Science topic

# Information Geometry - Science topic

This is a group for discussing information geometry. That is the field of study that uses tools from geometry to study statistics. Geometric methods can lead to greater insights in statistical estimation algorithms and understanding of various statistical tests from a new perspective. Will be of interest for geometers wishing to learn about statistics or vice versa.
Questions related to Information Geometry
Question
How those algorithms mentioned above performs if we consider a long DNA sequence as input. what actually happens and what will be the outcome?
It is a system designed to capture, store, manipulate, analyze, manage, and present spatial or geographic data.
Question
• Let (M,g,∇,J) be a Kaehlerian manifold with almost complex structure J and ∇ a torsion free affine connection of M. The dual (conjugate) connection ∇* of ∇ is defined by Xg(Y,Z)=g(∇XY,Z)+g(X,∇*YZ).
• The question is whether J is ∇*-parallel.
• A remark: ∇XJY=J∇*YZ.
Let (M,g,J) be an almost Hermitian manifold and ∇ a torsion free affine connection on M. Then we have:
g(JX,Y)+g(X,JY)=0.                   (1)
Using now (1) and the definition of the conjugate connection ∇* of ∇, namely
Xg(Y,Z)=g(∇XY,Z)+g(X,∇*YZ),     (2)
it follows easily that
g((∇zJ)X,Y)+g(X,(∇*ZJ)Y)=0.       (3)
Hence we derive from (3) that J is parallel with respect to ∇ if and only if J is parallel with respect to ∇*.
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