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Case-based games learning strategies to improve conceptual understanding in mathematics 5

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Case-based games learning strategies to improve conceptual u...

5th Seminar Nasional Matematika dan Pendidikan Matematika, SENATIK 2020

作者： Asfar, A.M.I.T. Asfar, A.M.I.A. Department of Mathematics Education Stkip Muhammadiyah Bone Indonesia Program Science Education Universitas Negeri Makassar Indonesia Department of Chemical Engineering of Politeknik Negeri Ujung Pandang Indonesia

Case-Based Games Learning (CBGL) is a strategy of active learning in which the students implement knowledge and analytical skill related to the real complex situation (contextual) and relevant with subject lessons. Give case-based task or question routinely can help students to solve case-based mathematics problems. This study aims to analyze the effectiveness of CBGL using Quizizz dan Case Base Learning (CBL) without Quizizz based on students' conceptual understanding in mathematics by finding out the percentage of the correct answer. Students were grouping by using a purposive sampling method based on the conceptual understanding indicator. The result of this study is the average conceptual understanding CBGL using Quizizz application strategy is more effective than CBL without Quizizz application in evaluating student work results quickly, precisely, and accurately. Therefore the use of Quizzes application with CBGL was more effective than CBL in assessing the work result quickly, right, and accurately. © Published under licence by IOP Publishing Ltd.

关键词： Students

Hyperbolic procrustes analysis using riemannian geometry 21

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Hyperbolic procrustes analysis using riemannian geometry

Proceedings of the 35th International Conference on Neural Information Processing Systems

作者： Ya-Wei Eileen Lin Yuval Kluger Ronen Talmon Viterbi Faculty of Electrical and Computer Engineering Technion Program in Applied Mathematics Yale University and Interdepartmental Program in Computational Biology and Bioinformatics Yale University and Department of Pathology Yale University

ISBN: (纸本)9781713845393

Label-free alignment between datasets collected at different times, locations, or by different instruments is a fundamental scientific task. Hyperbolic spaces have recently provided a fruitful foundation for the development of informative representations of hierarchical data. Here, we take a purely geometric approach for label-free alignment of hierarchical datasets and introduce hyperbolic Procrustes analysis (HPA). HPA consists of new implementations of the three prototypical Procrustes analysis components: translation, scaling, and rotation, based on the Riemannian geometry of the Lorentz model of hyperbolic space. We analyze the proposed components, highlighting their useful properties for alignment. The efficacy of HPA, its theoretical properties, stability and computational efficiency are demonstrated in simulations. In addition, we showcase its performance on three batch correction tasks involving gene expression and mass cytometry data. Specifically, we demonstrate high-quality unsupervised batch effect removal from data acquired at different sites and with different technologies that outperforms recent methods for label-free alignment in hyperbolic spaces.

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Cross-system biological image quality enhancement based on the generative adversarial network as a foundation for establishing a multi-institute microscopy cooperative network

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arXiv 2024年

作者： Panek, Dominik Rząca, Carina Szczypior, Maksymilian Sorysz, Joanna Misztal, Krzysztof Baster, Zbigniew Rajfur, Zenon Doctoral School of Exact and Natural Sciences Jagiellonian University ul. Lojasiewicza 11 Kraków30-348 Poland Department of Molecular and Interfacial Biophysics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Lojasiewicza 11 Kraków30‑348 Poland Undergraduate Program in Biophysics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Lojasiewicza 11 Kraków30‑348 Poland Undergraduate program in Biomedical Engineering Faculty of Electrical Engineering Automatics Computer Science and Biomedical Engineering AGH University of Science and Technology Al. A. Mickiewicza 30 Building B-1 Kraków30-059 Poland Division of Computational Mathematics Faculty of Mathematics and Computer Science Jagiellonian University 6 Lojasiewicza St. Kraków Poland

High-quality fluorescence imaging of biological systems is limited by processes like photobleaching and phototoxicity, and also in many cases, by limited access to the latest generations of microscopes. Moreover, low temporal resolution can lead to a motion blur effect in living systems. Our work presents a deep learning (DL) generative-adversarial approach to the problem of obtaining high-quality (HQ) images based on their low-quality (LQ) equivalents. We propose a generative-adversarial network (GAN) for contrast transfer between two different separate microscopy systems: a confocal microscope (producing HQ images) and a wide-field fluorescence microscope (producing LQ images). Our model proves that such transfer is possible, allowing us to receive HQ-generated images characterized by low mean squared error (MSE) values, high structural similarity index (SSIM), and high peak signal-to-noise ratio (PSNR) values. For our best model in the case of comparing HQ-generated images and HQ-ground truth images, the median values of the metrics are 6·10-4, 0.9413, and 31.87, for MSE, SSIM, and PSNR, respectively. In contrast, in the case of comparison between LQ and HQ ground truth median values of the metrics are equal to 0.0071, 0.8304, and 21.48 for MSE, SSIM, and PSNR respectively. Therefore, we observe a significant increase ranging from 14% to 49% for SSIM and PSNR respectively. These results, together with other single-system cross-modality studies, provide proof of concept for further implementation of a cross-system biological image quality enhancement. © 2024, CC BY-SA.

