Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamical systems with nonlocal characteristics. Recent progress at the intersection of FDEs and deep learning has catalyzed a new wave of innovative models, demonstrating the potential to address challenges such as graph representation learning. However, training neural FDEs has primarily relied on direct differentiation through forward-pass operations in FDE numerical solvers, leading to increased memory usage and computational complexity, particularly in large-scale applications. To address these challenges, we propose a scalable adjoint backpropagation method for training neural FDEs by solving an augmented FDE backward in time, which substantially reduces memory requirements. This approach provides a practical neural FDE toolbox and holds considerable promise for diverse applications. We demonstrate the effectiveness of our method in several tasks, achieving performance comparable to baseline models while significantly reducing computational overhead.

Neural differential equation models have garnered significant attention in recent years for their effectiveness in machine learning applications.Among these, fractional differential equations (FDEs) have emerged as a promising tool due to their ability to capture memory-dependent dynamics, which are often challenging to model with traditional integer-order approaches.While existing models have primarily focused on constant-order fractional derivatives, variable-order fractional operators offer a more flexible and expressive framework for modeling complex memory patterns. In this work, we introduce the Neural Variable-Order Fractional Differential Equation network (NvoFDE), a novel neural network framework that integrates variable-order fractional derivatives with learnable neural networks.Our framework allows for the modeling of adaptive derivative orders dependent on hidden features, capturing more complex feature-updating dynamics and providing enhanced flexibility. We conduct extensive experiments across multiple graph datasets to validate the effectiveness of our approach.Our results demonstrate that NvoFDE outperforms traditional constant-order fractional and integer models across a range of tasks, showcasing its superior adaptability and performance.

Additionally, Zopf et al. [2] introduced The evaluation of layer importance in deep learning has been an Layer-wise Relevance Propagation (LRP), including its variants, active area of research, with significant implications for model to analyze the flow of information in complex neural networks, optimization and interpretability. Recently, large language models providing a more nuanced understanding of each layer's contribution (LLMs) have gained prominence across various domains, yet limited to the model's decisions. Furthermore, the work of Mencía studies have explored the functional importance and performance et al. [12] highlighted the significance of Contextual Importance contributions of individual layers within LLMs, especially from Measures(CIM), which integrate contextual information to dynamically the perspective of activation distribution. In this work, we propose evaluate the importance of each layer based on specific input the Activation Variance-Sparsity Score (AVSS), a novel metric conditions, thus overcoming the limitations of static assessment combining normalized activation variance and sparsity to assess methods. However, these approaches often struggle to fully capture each layer's contribution to model performance. By identifying and the intricate activation distributions and redundancy within large removing approximately the lowest 25% of layers based on AVSS, language models, limiting their effectiveness in identifying less we achieve over 90% of original model performance across tasks critical layers.

Spiking Neural Networks (SNNs) capture the information processing mechanism of the brain by taking advantage of spiking neurons, such as the Leaky Integrate-and-Fire (LIF) model neuron, which incorporates temporal dynamics and transmits information via discrete and asynchronous spikes. However, the simplified biological properties of LIF ignore the neuronal coupling and dendritic structure of real neurons, which limits the spatio-temporal dynamics of neurons and thus reduce the expressive power of the resulting SNNs. In this work, we leverage a more biologically plausible neural model with complex dynamics, i.e., a pulse-coupled neural network (PCNN), to improve the expressiveness and recognition performance of SNNs for vision tasks. The PCNN is a type of cortical model capable of emulating the complex neuronal activities in the primary visual cortex. We construct deep pulse-coupled neural networks (DPCNNs) by replacing commonly used LIF neurons in SNNs with PCNN neurons. The intra-coupling in existing PCNN models limits the coupling between neurons only within channels. To address this limitation, we propose inter-channel coupling, which allows neurons in different feature maps to interact with each other. Experimental results show that inter-channel coupling can efficiently boost performance with fewer neurons, synapses, and less training time compared to widening the networks. For instance, compared to the LIF-based SNN with wide VGG9, DPCNN with VGG9 uses only 50%, 53%, and 73% of neurons, synapses, and training time, respectively. Furthermore, we propose receptive field and time dependent batch normalization (RFTD-BN) to speed up the convergence and performance of DPCNNs.

The study of complex networks has significantly advanced our understanding of community structures which serves as a crucial feature of real-world graphs. Detecting communities in graphs is a challenging problem with applications in sociology, biology, and computer science. Despite the efforts of an interdisciplinary community of scientists, a satisfactory solution to this problem has not yet been achieved. This review article delves into the topic of community detection in graphs, which serves as a crucial role in understanding the organization and functioning of complex systems. We begin by introducing the concept of community structure, which refers to the arrangement of vertices into clusters, with strong internal connections and weaker connections between clusters. Then, we provide a thorough exposition of various community detection methods, including a new method designed by us. Additionally, we explore real-world applications of community detection in diverse networks. In conclusion, this comprehensive review provides a deep understanding of community detection in graphs. It serves as a valuable resource for researchers and practitioners in multiple disciplines, offering insights into the challenges, methodologies, and applications of community detection in complex networks.

