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Taylor dispersion in variable-density, variable-viscosity pulsatile flows

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arXiv 2025年

作者： Rajamanickam, Prabakaran Weiss, Adam D. Department of Mathematics and Statistics University of Strathclyde GlasgowG1 1XQ United Kingdom ATA Engineering Inc. San Diego92128 United States

The phenomenon of Taylor or shear-induced dispersion of a non-passive scalar field in a pulsatile pipe flow is investigated, accounting for the scalar field’s influence on fluid density and transport coefficients. By employing multiple scale analysis, an effective one-dimensional, unsteady mixing problem for the scalar field is obtained, which includes the diffusion coefficient for shear-induced dispersion. The resulting governing equations are applicable to a range of scalar transport problems in pulsatile pipe flows. Copyright © 2025, The Authors. All rights reserved.

关键词： Pulsatile flow

GLOBAL SOLUTIONS TO THE SUPERCOOLED STEFAN PROBLEM WITH BLOW-UPS: REGULARITY AND UNIQUENESS

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Probability and Mathematical Physics

Probability and Mathematical Physics 2022年第1期3卷 171-213页

作者： Delarue, François Nadtochiy, Sergey Shkolnikov, Mykhaylo Laboratoire J.A.Dieudonné Université de Nice Sophia-Antipolis UMR CNRS-UNS No. 7351 Nice France Department of Applied Mathematics Illinois Institute of Technology Rettaliata Engineering Center Chicago IL United States ORFE Department Bendheim Center for Finance Program in Applied and Computational Mathematics Princeton University Princeton NJ United States

We consider the supercooled Stefan problem, which captures the freezing of a supercooled liquid, in one space dimension. A probabilistic reformulation of the problem allows us to define global solutions, even in the presence of blow-ups of the freezing rate. We provide a complete description of such solutions, by relating the temperature distribution in the liquid to the regularity of the ice growth process. The latter is shown to transition between (i) continuous differentiability, (ii) Hölder continuity, and (iii) discontinuity. In particular, in the second regime we rediscover the square root behavior of the growth process pointed out by Stefan in his seminal 1889 paper for the ordinary Stefan problem. In our second main theorem, we establish the uniqueness of the global solutions, a first result of this kind in the context of growth processes with singular self-excitation when blow-ups are present. © 2022 Mathematical Sciences Publishers.

关键词： blow-ups free boundary problem heat equation interacting particle systems mean-field interaction physical solutions probabilistic reformulation self-excitation supercooled Stefan problem zero set

A Unifying Generator Loss Function for Generative Adversarial Networks

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arXiv 2023年

作者： Veiner, Justin Alajaji, Fady Gharesifard, Bahman Department of Mathematics and Statistics Queen's University KingstonON Canada Department of Electrical and Computer Engineering University of California Los AngelesCA United States

A unifying α-parametrized generator loss function is introduced for a dual-objective generative adversarial network (GAN), which uses a canonical (or classical) discriminator loss function such as the one in the original GAN (VanillaGAN) system. The generator loss function is based on a symmetric class probability estimation type function, Lα, and the resulting GAN system is termed Lα-GAN. Under an optimal discriminator, it is shown that the generator's optimization problem consists of minimizing a Jensen-fα-divergence, a natural generalization of the Jensen-Shannon divergence, where fα is a convex function expressed in terms of the loss function Lα. It is also demonstrated that this Lα−GAN problem recovers as special cases a number of GAN problems in the literature, including VanillaGAN, Least Squares GAN (LSGAN), Least kth order GAN (LkGAN) and the recently introduced (αD, αG)-GAN with αD = 1. Finally, experimental results are conducted on three datasets, MNIST, CIFAR-10, and Stacked MNIST to illustrate the performance of various examples of the Lα−GAN system. © 2023, CC BY.

关键词： Generative adversarial networks

Event-Based Multi-Modal Fusion for Online Misinformation Detection in High-Impact Events

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Event-Based Multi-Modal Fusion for Online Misinformation Det...

