We show that if all the even exponents of an odd perfect number N are equal to 2 except for one, then 3^23,000,000,000 divides N .
This paper proposes a quantum algorithm for the capacitated vehicle routing problem with time windows (CVRPTW) based on Grover Search framework. This problem is often faced by Postal services in the context of package delivery or other time-sensitive operations. We provide an implementation on gate based quantum computer of a model inspired by classical route first, cluster second technique. The quantum paradigm allows to overcome suboptimality inherent property of this decomposition. In the current NISQ (Noisy Intermediate-Scale Quantum) era, the most important limitation is the number of available qubits which makes time windows and capacity constraints hard to tackle. We introduce a qubit-efficient split-inspired modeling which adds only a linear number of decision qubits to standard quantum formulations for Traveling Salesman Problem (TSP).
This is a corrigendum for the article “Life Cycle Assessment of Edge Data Centers: Cash Study in Presence of Renewable Energy and Refurbished Services” published in ACM J. Comput. Sustain. Soc. 3, 2, Article 9 (April 2025), 29 pages.
Understanding driving scenes and communicating automated vehicle decisions are key requirements for trustworthy automated driving. In this article, we introduce the Qualitative Explainable Graph (QXG), which is a unified symbolic and qualitative representation for scene understanding in urban mobility. The QXG enables interpreting an automated vehicle's environment using sensor data and machine learning models. It utilizes spatio-temporal graphs and qualitative constraints to extract scene semantics from raw sensor inputs, such as LiDAR and camera data, offering an interpretable scene model. A QXG can be incrementally constructed in real-time, making it a versatile tool for in-vehicle explanations across various sensor types. Our research showcases the potential of QXG, particularly in the context of automated driving, where it can rationalize decisions by linking the graph with observed actions. These explanations can serve diverse purposes, from informing passengers and alerting vulnerable road users to enabling post-hoc analysis of prior behaviors.
Thanks to recent promising advances in AI, automated segmentation of imaging datasets has made significant strides. However, the evaluation and curation of 3D and 3D+t datasets remain extremely challenging and highly resource-intensive. We present MorphoNet 2.0, a major conceptual and technical evolution designed to facilitate the segmentation, self-evaluation, and correction of 3D images. The application is accessible to non-programming biologists through user-friendly graphical interfaces and works on all major operating systems. We showcase its power in enhancing segmentation accuracy and boosting interpretability across five previously published segmented datasets. This new approach is crucial for producing ground-truth datasets of discovery-level scientific quality, critical for training and benchmarking advanced AI-driven segmentation tools, as well as for competitive challenges.
