Among biological networks, co-expression networks have been widely studied. One of the most commonly used pipelines for the construction of co-expression networks is weighted gene co-expression network analysis (WGCNA), which can identify highly co-expressed clusters of genes (modules). WGCNA identifies gene modules using hierarchical clustering. The major drawback of hierarchical clustering is that once two objects are clustered together, it cannot be reversed; thus, re-adjustment of the unbefitting decision is impossible. In this paper, we calculate the similarity matrix with the distance correlation for WGCNA to construct a gene co-expression network, and present a new approach called the k-module algorithm to improve the WGCNA clustering results. This method can assign all genes to the module with the highest mean connectivity with these genes. This algorithm re-adjusts the results of hierarchical clustering while retaining the advantages of the dynamic tree cut method. The validity of the algorithm is verified using six datasets from microarray and RNA-seq data. The k-module algorithm has fewer iterations, which leads to lower complexity. We verify that the gene modules obtained by the k-module algorithm have high enrichment scores and strong stability. Our method improves upon hierarchical clustering, and can be applied to general clustering algorithms based on the similarity matrix, not limited to gene co-expression network analysis.

Accurate segmentation of the lesion area from MRI images is essential for diagnosing bladder cancer. However, the precise segmentation of bladder tumors remains a massive challenge due to their similar intensity distributions, various tumor morphologies, and blurred boundaries. While some seminal studies, such as those using CNNs combined with transformer segmentation methods, have made significant progress, (1) how to reduce the computational complexity of the self-attention mechanism in the transformer while maintaining performance and (2) how to build a better global feature fusion process to improve segmentation performance still require further exploration. Considering the complexity of bladder MRI images, we developed a lightweight context-aware network (LCANet) to automatically segment bladder lesions from MRI images. Specifically, the local detail encoder generates local-level details of the lesion, the lightweight transformer encoder models the global-level features with different resolutions, the pyramid scene parsing module extracts high-level and multiscale semantic features, and the decoder provides high-resolution segmentation results by fusing local-level details with global-level cues at the channel level. A series of empirical studies on T2-weighted MRI images from 86 patients show that LCANet achieves an overall Jaccard index of 89.39%, a Dice similarity coefficient of 94.08%, and a Class pixel accuracy of 94.10%. These advantages show that our method is an efficient tool that can assist in reducing the heavy workload of radiologists.

The precise segmentation of bladder tumors from MRI is essential for bladder cancer diagnosis and personalized therapy selection. Limited by the properties of tumor morphology, achieving precise segmentation from MRI images remains challenging. In recent years, deep convolutional neural networks have provided a promising solution for bladder tumor segmentation from MRI. However, deep-learning-based methods still face two weakness: (1) multi-scale feature extraction and utilization are inadequate, being limited by the learning approach. (2) The establishment of explicit long-distance dependence is difficult due to the limited receptive field of convolution kernels. These limitations raise challenges in the learning of global semantic information, which is critical for bladder cancer segmentation. To tackle the problem, a newly auxiliary segmentation algorithm integrating a multi-scale encoder and decoder with a transformer is proposed, which is called MSEDTNet. Specifically, the designed encoder with multi-scale pyramidal convolution (MSPC) is utilized to generate compact feature maps which capture the richly detailed local features of the image. Furthermore, the transformer bottleneck is then leveraged to model the long-distance dependency between high-level tumor semantics from a global space. Finally, a decoder with a spatial context fusion module (SCFM) is adopted to fuse the context information and gradually produce high-resolution segmentation results. The experimental results of T2-weighted MRI scans from 86 patients show that MSEDTNet achieves an overall Jaccard index of 83.46%, a Dice similarity coefficient of 92.35%, and a complexity less than that of other, similar models. This suggests that the method proposed in this article can be used as an efficient tool for clinical bladder cancer segmentation.

This paper focuses on finite-horizon optimum state feedback control problems for interconnected systems of two players involved with asymmetric one-step delay information. For the finite horizon optimum decentralized control problem, a crucial and adequate condition is derived by using Pontryagin’s maximum principle. Under this framework, player 1 transmits its state and control input data with a one-step delay to the controller of player 2, while player 1’s controller does not have access to the real-time or delayed states and control inputs of player 2, resulting in an asymmetric information structure characterized by a one-step delay Then, the solutions to the forward and backward stochastic difference equations are derived. A target tracking system is given in numerical examples to verify the proposed algorithm.

Special polynomials (e.g. Hermite polynomials) are very important for the development of physics and mathematics. As a further extension of ordinary Hermite polynomials, we introduce new generalized Hermite polynomials with three variables and find their generating functions using the operator ordering method in quantum optics. Also, some new operator identities and integral formulas are obtained. As applications, the normalization, Wigner functions and evolutions for certain quantum states are analytically presented. These analytical results can provide conveniences for numerically studying the properties and applications of such quantum states.