South Westphalia University of Applied Sciences

Modern multimodal systems deployed in industrial and safety-critical environments must remain reliable under partial sensor failures, signal degradation, or cross-modal inconsistencies. This work introduces a mathematically grounded framework for fault-tolerant multimodal representation learning that unifies self-supervised anomaly detection and error correction within a single architecture. Building upon a theoretical analysis of perturbation propagation, we derive Lipschitz- and Jacobian-based criteria that determine whether a neural operator amplifies or attenuates localized faults. Guided by this theory, we propose a two-stage self-supervised training scheme: pre-training a multimodal convolutional autoencoder on clean data to preserve localized anomaly signals in the latent space, and expanding it with a learnable compute block composed of dense layers for correction and contrastive objectives for anomaly identification. Furthermore, we introduce layer-specific Lipschitz modulation and gradient clipping as principled mechanisms to control sensitivity across detection and correction modules. Experimental results on multimodal fault datasets demonstrate that the proposed approach improves both anomaly detection accuracy and reconstruction under sensor corruption. Overall, this framework bridges the gap between analytical robustness guarantees and practical fault-tolerant multimodal learning.

OBJECTIVES:The Ixworth chicken is a British dual-purpose breed and mostly maintained by small-scale farmers. Due to legislation regarding the ban on male chick culling in European countries, such as in Germany, renewed interest has arisen in rearing dual-purpose chickens that provide both meat and eggs from the same genetic line. This dataset was generated within the scope of projects aiming to evaluate the viability of dual-purpose breeds for sustainable and welfare-oriented poultry production. One of the objectives was to characterize the genetic potential of the Ixworth chicken as a model for breeding programs that combine conservation and practical use in ecological farming systems. DATA DESCRIPTION:Liver samples from 49 male Ixworth chickens were collected after scheduled slaughter at the Campus Frankenforst of the Faculty of Agricultural, Nutritional and Engineering Sciences of the University of Bonn, Germany. Genomic DNA was extracted and subjected to whole-genome resequencing using the Illumina NovaSeq 6000 platform. The dataset provides high-resolution genomic information on a rare breed with a pure dual-purpose background. This resource represents the first public sequencing dataset of the Ixworth chicken and thus offers a valuable foundation for future studies on genetic diversity, conservation genomics, and breeding strategies for sustainable poultry production.

Ensuring the stability and robustness of multimodal autoencoders is critical for their optimization and deployment in safety-critical industrial environments. This paper presents a rigorous analysis of Lipschitz properties in multimodal fusion, identifying theoretical vulnerabilities in standard summation and concatenation strategies. We derive explicit Lipschitz bounds for these methods, demonstrating their susceptibility to gradient instability and noise propagation as the number of modalities increases. To address this, we introduce a Lipschitz-regularized attention-based fusion mechanism that explicitly bounds gradient sensitivity through spectral normalization and dimension scaling. Empirical validation on four industrial robotic datasets, including the real-world RoboMNIST dataset, confirms our theoretical findings. On the RoboMNIST dataset, our method achieves an improvement of 54.7% in bimodal and 57.4% in trimodal reconstruction over standard attention, alongside a 20.5% gain in subordinated fault detection, while effectively regularizing the Lipschitz of the gradients.

This paper addresses the question of how many autonomous aerial vehicles (UAVs or drones) can safely operate within a bounded three-dimensional airspace. First, we derive the absolute mathematical limits on drone density using geometric arguments from sphere packing and covering theory. Then, we verify these limits empirically by simulating a swarm controlled via model predictive control. We incrementally increase the number of drones until motion becomes impossible. Each drone is modeled as a double-integrator system with a bounded speed and acceleration and is surrounded by a radius spherical safety zone r>0. The drones are controlled via model predictive control with hard separation constraints. We formalize complete blockage as the loss of any feasible non-trivial trajectory set, either due to geometric crowding or dynamic limitations. Using tools from discrete geometry, we establish absolute upper bounds on a safe population via sphere-packing results and sufficient conditions for total immobilization via sphere-covering arguments. We extend these static bounds by incorporating dynamics through stopping-distance analysis, leading to an inflated exclusion radius that captures the effect of finite control authority. In addition, we prove min-cut style flow-capacity bounds that limit feasible throughput across bottlenecks and derive horizon-dependent conflict-graph conditions that capture MPC infeasibility at high densities. These results provide a rigorous theoretical framework for determining the transition from feasible multi-drone operation to inevitable gridlock, offering explicit quantitative thresholds that can inform airspace design, drone density regulation, and the tuning of predictive controllers. We evaluate our theoretical findings with a simulation environment.

Purpose Provide the theoretical foundation and the first practical demonstration of spatiotemporal encoding (SPEN) using additional nonlinear gradient hardware.Methods The quadratic phase profile can be generated either by a chirped-RF pulse combined with a constant gradient or, directly, by a quadratic gradient pulse. Both a conventional chirped-RF and a novel SPEN method using a custom-built matrix gradient coil for quadratic phase generation were implemented and integrated into a spin-echo echo-planar-imaging (SE-EPI) sequence using Pulseq. The methods were compared through phantom imaging experiments performed on a 3T MRI system.Results The required quadratic phase profile for SPEN was successfully generated using the nonlinear gradient coil, resulting in images of comparable quality. This quadratic gradient-based approach was achieved while exploiting the advantages of SPEN and overcoming current SAR and minimal TE limitations arising from the use of chirped-RF pulses.Conclusion The generation of the SPEN-defining quadratic phase using nonlinear gradients is an advantageous alternative to conventional methods. This approach enables improved clinical applicability of SPEN, particularly for 3D and high-field MRI, by mitigating critical safety and timing limitations. Additionally, an implementation of the conventional method is provided open-source to support further research.