Community detection becomes an important problem with the booming of social networks. The Medoid-Shift algorithm preserves the benefits of Mean-Shift and can be applied to problems based on distance matrix, such as community detection. One drawback of the Medoid-Shift algorithm is that there may be no data points within the neighborhood region defined by a distance parameter. To deal with the community detection problem better, a new algorithm called Revised Medoid-Shift (RMS) in this work is thus proposed. During the process of finding the next medoid, the RMS algorithm is based on a neighborhood defined by KNN, while the original Medoid-Shift is based on a neighborhood defined by a distance parameter. Since the neighborhood defined by KNN is more stable than the one defined by the distance parameter in terms of the number of data points within the neighborhood, the RMS algorithm may converge more smoothly. In the RMS method, each of the data points is shifted towards a medoid within the neighborhood defined by KNN. After the iterative process of shifting, each of the data point converges into a cluster center, and the data points converging into the same center are grouped into the same cluster. The RMS algorithm is tested on two kinds of datasets including community datasets with known ground truth partition and community datasets without ground truth partition respectively. The experiment results show sthat the proposed RMS algorithm generally produces betster results than Medoid-Shift and some state-of-the-art together with most classic community detection algorithms on different kinds of community detection datasets.

Wind energy is a widely distributed, renewable, and environmentally friendly energy source that plays a crucial role in mitigating global warming and addressing energy shortages. Nevertheless, wind power generation is characterized by volatility, intermittence, and randomness, which hinder its ability to serve as a reliable power source for the grid. Accurate wind power forecasting is crucial for developing a new power system that heavily relies on renewable energy sources. However, traditional wind power forecasting systems primarily focus on ultra-short-term or short-term forecasts, limiting their ability to address the diverse adjustment requirements of the power system simultaneously. To overcome these challenges, We propose an automatic framework capable of forecasting wind power across multi-time scale. The framework based on the tree-structured Parzen estimator (TPE) and temporal fusion transformer (TFT) that can provide ultra-short-term, short-term and medium-term wind power forecasting power.Our approach employs the TFT for wind power forecasting and categorizes features based on their properties. Additionally, we introduce a generic algorithm to simultaneously fine-tune the hyperparameters of the decomposition method and model. We evaluate the performance of our framework by conducting ablation experiments using three commonly used decomposition algorithms and six state-of-the-art models for forecasting multi-time scale. The experimental results demonstrate that our proposed method considerably improves prediction accuracy on the public dataset Engie https://opendata-renewables.engie.com. Compared to the second-best state-of-the-art model, our approach exhibits a reduction of 31.75% and 28.74% in normalized mean absolute error (nMAE) for 24-hour forecasting, and 20.79% and 16.93% in nMAE for 48-hour forecasting, respectively.

NASA might not even hit its new 2025 moon deadline, an expert has warned, amid fears China could now beat the US to the lunar surface this decade. It comes just hours after the US space agency revealed that its plans to send the first woman and first person of colour to Earth's only natural satellite had been delayed by a year. Seven months of litigation over the Blue Origin lawsuit, the coronavirus pandemic and unexpected cost increases have all played a part in the schedule change. But Dr Erin Macdonald, a Scottish-American astrophysicist and aerospace engineer, agreed with NASA Administrator Bill Nelson that a lack of finances and an unrealistic target set by Donald Trump's government in 2019 was also to blame. She told BBC Radio 4's Today programme: 'The budget that they were awarded to do this under the previous administration wasn't really sufficient to get everything completed in the timeline they were given.'

Stunning footage of the Zhurong rover beginning its exploration of the surface of Mars has been released by the China National Space Administration (CNSA). The clips of the six-wheeled rover trundling across the Red Planet were captured by a wireless camera that the rover had placed on the ground. They were then relayed back to Earth via the Tianwen-1 satellite which brought the rover to Mars and is presently orbiting the Red Planet. Also released yesterday was previously unseen footage from the Zhurong rover's landing back on May 15 -- and its deployment from the Lander platform on May 22. Footage and photos were relayed back to Earth via the Tianwen-1 satellite which brought the rover to Mars and is presently orbiting the Red Planet. Pictured: part of a panorama of the Martian surface taken by Zhurong.

Russia and China have committed to work together on a moon base and lunar space station, but it will not be ready to house astronauts until at least 2036, the two countries said. Known as the International Lunar Research Station (ILRS), it will consist of a surface moon base and station in lunar orbit, with construction expected to start in 2026. The two nations have asked other international agencies to join them in the project, which will also include rovers and'hopping robots' to aid eventual inhabitants. NASA is working with the European Space Agency (ESA), as well as Canada and Japan on the Lunar Gateway, a modular crewed space station designed to operate in orbit around the moon and help astronauts reach the lunar surface from 2024. While Russia and China are working together on the moon, the two will compete in low Earth orbit, with both planning their own space station to rival the International Space Station (ISS).