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PiRL: Participant-Invariant Representation Learning for Healthcare Using Maximum Mean Discrepancy and Triplet Loss

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arXiv 2023年

作者： Cao, Zhaoyang Yu, Han Yang, Huiyuan Sano, Akane Department of Computational and Applied Mathematics Rice University Houston United States Department of Electrical and Computer Engineering Rice University Houston United States

Due to individual heterogeneity, person-specific models are usually achieving better performance than generic (one-size-fits-all) models in data-driven health applications. However, generic models are usually preferable in real-world applications, due to the difficulties of developing person-specific models, such as new-user-adaptation issues and system complexities. To improve the performance of generic models, we propose a Participant-invariant Representation Learning (PiRL) framework, which utilizes maximum mean discrepancy (MMD) loss and domain-adversarial training to encourage the model to learn participant-invariant representations. Further, to avoid trivial solutions in the learned representations, a triplet loss based constraint is used for the model to learn the label-distinguishable embeddings. The proposed framework is evaluated on two public datasets (CLAS and Apnea-ECG), and significant performance improvements are achieved compared to the baseline models. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning

Sample-based robust model reduction for non-linear systems biology models

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Sample-based robust model reduction for non-linear systems b...

93rd Annual Meeting of the International Association of applied mathematics and Mechanics, GAMM 2023

作者： Falkenhagen, Undine Himpe, Christian Knöchel, Jane Kloft, Charlotte Huisinga, Wilhelm Institute of Mathematics University of Potsdam Potsdam Germany Graduate Research Training Program PharMetrX: Pharmacometrics & Computational Disease Modelling Freie Universität Berlin and University of Potsdam Potsdam Germany Mathematics Münster University of Münster Muenster Germany Department of Clinical Pharmacy and Biochemistry Institute of Pharmacy Freie Universität Berlin Berlin Germany

Complex non-linear systems biology models comprise relevant knowledge on processes of pharmacological interest. They are, however, too complex to be used in inferential settings, for example, to allow for the estimation of patient-specific parameters for individual dose optimisation. Thus, there is a need for simple models with interpretable components to infer the drug effect in a clinical setting. In particular, it is essential to accurately quantify and simulate the interindividual variability in the drug response in order to account for covari-ates like body weight, age and genetic disposition. To this end, non-linear model order reduction and simplification methods can be used if they maintain model interpretability during reduction and consider an entire population rather than just a single reference individual. We present a sample-based approach for robust model order reduction and propose two improvements for efficiency. In particular, we introduce a new sampling method to generate the virtual population based on transformed latin hypercube sampling. Thereby, the sample is stratified in the relevant parameter-space directions, which are identified using empirical observability Gramians. We illustrate our approach in application to a blood coagulation pathway model, where we reduce the complexity from a 62-dimensional highly non-linear to a six-dimensional and a nine-dimensional system of ordinary differential equations for two scenarios, respectively. © 2023 The Authors. Proceedings in applied mathematics & Mechanics published by Wiley-VCH GmbH.

关键词： Nonlinear systems

STEERABLE TRANSFORMERS FOR VOLUMETRIC DATA

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arXiv 2024年

作者： Kundu, Soumyabrata Kondor, Risi Department of Statistics University of Chicago ChicagoIL60637 United States Department of Computer Science Department of Statistics Computational and Applied Mathematics University of Chicago ChicagoIL60637 United States

In this work we introduce Steerable Transformers, an extension of the Vision Transformer mechanism that maintains equivariance to the special Euclidean group SE(d). We propose an equivariant attention mechanism that operates on features extracted by steerable convolutions. Operating in Fourier space, our network utilizes Fourier space non-linearities. Our experiments in both two and three dimensions show that adding steerable transformer layers to steerable convolutional networks enhances performance. © 2024, CC BY.

