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Let observations represent the features for the frames.
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Let the observations representing copy numbers in p genomic loci be y= y1,…, y p ), ordered according to genomic position.
Let the observations y 1 : M ∈ Y 1 : M with f Y 1 : M (y 1 : M ) > 0 be given.
In this first analysis, we have retained a large range of values for the entrainment coefficients (indeed, a larger range than found in existing experimental studies) to avoid discounting plausible values from the study, and have taken ranges for k s and k w and no further probability judgements to let the observations induce constraints.
Take the time to become fully aware of your surroundings and let your observations seep into your work.
Let the observation space be Y = L 2 ( 0, T ; H ) with H = L 2.
Let the observation vector x ~ ( n ) ∈ ℝ N, where x ~ ( n ) = [ x ~ ( n − 1 ) x ~ ( n − 1 ) ⋯ x ~ ( n − N ) ] T, be an incomplete version of x(n).
We now let the observation data (bar{u} x,t)=sinpi t sinpi x), and consider problem (2.1 - 2.2 2.1 - 2.2ct analytical solution: ubigl(q^{ast}bigr)=sinpi t sinpi x,qquad zbigl(q^{ast} bigr)=0,quad q^{ast}=0.
Let h index observations with x observed and j index observations with x missing.
It all works because he lets his observations lead the way.
This was decades before one was supposed to air such observations, let alone politics, in a Big Brother world.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com