IEEE International Conference on Big Data

作者： Javad Rajabi Sunday Okechukwu Ahmad Mousavi Roberto Corizzo Charles C. Cavalcante Zois Boukouvalas Department of Computer Science American University Washington DC USA Department of Mathematics and Statistics American University Washington DC USA Department of Teleinformatics Engineering Federal University of Ceará Fortaleza Ceará Brazil

ISBN: (数字)9798350362480

ISBN: (纸本)9798350362497

Social media platforms are pivotal in information dissemination but also contribute to the rapid spread of misinformation, especially during high-impact events like natural disasters, terrorist attacks, and political unrest. While recent advances in multi-modal learning have enhanced misinformation detection by integrating features from various modalities (e.g., text, images), certain areas remain under-explored, particularly the use of event-based multi-modal data. This paper introduces a novel approach to misinformation detection on social media using an event-based multi-modal learning framework. Our method extends beyond traditional techniques by employing latent variable modeling to capture non-linear associations in event-based multi-modal data and to generate joint features between events for classification. This approach enhances misinformation detection and enables the contextual understanding of terms across different events. We provide a detailed analysis of our dataset preparation, methodology, and results, demonstrating the effectiveness of our framework on a widely-used dataset of tweets from high-impact events. The paper concludes with insights into potential enhancements and future directions in multi-modal misinformation detection.

关键词： Event detection Social networking (online) Terrorism Disasters Big Data Feature extraction Vectors Data models Fake news

ELFATT: Efficient Linear Fast Attention for Vision Transformers

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arXiv 2025年

作者： Wu, Chong Che, Maolin Xu, Renjie Ran, Zhuoheng Yan, Hong Department of Electrical Engineering Centre for Intelligent Multidimensional Data Analysis City University of Hong Kong Kowloon Hong Kong School of Mathematics and Statistics Guizhou University Guiyang550025 China

The attention mechanism is the key to the success of transformers in different machine learning tasks. However, the quadratic complexity with respect to the sequence length of the vanilla softmax-based attention mechanism becomes the major bottleneck for the application of long sequence tasks, such as vision tasks. Although various efficient linear attention mechanisms have been proposed, they need to sacrifice performance to achieve high efficiency. What’s more, memory-efficient methods, such as FlashAttention-1-3, still have quadratic computation complexity which can be further improved. In this paper, we propose a novel efficient linear fast attention (ELFATT) mechanism to achieve low memory input/output operations, linear computational complexity, and high performance at the same time. ELFATT offers 4-7x speedups over the vanilla softmax-based attention mechanism in high-resolution vision tasks without losing performance. ELFATT is FlashAttention friendly. Using FlashAttention-2 acceleration, ELFATT still offers 2-3x speedups over the vanilla softmax-based attention mechanism on high-resolution vision tasks without losing performance. Even on edge GPUs, ELFATT still offers 1.6x to 2.0x speedups compared to state-of-the-art attention mechanisms in various power modes from 5W to 60W. Furthermore, ELFATT can be used to enhance and accelerate diffusion tasks directly without training. Copyright © 2025, The Authors. All rights reserved.

关键词： Machine vision

Trustworthy Actionable Perturbations

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arXiv 2024年

作者： Friedbaum, Jesse Adiga, Sudarshan Tandon, Ravi Program in Applied Mathematics University of Arizona TucsonAZ United States Department of Electrical and Computer Engineering University of Arizona TucsonAZ United States

Counterfactuals, or modified inputs that lead to a different outcome, are an important tool for understanding the logic used by machine learning classifiers and how to change an undesirable classification. Even if a counterfactual changes a classifier’s decision, however, it may not affect the true underlying class probabilities, i.e. the counterfactual may act like an adversarial attack and "fool" the classifier. We propose a new framework for creating modified inputs that change the true underlying probabilities in a beneficial way which we call Trustworthy Actionable Perturbations (TAP). This includes a novel verification procedure to ensure that TAP change the true class probabilities instead of acting adversarially. Our framework also includes new cost, reward, and goal definitions that are better suited to effectuating change in the real world. We present PAClearnability results for our verification procedure and theoretically analyze our new method for measuring reward. We also develop a methodology for creating TAP and compare our results to those achieved by previous counterfactual methods. © 2024, CC BY.

