We establish closed-form enumeration formulas for chromatic feature vectors of 2-trees under the bichromatic triangle constraint. These efficiently computable structural features derive from constrained graph colorings where each triangle uses exactly two colors, forbidding monochromatic and rainbow triangles, a constraint arising in distributed systems where components avoid complete concentration or isolation. For theta graphs Theta_n, we prove r_k(Theta_n) = S(n-2, k-1) for k >= 3 (Stirling numbers of the second kind) and r_2(Theta_n) = 2^(n-2) + 1, computable in O(n) time. For fan graphs Phi_n, we establish r_2(Phi_n) = F_{n+1} (Fibonacci numbers) and derive explicit formulas r_k(Phi_n) = sum_{t=k-1}^{n-1} a_{n-1,t} * S(t, k-1) with efficiently computable binomial coefficients, achieving O(n^2) computation per component. Unlike classical chromatic polynomials, which assign identical features to all n-vertex 2-trees, bichromatic constraints provide informative structural features. While not complete graph invariants, these features capture meaningful structural properties through connections to Fibonacci polynomials, Bell numbers, and independent set enumeration. Applications include Byzantine fault tolerance in hierarchical networks, VM allocation in cloud computing, and secret-sharing protocols in distributed cryptography.

X-ray Absorption Spectroscopy (XAS) is a powerful technique for probing local atomic environments, yet its interpretation remains limited by the need for expert-driven analysis, computationally expensive simulations, and element-specific heuristics. Recent advances in machine learning have shown promise for accelerating XAS interpretation, but many existing models are narrowly focused on specific elements, edge types, or spectral regimes. In this work, we present XAStruct, a learning-based system capable of both predicting XAS spectra from crystal structures and inferring local structural descriptors from XAS input. XAStruct is trained on a large-scale dataset spanning over 70 elements across the periodic table, enabling generalization to a wide variety of chemistries and bonding environments. The framework includes the first machine learning approach for predicting neighbor atom types directly from XAS spectra, as well as a generalizable regression model for mean nearest-neighbor distance that requires no element-specific tuning. By combining deep neural networks for complex structure property mappings with efficient baseline models for simpler tasks, XAStruct offers a scalable and extensible solution for data-driven XAS analysis and local structure inference. The source code will be released upon paper acceptance.

In recent years, pre-trained graph neural networks (GNNs) have been developed as general models which can be effectively fine-tuned for various potential downstream tasks in materials science, and have shown significant improvements in accuracy and data efficiency. The most widely used pre-training methods currently involve either supervised training to fit a general force field or self-supervised training by denoising atomic structures equilibrium. Both methods require datasets generated from quantum mechanical calculations, which quickly become intractable when scaling to larger datasets. Here we propose a novel pre-training objective which instead uses cheaply-computed structural fingerprints as targets while maintaining comparable performance across a range of different structural descriptors. Our experiments show this approach can act as a general strategy for pre-training GNNs with application towards large scale foundational models for atomistic data.

X-ray absorption spectroscopy (XAS) is a powerful technique to probe the electronic and structural properties of materials. With the rapid growth in both the volume and complexity of XAS datasets driven by advancements in synchrotron radiation facilities, there is an increasing demand for advanced computational tools capable of efficiently analyzing large-scale data. To address these needs, we introduce XASDAML,a flexible, machine learning based framework that integrates the entire data-processing workflow-including dataset construction for spectra and structural descriptors, data filtering, ML modeling, prediction, and model evaluation-into a unified platform. Additionally, it supports comprehensive statistical analysis, leveraging methods such as principal component analysis and clustering to reveal potential patterns and relationships within large datasets. Each module operates independently, allowing users to modify or upgrade modules in response to evolving research needs or technological advances. Moreover, the platform provides a user-friendly interface via Jupyter Notebook, making it accessible to researchers at varying levels of expertise. The versatility and effectiveness of XASDAML are exemplified by its application to a copper dataset, where it efficiently manages large and complex data, supports both supervised and unsupervised machine learning models, provides comprehensive statistics for structural descriptors, generates spectral plots, and accurately predicts coordination numbers and bond lengths. Furthermore, the platform streamlining the integration of XAS with machine learning and lowering the barriers to entry for new users.

