Conditional score-based diffusion model (SBDM) is for conditional generation of target data with paired data as condition, and has achieved great success in image translation. However, it requires the paired data as condition, and there would be insufficient paired data provided in real-world applications.

Conditional score-based diffusion model (SBDM) is for conditional generation of target data with paired data as condition, and has achieved great success in image translation. However, it requires the paired data as condition, and there would be insufficient paired data provided in real-world applications. To tackle the applications with partially paired or even unpaired dataset, we propose a novel Optimal Transport-guided Conditional Score-based diffusion model (OTCS) in this paper. We build the coupling relationship for the unpaired or partially paired dataset based on $L_2$-regularized unsupervised or semi-supervised optimal transport, respectively. Based on the coupling relationship, we develop the objective for training the conditional score-based model for unpaired or partially paired settings, which is based on a reformulation and generalization of the conditional SBDM for paired setting. With the estimated coupling relationship, we effectively train the conditional score-based model by designing a ``resampling-by-compatibility'' strategy to choose the sampled data with high compatibility as guidance. Extensive experiments on unpaired super-resolution and semi-paired image-to-image translation demonstrated the effectiveness of the proposed OTCS model. From the viewpoint of optimal transport, OTCS provides an approach to transport data across distributions, which is a challenge for OT on large-scale datasets. We theoretically prove that OTCS realizes the data transport in OT with a theoretical bound.

Conditional score-based diffusion model (SBDM) is for conditional generation of target data with paired data as condition, and has achieved great success in image translation. However, it requires the paired data as condition, and there would be insufficient paired data provided in real-world applications. To tackle the applications with partially paired or even unpaired dataset, we propose a novel Optimal Transport-guided Conditional Score-based diffusion model (OTCS) in this paper. We build the coupling relationship for the unpaired or partially paired dataset based on L_2 -regularized unsupervised or semi-supervised optimal transport, respectively. Based on the coupling relationship, we develop the objective for training the conditional score-based model for unpaired or partially paired settings, which is based on a reformulation and generalization of the conditional SBDM for paired setting.

Advancements in electronic technology and control algorithms have enabled precise flight control techniques, transforming bionic aircraft from principle imitation to comprehensive resemblance. This paper introduces the Minimal Biorobotic Stealth Distance (MBSD), a novel quantitative metric to evaluate the bionic resemblance of biorobotic aircraft. Current technological limitations prevent dragonfly-inspired aircrafts from achieving optimal performance at biological scales. To address these challenges, we use the DDD-1 dragonfly-inspired aircraft, a hover-capable directdrive aircraft, to explore the impact of the MBSD on aircraft design. Key contributions of this research include: (1) the establishment of the MBSD as a quantifiable and operable evaluation metric that influences aircraft design, integrating seamlessly with the overall design process and providing a new dimension for optimizing bionic aircraft, balancing mechanical attributes and bionic characteristics; (2) the creation and analysis of a typical aircraft in four directions: essential characteristics of the MBSD, its coupling relationship with existing performance metrics (Longest Hover Duration and Maximum Instantaneous Forward Flight Speed), multi-objective optimization, and application in a typical mission scenario; (3) the construction and validation of a full-system model for the direct-drive dragonfly-inspired aircraft, demonstrating the design model's effectiveness against existing aircraft data. Detailed calculations of the MBSD consider appearance similarity, dynamic similarity, and environmental similarity. Experimental results indicate that the MBSD value correlates with bionic resemblance and is influenced by design parameters like wingspan, flapping frequency, and amplitude.

Complex applications such as big data analytics involve different forms of coupling relationships that reflect interactions between factors related to technical, business (domain-specific) and environmental (including socio-cultural and economic) aspects. There are diverse forms of couplings embedded in poor-structured and ill-structured data. Such couplings are ubiquitous, implicit and/or explicit, objective and/or subjective, heterogeneous and/or homogeneous, presenting complexities to existing learning systems in statistics, mathematics and computer sciences, such as typical dependency, association and correlation relationships. Modeling and learning such couplings thus is fundamental but challenging. This paper discusses the concept of coupling learning, focusing on the involvement of coupling relationships in learning systems. Coupling learning has great potential for building a deep understanding of the essence of business problems and handling challenges that have not been addressed well by existing learning theories and tools. This argument is verified by several case studies on coupling learning, including handling coupling in recommender systems, incorporating couplings into coupled clustering, coupling document clustering, coupled recommender algorithms and coupled behavior analysis for groups.