Memristors have emerged as promising candidates for multilevel data storage, in-memory processing, and neural networks since their intrinsic programmability of resistance states under applied stimuli has been well revealed in memristor modeling. However, the programming uncertainty arising from the inherently stochastic nature of the device itself has been overlooked in previous modeling approaches. This omission hinders the incorporation of memristor stochasticity into time-domain circuit simulation. To address this issue, we propose a behavior model that incorporates real-time programming stochasticity. Our model stands out for several attributes: 1) programming stochasticity is included and exhibited in its resistance change over time; 2) its stochastic behavior is depicted by the summation of its deterministic behaviors and a noise signal; and 3) both deterministic behaviors and noise amplitudes depending on the pulse amplitude v and the memristor resistance R are determined by sufficient characterization data of our in-house TiO2 devices in a data-driven method. Consequently, our model is validated as highly matched to the characterized memristor device in terms of time-domain resistance evolution. Additionally, the modeling process can be adapted to different memristors with significant device variations. Furthermore, the model is transformed into the standard Verilog-A style for in-circuit simulation. To demonstrate its compatibility with system-level circuit simulation, a mixed-signal CMOS circuit is designed. This circuit explores the feasibility of storing multibit data within a single memristor, while considering its stochasticity.

Time series regression models are typically trained using the mean squared error (MSE) and thus rely critically on time-aligned reference data. However, the MSE loss is often inadequate when processing real-world data, such as physiological signals, as misalignment between two signals can cause a large change in MSE, thus severely inhibiting convergence. This is regularly compounded by time varying drifts between different modalities and such as photoplethysmography, electrocardiography, blood pressure and respiration. Indeed, these exhibit fluctuating time delays even when taken from the same individual across different body positions and at different times of the day. To this end, we introduce the concept of segmented error minimisation (SEMI), a new loss function which accounts for differing time delays among the variables. The SEMI is examined both through simulations, and via a denoising convolutional autoencoder with synthetic data. It is then finally verified in the real-world application of the denoising of wearable photoplethysmography with a reference signal.