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SUMMARY:Marty Golubitsky (Ohio State University)
DTSTART:20231214T163000Z
DTEND:20231214T170000Z
DTSTAMP:20260421T124113Z
UID:MoRN/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MoRN/86/">Ho
 meostasis in Input-Output Networks</a>\nby Marty Golubitsky (Ohio State Un
 iversity) as part of Seminar on the Mathematics of Reaction Networks\n\n\n
 Abstract\nA typical example of homeostasis occurs in warm-blooded mammals 
 where the animal’s internal body temperature $x_o$ is held approximated 
 constant on variation of the external ambient temperature I.\n\nOur mathem
 atical study of homeostasis focuses on networks of differential equations.
  First\, we assume that the network has an input node $(x_i)$\, an output 
 node $(x_o)$ \, and a set of n regulatory nodes $(x_{r_1}\, …\, x_{r_n})
 $ where only the input node depends explicitly on an external ambient para
 meter $I$. Second\, we assume that there exists a stable equilibrium that 
 leads to an input-output function $x_o(I)$. Third\, we replace homeostasis
  (where the output is held approximately constant on variation of $I$) by 
 infinitesimal homeostasis (where the derivative $(dx_o/dI)$ vanishes).\n\n
 We use graph theoretic methods to classify infinitesimal homeostasis. Firs
 t\, we show that there are three kinds of three-node network motif (feedfo
 rward loops\, substrate inhibition\, and negative feedback loops) each of 
 which leads to a different kind of homeostasis. Second\, we show that ever
 y network leads to a unique set of possible patterns of infinitesimal home
 ostasis.  Where possible\, we illustrate our results through example.\n
LOCATION:https://researchseminars.org/talk/MoRN/86/
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