Crystal structures can be simplified as a periodic point set that repeats across three-dimensional space along an underlying lattice. Traditionally, crystal representation methods rely on descriptors such as lattice parameters, symmetry, and space groups to characterize the structure. However, in reality, atoms in materials always vibrate above absolute zero, causing their positions to fluctuate continuously. This dynamic behavior disrupts the fundamental periodicity of the lattice, making crystal graphs based on static lattice parameters and conventional descriptors discontinuous under slight perturbations. Chemists proposed the pairwise distance distribution (PDD) method to address this. However, the completeness of PDD requires defining a large number of neighboring atoms, leading to high computational costs. Additionally, PDD does not account for atomic information, making it challenging to apply it directly to crystal material property prediction tasks. To tackle these challenges, we introduce the atom-weighted Pairwise Distance Distribution (WPDD) and Unit cell Pairwise Distance Distribution (UPDD) for the first time, applying them to the construction of multi-edge crystal graphs. We demonstrate the continuity and general completeness of crystal graphs under slight atomic position perturbations. Moreover, by modeling PDD as global information and integrating it into matrix-based message passing, we significantly reduce computational costs. Comprehensive evaluation results show that WPDDFormer achieves state-of-the-art predictive accuracy across tasks on benchmark datasets such as the Materials Project and JARVIS-DFT.

Diffusion generative models (DMs) have achieved promising results in image and graph generation. However, real-world graphs, such as social networks, molecular graphs, and traffic graphs, generally share non-Euclidean topologies and hidden hierarchies. For example, the degree distributions of graphs are mostly power-law distributions. The current latent diffusion model embeds the hierarchical data in a Euclidean space, which leads to distortions and interferes with modeling the distribution. Instead, hyperbolic space has been found to be more suitable for capturing complex hierarchical structures due to its exponential growth property. In order to simultaneously utilize the data generation capabilities of diffusion models and the ability of hyperbolic embeddings to extract latent hierarchical distributions, we propose a novel graph generation method called, Hyperbolic Graph Diffusion Model (HGDM), which consists of an auto-encoder to encode nodes into successive hyperbolic embeddings, and a DM that operates in the hyperbolic latent space. HGDM captures the crucial graph structure distributions by constructing a hyperbolic potential node space that incorporates edge information. Extensive experiments show that HGDM achieves better performance in generic graph and molecule generation benchmarks, with a 48% improvement in the quality of graph generation with highly hierarchical structures.

The multi-view/multi-modal features are commonly used in neuroimaging classification because they could provide complementary information to each other and thus result in better classification performance than single-view features. However, it is very challenging to effectively integrate such rich features, since straightforward concatenation or singleview spectral embedding methods rarely leads to physically meaningful integration. In this paper, we present a supervised multi-view/multi-modal spectral embedding method (SMSE) for neuroimaging classification. This method embeds the high dimensional multi-view features derived from multi-modal neuroimaging data into a low dimensional feature space and preserves the optimal local embeddings among different views. The proposed SMSE algorithm, validated using three groups of neuroimaging data, is able to achieve significant classification improvement over the state-of-the-art multi-view spectral embedding methods.

Accurate neuroimaging feature extraction is essential for effective content-based management of the large neuroimaging databases, as well as achieving improved diagnosis. In this paper, we presented a multiscale and multi-orientation neuroimaging feature extraction algorithm with degenerative patterns for content-based 3D neuroimaging analysis and retrieval, based on the localized 3D Gabor wavelets. Our proposed approach was evaluated with 209 3D clinical neurological imaging studies and compared with the 3D discrete curvelet transform based method and the 3D spatial grey level co-occurrence matrices based method. The preliminary results suggested that our algorithm could support more reliable 3D neuroimaging retrieval.

The volume and complexity of neurological images have significantly increased, which leads to challenges in efficient data management and retrieval. In this paper, we developed a new content-based image retrieval framework with the localized multiscale Discrete Curvelet Transform (DCvT) features extracted from parametric neurological images. We also compared the performance of three different irregular-to-regular shape padding methods. 142 patient data with neurodegenerative disorders were used in the evaluation. The preliminary results show that our proposed framework supports fast neuroimaging retrieval, and the orthographic projection method can reduce the computational complexity and has a great potential to improve the retrieval for indefinite cases.

Functional neuroimaging has an important role in non-invasive diagnosis of neurodegenerative disorders. There are now large volumes of imaging data generated by functional imaging technologies and so there is a need to efficiently manage and retrieve these data. In this paper, we propose a new scheme for efficient 3D content-based neurological image retrieval. 3D pathology-centric masks were adaptively designed and applied for extracting CMRGlc (cerebral metabolic rate of glucose consumption) texture features with volumetric co-occurrence matrices from neurological FDG PET images. Our results, using 93 clinical dementia studies, show that our approach offers a robust and efficient retrieval mechanism for relevant clinical cases and provides advantages in image data analysis and management.

Functional imaging can provide quantitative functional parameters to aid early diagnosis. Low signal to noise ratio (SNR) in functional imaging, especially for single photon emission computed tomography, poses a challenge in generating voxel-wise parametric images due to unreliable or physiologically meaningless parameter estimates. Our aim was to systematically investigate the performance of our recently proposed adaptive fuzzy clustering (AFC) technique, which applies standard fuzzy clustering to sub-divided data. Monte Carlo simulations were performed to generate noisy dynamic SPECT data with quantitative analysis for the fitting using the general linear least square method (GLLS) and enhanced model-aided GLLS methods. The results show that AFC substantially improves computational efficiency and obtains improved reliability as standard fuzzy clustering in estimating parametric images but is prone to slight underestimation. Normalization of tissue time activity curves may lead to severe overestimation for small structures when AFC is applied.

Dual modality PET/CT has now essentially replaced PET in clinical practice and provided an opportunity to improve image segmentation through the high resolution, lower noise CT data. Thus far most research efforts have concentrated on segmentation of PET-only data. In this work we propose a systematic solution for the automated segmentation of brain PET/CT images into gray, white matter and CSF regions with the MAP-MRF model. Our approach takes advantage of the full information available from the combined scan. A PET/CT image pair and its segmentation result are modelled as a random field triplet, and segmentation is eventually achieved by solving a maximum a posteriori (MAP) problem using the expectation-maximization (EM) algorithm with simulated annealing. We compared the novel algorithm to two widely used PET-only based segmentation methods in the SPM5 toolbox and the VBM toolbox for simulation and patient data. Our results suggest that using the proposed approach substantially improves the accuracy of the delineation of brain structures.

Dynamic single photon emission computed tomography (SPECT) has demonstrated the potential to quantitatively estimate physiological parameters in the brain and the heart. The generalized linear least square (GLLS) method is a well-established method for solving linear compartment models with fast computational speed. However, the high level of noise intrinsic in the SPECT data leads to reliability and instability problems of GLLS for generating parametric images. An integrated method is proposed to restrict the noise in both the temporal and spatial domains to estimate multiple parametric images for dynamic SPECT. This method comprises three steps which are optimum image sampling schedule in the projection space, cluster analysis applied postreconstruction and parametric image generation with GLLS. The simulation and experimental studies for the neuronal nicotine acetylcholine receptor tracer of 5-[123I]-iodo-A-85380 were employed to evaluate the performance of the proposed method. The results of influx rate of K1 and volume of distribution of Vd demonstrated that the integrated method was successful in generating low noise parametric images for high noise SPECT data without enhancing the partial volume effect. Furthermore, the integrated method is computationally efficient for potential clinical applications.