Hello,
Just for clarification: Is it correct that the \theta coefficients in eq. (7) of the whitepaper also depend on i? Maybe an additional index would be helpful.
Best regards
Robert
Adding to the question: Do θj and θj,k in equation 7 of whitepaper vary with both 'i' (i=1,2,.....d) and time 't'?
Thanks
Hi Robert,
thank you for your question. The F_1,...,F_12 functions that define the ODE systems are all members of the \mathcal{F}-class of functions which is defined in Equation (7), though the \theta_j and \theta_j,k coefficients may be different between systems. The \theta_j and \theta_j,k coefficients are all real numbers and do not vary over time (t).
We hope this helps!
Søren
Posted by: LearningByDoing @ July 12, 2021, 6:26 a.m.Hi Søren,
Thank you very much for your reply.
Each F \in \mathcal{F} has d components and the definition in (7) states
F_i(Z) = \sum_{j=1}^d \theta_j Z_j + \sum_{k,j=1}^d \theta_{j,k} Z_j Z_k for i = 1,\dots,d
It would be possible that \theta_j and \theta_{j,k} are indeed independent of i, but I suppose that the coefficients also depend on i. Is this correct?
Robert
Posted by: rho1101 @ July 12, 2021, 6:41 a.m.Hi Robert,
I misunderstood your question - thanks for getting back. Yes, the theta coefficients may indeed be different between coordinate functions of F (indexed by i in Equation (7)). We will change the notation to make this clear in an updated version of the white paper).
Søren
Posted by: LearningByDoing @ July 12, 2021, 6:58 a.m.So just to be clear, you have made sure that the thetas used to generate the data actually satisfy all physical constraints?
Posted by: Funko @ July 13, 2021, 4:09 p.m.Thank you for the question. The thetas were derived using mass-action kinetics as described in the whitepaper.
We hope this helps.
Søren
Posted by: LearningByDoing @ July 13, 2021, 6:32 p.m.Thank you for the answer!
As a follow-up, are there any further assumptions which are not explicitly stated in the whitepaper? Is e.g. the Lotka-Volterra model part of the class of ODEs?
Posted by: Funko @ July 13, 2021, 6:56 p.m.It's important that all participants have access to the same information regarding the data-generating processes. For this reason, all details on the data-generating processes that are available to participants can be found in the whitepaper, tutorial, or starter kit. We gladly receive questions in these Forums, however, we will mostly be able to give specific answers when questions relate to technical issues or ask for clarification of statements found in the provided materials (e.g., in the case of typos).
Søren
Posted by: LearningByDoing @ July 13, 2021, 9:19 p.m.Great, thanks!
So I'm guessing that any further ambiguity in the white paper is intentional?
Posted by: Funko @ July 14, 2021, 7:26 a.m.