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Neuromorphic computing (NC) is a promising candidate for artificial intelligence applications. To realize NC, electronic analogues of brain components, such as synapses and neurons, must be designed. In spintronics, domain wall (DW) based magnetic tunnel junctions - which offer both synaptic and neuronal functionalities - are one of the promising candidates. An electronic neuron should exhibit leaky-integrate-fire functions similar to their biological counterparts. However, most experimental studies focused only on the integrate-and-fire functions, overlooking the leaky function. Here, we report on a domain wall neuron device that achieves integration using spin-orbit torque-induced domain wall motion and a leaky function via synthetic antiferromagnetic coupling. By fabricating Hall bar devices in a special geometry, we could achieve these two functionalities. During the leaky process, the maximum DW velocity achieved was 2500 {\mu}m/s. The proposed design utilizes materials used in STT-MRAM fabrication and is compatible with CMOS fabrication. Therefore, this neuron can be readily integrated into NC., Comment: 15 pages, 4 Figures, 1 Table

We employ the Bayesian improved cross entropy (BiCE) method for rare event estimation in static networks and choose the categorical mixture as the parametric family to capture the dependence among network components. At each iteration of the BiCE method, the mixture parameters are updated through the weighted maximum a posteriori (MAP) estimate, which mitigates the overfitting issue of the standard improved cross entropy (iCE) method through a novel balanced prior, and we propose a generalized version of the expectation-maximization (EM) algorithm to approximate this weighted MAP estimate. The resulting importance sampling distribution is proved to be unbiased. For choosing a proper number of components $K$ in the mixture, we compute the Bayesian information criterion (BIC) of each candidate $K$ as a by-product of the generalized EM algorithm. The performance of the proposed method is investigated through a simple illustration, a benchmark study, and a practical application. In all these numerical examples, the BiCE method results in an efficient and accurate estimator that significantly outperforms the standard iCE method and the BiCE method with the independent categorical distribution.

We propose a modification of the improved cross entropy (iCE) method to enhance its performance for network reliability assessment. The iCE method performs a transition from the nominal density to the optimal importance sampling (IS) density via a parametric distribution model whose cross entropy with the optimal IS is minimized. The efficiency and accuracy of the iCE method are largely influenced by the choice of the parametric model. In the context of reliability of systems with independent multi-state components, the obvious choice of the parametric family is the categorical distribution. When updating this distribution model with standard iCE, the probability assigned to a certain category often converges to 0 due to lack of occurrence of samples from this category during the adaptive sampling process, resulting in a poor IS estima tor with a strong negative bias. To circumvent this issue, we propose an algorithm termed Bayesian improved cross entropy method (BiCE). Thereby, the posterior predictive distribution is employed to update the parametric model instead of the weighted maximum likelihood estimation approach employed in the original iCE method. A set of numerical examples illustrate the efficiency and accuracy of the proposed method.