and action imitation, while high-level skill cognition explicitly guides low-level primitive actions, providing robustness and reliability to the entire skill IL process. We evaluated our method on MuJoCo and RLBench benchmarks, as well as on the obstacle avoidance and point-goal navigation tasks for quadrupedal robot locomotion. Experimental results show that our CasIL consistently achieves competitive and robust skill imitation capability compared to other counterparts in a variety of long-horizon robotic tasks

Dynamic Extra Buses Scheduling Strategy in Public Transport

This paper presents a dynamic extra buses scheduling strategy to improve the transit service of transit routes. In this strategy, in order to decide when to dispatch an extra bus, the service reliability of transit route is assessed firstly. A model aimed at maximizing the benefit of the extra buses scheduling strategy is constructed to determine how many stops extra buses need to skip from the terminal to accommodate passengers at the following stops. A heuristic algorithm is defined and implemented to estimate the service reliability of transit route and to optimize the initial stop of extra buses scheduling strategy. Finally, the strategy is tested on two examples: a simple and a real-life transit route in the Dalian city in China. The results show that the extra buses scheduling strategy based on terminal stops with a reasonable threshold can save 8.01% waiting time of passengers

Rethink Baseline of Integrated Gradients from the Perspective of Shapley Value

Numerous approaches have attempted to interpret deep neural networks (DNNs) by attributing the prediction of DNN to its input features. One of the well-studied attribution methods is Integrated Gradients (IG). Specifically, the choice of baselines for IG is a critical consideration for generating meaningful and unbiased explanations for model predictions in different scenarios. However, current practice of exploiting a single baseline fails to fulfill this ambition, thus demanding multiple baselines. Fortunately, the inherent connection between IG and Aumann-Shapley Value forms a unique perspective to rethink the design of baselines. Under certain hypothesis, we theoretically analyse that a set of baseline aligns with the coalitions in Shapley Value. Thus, we propose a novel baseline construction method called Shapley Integrated Gradients (SIG) that searches for a set of baselines by proportional sampling to partly simulate the computation path of Shapley Value. Simulations on GridWorld show that SIG approximates the proportion of Shapley Values. Furthermore, experiments conducted on various image tasks demonstrate that compared to IG using other baseline methods, SIG exhibits an improved estimation of feature's contribution, offers more consistent explanations across diverse applications, and is generic to distinct data types or instances with insignificant computational overhead.Comment: 12 page

Interferon regulatory factor 2 binding protein 2b regulates neutrophil versus macrophage fate during zebrafish definitive myelopoiesis

International audienceInterferon regulatory factor 2 binding protein 2b regulates neutrophil versus macrophage fate during zebrafish definitive myelopoiesis

Chemically programmed metabolism drives a superior cell fitness for cartilage regeneration

The rapid advancement of cell therapies underscores the importance of understanding fundamental cellular attributes. Among these, cell fitness—how transplanted cells adapt to new microenvironments and maintain functional stability in vivo—is crucial. This study identifies a chemical compound, FPH2, that enhances the fitness of human chondrocytes and the repair of articular cartilage, which is typically nonregenerative. Through drug screening, FPH2 was shown to broadly improve cell performance, especially in maintaining chondrocyte phenotype and enhancing migration. Single-cell transcriptomics indicated that FPH2 induced a super-fit cell state. The mechanism primarily involves the inhibition of carnitine palmitoyl transferase I and the optimization of metabolic homeostasis. In animal models, FPH2-treated human chondrocytes substantially improved cartilage regeneration, demonstrating well-integrated tissue interfaces in rats. In addition, an acellular FPH2-loaded hydrogel proved effective in preventing the onset of osteoarthritis. This research provides a viable and safe method to enhance chondrocyte fitness, offering insights into the self-regulatory mechanisms of cell fitness