关键词： Fluorescence imaging

Benchmarking the Immersed Boundary Method for Viscoelastic Flows

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arXiv 2023年

作者： Gruninger, Cole Barrett, Aaron Fang, Fuhui Forest, M. Gregory Griffith, Boyce E. Department of Mathematics University North Carolina Chapel HillNC United States Department of Mathematics University of Utah Salt Lake CityUT United States Department of Applied Physical Sciences University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used for the simulation of biological fluid dynamics and other modeling scenarios where a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems with viscous incompressible fluids, it also can be applied to visoelastic fluids, and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constuitive equation. However, to date, relatively little work has explored the accuracy or convergence properties of the numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using the idealized Oldroyd-B and more realistic, polymer-entanglement-based Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime. Copyright © 2023, The Authors. All rights reserved.

关键词： Benchmarking

Sensitivity Analysis for Verification of an Anaerobic Digestion Model

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International Journal of applied and Computational mathematics 2020年第2期6卷 1-12页

作者： Silva, M.I. De Bortoli, A.L. Graduate Program in Applied Mathematics Federal Univ. of Rio Grande do Sul Av. Bento Gonçalves 9500 Porto Alegre RS Brazil Graduate Program in Chemical Engineering Federal Univ. of Rio Grande do Sul Porto Alegre Brazil

In this article, the first-order sensitivity coefficients for a system of stiff nonlinear differential equations from the anaerobic digestion model are calculated. In this approach, the auxiliary equations used to calculate the sensitivity coefficients are solved separately from the model equations, using the same time steps and numerical approximations used in the calculation of the model solution by the Rosenbrock method of order four. The results show the importance of each reaction for each species involved in the model. © 2020, Springer Nature India Private Limited.

关键词： Anaerobic digestion chemical kinetics Differential equations system Rosenbrock method Sensitivity analysis Simulation

Antithetic Multilevel Methods for Elliptic and Hypo-Elliptic Diffusions with Applications

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arXiv 2024年

作者： Iguchi, Yuga Jasra, Ajay Maama, Mohamed Beskos, Alexandros Department of Statistical Science University College London LondonWC1E 6BT United Kingdom School of Data Science The Chinese University of Hong Kong Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we present a new antithetic multilevel Monte Carlo (MLMC) method for the estimation of expectations with respect to laws of diffusion processes that can be elliptic or hypo-elliptic. In particular, we consider the case where one has to resort to time discretization of the diffusion and numerical simulation of such schemes. Motivated by recent developments, we introduce a new MLMC estimator of expectations, which does not require simulation of intractable Lévy areas but has a weak error of order 2 and achieves the optimal computational complexity. We then show how this approach can be used in the context of the filtering problem associated to partially observed diffusions with discrete time observations. We illustrate with numerical simulations that our new approaches provide efficiency gains for several problems relative to some existing methods. © 2024, CC BY.

关键词： Diffusion

Obstacles on the Pathway Towards chemical programmability Using Agglomerations of Droplets 15th

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Obstacles on the Pathway Towards Chemical Programmability Us...

15th International Workshop on Artificial Life and Evolutionary Computation, WIVACE 2021

作者： Schneider, Johannes Josef Faggian, Alessia Matuttis, Hans-Georg Barrow, David Anthony Li, Jin Holler, Silvia Casiraghi, Federica Sanahuja, Lorena Cebolla Hanczyc, Martin Michael Eschle, Patrik Weyland, Mathias Sebastian Flumini, Dandolo Eggenberger Hotz, Peter Füchslin, Rudolf Marcel Institute of Applied Mathematics and Physics School of Engineering Zurich University of Applied Sciences Technikumstr. 9 Winterthur8401 Switzerland Laboratory for Artificial Biology Department of Cellular Computational and Integrative Biology University of Trento Via Sommarive 9 Povo38123 Italy Department of Mechanical Engineering and Intelligent Systems The University of Electrocommunications Chofu Chofugaoka 1-5-1 Tokyo182-8585 Japan Laboratory for Microfluidics and Soft Matter Microengineering Cardiff School of Engineering Cardiff University Queen’s Buildings 14-17 The Parade CardiffCF24 3AA United Kingdom Chemical and Biological Engineering University of New Mexico MSC01 1120 AlbuquerqueNM87131-0001 United States European Centre for Living Technology Ca’ Bottacin Dorsoduro 3911 Calle Crosera Venice30123 Italy

