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Selective Cascade of Residual ExtraTrees

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SN Computer Science 2020年第6期1卷 354页

作者： Liu, Qimin Liu, Fang Department of Psychology and Human Development Vanderbilt University Nashville TN United States Department of Applied and Computational Mathematics & Statistics University of Notre Dame Notre Dame IN United States

We propose a novel tree-based ensemble method named Selective Cascade of Residual ExtraTrees (SCORE). SCORE draws inspiration from representation learning, incorporates regularized regression with variable selection features, and utilizes boosting to improve prediction and reduce generalization errors. We also develop a variable importance measure to increase the explainability of SCORE. Our computer experiments show that SCORE provides comparable or superior performance in prediction against ExtraTrees, random forest, gradient boosting machine, and neural networks;and the proposed variable importance measure for SCORE is comparable to studied benchmark methods. Finally, the predictive performance of SCORE remains stable across hyper-parameter values, suggesting potential robustness to hyper-parameter specification. © 2020, Springer Nature Singapore Pte Ltd.

关键词： Boosting Ensemble learning Explainability Extremely randomized trees Regularized regression Variable importance measure

Vision Transformer Pruning Via Matrix Decomposition

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arXiv 2023年

作者： Sun, Tianyi Committee on Computational and Applied Mathematics Department of Computer Science Department of Statistics University of Chicago United States

This is a further development of Vision Transformer Pruning [36] via matrix decomposition. The purpose of the Vision Transformer Pruning is to prune the dimension of the linear projection of the dataset by learning their associated importance score in order to reduce the storage, run-time memory, and computational demands. In this paper we further reduce dimension and complexity of the linear projection by implementing and comparing several matrix decomposition methods while preserving the generated important features. We end up selected the Singular Value Decomposition as the method to achieve our goal by comparing the original accuracy scores in the original Github repository and the accuracy scores of using those matrix decomposition methods, including Singular Value Decomposition, four versions of QR Decomposition, and LU factorization. © 2023, CC BY.

关键词： Singular value decomposition

Point forces in elasticity equation and their alternatives in multi dimensions

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mathematics AND COMPUTERS IN SIMULATION 2022年第0期199卷 182-201页

作者： Peng, Q. Vermolen, F. J. [a]Mathematical Institute Leiden University Niels Bohrweg 1 2333 CA Leiden The Netherlands [b]Delft Institute of Applied Mathematics Delft University of Technology Mekelweg 4 2628 CD Delft The Netherlands [c]Computational Mathematics Group Department of Statistics and Mathematics Hasselt University Agoralaan Gebouw D 3590 Diepenbeek Belgium

Deep dermal wounds induce skin contraction as a result of the traction forcing exerted by (myo)fibroblasts on their immediate environment. These (myo)fibroblasts are skin cells that are responsible for the regeneration of collagen that is necessary for the integrity of skin We consider several mathematical issues regarding models that simulate traction forces exerted by (myo)fibroblasts. Since the size of cells (e.g. (myo)fibroblasts) is much smaller than the size of the domain of computation, one often considers point forces, modelled by Dirac Delta distributions on boundary segments of cells to simulate the traction forces exerted by the skin cells. In the current paper, we treat the forces that are directed normal to the cell boundary and toward the cell centre. Since it can be shown that there exists no smooth solution, at least not in H1 for solutions to the governing momentum balance equation, we analyse the convergence and quality of approximation. Furthermore, the expected finite element problems that we get necessitate to scrutinize alternative model formulations, such as the use of smoothed Dirac Delta distributions, or the so-called smoothed particle approach as well as the so-called 'hole' approach where cellular forces are modelled through the use of (natural) boundary conditions. In this paper, we investigate and attempt to quantify the conditions for consistency between the various approaches. This has resulted into error analyses in the L2-norm of the numerical solution based on Galerkin principles that entail Lagrangian basis functions. The paper also addresses well-posedness in terms of existence and uniqueness. The current analysis has been performed for the linear steady-state (hence neglecting inertia and damping) momentum equations under the assumption of Hooke's law. (C) 2022 The Author(s). Published by Elsevier B.V. on behalf of International Association for mathematics and Computers in Simulation (IMACS).

