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Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
Rotation averaging (RA) is a fundamental problem in robotics and computer vision. In RA, the goal is to estimate a set of $N$ unknown orientations $R_{1}, ..., R_{N} \in SO(3)$, given noisy measurements $R_{ij} \sim R^{-1}_{i} R_{j}$ of a…
The intrinsic modularity and reconfigurability of modular reconfigurable robots (MRR) confer advantages such as versatility, fault tolerance, and economic efficacy, thereby showcasing considerable potential across diverse applications. The…
The multiscale entanglement renormalization ansatz (MERA) provides a constructive algorithm for realizing wavefunctions that are inherently scale invariant. Unlike conformally invariant partition functions however, the finite bond dimension…
To some braiding R of Hecke type (a Hecke symmetry) we put into correspondence an associative algebra called the modified Reflection Equation Algebra (mREA). We construct a series of matrices L_(m), m=1,2,... with entries belonging to mREA…
The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of…
We present a novel approach for the construction of basis functions to be employed in selective or adaptive h-refined finite element applications with arbitrary-level hanging node configurations. Our analysis is not restricted to…
In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few non-uniform (multichannel) measurements using structured low-rank matrix completion formulation.…
We discuss how generalized multiresolution analyses (GMRAs), both classical and those defined on abstract Hilbert spaces, can be classified by their multiplicity functions $m$ and matrix-valued filter functions $H$. Given a natural number…
While Retrieval-Augmented Generation (RAG) augments Large Language Models (LLMs) with external knowledge, conventional single-agent RAG remains fundamentally limited in resolving complex queries demanding coordinated reasoning across…
Low-Rank Adaptation (LoRA) has emerged as a widely adopted technique in text-to-image models, enabling precise rendering of multiple distinct elements, such as characters and styles, in multi-concept image generation. However, current…
Multimodal Large Language Models (MLLMs) have significantly advanced AI-assisted medical diagnosis, but they often generate factually inconsistent responses that deviate from established medical knowledge. Retrieval-Augmented Generation…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
Retrieval-Augmented Generation (RAG) has become a core paradigm in document question answering tasks. However, existing methods have limitations when dealing with multimodal documents: one category of methods relies on layout analysis and…
With more open-source models available for diverse tasks, model merging has gained attention by combining models into one, reducing training, storage, and inference costs. Current research mainly focuses on model merging for full…
A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…
Multi-hop question answering (QA) necessitates multi-step reasoning and retrieval across interconnected subjects, attributes, and relations. Existing retrieval-augmented generation (RAG) methods struggle to capture these structural…
We extend the classical deconvolution framework in Rn to the case with a pseudodifferential-like solution operator with a symbol depending on both the base and cotangent variable. Our framework enables deconvolution with spatially varying…
Combining pre-trained expert models offers substantial potential for scalable multimodal reasoning, but building a unified framework remains challenging due to the increasing diversity of input modalities and task complexity. For instance,…