IMA Journal of Applied Mathematics最新文献_第2页

Reaction dynamics and early-time behaviour of chemical decontamination 化学净化的反应动力学和早期行为

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2024-01-25 DOI: 10.1093/imamat/hxae001

S Murphy, M Vynnycky, S L Mitchell, D O’Kiely

{"title":"Reaction dynamics and early-time behaviour of chemical decontamination","authors":"S Murphy, M Vynnycky, S L Mitchell, D O’Kiely","doi":"10.1093/imamat/hxae001","DOIUrl":"https://doi.org/10.1093/imamat/hxae001","url":null,"abstract":"When a hazardous chemical soaks into a porous material such as a concrete floor, it can be difficult to remove. One approach is chemical decontamination, where a cleanser is added to react with and neutralise the contaminating agent. The goal of this paper is to investigate the reaction dynamics and the factors that affect the efficacy of the decontamination procedure. We consider a one-dimensional porous medium initially saturated with an oil-based agent. An aqueous cleanser is applied at the surface, so the two chemicals are immiscible and a boundary forms between them. A neutralising reaction takes place at this boundary in which cleanser and agent are consumed and reaction products are created. This is a Stefan problem, and the boundary between the cleanser and agent moves as the reaction proceeds. Reaction products formed at the interface may dissolve in one or both liquids. This may temporarily prevent cleanser and/or agent from reaching the reaction site, so diffusion of the chemical species, in particular the diffusion of product from the interface, plays a key role. The scenario described above was considered previously by ?? in the limit where the depth of the porous medium is large compared to the length scale over which concentrations vary inside the medium. Here, we present results that are valid for any ratio between these length scales and an analysis of agent removal times for various dimensionless parameter regimes. We also highlight the emergence of a boundary layer associated with diffusion in the oil phase for early times, where the thickness of the boundary layer is directly proportional to the square root of the time variable.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"11 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139584709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Bubble Model for the Gating of Kv Channels Kv 通道门控的气泡模型

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2024-01-25 DOI: 10.1093/imamat/hxae002

Zilong Song, Robert Eisenberg, Shixin Xu, Huaxiong Huang

引用次数: 0

Correction to: Initial-boundary value problem for a fractional heat equation on an interval 更正：区间上分式热方程的初始边界值问题

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2023-12-02 DOI: 10.1093/imamat/hxad036

引用次数: 0

Analyzing inexact hypergradients for bilevel learning 分析两层学习的非精确超梯度

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2023-12-01 DOI: 10.1093/imamat/hxad035

Matthias J Ehrhardt, Lindon Roberts

引用次数: 0

Interfacial growth morphologies in dense eutectic crystal mushes 致密共晶糊状中界面生长形态

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2023-12-01 DOI: 10.1093/imamat/hxad033

A C Fowler, Marian B Holness

引用次数: 0

A unified and constructive framework for the universality of neural networks 为神经网络的普遍性提供了一个统一的、建设性的框架

4区数学

IMA Journal of Applied Mathematics Pub Date : 2023-11-11 DOI: 10.1093/imamat/hxad032

Tan Bui-Thanh

{"title":"A unified and constructive framework for the universality of neural networks","authors":"Tan Bui-Thanh","doi":"10.1093/imamat/hxad032","DOIUrl":"https://doi.org/10.1093/imamat/hxad032","url":null,"abstract":"Abstract One of the reasons why many neural networks are capable of replicating complicated tasks or functions is their universal approximation property. Though the past few decades have seen tremendous advances in theories of neural networks, a single constructive and elementary framework for neural network universality remains unavailable. This paper is an effort to provide a unified and constructive framework for the universality of a large class of activation functions including most of the existing ones. At the heart of the framework is the concept of neural network approximate identity (nAI). The main result is: any nAI activation function is universal in the space of continuous functions on compacta. It turns out that most of the existing activation functions are nAI, and thus universal. The framework induces several advantages over the contemporary counterparts. First, it is constructive with elementary means from functional analysis, probability theory, and numerical analysis. Second, it is one of the first unified and constructive attempts that is valid for most of the existing activation functions. Third, it provides new proofs for most activation functions. Fourth, for a given activation and error tolerance, the framework provides precisely the architecture of the corresponding one-hidden neural network with a predetermined number of neurons and the values of weights/biases. Fifth, the framework allows us to abstractly present the first universal approximation with a favorable non-asymptotic rate. Sixth, our framework also provides insights into the developments, and hence providing constructive derivations, of some of the existing approaches.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"7 16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135086306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Reduced Landau-de Gennes Study for Nematic Equilibria in Three-Dimensional Prisms 三维棱镜中向列平衡的简化Landau-de Gennes研究

4区数学

IMA Journal of Applied Mathematics Pub Date : 2023-11-08 DOI: 10.1093/imamat/hxad031

Yucen Han, Baoming Shi, Lei Zhang, Apala Majumdar

引用次数: 1

Initial-boundary value problem for a fractional heat equation on an interval 区间上分数阶热方程的初边值问题

4区数学

IMA Journal of Applied Mathematics Pub Date : 2023-11-04 DOI: 10.1093/imamat/hxad029

Y Peña Pérez, J Sánchez Ortíz, F J Ariza Hernández, M P Árciga Alejandre

引用次数: 0

Application of the topological sensitivity method to the detection of Breast cancer 拓扑灵敏度法在乳腺癌检测中的应用

4区数学

IMA Journal of Applied Mathematics Pub Date : 2023-10-23 DOI: 10.1093/imamat/hxad028

Sabeur Mansouri, Mohamed BenSalah

引用次数: 0

The feasibility and inevitability of stealth attacks 隐身攻击的可行性和必然性

4区数学

IMA Journal of Applied Mathematics Pub Date : 2023-10-19 DOI: 10.1093/imamat/hxad027

Ivan Yu. Tyukin, Desmond J. Higham, Eliyas Woldegeorgis, Alexander N. Gorban

{"title":"The feasibility and inevitability of stealth attacks","authors":"Ivan Yu. Tyukin, Desmond J. Higham, Eliyas Woldegeorgis, Alexander N. Gorban","doi":"10.1093/imamat/hxad027","DOIUrl":"https://doi.org/10.1093/imamat/hxad027","url":null,"abstract":"Abstract We develop and study new adversarial perturbations that enable an attacker to gain control over decisions in generic Artificial Intelligence (AI) systems including deep learning neural networks. In contrast to adversarial data modification, the attack mechanism we consider here involves alterations to the AI system itself. Such a stealth attack could be conducted by a mischievous, corrupt or disgruntled member of a software development team. It could also be made by those wishing to exploit a “democratization of AI” agenda, where network architectures and trained parameter sets are shared publicly. We develop a range of new implementable attack strategies with accompanying analysis, showing that with high probability a stealth attack can be made transparent, in the sense that system performance is unchanged on a fixed validation set which is unknown to the attacker, while evoking any desired output on a trigger input of interest. The attacker only needs to have estimates of the size of the validation set and the spread of the AI’s relevant latent space. In the case of deep learning neural networks, we show that a one neuron attack is possible—a modification to the weights and bias associated with a single neuron—revealing a vulnerability arising from over-parameterization. We illustrate these concepts using state of the art architectures on two standard image data sets. Guided by the theory and computational results, we also propose strategies to guard against stealth attacks.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135666553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 13