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The Central Nervous System (CNS) acts as the main element of the biological system, regulating and commanding numerous organs in the human body. Neurons play a crucial role in the central nervous system, and it is necessary to thoroughly examine, replicate, simulate, and integrate various aspects of the CNS to develop a comprehensive neuronal system that can mimic the actual nervous system. In this research, a neuron model called the Quartic Neuron Model is employed to imitate the fundamental nervous functions of the human brain. The proposed method, known as Digital-QNM (D-QNM) is accomplished by employing power-2 based approximation and linear approaches to modify the fourth-degree function. These power-2 based functions are digital-friendly terms (high-accurate, low-cost and leads to high-frequency implementation). By eliminating the high-cost function, the presented model offers advantages such as low error, high speed, and efficient resource utilization compared to the basic main state. In order to validate the final hardware design, a digital FPGA board (specifically, the Xilinx Virtex-5 FPGA board) is employed. The process of digitally synthesizing the hardware demonstrates that our proposed approach can replicate the QNM with improved frequency, performance, and reduced hardware costs. The implementation outcomes show a significant reduction of 98% in FPGA resources cost and a higher operating frequency of the suggested model, reaching 190 MHz. This frequency is considerably higher than the original model’s 105 MHz.

In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of SU(2), U(2), SO(3), SO(3) × S1and Spinℂ(3). We define the rotation vectors (numbers) of the left actions induced by the elements in the maximal tori of these groups, and utilize rotation vectors (numbers) to give the topologically conjugate classification of the left actions. Algebraic conjugacy and smooth conjugacy are also considered. As a by-product, we show that for any homeomorphism f: L(p, −1) × S1→ L(p, −1) × S1, the induced isomorphism (τ◦ f◦ i)* maps each element in the fundamental group of L(p, −1) to itself or its inverse, where i: L(p, −1) → L(p, −1) × S1is the natural inclusion and τ: L(p, −1) × S1→ L(p, −1) is the projection.