Activation functions are critical components in deep neural networks, directly influencing gradient flow, training stability, and model performance. Traditional functions like ReLU suffer from dead neuron problems, while sigmoid and tanh exhibit vanishing gradient issues. We introduce two novel hybrid activation functions: S3 (Sigmoid-Softsign) and its improved version S4 (smoothed S3). S3 combines sigmoid for negative inputs with softsign for positive inputs, while S4 employs a smooth transition mechanism controlled by a steepness parameter k. We conducted comprehensive experiments across binary classification, multi-class classification, and regression tasks using three different neural network architectures. S4 demonstrated superior performance compared to nine baseline activation functions, achieving 97.4% accuracy on MNIST, 96.0% on Iris classification, and 18.7 MSE on Boston Housing regression. The function exhibited faster convergence (-19 for ReLU) and maintained stable gradient flow across network depths. Comparative analysis revealed S4's gradient range of [0.24, 0.59] compared to ReLU's 18% dead neurons in deep networks. The S4 activation function addresses key limitations of existing functions through its hybrid design and smooth transition mechanism. The tunable parameter k allows adaptation to different tasks and network depths, making S4 a versatile choice for deep learning applications. These findings suggest that hybrid activation functions represent a promising direction for improving neural network training dynamics.

This paper introduces KZImputer, a novel adaptive imputation method for univariate time series designed for short to medium-sized missed points (gaps) (1-5 points and beyond) with tailored strategies for segments at the start, middle, or end of the series. KZImputer employs a hybrid strategy to handle various missing data scenarios. Its core mechanism differentiates between gaps at the beginning, middle, or end of the series, applying tailored techniques at each position to optimize imputation accuracy. The method leverages linear interpolation and localized statistical measures, adapting to the characteristics of the surrounding data and the gap size. The performance of KZImputer has been systematically evaluated against established imputation techniques, demonstrating its potential to enhance data quality for subsequent time series analysis. This paper describes the KZImputer methodology in detail and discusses its effectiveness in improving the integrity of time series data. Empirical analysis demonstrates that KZImputer achieves particularly strong performance for datasets with high missingness rates (around 50% or more), maintaining stable and competitive results across statistical and signal-reconstruction metrics. The method proves especially effective in high-sparsity regimes, where traditional approaches typically experience accuracy degradation.

As the 400 employees of GSC Game World, creators of the hit video game Stalker, filtered into their Kyiv office in January 2022, most didn't even notice the strange buses parked around the corner. While tensions were growing with their neighbours across the border, the frost-coated shlep to the office felt almost normal. Or so they told themselves. As whispers of war spread throughout the country, regular reassurances from their business partners – and President Zelenskiy – made it seem foolish to worry. Life, they were told, would carry on as usual.