The removal of leaked radioactive iodine isotopes in humid environments holds significant importance in nuclear waste management and nuclear accident mitigation. In this study, high - throughput computational screening and machine learning were combined to reveal the iodine capture performance of 1816 metal - organic framework (MOF) materials under humid air conditions. First ly, the relationship between the structural characteristics of MOF materials (including density, surface area and pore features) and their adsorption properties was explored, with the aim of identifying the optimal structural parameters for iodine capture. Subsequently, two machine learning regression algorithms - Random Forest and CatBoos t, were employed to predict the iodine adsorption capabilities of MOF materials. In addition to 6 structural features, 25 molecular features (encompassing the types of metal and ligand atoms as well as bonding modes) and 8 chemical features (including heat of adsorption and Henry's coefficient) were incorporated to enhance the predicti on accuracy of the machine learning algorithms . Feature importance was assessed to determine the relative influence of various features on iodine adsorption performance, in which the Henry's coefficient and heat of adsorption to iodine were found the two most crucial chemical factors. Furthermore, four types of molecular fingerprint s were introduced for provid ing comprehensive and detailed structural information of MOF materials. The top 20 most significant MACCS molecul ar fingerprints were picked out, revealing that the presence of six - membered ring structures and nitrogen atoms in the MOF framework were the key structural factors that enhance d iodine adsorption, followed by the existence of oxygen atoms. This work combine d high - throughput computation, machine learning, and molecular fingerprints to comprehensively and systematically elucidate the multifaceted factors influencing the iodine adsorption performance of MOFs in humid environments, offering prof ound insight ful guidelines for screening and structural design of advanced MOF materials.

Detecting underlying clusters from large-scale data plays a central role in machine learning research. In this paper, we attempt to tackle clustering problems for complex data of multiple distributions and large multi-scales. To this end, we develop an algorithm named Zeta l -links, or Zell which consists of two parts: Zeta merging with a similarity graph and an initial set of small clusters derived from local l -links of the graph. More specifically, we propose to structurize a cluster using cycles in the associated subgraph. A mathematical tool, Zeta function of a graph, is introduced for the integration of all cycles, leading to a structural descriptor of the cluster in determinantal form.

Detecting underlying clusters from large-scale data plays a central role in machine learning research. In this paper, we attempt to tackle clustering problems for complex data of multiple distributions and large multi-scales. To this end, we develop an algorithm named Zeta $l$-links, or Zell which consists of two parts: Zeta merging with a similarity graph and an initial set of small clusters derived from local $l$-links of the graph. More specifically, we propose to structurize a cluster using cycles in the associated subgraph. A mathematical tool, Zeta function of a graph, is introduced for the integration of all cycles, leading to a structural descriptor of the cluster in determinantal form.

Humans easily recognize object parts and their hierarchical structure by watching how they move; they can then predict how each part moves in the future. In this paper, we propose a novel formulation that simultaneously learns a hierarchical, disentangled object representation and a dynamics model for object parts from unlabeled videos. Our Parts, Structure, and Dynamics (PSD) model learns to, first, recognize the object parts via a layered image representation; second, predict hierarchy via a structural descriptor that composes low-level concepts into a hierarchical structure; and third, model the system dynamics by predicting the future. Experiments on multiple real and synthetic datasets demonstrate that our PSD model works well on all three tasks: segmenting object parts, building their hierarchical structure, and capturing their motion distributions.

Motivation: Analysis of relationships of drug structure to biological response is key to understanding off-target and unexpected drug effects, and for developing hypotheses on how to tailor drug thera-pies. New methods are required for integrated analyses of a large number of chemical features of drugs against the corresponding genome-wide responses of multiple cell models. Results: In this paper, we present the first comprehensive multi-set analysis on how the chemical structure of drugs impacts on ge-nome-wide gene expression across several cancer cell lines (CMap database). The task is formulated as searching for drug response components across multiple cancers to reveal shared effects of drugs and the chemical features that may be responsible. The com-ponents can be computed with an extension of a very recent ap-proach called Group Factor Analysis (GFA). We identify 11 compo-nents that link the structural descriptors of drugs with specific gene expression responses observed in the three cell lines, and identify structural groups that may be responsible for the responses. Our method quantitatively outperforms the limited earlier studies on CMap and identifies both the previously reported associations and several interesting novel findings, by taking into account multiple cell lines and advanced 3D structural descriptors. The novel observations include: previously unknown similarities in the effects induced by 15-delta prostaglandin J2 and HSP90 inhibitors, which are linked to the 3D descriptors of the drugs; and the induction by simvastatin of leukemia-specific anti-inflammatory response, resem-bling the effects of corticosteroids.

Detecting underlying clusters from large-scale data plays a central role in machine learning research. In this paper, we attempt to tackle clustering problems for complex data of multiple distributions and large multi-scales. To this end, we develop an algorithm named Zeta $l$-links, or Zell which consists of two parts: Zeta merging with a similarity graph and an initial set of small clusters derived from local $l$-links of the graph. More specifically, we propose to structurize a cluster using cycles in the associated subgraph. A mathematical tool, Zeta function of a graph, is introduced for the integration of all cycles, leading to a structural descriptor of the cluster in determinantal form. The popularity character of the cluster is conceptualized as the global fusion of variations of the structural descriptor by means of the leave-one-out strategy in the cluster. Zeta merging proceeds, in the agglomerative fashion, according to the maximum incremental popularity among all pairwise clusters. Experiments on toy data, real imagery data, and real sensory data show the promising performance of Zell. The $98.1\%$ accuracy, in the sense of the normalized mutual information, is obtained on the FRGC face data of 16028 samples and 466 facial clusters. The MATLAB codes of Zell will be made publicly available for peer evaluation.