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CATEGORIES:CUED Control Group Seminars
SUMMARY:Who’s Afraid of Fractional Order Laplace? - Clara
Ionescu\, Ghent University
DTSTART;TZID=Europe/London:20150408T140000
DTEND;TZID=Europe/London:20150408T150000
UID:TALK57914AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/57914
DESCRIPTION:We are now in the pioneering position where clinic
ians with their stethoscopes poised over the healt
hy heart\, radiologists tracking the blood flow\,
and physiologists probing the nervous system\, are
all exploring the frontiers of chaos and fractals
. Two concepts are necessary to be introduced: a)
chaos theory says that a very minor disturbance in
initial conditions leads to an entirely different
outcome\; and b) fractals are self-similar struct
ures on many or all scales (i.e. the principle of
regularity and order) [1\,2\,3]. These topics are
central concepts in the new discipline of nonlinea
r dynamics developed in physics and mathematics –
see Figure 1.\n\nHowever\, the most compelling app
lications of these abstract concepts are not in th
e physical sciences [4]\, but in medicine\, where
fractals and chaos may change radically long-held
views about order and variability in health and di
sease [5]. A transition to a more ordered or less
complicated state may be an indicative of disease
(or equivalent a change in the nominal activity).
Investigators have\, only in the past 5 years or s
o\, discovered that the heart and other physiologi
cal systems may behave most erratically when they
are young and healthy (i.e. random fractal propert
ies\, power law dynamics\, can be well characteriz
ed by cascaded impedance models). Counter-intuitiv
ely\, increasingly regular dynamic patterns accomp
any aging and disease (i.e by using Fourier analys
is tools one can detect these locked dynamics) [6\
,7\,8].\n\nThe last decades have shown an increase
d interest in the research community to employ par
ametric model structures of fractional-order for a
nalyzing nonlinear biological systems [8]. The con
cept of fractional-order (FO) -- or non-integer or
der -- systems refers to those dynamical systems w
hose model structure contains arbitrary order deri
vatives and/or integrals [9\,10\,11]. The dynamica
l systems whose model can be approximated in a nat
ural way using FO terms\, exhibit specific feature
s: viscoelasticity\, diffusion and fractal structu
re [12\,13\,14].\n \nHowever\, the theoretical con
cepts of fractals\, chaos and multiscale analysis
have not yet been enabled breakthrough mainly due
to a lack of awareness within the research communi
ty.\n\nFor further details of the speaker and deta
ils of referenced work\, see http://www-control.en
g.cam.ac.uk/Main/ControlSeminarSlides or contact <
a href="http://talks.cam.ac.uk/user/show/33890">Ti
m Hughes.
LOCATION:Cambridge University Engineering Department\, LR3B
CONTACT:Tim Hughes
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