ISBN: (纸本)9783031239281

We aim at planning and creating specific agglomerations of droplets to study synergic communication using these as programmable units. In this paper, we give an overview of preliminary obstacles for the various research issues, namely of how to create droplets, how to set up droplet agglomerations using DNA technology, how to prepare them for confocal microscopy, how to make a computer see droplets on photos, how to analyze networks of droplets, how to perform simulations mimicking experiments, and how to plan specific agglomerations of droplets. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Drops

Modeling CO2 solubility in polyethylene glycol polymer using data driven methods

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Separation Science and Technology (Philadelphia) 2025年第11期60卷 1451-1470页

作者： Lei, YunLi Sead, Fadhel F. Sur, Dharmesh Yadav, Anupam Ballal, Suhas Singh, Abhayveer Krithiga, T. Kumar, Akshay Yuldashev, Farrukh Ahmad, Irfan Sherzod, Samim Guangxi Technological College of Machinery and Electricity Nanning China Department of Dentistry College of Dentistry The Islamic University Iraq Department of medical analysis Medical laboratory technique college the Islamic University of Al Diwaniyah Al Diwaniyah Iraq Department of medical analysis Medical laboratory technique college the Islamic University of Babylon Babylon Iraq Department of Chemical Engineering Faculty of Engineering & Technology Marwadi University Research Center Rajkot India Department of Computer engineering and Application GLA University Mathura India Bangalore India Centre for Research Impact & Outcome Chitkara University Institute of Engineering and Technology Chitkara University Rajpura India Department of Chemistry Sathyabama Institute of Science and Technology Chennai India Department of Mathematics Graphic Era Hill University Dehradun India Graphic Era Deemed to be University Dehradun India Department of Informatics and Its Teaching Methods Tashkent State Pedagogical University Tashkent Uzbekistan Department of Clinical Laboratory Sciences College of Applied Medical Sciences King Khalid University Abha Saudi Arabia Faculty of Engineering Nangarhar University Nangarhar Afghanistan

The solubility of CO2 in polyethylene glycol (PEG) polymer is a critical parameter for optimizing its use in various industrial processes, underscoring the need for precise predictive models. In this research, a Random Forest (RF) machine learning model is meticulously tuned through four sophisticated optimization algorithms: Batch Bayesian Optimization (BBO), Self-Adaptive Differential Evolution (SADE), Bayesian Probability Improvement (BPI), and Gaussian Processes Optimization (GPO). The model leverages a dataset of 164 experimental samples, incorporating essential input parameters such as pressure, PEG molar mass, and temperature to predict CO2 solubility. To prevent overfitting, K-fold cross-validation is applied throughout model training. The efficacy of each optimization method is evaluated using computational runtime and performance metrics, including R-squared (R2), mean squared error (MSE), and average absolute relative error (AARE%). Correlation analysis indicates that pressure has a moderate positive relationship with CO2 solubility (correlation coefficient: 0.58), while PEG molar mass and temperature exhibit weaker associations (0.2 and 0.05, respectively). Among the optimization techniques, RF-BPI proves to be the most effective, delivering superior predictive performance. The results show RF-BPI achieves an R2 of 0.9625 for the training set and 0.9307 for the test set, surpassing other methods. For benchmarking, a conventional multiple linear regression (LR) model was tested, demonstrating significantly lower accuracy (R2 notably inferior to RF-BPI’s 0.9307 on the test set). In terms of computational efficiency, BPI records the shortest runtime (63.9 seconds), while SADE is the least efficient, requiring 2370.2 seconds. Sensitivity analysis further clarifies the relative impact of each input variable on CO2 solubility, affirming the power of data-driven approaches in modeling complex systems. The created models can be seen as promising predictive tools

关键词： Mean square error

Reliable extrapolation of deep neural operators informed by physics or sparse observations

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arXiv 2022年

作者： Zhu, Min Zhang, Handi Jiao, Anran Karniadakis, George Em Lu, Lu Department of Chemical and Biomolecular Engineering University of Pennsylvania PhiladelphiaPA19104 United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Computer and Information Science University of Pennsylvania PhiladelphiaPA19104 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States School of Engineering Brown University ProvidenceRI02912 United States

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity via the 2-Wasserstein distance between two function spaces and propose a new behavior of bias-variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information—the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed. © 2022, CC BY-NC-ND.

关键词： Extrapolation