3 research outputs found
Information Surfaces in Systems Biology and Applications to Engineering Sustainable Agriculture
Systems biology of plants offers myriad opportunities and many challenges in
modeling. A number of technical challenges stem from paucity of computational
methods for discovery of the most fundamental properties of complex dynamical
systems. In systems engineering, eigen-mode analysis have proved to be a
powerful approach. Following this philosophy, we introduce a new theory that
has the benefits of eigen-mode analysis, while it allows investigation of
complex dynamics prior to estimation of optimal scales and resolutions.
Information Surfaces organizes the many intricate relationships among
"eigen-modes" of gene networks at multiple scales and via an adaptable
multi-resolution analytic approach that permits discovery of the appropriate
scale and resolution for discovery of functions of genes in the model plant
Arabidopsis. Applications are many, and some pertain developments of crops that
sustainable agriculture requires.Comment: 24 Pages, DoCEIS 1
On the Geometry of Maximum Entropy Problems
We show that a simple geometric result suffices to derive the form of the
optimal solution in a large class of finite and infinite-dimensional maximum
entropy problems concerning probability distributions, spectral densities and
covariance matrices. These include Burg's spectral estimation method and
Dempster's covariance completion, as well as various recent generalizations of
the above. We then apply this orthogonality principle to the new problem of
completing a block-circulant covariance matrix when an a priori estimate is
available.Comment: 22 page