[Amath-seminars] Thursday Seminar, 4-5pm Dem 104
Loyce M. Adams
lma3 at uw.edu
Tue Jan 17 14:48:35 PST 2017
Hi All,
The speaker in our first Thursday Seminar this quarter is Prof.
Zhaohua Wu from Florida State. Please see his title and abstract
below. See you there!
Loyce Adams
-----
Speaker: Professor Zhaohua Wu
Florida State University
Holo-spectrum: A Method for Quantifying Nonlinear Interactions Hidden
in a Time Series
The early usage of trigonometric functions can be traced back to at
least 17th century BC. It was Bhaskara II of the 12th century CE who
first proved the mathematical equivalence between the sum of two
trigonometric functions of any given angles and the product of two
trigonometric functions of related angles, which has been taught these
days in middle school classroom. The additive perspective of
trigonometric functions led to the development of the Fourier
transform that is used to express any functions as the sum of a set of
trigonometric functions and opened a new mathematical field called
harmonic analysis. Unfortunately, Fourier’s sum cannot directly
express nonlinear interactions between trigonometric components of
different periods, and thereby lacking the capability of quantifying
nonlinear interactions in dynamical systems.
In this talk, the speaker will introduce the Huang transform and
Holo-spectrum which were pioneered by Norden Huang and emphasizes the
multiplicative perspective of trigonometric functions in expressing
any function. Holo-spectrum is a multi-dimensional spectral expression
of a time series that explicitly identifies the interactions among
different scales and quantifies nonlinear interactions hidden in a
time series. Along with this introduction, the developing concepts of
physical, rather than mathematical, analysis of data will be
explained.
Various enlightening applications of Holo-spectrum analysis in
atmospheric and climate studies will also be presented.
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