This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from N independent trajectories. We propose a neural network-based estimator and derive a non-asymptotic convergence rate, decomposed into a training error, an approximation error, and a diffusion-related term scaling as log N/N. For compositional drift functions, we establish an explicit rate. In the numerical experiments, we consider a drift function with local fluctuations generated by a double-layer compositional structure featuring local oscillations, and show that the empirical convergence rate becomes independent of the input dimension d. Compared to the B-spline method, the neural network estimator achieves better convergence rates and more effectively captures local features, particularly in higher-dimensional settings.

Spiking neural membrane systems (SNP systems) are distributed parallel computing models inspired by neuronal spike mechanisms. Traditional SNP systems execute rules serially within each neuron, limiting their efficiency. This paper introduces MNSNP systems, a novel variant where neurons can distinguish spike sources and execute multiple rules in parallel at one time step. MNSNP systems maintain global distributed parallelism while integrating local parallelism, significantly enhancing information processing capabilities. Computational completeness is demonstrated, proving MNSNP systems as Turing universal devices for number generation, acceptance, and function computation. Compared to existing models, MNSNP systems require fewer neurons (only 60 for universal computation), showcasing resource efficiency. An application in smoke detection achieves an AUC value of 0.9840, demonstrating practical utility. This work advances SNP systems by introducing multiplexing, paving the way for applications in robotics, feature recognition, and real-time processing.

3D human pose estimation (HPE) is crucial due to its extensive applications. While current 3D HPE methods focus on human skeleton topology for accuracy, they often overlook joint angle information, which is vital in 2D-to-3D pose lifting. This paper introduces the Joint Angle Network (JANE) model to leverage joint angle features from 2D poses. We propose an angle graph convolution module to extract joint angle features and a multi-stage parallel fusion module to integrate these features with input image data. Experiments on Human3.6M show that our method improves accuracy by 8.7% and 2.6% over non-spatiotemporal baselines using 2D ground truth and 2D pose detectors, respectively.

Spiking neural membrane systems (or spiking neural P systems, SNP systems) are a new type of computation model which have attracted the attention of plentiful scholars for parallelism, time encoding, interpretability and extensibility. The original SNP systems only consider the time delay caused by the execution of rules within neurons, but not caused by the transmission of spikes via synapses between neurons and its adaptive adjustment. In view of the importance of time delay for SNP systems, which are a time encoding computation model, this study proposes SNP systems with adaptive synaptic time delay (ADSNP systems) based on the dynamic regulation mechanism of synaptic transmission delay in neural systems. In ADSNP systems, besides neurons, astrocytes that can generate adenosine triphosphate (ATP) are introduced. After receiving spikes, astrocytes convert spikes into ATP and send ATP to the synapses controlled by them to change the synaptic time delays. The Turing universality of ADSNP systems in number generating and accepting modes is proved. In addition, a small universal ADSNP system using 93 neurons and astrocytes is given. The superiority of the ADSNP system is demonstrated by comparison with the six variants. Finally, an ADSNP system is constructed for credit card fraud detection, which verifies the feasibility of the ADSNP system for solving real-world problems. By considering the adaptive synaptic delay, ADSNP systems better restore the process of information transmission in biological neural networks, and enhance the adaptability of SNP systems, making the control of time more accurate.

Since the spiking neural P system (SN P system) was proposed in 2006, it has become a research hotspot in the field of membrane computing. The SN P system performs computations through the encoding, processing, and transmission of spiking information and can be regarded as a third-generation neural network. As a variant of the SN P system, the global asynchronous numerical spiking neural P system (ANSN P system) is adaptable to a broader range of application scenarios. However, in biological neuroscience, some neurons work synchronously within a community to perform specific functions in the brain. Inspired by this, our work investigates a global asynchronous spiking neural P system (ANSN P system) that incorporates certain local synchronous neuron sets. Within these local synchronous sets, neurons must execute their production functions simultaneously, thereby reducing dependence on thresholds and enhancing control uncertainty in ANSN P systems. By analyzing the ADD, SUB, and FIN modules in the generating mode, as well as the INPUT and ADD modules in the accepting mode, this paper demonstrates the novel system's computational capacity as both a generator and an acceptor. Additionally, this paper compares each module to those in other SN P systems, considering the maximum number of neurons and rules per neuron. The results show that this new ANSN P system is at least as effective as the existing SN P systems.

P systems (SNP systems), one of the parallel and distributed computing models with biological interpretability, have been a hot research topic in bio-inspired computational models in recent years. To improve the stability of the models, this study introduces microglia in the biological nervous system into SNP systems and proposes SNP systems with microglia (MSNP systems). In MSNP systems, besides neurons, another cell type named microglia is introduced. Microglia can help neurons in the range of action maintain homeostasis and prevent excitotoxicity, i.e., excessive excitability. Specifically, microglia use a new microglial maintenance rule to lower the number of spikes in neurons within their range of action when it is too high. The computational capability and efficiency of MSNP systems are also proved. This study makes SNP systems more stable and avoids data overflow or data explosion problems to some degree.