关键词： Point forces Dirac delta distribution Singular solution Immersed boundary approach "Hole" approach Smoothed particle approach

Snow topography on undeformed Arctic sea ice captured by an idealized "snow dune" model

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arXiv 2022年

作者： Popović, Predrag Finkel, Justin Silber, Mary C. Abbot, Dorian S. The University Of Chicago The Department Of The Geophysical Sciences United States The University Of Chicago Committee On Computational And Applied Mathematics United States The University Of Chicago Department Of Statistics Committee On Computational And Applied Mathematics United States

Our ability to predict the future of Arctic sea ice is limited by ice's sensitivity to detailed surface conditions such as the distribution of snow and melt ponds. Snow on top of the ice decreases ice's thermal conductivity, increases its reflectivity (albedo), and provides a source of meltwater for melt ponds during summer that decrease the ice's albedo. In this paper, we develop a simple model of pre-melt snow topography that accurately describes snow cover of flat, undeformed Arctic sea ice on several study sites for which data was available. The model considers a surface that is a sum of randomly sized and placed "snow dunes" represented as Gaussian mounds. This model generalizes the "void model" of Popović et al. [1] and, as such, accurately describes the statistics of melt pond geometry. We test this model against detailed LiDAR measurements of the pre-melt snow topography. We show that the model snow-depth distribution is statistically indistinguishable from the measurements on flat ice, while small disagreement exists if the ice is deformed. We then use this model to determine analytic expressions for the conductive heat flux through the ice and for melt pond coverage evolution during an early stage of pond formation. We also formulate a criterion for ice to remain pond-free throughout the summer. Results from our model could be directly included in large-scale models, thereby improving our understanding of energy balance on sea ice and allowing for more reliable predictions of Arctic sea ice in a future climate. © 2022, CC BY.

关键词： Snow

Solving cluster moment relaxation with hierarchical matrix

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arXiv 2024年

作者： Wang, Yi Khoo, Yuehaw Department of Statistics University of Chicago United States Department of Statistics and Committee on Computational and Applied Mathematics University of Chicago United States

Convex relaxation methods are powerful tools for studying the lowest energy of many-body problems. By relaxing the representability conditions for marginals to a set of local constraints, along with a global semidefinite constraint, a polynomial-time solvable semidefinite program (SDP) that provides a lower bound for the energy can be derived. In this paper, we propose accelerating the solution of such an SDP relaxation by imposing a hierarchical structure on the positive semidefinite (PSD) primal and dual variables. Furthermore, these matrices can be updated efficiently using the algebra of the compressed representations within an augmented Lagrangian method. We achieve quadratic and even near-linear time per-iteration complexity. Through experimentation on the quantum transverse field Ising model, we showcase the capability of our approach to provide a sufficiently accurate lower bound for the exact ground-state energy. Copyright © 2024, The Authors. All rights reserved.

关键词： Ising model

Numerically testing generically reduced projective schemes for the arithmetic gorenstein property 6th

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Numerically testing generically reduced projective schemes f...

6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015

作者： Daleo, Noah S. Hauenstein, Jonathan D. Department of Mathematics Worcester State University WorcesterMA01602 United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States

ISBN: (纸本)9783319328584

Let X ⊂ n be a generically reduced projective scheme. A fundamental goal in computational algebraic geometry is to compute information about X even when defining equations for X are not known. We use numerical algebraic geometry to develop a test for deciding if X is arithmetically Gorenstein and apply it to three secant varieties. © Springer International Publishing Switzerland 2016.

