Recently, "pre-training and fine-tuning'' has been adopted as a standard workflow for many graph tasks since it can take general graph knowledge to relieve the lack of graph annotations from each application. However, graph tasks with node level, edge level, and graph level are far diversified, making the pre-training pretext often incompatible with these multiple tasks. This gap may even cause a "negative transfer'' to the specific application, leading to poor results. Inspired by the prompt learning in natural language processing (NLP), which has presented significant effectiveness in leveraging prior knowledge for various NLP tasks, we study the prompting topic for graphs with the motivation of filling the gap between pre-trained models and various graph tasks. In this paper, we propose a novel multi-task prompting method for graph models. Specifically, we first unify the format of graph prompts and language prompts with the prompt token, token structure, and inserting pattern. In this way, the prompting idea from NLP can be seamlessly introduced to the graph area. Then, to further narrow the gap between various graph tasks and state-of-the-art pre-training strategies, we further study the task space of various graph applications and reformulate downstream problems to the graph-level task. Afterward, we introduce meta-learning to efficiently learn a better initialization for the multi-task prompt of graphs so that our prompting framework can be more reliable and general for different tasks. We conduct extensive experiments, results from which demonstrate the superiority of our method.

MicroRNAs (simply miRNAs) are derived from larger hairpin RNA precursors and play essential regular roles in both animals and plants. A number of computational methods for miRNA genes finding have been proposed in the past decade, yet the problem is far from being tackled, especially when considering the imbalance issue of known miRNAs and unidentified miRNAs, and the pre-miRNAs with multi-loops or higher minimum free energy (MFE). This paper presents a new computational approach, miRenSVM, for finding miRNA genes. Aiming at better prediction performance, an ensemble support vector machine (SVM) classifier is established to deal with the imbalance issue, and multi-loop features are included for identifying those pre-miRNAs with multi-loops. We collected a representative dataset, which contains 697 real miRNA precursors identified by experimental procedure and other computational methods, and 5428 pseudo ones from several datasets. Experiments showed that our miRenSVM achieved a 96.5% specificity and a 93.05% sensitivity on the dataset. Compared with the state-of-the-art approaches, miRenSVM obtained better prediction results. We also applied our method to predict 14 Homo sapiens pre-miRNAs and 13 Anopheles gambiae pre-miRNAs that first appeared in miRBase13.0, MiRenSVM got a 100% prediction rate. Furthermore, performance evaluation was conducted over 27 additional species in miRBase13.0, and 92.84% (4863/5238) animal pre-miRNAs were correctly identified by miRenSVM. MiRenSVM is an ensemble support vector machine (SVM) classification system for better detecting miRNA genes, especially those with multi-loop secondary structure.

The explicit determinations of the mean first-passage time (MFPT) for trapping problem are limited to some simple structure, e.g., regular lattices and regular geometrical fractals, and determining MFPT for random walks on other media, especially complex real networks, is a theoretical challenge. In this paper, we investigate a simple random walk on the the pseudofractal scale-free web (PSFW) with a perfect trap located at a node with the highest degree, which simultaneously exhibits the remarkable scale-free and small-world properties observed in real networks. We obtain the exact solution for the MFPT that is calculated through the recurrence relations derived from the structure of PSFW. The rigorous solution exhibits that the MFPT approximately increases as a power-law function of the number of nodes, with the exponent less than 1. We confirm the closed-form solution by direct numerical calculations. We show that the structure of PSFW can improve the efficiency of transport by diffusion, compared with some other structure, such as regular lattices, Sierpinski fractals, and T-graph. The analytical method can be applied to other deterministic networks, making the accurate computation of MFPT possible.

Single-cell RNA sequencing (scRNA-seq) permits researchers to study the complex mechanisms of cell heterogeneity and diversity. Unsupervised clustering is of central importance for the analysis of the scRNA-seq data, as it can be used to identify putative cell types. However, due to noise impacts, high dimensionality and pervasive dropout events, clustering analysis of scRNA-seq data remains a computational challenge. Here, we propose a new deep structural clustering method for scRNA-seq data, named scDSC, which integrate the structural information into deep clustering of single cells. The proposed scDSC consists of a Zero-Inflated Negative Binomial (ZINB) model-based autoencoder, a graph neural network (GNN) module and a mutual-supervised module. To learn the data representation from the sparse and zero-inflated scRNA-seq data, we add a ZINB model to the basic autoencoder. The GNN module is introduced to capture the structural information among cells. By joining the ZINB-based autoencoder with the GNN module, the model transfers the data representation learned by autoencoder to the corresponding GNN layer. Furthermore, we adopt a mutual supervised strategy to unify these two different deep neural architectures and to guide the clustering task. Extensive experimental results on six real scRNA-seq datasets demonstrate that scDSC outperforms state-of-the-art methods in terms of clustering accuracy and scalability. Our method scDSC is implemented in Python using the Pytorch machine-learning library, and it is freely available at https://github.com/DHUDBlab/scDSC.

A vast variety of real-life networks display the ubiquitous presence of scale-free phenomenon and small-world effect, both of which play a significant role in the dynamical processes running on networks. Although various dynamical processes have been investigated in scale-free small-world networks, analytical research about random walks on such networks is much less. In this paper, we will study analytically the scaling of the mean first-passage time (MFPT) for random walks on scale-free small-world networks. To this end, we first map the classical Koch fractal to a network, called Koch network. According to this proposed mapping, we present an iterative algorithm for generating the Koch network; based on which we derive closed-form expressions for the relevant topological features, such as degree distribution, clustering coefficient, average path length, and degree correlations. The obtained solutions show that the Koch network exhibits scale-free behavior and small-world effect. Then, we investigate the standard random walks and trapping issue on the Koch network. Through the recurrence relations derived from the structure of the Koch network, we obtain the exact scaling for the MFPT. We show that in the infinite network order limit, the MFPT grows linearly with the number of all nodes in the network. The obtained analytical results are corroborated by direct extensive numerical calculations. In addition, we also determine the scaling efficiency exponents characterizing random walks on the Koch network.