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UID:6ba51518921c076783460437868a0ac6
CATEGORIES:Applied and Computational Math Seminar
CREATED:20230125T004659
SUMMARY:Rigorous topological dynamics for Gaussian processes and Brownian motion
LOCATION:Hill 705
DESCRIPTION:<div style="border: 0px; font-style: normal; font-weight: 400; font-size: 1
 6px; line-height: inherit; font-family: Calibri, Arial, Helvetica, sans-ser
 if; margin: 0px; padding: 0px; vertical-align: baseline; color: #000000; le
 tter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text
 -transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span
  style="border: 0px; font-style: inherit; font-variant: inherit; font-weigh
 t: inherit; font-size: 12pt; line-height: inherit; font-family: Calibri, Ar
 ial, Helvetica, sans-serif; margin: 0px; padding: 0px; vertical-align: base
 line; color: black; background-color: white;">We consider the problem of un
 derstanding a dynamical system via finite samples of that system.&nbsp; The
  most straightforward approach to addressing this problem is to use the dat
 a to generate a model and then analyze the dynamics of that model using sta
 ndard techniques.&nbsp; However, because long term dynamics may qualitative
 ly change under arbitrarily small perturbations of a system it is unclear h
 ow reliable the conclusions that we arrive at in this manner will be; that 
 is, it is difficult to quantify the probability that the predictions we mak
 e are correct.&nbsp;&nbsp;<br aria-hidden="true"></span></div><div style="b
 order: 0px; font-style: normal; font-weight: 400; font-size: 16px; line-hei
 ght: inherit; font-family: Calibri, Arial, Helvetica, sans-serif; margin: 0
 px; padding: 0px; vertical-align: baseline; color: #000000; letter-spacing:
  normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: n
 one; white-space: normal; widows: 2; word-spacing: 0px;"><span style="borde
 r: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; f
 ont-size: 12pt; line-height: inherit; font-family: Calibri, Arial, Helvetic
 a, sans-serif; margin: 0px; padding: 0px; vertical-align: baseline; color: 
 black; background-color: white;"></span></div><div style="border: 0px; font
 -style: normal; font-weight: 400; font-size: 16px; line-height: inherit; fo
 nt-family: Calibri, Arial, Helvetica, sans-serif; margin: 0px; padding: 0px
 ; vertical-align: baseline; color: #000000; letter-spacing: normal; orphans
 : 2; text-align: start; text-indent: 0px; text-transform: none; white-space
 : normal; widows: 2; word-spacing: 0px;"><span style="border: 0px; font-sty
 le: inherit; font-variant: inherit; font-weight: inherit; font-size: 12pt; 
 line-height: inherit; font-family: Calibri, Arial, Helvetica, sans-serif; m
 argin: 0px; padding: 0px; vertical-align: baseline; color: black; backgroun
 d-color: white;">In recent work, Batko et al. address this problem by combi
 ning Gaussian processes with multivalued dynamics.&nbsp; This talk will dis
 cuss this general framework as well as considering the special case of a We
 iner process that is conditioned to pass through a finite set of points and
  the dynamics generated by iterating a sample path from this process.&nbsp;
  In both the general and special cases, topological techniques (Conley theo
 ry) are used to characterize the global dynamics and deduce the existence, 
 structure and approximate location of invariant sets. &nbsp;Most importantl
 y, these techniques determine the probability (or confidence) that this cha
 racterization is correct. &nbsp;</span></div>
CONTACT:Cameron Thieme
DTSTAMP:20260828T093431
DTSTART;TZID=America/New_York:20230131T110000
DTEND;TZID=America/New_York:20230131T120000
SEQUENCE:0
TRANSP:OPAQUE
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