Naga: Vedic Encoding for Deep State Space Models

This paper presents Naga, a deep State Space Model (SSM) encoding approach inspired by structural concepts from Vedic mathematics. The proposed method introduces a bidirectional representation for time series by jointly processing forward and time-reversed input sequences. These representations are then combined through an element-wise (Hadamard) interaction, resulting in a Vedic-inspired encoding that enhances the model's ability to capture temporal dependencies across distant time steps. We evaluate Naga on multiple long-term time series forecasting (LTSF) benchmarks, including ETTh1, ETTh2, ETTm1, ETTm2, Weather, Traffic, and ILI. The experimental results show that Naga outperforms 28 current state of the art models and demonstrates improved efficiency compared to existing deep SSM-based approaches. The findings suggest that incorporating structured, Vedic-inspired decomposition can provide an interpretable and computationally efficient alternative for long-range sequence modeling.

S4D-Bio Audio Monitoring of Bone Cement Disintegration in Pulsating Fluid Jet Surgery under Laboratory Conditions

This study investigates a pulsating fluid jet as a novel precise, minimally invasive and cold technique for bone cement removal. We utilize the pulsating fluid jet device to remove bone cement from samples designed to mimic clinical conditions. The effectiveness of long nozzles was tested to enable minimally invasive procedures. Audio signal monitoring, complemented by the State Space Model (SSM) S4D-Bio, was employed to optimize the fluid jet parameters dynamically, addressing challenges like visibility obstruction from splashing. Within our experiments, we generate a comprehensive dataset correlating various process parameters and their equivalent audio signals to material erosion. The use of SSMs yields precise control over the predictive erosion process, achieving 98.93 \% accuracy. The study demonstrates on the one hand, that the pulsating fluid jet device, coupled with advanced audio monitoring techniques, is a highly effective tool for precise bone cement removal. On the other hand, this study presents the first application of SSMs in biomedical surgery technology, marking a significant advancement in the application. This research significantly advances biomedical engineering by integrating machine learning combined with pulsating fluid jet as surgical technology, offering a novel, minimally invasive, cold and adaptive approach for bone cement removal in orthopedic applications.