COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS纯数学与应用数学通讯
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS(英文缩写 COMMUN PUR APPL MATH),ISSN 0010-3640,eISSN 1097-0312,中文译名:纯数学与应用数学通讯 是一本学术期刊。本页汇总该期刊的最新影响因子、分区信息以及最新收录于 PubMed 的文献,帮助您快速了解期刊全貌。
发文量统计区间：2025-11-01 至 2026-10-31，按本站收录文献的发表日期统计。
期刊介绍
历年影响因子趋势
| JCR 数据年份 | 影响因子 | JCR 分区 |
|---|---|---|
| 2021 | 2.774 | Q1 |
| 2022 | 3.000 | Q1 |
| 2023 | 3.100 | Q1 |
| 2024 | 2.700 | Q1 |
| 2025 | 3.500 | Q1 |
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS 最新收录文献
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1. Electrophysiology.
PMID:日期:2013-10-09Electrical signaling is a fast mode of communication for cells within an organism. We are concerned here with the formulation and analysis of mathematical models that are used to describe this important class of physiological processes. These models generally take the form of partial differential equations that are descendants of those introduced by Hodgkin and Huxley to describe the propagation of an action potential along the squid giant axon. We review that work here and then go on to describe more recent variations on the Hodgkin-Huxley theme, including the three-dimensional bidomain (and monodomain) equations for cardiac electrophysiology, multiscale models for the heart that take cellular structure into account near the action potential wavefront, and finally a more detailed reformulation of electrophysiology in terms of electrodiffusion.
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2. Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Detection.
PMID:日期:2013-09We review some widely studied models and firing dynamics for neuronal systems, both at the single cell and network level, and dynamical systems techniques to study them. In particular, we focus on two topics in mathematical neuroscience that have attracted the attention of mathematicians for decades: single-cell excitability and bursting. We review the mathematical framework for three types of excitability and onset of repetitive firing behavior in single-neuron models and their relation with Hodgkin's classification in 1948 of repetitive firing properties. We discuss the mathematical dissection of bursting oscillations using fast/slow analysis and demonstrate the approach using single-cell and mean-field network models. Finally, we illustrate the properties of Type III excitability in which case repetitive firing for constant or slow inputs is absent. Rather, firing is in response only to rapid enough changes in the stimulus. Our case study involves neuronal computations for sound localization for which neurons in the auditory brain stem perform extraordinarily precise coincidence detection with submillisecond temporal resolution.
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3. Vector Diffusion Maps and the Connection Laplacian.
PMID:日期:2012-08We introduce (VDM), a new mathematical framework for organizing and analyzing massive high-dimensional data sets, images, and shapes. VDM is a mathematical and algorithmic generalization of diffusion maps and other nonlinear dimensionality reduction methods, such as LLE, ISOMAP, and Laplacian eigenmaps. While existing methods are either directly or indirectly related to the heat kernel for functions over the data, VDM is based on the heat kernel for vector fields. VDM provides tools for organizing complex data sets, embedding them in a low-dimensional space, and interpolating and regressing vector fields over the data. In particular, it equips the data with a metric, which we refer to as the . In the manifold learning setup, where the data set is distributed on a low-dimensional manifold ℳ embedded in ℝ , we prove the relation between VDM and the connection Laplacian operator for vector fields over the manifold.