Abstract In recent years, the development of microelectrode arrays and multichannel recordings has provided opportunities for high‐precision detection in signal processing. The study of neuronal frontal potentials has been rapidly emerging as an important component in brain‐computer interface and neuroscience research. Neuronal spike detection provides a basis for neuronal discharge analysis and nucleus cluster identification; its accuracy depends on feature extraction and classification, which affect neuronal decoding analysis. However, improving the detection accuracy of spike potentials in highly noisy signals remains a problem. IThe authors propose a heuristic adaptive threshold spike‐detection algorithm that removes noise and reduces the phase shift using a zero‐phase Butterworth infinite impulse response filter. Next, heuristic thresholding is applied to obtain spike points, remove repetitions, and achieve robust spike detection. The proposed algorithm achieved an average accuracy of 95.40% using extracellular spiked datasets and effectively detected spikes.

Spatial-temporal relation reasoning is a significant yet challenging problem for video action recognition. Previous works typically apply local operations like 2D or 3D CNNs to conduct space-time interactions in video sequences, or simply capture space-time long-range relations of a single fixed scale. However, this is inadequate for obtaining a comprehensive action representation. Besides, most models treat all input frames equally for the final classification, without selecting key frames and motion-sensitive regions. This introduces irrelevant video content and hurts the performance of models. In this paper, we propose a generic Spatial-Temporal Pyramid Graph Network (STPG-Net) to adaptively capture long-range spatial-temporal relations in video sequences at multiple scales. Specifically, we design a temporal attention (TA) module and a spatial-temporal attention (STA) module to learn the contribution of each frame and each space-time region to an action at a feature level, respectively. We then apply the selected key information to build spatial-temporal pyramid graphs for long-range relation reasoning and more comprehensive action representation learning. STPG-Net can be flexibly integrated into 2D and 3D backbone networks in a plug-and-play manner. Extensive experiments show that it brings consistent improvements over many challenging baselines on several standard action recognition benchmarks (i.e., Something-Something V1 & V2, and FineGym), demonstrating the effectiveness of our approach.

In many fields such as computer animation, computer graphics, machine vision, robotics, virtual reality and CAD/CAM, it is a common problem to detect the positional relationship between two planar conics. Based on the generalized characteristic polynomial and the affine invariants of two conics, explicit conditions are derived for classifying the various positional relationships between an ellipse and a parabola, namely, separation, exterior tangency, intersection, interior tangency and inclusion. The explicit conditions can be expressed in terms of the coefficients of the quadratic forms representing the ellipse and the parabola.

We use two approaches to solve the perspective-three-point (P3P) problem: the algebraic approach and the geometric approach. In the algebraic approach, we use Wu-Ritt's zero decomposition algorithm to give a complete triangular decomposition for the P3P equation system. This decomposition provides the first complete analytical solution to the P3P problem. We also give a complete solution classification for the P3P equation system, i.e., we give explicit criteria for the P3P problem to have one, two, three, and four solutions. Combining the analytical solutions with the criteria, we provide an algorithm, CASSC, which may be used to find complete and robust numerical solutions to the P3P problem. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions.