Jyh-Charn Liu

Recent advances in computational chemistry, machine learning, and large-scale virtual screening have rapidly expanded the accessible chemical space, increasing the need for interpretable molecular representations that capture the hierarchical topological structure of molecules. Existing formats, such as Simplified Molecular Input Line Entry System (SMILES) strings and MOL files, effectively encode molecular graphs but provide limited support for representing the multi-level structural information needed for complex downstream tasks. To address these challenges, we introduce HiFrAMes, a novel graph–theoretic hierarchical molecular fragmentation framework that decomposes molecular graphs into chemically meaningful substructures and organizes them into hierarchical scaffold representations. HiFrAMes is implemented as a four-stage pipeline consisting of leaf and ring chain extraction, ring mesh reduction, ring enumeration, and linker detection, which iteratively transforms raw molecular graphs into interpretable abstract objects. The framework decomposes molecules into chains, rings, linkers, and scaffolds while retaining global topological relationships. We apply HiFrAMes to both complex and drug-like molecules to generate molecular fragments and scaffold representations that capture structural motifs at multiple levels of abstraction. The resulting fragments are evaluated using selection criteria established in the fragment-based drug discovery literature and qualitative case studies to demonstrate their suitability for downstream computational tasks.

In scientific documents, molecule structure information is usually delivered by chemical structure images. Although convenient for human interpretation, the image‐based molecule structure depiction is not a machine‐readable format, blocking productivity improvements in many fields including chemical data mining and drug discovery. Molecule structures can be modeled as graphs with atoms as nodes and bonds as edges. Following this intuitive modeling, optical chemical structure recognition (OCSR) can be achieved by first detecting individual atoms and bonds and then assembling into a graph. However, the challenges in decision ambiguity due to false positives and spatial proximity during graph assembly is rarely explained and explicitly addressed. In this work, we present a rule‐based probabilistic OCSR model to explain and tackle the ambiguity challenges in graph assembly. We developed a novel line detection algorithm for precise bond line identification, and designed a candidate mechanism with probabilistic graph to resolve atom/bond ambiguity. The proposed model is evaluated with popular large image datasets and achieved outperforming recognition accuracy compared to state‐of‐the‐art solutions.

A z-curve is the set of points on Earth’s surface that have identical pseudoranges to Global Navigation Satellite Systems (GNSS) satellites (A, B). The zero Time Difference of Arrival (TDOA) model eliminates common mode errors in signal transmission and the clock bias of GNSS receivers. Building upon a static model of z-surfaces and z-curves, this paper presents a dynamic model for migration of z-surfaces and z-curves with respect to satellite motions and atmospheric changes. Specifically, we use geometric transformation matrices and numerical solvers to describe the migration of the satellite Terrestrial Service Volume (TSV) model, z-surface, and z-curve. Affine transformations are applied to TSV and z-surface migrations, while for z-curve migration, we adopt a modified Newton’s method and a 4th-order Runge-Kutta method to align z-curve points on ground and within satellite coverage. These migration functions are validated using Global Positioning System (GPS) data.

In this paper we propose a deep neural network model with an encoder-decoder architecture that translates images of math formulas into their LaTeX markup sequences. The encoder is a convolutional neural network (CNN) that transforms images into a group of feature maps. To better capture the spatial relationships of math symbols, the feature maps are augmented with 2D positional encoding before being unfolded into a vector. The decoder is a stacked bidirectional long short-term memory (LSTM) model integrated with the soft attention mechanism, which works as a language model to translate the encoder output into a sequence of LaTeX tokens. The neural network is trained in two steps. The first step is token-level training using the Maximum-Likelihood Estimation (MLE) as the objective function. At completion of the token-level training, the sequence-level training objective function is employed to optimize the overall model based on the policy gradient algorithm from reinforcement learning. Our design also overcomes the exposure bias problem by closing the feedback loop in the decoder during sequence-level training, i.e., feeding in the predicted token instead of the ground truth token at every time step. The model is trained and evaluated on the IM2LATEX-100K dataset and shows state-of-the-art performance on both sequence-based and image-based evaluation metrics.