filmov
tv
7th HLF – Lecture: Stephen Smale
Показать описание
Stephen Smale: “The Mathematics of the Heart Beat”
Myocites, a class of heart cells, when put into a petri dish will oscillate independently, but after some time, nearby cells will have similar oscillatory behavior. Our goal is to give a mathematical model of synchronization to help understand this phenomenon.
Important work on this subject goes back to Huygens more than 350 years ago (pre-Newton). More recently, Turing (morphogenesis), Winfree, and Strogatz, (a one-time post-doc of my student Nancy Kopell) made contributions to these studies.
Here we focus especially on the work of Kuramoto on the collective behavior of phases. We will give a geometric analysis of Kuramoto's ordinary differential equations. Starting from the graph Laplacian of the cellular architecture of the heart, and a "hard-wiring" hypothesis of the associated genome dynamics, we obtain a phase setting of Kuramoto equations to obtain a "beating in unison" result.
This video is also available on another stream:
The opinions expressed in this video do not necessarily reflect the views of the Heidelberg Laureate Forum Foundation or any other person or associated institution involved in the making and distribution of the video.
More information to the Heidelberg Laureate Forum:
Myocites, a class of heart cells, when put into a petri dish will oscillate independently, but after some time, nearby cells will have similar oscillatory behavior. Our goal is to give a mathematical model of synchronization to help understand this phenomenon.
Important work on this subject goes back to Huygens more than 350 years ago (pre-Newton). More recently, Turing (morphogenesis), Winfree, and Strogatz, (a one-time post-doc of my student Nancy Kopell) made contributions to these studies.
Here we focus especially on the work of Kuramoto on the collective behavior of phases. We will give a geometric analysis of Kuramoto's ordinary differential equations. Starting from the graph Laplacian of the cellular architecture of the heart, and a "hard-wiring" hypothesis of the associated genome dynamics, we obtain a phase setting of Kuramoto equations to obtain a "beating in unison" result.
This video is also available on another stream:
The opinions expressed in this video do not necessarily reflect the views of the Heidelberg Laureate Forum Foundation or any other person or associated institution involved in the making and distribution of the video.
More information to the Heidelberg Laureate Forum:
0:37:08
0:53:34
0:43:14
0:54:03
1:50:52
0:47:20
1:36:17
1:08:27
0:55:21
0:45:08
2:41:26
0:44:41
0:01:22
1:19:11
1:17:06
0:25:29
0:00:23
0:38:39
0:47:53
1:17:07
0:00:12
0:14:57
0:11:10
0:14:24