关键词： Algebra

PARAMETERIZED VIETORIS-RIPS FILTRATIONS VIA COVERS

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arXiv 2022年

作者： Nelson, Bradley J. Department of Statistics Committee on Computational and Applied Mathematics University of Chicago ChicagoIL60637 United States

A challenge in computational topology is to deal with large filtered geometric complexes built from point cloud data such as Vietoris-Rips filtrations. This has led to the development of schemes for parallel computation and compression which restrict simplices to lie in open sets in a cover of the data. We extend the method of acyclic carriers to the setting of persistent homology to give detailed bounds on the relationship between Vietoris-Rips filtrations restricted to covers and the full construction. We show how these complexes can be used to study data over a base space and use our results to guide the selection of covers of data. We demonstrate these techniques on a variety of covers, and show the utility of this construction in investigating higher-order homology of a model of high-dimensional image *** Codes 55N31 (Primary), 68T09 (Secondary) © 2022, CC BY.

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MatterChat: A Multi-Modal LLM for Material Science

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arXiv 2025年

作者： Tang, Yingheng Xu, Wenbin Cao, Jie Ma, Jianzhu Gao, Weilu Farrell, Steve Erichson, Benjamin Mahoney, Michael W. Nonaka, Andy Yao, Zhi Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States NSF National AI Institute for Student-AI Teaming University of Colorado at Boulder Boulder United States Institute for AI Industry Research Tsinghua University Beijing China Department of Electrical and Computer Engineering The University of Utah Salt Lake CityUT United States Scientific Data Division Lawrence Berkeley National Laboratory BerkeleyCA United States International Computer Science Institute BerkeleyCA United States Department of Statistics University of California at Berkeley BerkeleyCA United States

Understanding and predicting the properties of inorganic materials is crucial for accelerating advancements in materials science and driving applications in energy, electronics, and beyond. Integrating material structure data with language-based information through multi-modal large language models (LLMs) offers great potential to support these efforts by enhancing human–AI interaction. However, a key challenge lies in integrating atomic structures at full resolution into LLMs. In this work, we introduce MatterChat, a versatile structure-aware multi-modal LLM that unifies material structural data and textual inputs into a single cohesive model. MatterChat employs a bridging module to effectively align a pretrained machine learning interatomic potential with a pretrained LLM, reducing training costs and enhancing flexibility. Our results demonstrate that MatterChat significantly improves performance in material property prediction and human-AI interaction, surpassing general-purpose LLMs such as GPT-4. We also demonstrate its usefulness in applications such as more advanced scientific reasoning and step-by-step material synthesis. © 2025, CC BY.

关键词： Materials properties

Chaos,Transport and Mesh Convergence for Fluid Mixing

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Acta Mathematicae Applicatae Sinica 2008年第3期24卷 355-368页

作者： H. Lim Y. Yu J. Glimm X.L. Li D.H. Sharp Department of Applied Mathematics and Statistics Stony Brook University Stony Brook NY 11794-3600 USA Computational Science Center Brookhaven National Laboratory Upton N~ 11793-6000 USA Los Alamos National Laboratory Los Alamos NM USA

Chaotic mixing of distinct fluids produces a convoluted structure to the interface separating these fluids. For miscible fluids （as considered here）, this interface is defined as a 50% mass concentration isosurface. For shock wave induced （Richtmyer-Meshkov） instabilities, we find the interface to be increasingly complex as the computational mesh is refined. This interfacial chaos is cut off by viscosity, or by the computational mesh if the Kolmogorov scale is small relative to the mesh. In a regime of converged interface statistics, we then examine mixing, i.e. concentration statistics, regularized by mass diffusion. For Schmidt numbers significantly larger than unity, typical of a liquid or dense plasma, additional mesh refinement is normally needed to overcome numerical mass diffusion and to achieve a converged solution of the mixing problem. However, with the benefit of front tracking and with an algorithm that allows limited interface diffusion, we can assure convergence uniformly in the Schmidt number. We show that different solutions result from variation of the Schmidt number. We propose subgrid viscosity and mass diffusion parameterizations which might allow converged solutions at realistic grid levels.

关键词： Schmidt number mass diffusion turbulence multiphase flow