Early detection of aseptic or septic loosening of hip endoprostheses is clinically crucial but still relies primarily on projection radiography, which lacks sensitivity for sub-millimetre interlayers at the bone–implant interface. Recent work by Lützelberger et al. demonstrated that ultrasound interferometry enables quantification of the width of this interface by analysing frequency-domain interference patterns of reflections from the soft-tissue gap. However, several open theoretical questions remained, particularly regarding the fundamental detection limits for small gap widths and the optimal choice of excitation frequency. This work provides a mathematical analysis of (i) the minimal resolvable gap width based on the Gabor limit, bandwidth constraints, and the signal-to-noise ratio (SNR) and (ii) the optimal operating frequency considering attenuation in soft tissue and the limited thickness of the cortical bone layer. The results show that an excitation frequency around 3 MHz represents an optimum here. Furthermore, closed-form expressions for the minimum detectable width are derived, predicting detection thresholds in the range of 156–212 µm for different SNR conditions – consistent with previously reported experimental results. These findings provide theoretical justification for system design choices in interferometric ultrasound for implant-integration monitoring.

LectureChat extends the WikiChat conversational AI system by integrating multilingual university lecture transcripts alongside

Wikipedia content. The demo showcases a dual retrieval architecture that combines structured encyclopedic knowledge with academic lecture

material, leveraging multiple segmentation strategies and cross index reconciliation to improve retrieval quality. The system maintains separate

citation spaces for Wikipedia (numeric) and lectures (alphabetic) and preserves temporal provenance for direct video navigation. We present

the overall architecture, interaction flow, implementation details, and a reproducibility plan.

Bone fractures represent an increasing medical and social challenge, particularly due to falls and osteoporosis in the elderly. Among these, tibial (shinbone) fractures are the most clinically significant. Proper clinical management requires assessing whether biological healing progresses well and determining when sucient stiness and stability are regained – for example, to decide when to remove artificial fixation. Currently, fracture healing is mainly monitored through functional tests and X-ray imaging, which involves radiation, is costly, and provides no direct information about the mechanical stiness of the healing bone. To overcome these limitations, we propose an ultrasonic approach for continuous monitoring the elasticity changes of the fracture regions during the healing process. By evaluating the propagation characteristics of guided acoustic Lamb waves travelling through the fracture region, our method aims to enable tracking of the healing progress and prediction of the remaining healing time. Using phantom materials that replicate various bone anatomies and fracture types, we obtained initial experimental results with a single-element transmitter–receiver ultrasonic setup, showing excellent agreement with theoretical predictions. In future work, we aim to increase the realism of our phantoms by including various soft-tissue layers and to advance both hardware and software toward an integrated medical device.

Nonlinear optimisation techniques are commonly employed to minimise complex cost functions, with their effectiveness determined largely by the structure of the underlying error landscape. These methods require initial parameter values, and in the presence of multiple local minima, they are prone to becoming trapped in suboptimal regions. The likelihood of locating the global minimum increases substantially when the initialisation lies within its corresponding basin of attraction. Consequently, high-quality initial parameters are critical for successful optimisation. This technical report outlines a new strategy for selecting suitable initial parameters for a trigonometric model and unevenly sampled data, ensuring that the optimisation procedure starts sufficiently close to the global minimum. The proposed parameter estimation approach is strictly NI-based, interpretable, and explainable. It targets at complicated cases which include: samples with strong random noise, samples with only few covered periods, and samples which cover only a fraction of one period. Special attention is put on the frequency estimation. It can be shown that an estimation of initial parameters with sufficient accuracy is possible down to a signal-noise-ratio of 1.4 dB at much lower computational costs than the Lomb-Scargle-periodogram method requires.