Let G be a graph and denote its vertex set and edge set by V ( G ) and E ( G ) , respectively. For a vertex v i ∈ V ( G ) , let d i denote its degree. A broad class of numerical parameters for graphs is given by BID ϑ ( G ) = ∑ v i v j ∈ E ( G ) ϑ ( d i , d j ) , where the function ϑ is symmetric and it assigns a real value to each pair of degrees of adjacent vertices of G . Such graph parameters are known as bond incident degree (BID) indices. The family BID ϑ specializes to the general atom–bond connectivity index ABC α when ϑ ( d i , d j ) = ( ( d i + d j − 2 ) d i − 1 d j − 1 ) α , for any real parameter α ; in particular, the choice α = 1 2 yields the classical atom–bond connectivity index. In their work (Chen and Hao, 2018), Chen and Hao posed the problem of identifying those graphs from the class of all connected graphs of fixed order with prescribed edge or vertex connectivity that attain the maximum value of ABC α for any α with 0 < α ≤ 1 2 . The present article resolves the aforementioned problem by providing a general result for BID ϑ under some suitable conditions imposed on ϑ . These conditions are fulfilled not only by ABC α for 0 < α ≤ 1 2 , but also by many other existing particular BID indices, such as the reformulated first Zagreb index, the Sombor index and its reduced form, the Euler–Sombor index, the inverse sum indeg index, the Zagreb–Sombor index, the reciprocal sum-connectivity index, the reciprocal Randić index, and the elliptic Sombor index.

Nighttime object detection is essential for road, urban, and traffic perception, where detectors are typically required to recognize a predefined set of categories under a closed-set protocol. However, severe illumination degradation, noise amplification, and weak textures make visual evidence unreliable, leading to semantic ambiguity and missed detections. To address this issue, we propose Night-Mamba-World, a knowledge-guided framework that incorporates open-vocabulary priors into closed-set nighttime object detection, thereby effectively complementing degraded visual features with language-aligned semantic knowledge. Night-Mamba-World unifies language-aligned open-vocabulary priors, frequency adaptation, illumination-guided state-space aggregation, and inference-time prompt calibration within a single detection framework. Night-Mamba-World consists of three modules. Visual Fourier Prompt Tuning (VFPT) mitigates illumination-style mismatch while preserving phase-based structural information. Retinex-Guided Mamba-PAN (RG-Mamba-PAN) enhances long-range context aggregation in dark and weak texture regions through illumination-guided state-space modeling. ModPrompt further improves robustness to varying nighttime conditions via online prompt calibration during inference. Experiments on ExDark, LLVIP, and BDD100 K demonstrate that Night-Mamba-World achieves consistent improvements across diverse nighttime scenarios, reaching 0.831$mAP_{50}$on ExDark, 0.929$mAP_{50}$on LLVIP, and 0.545$mAP_{50}$on BDD100 K. It also maintains deployment-oriented efficiency with 49.564 M parameters, 91.451 G FLOPs, 13.972 ms latency, and 71.57 FPS.

Large labeled datasets are required for training a powerful semantic segmentation model. However, it is very expensive to construct pixel-wise annotated images. In this work, we propose a general batch mode active learning algorithm for semantic segmentation which automatically selects important samples to be labeled for building a competitive classifier. In our approach the edge information of an image is first introduced as a new selecting clue of active learning, which can measure the essential information relevant to segmentation performance. In addition, we also incorporate the informativeness based on Query by Committee (QBC) and representativeness criteria in our algorithm. We combine three clues to select a batch of samples during each iteration. It is shown that the image edge information is significant for the active learning for semantic segmentation in the experiments. And we also demonstrate the performance of our method outperforms the state of the art active learning approaches on the datasets of CamVid, Stanford Background and PASCAL VOC 2012.

Heterogeneous transfer clustering can translate knowledge from some related heterogeneous source domains to the target domain without any supervision. Existing works usually use a large amount of complete co-occurrence data to learn the projection functions mapping heterogeneous data to a common latent feature subspace. However, in many real applications, it is not practical to collect abundant co-occurrence data, while the available co-occurrence data are always incomplete. Another commonly encountered problem is that the complex structure of real heterogeneous data may result in substantial degeneration in clustering performance. To address these issues, we propose a heterogeneous transfer clustering method specifically designed for partial co-occurrence data (HTCPC). It is superior to the existing methods in three facets. First, HTCPC fully uses the partial co-occurrence data in both source and target domains to learn a latent space, maximally extracting useful knowledge for clustering from limited information. Second, it incorporates multi-layer hidden representations, accurately preserving the complex hierarchical structure of data. Third, it enforces approximately orthogonal constraint in representations, effectively characterizing the latent subspace with minimal redundancy. An efficient algorithm has been derived and implemented to realize the proposed HTCPC. A series of experiments on the real datasets have illustrated the advantage of the proposed approach compared with state-of-the-art methods.

Semantic segmentation is a task that heavily relies on the annotated data. The image annotation cost is very expensive. While active learning aims to select the most valuable samples by an iterative procedure. It can reduce the annotation cost and improve the performance of classification. In semantic segmentation, its more common to select a batch of instances instead of a single instance at each iteration. In this paper, we propose a novel batch mode active learning algorithm for semantic segmentation. Different from the previous active learning algorithms for the image classification, we first introduce a new selecting criterion : the image prior of nonlocal self-similarity. It can measure the interaction between the pixels of the image. We combine the informativeness and representativeness with the criterion of nonlocal self-similarity to complete the selection of images at each iteration. In addition, we also use the model uncertainty to measure the information of samples. The model uncertainty is captured by using Monte Carlo Dropout in the semantic segmentation model. In this work, we evaluate our method on the CamVid and PASCAL VOC 2012 datasets. The importance of the nonlocal self-similarity is also assessed. The experiments demonstrate that our algorithm outperforms current state-of-the-art active learning methods over the segmentation performance.