Search for: All records

Identifying novel and functional RNA structures remains a significant challenge in RNA motif design and is crucial for developing RNA-based therapeutics. Here we introduce a computational topology-based approach with unsupervised machine-learning algorithms to estimate the database size and content of RNA-like graph topologies. Specifically, we apply graph theory enumeration to generate all 110,667 possible 2D dual graphs for vertex numbers ranging from 2 to 9. Among them, only 0.11% (121 dual graphs) correspond to approximately 200,000 known RNA atomic fragments/substructures (collected in 2021) using the RNA-as-Graphs (RAG) framework. The remaining 99.89% of the dual graphs may be RNA-like or non-RNA-like. To determine which dual graphs in the 99.89% hypothetical set are more likely to be associated with RNA structures, we apply computational topology descriptors using the Persistent Spectral Graphs (PSG) method to characterize each graph using 19 PSG-based features and use clustering algorithms that partition all possible dual graphs into two clusters. The cluster with the higher percentage of known dual graphs for RNA is defined as the “RNA-like cluster, while the other is considered as “non-RNA-like. The distance between each dual graph and the center of the RNA-like cluster represents the likelihood of it belonging to RNA structures. From validation, our PSG-based RNA-like cluster includes 97.3% of the 121 known RNA dual graphs, suggesting good performance. Furthermore, 46.017% of the hypothetical RNAs are predicted to be RNA-like. Among the top 15 graphs identified as high-likelihood candidates for novel RNA motifs, 4 were confirmed from the RNA dataset collected in 2022. Significantly, we observe that all the top 15 RNA-like dual graphs can be separated into multiple subgraphs, whereas the top 15 non-RNA-like dual graphs tend not to have any subgraphs (subgraphs preserve pseudoknots and junctions). Moreover, a significant topological difference between top RNA-like and non-RNA-like graphs is evident when comparing their topological features (e.g., Betti-0 and Betti-1 numbers). These findings provide valuable insights into the size of the RNA motif universe and RNA design strategies, offering a novel framework for predicting RNA graph topologies and guiding the discovery of novel RNA motifs, perhaps anti-viral therapeutics by subgraph assembly. 

The multiscale topological learning framework, based on persistent topological Laplacians, captures complex interactions and enhances energy prediction accuracy in multi-atom systems. 

In recent years, magnetic particle imaging (MPI) has emerged as a promising imaging technique depicting high sensitivity and spatial resolution. It originated in the early 2000s where it proposed a new approach to challenge the low spatial resolution achieved by using relaxometry in order to measure the magnetic fields. MPI presents 2D and 3D images with high temporal resolution, non‐ionizing radiation, and optimal visual contrast due to its lack of background tissue signal. Traditionally, the images were reconstructed by the conversion of signal from the induced voltage by generating system matrix and X‐space based methods. Because image reconstruction and analyses play an integral role in obtaining precise information from MPI signals, newer artificial intelligence‐based methods are continuously being researched and developed upon. In this work, we summarize and review the significance and employment of machine learning and deep learning models for applications with MPI and the potential they hold for the future. Level of Evidence5 Technical EfficacyStage 1 

The cone penetration test (CPT) is one of the most popular in situ soil characterization tools. However, the test is often difficult to conduct in soils with high penetration resistance. To resolve the problem, a rotary CPT device has recently been adopted in practice by rotating the rod to increase the penetrability, particularly in deep dense sand. This study investigates the underlying mechanism of the rotation effects from a micromechanical perspective using models based on the discrete element method. With rotation, the cone penetration resistance ( q_c) decreases by up to 50%, while the cone torque resistance ( t_c) increases gradually. These results are also used to successfully assess existing theoretical solutions. The mechanical work required during penetration is observed to keep rising as the rotational velocity increases. Microscopic variables including particle displacement and velocity field show that rotation reduces the volume of disturbed soil during penetration and drives particles to rotate horizontally, while contact force chain and contact fabric indicate that rotation increases the number of radial and tangential contacts and the corresponding contact forces, forming a lateral stable structure around the shaft, which can reduce the force transmitted to the particles below the cone, thus decreasing the vertical penetration resistance. 

Regularized learning problems in Banach spaces, which often minimize the sum of a data fidelity term in one Banach norm and a regularization term in another Banach norm, is challenging to solve. We construct a direct sum space based on the Banach spaces for the fidelity term and the regularization term and recast the objective function as the norm of a quotient space of the direct sum space. We then express the original regularized problem as an optimization problem in the dual space of the direct sum space. It is to find the maximum of a linear function on a convex polytope, which may be solved by linear programming. A solution of the original problem is then obtained by using related extremal properties of norming functionals from a solution of the dual problem. Numerical experiments demonstrate that the proposed duality approach is effective for solving the regularization learning problems.