关键词： Convolution

Enhancing the Swanepoel method: precise envelope detection of thin-film transmission spectra

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Optics Express 2025年第6期33卷 13376-13400页

作者： Ballester, Manuel Marquez, Almudena P. Lopez-Tapia, Santiago Fernandez, Susana Bass, John Minkov, Dorian Wuersch, Christoph Willomitzer, Florian Marquez, Emilio Katsaggelos, Aggelos K. Computer Science Department Northwestern University EvanstonIL60208 United States Department of Mathematics Faculty of Science University of Cadiz Puerto Real11510 Spain Department of Electrical and Computer Engineering Northwestern University EvanstonIL60208 United States CIEMAT Avenida Complutense 40 Madrid28040 Spain Wyant College of Optical Sciences University of Arizona TucsonAZ85721 United States Sofia1000 Bulgaria Institute for Computational Engineering ICE OST Eastern Switzerland University of Applied Sciences Switzerland Department of Condensed-matter Physics Faculty of Science University of Cadiz Puerto Real11510 Spain

The Swanepoel method is a widely used optical technique for characterizing thin films through normal-incidence transmission measurements. A critical step in this approach involves extracting the upper and lower envelopes of the measured oscillatory spectrum. By analyzing the transmission spectrum and its corresponding envelopes, the Swanepoel procedure enables precise determination of the film refractive index and extinction coefficient. However, even minor inaccuracies in envelope construction can propagate significant errors into the final characterization results. To address this challenge, we present what we believe to be a novel physics-informed optimization algorithm for envelope detection. Our mathematical model reformulates the envelope detection problem as a global optimization task that enforces the physical properties of the Swanepoel envelopes. Extensive validation on fifty randomly generated transmission spectra demonstrates unprecedented accuracy: the method achieves root-mean-square errors (RMSE) below 0.10% for the upper envelope and 0.06% for the lower envelope (more than doubling the accuracy of current state-of-the-art approaches). Furthermore, the proposed model has been assessed with two experimental transmission spectra, demonstrating its robustness and accuracy with real noisy data. We have developed an open-source Python software package (see text below). This software includes not only our innovative envelope construction algorithm but also additional envelope drawing algorithms for comparison and an efficient implementation of the Swanepoel method, enabling complete optical characterization of thin films. © 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement.

关键词： Mean square error

Inverted pin beams for robust propagation through atmospheric turbulence

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Inverted pin beams for robust propagation through atmospheri...

CLEO: Science and Innovations in CLEO 2024, CLEO: S and I 2024 - Part of Conference on Lasers and Electro-Optics

作者： Droulias, Sotiris Loulakis, Michalis Papazoglou, Dimitris G. Tzortzakis, Stelios Chen, Zhigang Efremidis, Nikolaos K. Institute of Applied and Computational Mathematics Foundation for Research and Technology - Hellas Crete Heraklion70013 Greece Department of Digital Systems University of Piraeus Piraeus18534 Greece Institute of Electronic Structure and Laser Foundation for Research and Technology - Hellas P.O. Box 1527 Crete Heraklion71110 Greece Department of Materials Science and Technology University of Crete Crete Heraklion700 13 Greece MOE Key Laboratory of Weak-Light Nonlinear Photonics TEDA Applied Physics Institute School of Physics Nankai University Tianjin300457 China Collaborative Innovation Center of Extreme Optics Shanxi University Shanxi Taiyuan030006 China Department of Applied Mathematics University of Crete Heraklion71409 Greece

We introduce a new class of beams the "inverted pin beams". We show that in atmospheric turbulence inverted pin beams outperform (have reduced scintillations) other classes of beams in moderate to strong flu...

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MVMS-RCN: A Dual-Domain Unified CT Reconstruction with Multi-sparse-view and Multi-scale Refinement-correction

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arXiv 2024年

作者： Fan, Xiaohong Chen, Ke Yi, Huaming Yang, Yin Zhang, Jianping The School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China The Centre for Mathematical Imaging Techniques Department of Mathematical Sciences The University of Liverpool LiverpoolL6972L United Kingdom The School of Mathematics and Computational Science Xiangtan University Hunan National Applied Mathematics Center Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan411105 China

X-ray Computed Tomography (CT) is one of the most important diagnostic imaging techniques in clinical applications. Sparse-view CT imaging reduces the number of projection views to a lower radiation dose and alleviates the potential risk of radiation exposure. Most existing deep learning (DL) and deep unfolding sparse-view CT reconstruction methods: 1) do not fully use the projection data;2) do not always link their architecture designs to a mathematical theory;3) do not flexibly deal with multi-sparse-view reconstruction assignments. This paper aims to use mathematical ideas and design optimal DL imaging algorithms for sparse-view CT reconstructions. We propose a novel dual-domain unified framework that offers a great deal of flexibility for multi-sparse-view CT reconstruction through a single model. This framework combines the theoretical advantages of model-based methods with the superior reconstruction performance of DL-based methods, resulting in the expected generalizability of DL. We propose a refinement module that utilizes unfolding projection domain to refine full-sparse-view projection errors, as well as an image domain correction module that distills multi-scale geometric error corrections to reconstruct sparse-view CT. This provides us with a new way to explore the potential of projection information and a new perspective on designing network architectures. The multi-scale geometric correction module is end-to-end learnable, and our method could function as a plug-and-play reconstruction technique, adaptable to various applications. Extensive experiments demonstrate that our framework is superior to other existing state-of-the-art methods. Our source codes are available at https://***/fanxiaohong/MVMS-RCN. Copyright © 2024, The Authors. All rights reserved.

关键词： Geometry

DEEP LEARNING ALTERNATIVES OF THE KOLMOGOROV SUPERPOSITION THEOREM

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arXiv 2024年

作者： Guilhoto, Leonardo Ferreira Perdikaris, Paris Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mechanical Engineering & Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

This paper explores alternative formulations of the Kolmogorov Superposition Theorem (KST) as a foundation for neural network design. The original KST formulation, while mathematically elegant, presents practical challenges due to its limited insight into the structure of inner and outer functions and the large number of unknown variables it introduces. Kolmogorov-Arnold Networks (KANs) leverage KST for function approximation, but they have faced scrutiny due to mixed results compared to traditional multilayer perceptrons (MLPs) and practical limitations imposed by the original KST formulation. To address these issues, we introduce ActNet, a scalable deep learning model that builds on the KST and overcomes many of the drawbacks of Kolmogorov’s original formulation. We evaluate ActNet in the context of Physics-Informed Neural Networks (PINNs), a framework well-suited for leveraging KST’s strengths in low-dimensional function approximation, particularly for simulating partial differential equations (PDEs). In this challenging setting, where models must learn latent functions without direct measurements, ActNet consistently outperforms KANs across multiple benchmarks and is competitive against the current best MLP-based approaches. These results present ActNet as a promising new direction for KST-based deep learning applications, particularly in scientific computing and PDE simulation *** Codes 68T07, 65M99 © 2024, CC BY-NC-SA.

关键词： Deep learning

Unbiased and Multilevel Methods for a Class of Diffusions Partially Observed via Marked Point Processes

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arXiv 2023年

作者： Alvarez, Miguel Jasra, Ajay Ruzayqat, Hamza Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity driven by a diffusion, with the associated marks also depending upon the diffusion process. We assume that one must resort to time-discretizing the diffusion process and develop particle and multilevel particle filters to recursively approximate the filter. In particular, we prove that our multilevel particle filter can achieve a mean square error (MSE) of O(∈2) (∈ > 0 and arbitrary) with a cost of O(∈-2.5) versus using a particle filter which has a cost of O(∈-3) to achieve the same MSE. We then show how this methodology can be extended to give unbiased (that is with no time-discretization error) estimators of the filter, which are proved to have finite variance and with high-probability have finite cost. Finally, we extend our methodology to the problem of online static-parameter estimation. Key words: Unbiased Methods, Multilevel Monte Carlo, Non-Linear Filtering, Point Processes, Parameter *** Codes 60G55, 60G35, 62M20, 62F30 © 2023, CC BY.

关键词： Diffusion

Inverted pin beams for robust propagation through atmospheric turbulence

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Inverted pin beams for robust propagation through atmospheri...

2024 Conference on Lasers and Electro-Optics, CLEO 2024

ISBN: (纸本)9781957171395

关键词： Laser beams