Journal•ISSN: 0036-1399

# Siam Journal on Applied Mathematics

Society for Industrial and Applied Mathematics

About: Siam Journal on Applied Mathematics is an academic journal published by Society for Industrial and Applied Mathematics. The journal publishes majorly in the area(s): Boundary value problem & Nonlinear system. It has an ISSN identifier of 0036-1399. Over the lifetime, 5841 publications have been published receiving 230117 citations. The journal is also known as: Society for Industrial and Applied Mathematics journal on applied mathematics & Applied mathematics.

Topics: Boundary value problem, Nonlinear system, Differential equation, Partial differential equation, Population

##### Papers published on a yearly basis

##### Papers

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2,861 citations

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2,387 citations

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TL;DR: A simple model for synchronous firing of biological oscillators based on Peskin's model of the cardiac pacemaker is studied in this article, which consists of a population of identical integrate-and-fire oscillators, whose coupling between oscillators is pulsatile: when a given oscillator fires, it pulls the others up by a fixed amount, or brings them to the firing threshold, whichever is less.

Abstract: A simple model for synchronous firing of biological oscillators based on Peskin's model of the cardiac pacemaker (Mathematical aspects of heart physiology, Courant Institute of Mathematical Sciences, New York University, New York, 1975, pp. 268-278) is studied. The model consists of a population of identical integrate-and-fire oscillators. The coupling between oscillators is pulsatile: when a given oscillator fires, it pulls the others up by a fixed amount, or brings them to the firing threshold, whichever is less. The main result is that for almost all initial conditions, the population evolves to a state in which all the oscillators are firing synchronously. The relationship between the model and real communities of biological oscillators is discussed; examples include populations of synchronously flashing fireflies, crickets that chirp in unison, electrically synchronous pacemaker cells, and groups of women whose menstrual cycles become mutually synchronized.

2,025 citations

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TL;DR: In this paper, a correct proof for this fact is given, based on an alternative definition of the nucleolus, which is of some interest in its own right, and the proof is based on a definition of an alternative class of nucleoli.

Abstract: : In RM 23, a proof was given that the nucleolus is continuous as a function of the characteristic function. This proof is not correct; the author, at least, does not know how to complete it. In the paper a correct proof for this fact is given. The proof is based on an alternative definition of the nucleolus, which is of some interest in its own right. (Author)

1,729 citations

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TL;DR: An algorithm is presented which finds a p-median of a tree (for $p > 1$) in time $O(n^2 \cdot p^2 )$.

Abstract: It is shown that the problem of finding a p-median of a network is an $NP$-hard problem even when the network has a simple structure (e.g., planar graph of maximum vertex degree 3). However, results leading to efficient algorithms are presented when the network is a tree: In particular, we first show that a 1-median of a tree is identical to its w-centroid, and obtain Goldman’s $O(n)$ algorithm for finding a 1-median of a tree out of more general considerations. Then, we present an algorithm which finds a p-median of a tree (for $p > 1$) in time $O(n^2 \cdot p^2 )$.

1,333 citations