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Multilevel Monte Carlo Methods for the Grad-Shafranov Free Boundary Problem

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SSRN

SSRN 2023年

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costsby performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductionstypically on the order of 60 or more and possibly as large as 200. Adaptive gridding results in more accurate computation of geometric quantities such as x-points associated with the model. © 2023, The Authors. All rights reserved.

关键词： Monte Carlo methods

On the Effectiveness of Text and Image Embeddings in Multimodal Hate Speech Detection

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On the Effectiveness of Text and Image Embeddings in Multimo...

IEEE International Conference on Big Data

作者： Nora Lewis Charles C. Cavalcante Zois Boukouvalas Roberto Corizzo Department of Computer Science American University Washington DC USA Department of Teleinformatics Engineering Federal University of Ceará Fortaleza Ceará Brazil Department of Mathematics and Statistics American University Washington DC USA

ISBN: (数字)9798350362480

ISBN: (纸本)9798350362497

Social media content is increasingly subject to hate speech towards specific demographic groups. In this context, machine learning approaches appear relevant to detect malicious contents and support moderators in mitigation initiatives. However, many of the existing approaches are exclusively focused on the analysis of textual contents. On the other hand, studies that address multiple data modalities often rely on a single feature representation and a fully supervised learning setting. In this paper, we tackle multimodal hate speech detection resorting to different learning settings (one-class learning and binary classification). We also investigate the effectiveness of multiple deep learning model backbones and language models to extract embedding feature representations for text and image modalities. Our experiments with a real-world hate speech dataset show that there is a significant performance gap between one-class learning and binary classification, and that the choice of embedding representations for image and text modalities can impact the detection performance for different predictive models.

关键词： Deep learning Radio frequency Social networking (online) Prevention and mitigation Hate speech Supervised learning Predictive models Nearest neighbor methods Feature extraction Vectors

A numerical treatment through Bayesian regularization neural network for the chickenpox disease model

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Computers in Biology and Medicine 2025年 187卷 109807-109807页

作者： Sabir, Zulqurnain Mehmood, Muhammad Athar Umar, Muhammad Salahshour, Soheil Altun, Yener Arbi, Adnène Ali, Mohamed R. Department of Mathematics and Statistics Hazara University Mansehra Pakistan Department of Mathematics University of Gujrat Pakistan Faculty of Engineering and Natural Sciences Istanbul Okan University Istanbul Turkey Faculty of Engineering and Natural Sciences Bahcesehir University Istanbul Turkey Faculty of Economics and Administrative Sciences Department of Business Administration Yuzuncu Yil University Van Turkey EPT University of Carthage Carthage Tunisia Faculty of Engineering Benha National University Obour Campus Egypt Basic Engineering Science Department Benha Faculty of Engineering Benha University Benha Egypt

Objectives: The current research investigations designates the numerical solutions of the chickenpox disease model by applying a proficient optimization framework based on the artificial neural network. The mathematical form of the chickenpox disease model is divided into different categories of individuals, susceptible, vaccinated, infected, exposed, recovered, and infected with/without complications. Method: The construction of neural network is performed by using the single hidden layer and the optimization of Bayesian regularization. A dataset is assembled using the explicit Runge-Kutta technique for reducing the mean square error using the training 76 %, while 12 %, 12 % for validation and testing. The whole stochastic procedure is based on logistic sigmoid fitness function, single hidden layer structure with thirty neurons, along with the optimization capability of Bayesian regularization. Finding: The designed procedure's correctness and reliability is observed by results matching, negligible absolute error around 10−04 to 10−06, regression, error histogram, and state transmission. Moreover, the best performance values based on the mean square error are performed as 10−09 to 10−11. Novelty: The current neural network framework using the construction of a single hidden layer and the optimization of Bayesian regularization is applied first time to solve the chickenpox disease model. © 2025 Elsevier Ltd

关键词： Neural network models