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We introduce a novel Unsmoothed Aggregation (UA) Algebraic Multigrid (AMG) method combined with Preconditioned Conjugate Gradient (PCG) to overcome the limitations of Extended Position-Based Dynamics (XPBD) in high-resolution and…
Graph machine learning has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually…
Developing fully parametric building models for performance-based generative design tasks often requires proficiency in many advanced 3D modeling and visual programming, limiting its use for many building designers. Moreover, iterations of…
We describe a guided proceduralization framework that optimizes geometry processing on architectural input models to extract target grammars. We aim to provide efficient artistic workflows by creating procedural representations from…
Geometric ability is a significant challenge for large language models (LLMs) due to the need for advanced spatial comprehension and abstract thinking. Existing datasets primarily evaluate LLMs on their final answers, but they cannot truly…
Geometric problem solving, as a typical multimodal reasoning problem, has attracted much attention and made great progress recently, however most of works focus on plane geometry while usually fail in solid geometry due to 3D spatial…
We give a new algorithm for generating Greechie diagrams with arbitrary chosen number of atoms or blocks (with 2,3,4,... atoms) and provide a computer program for generating the diagrams. The results show that the previous algorithm does…
Large language models (LLMs) have demonstrated strong reasoning capabilities in text-based mathematical problem solving; however, when adapted to visual reasoning tasks, particularly geometric problem solving, their performance…
Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much…
Machine Learning (ML) is proving extremely beneficial in many healthcare applications. In pediatric oncology, retrospective studies that investigate the relationship between treatment and late adverse effects still rely on simple…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
Multimodal geometry reasoning requires models to jointly understand visual diagrams and perform structured symbolic inference, yet current vision--language models struggle with complex geometric constructions due to limited training data…
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…
The design and optimization of Printed Circuit Board (PCB) schematics is crucial for the development of high-quality electronic devices. Thereby, an important task is to optimize drafts by adding components that improve the robustness and…
We describe the second version (v2.0.0) of the code ADG that automatically (1) generates all valid off-diagonal Bogoliubov many-body perturbation theory diagrams at play in particle-number projected Bogoliubov many-body perturbation theory…
The Unified Modeling Language is a standardized visual language widely used for modeling and documenting the design of software systems. Although many tools generate UML diagrams from UML code, generating executable UML code from…
A method of constructing algebraic-geometric codes with many automorphisms arising from Galois points for algebraic curves is presented.
Symmetry in integer programming causes redundant search and is often handled with symmetry breaking constraints that remove as many equivalent solutions as possible. We propose an algebraic method which allows to generate a random family of…
In 3D scene understanding, deep learning models rely on large models and extensive training to capture basic geometric structures that are present in the 3D data. However, existing methods lack explicit mechanisms to incorporate geometric…
Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly…