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Multiple phenotypes of resting-state cognition are altered in insomnia disorder
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stable isotopeassisted metabolic flux analysis mfa powerful method estimate carbon flow partitioning metabolic networks core mfa parameter estimation problem wherein fluxes metabolite pool sizes model parameters estimated via optimization account measurements steadystate isotopicallynonstationary isotope labeling patterns mfa problems advance scale require efficient computational methods fast robust convergence structure mfa problem enables cast equalityconstrained nonlinear program nlp equality constraints constructed mfa model equations objective function defined sum squared residuals ssr model predictions set labeling measurements nlp solved using algebraic modeling language aml offers stateoftheart optimization solvers robust parameter estimation superior scalability large networks implemented manner optimization performed distinction state variables model parameters iteration optimization system state updated instead calculated explicitly scratch occurs concurrently improvement model parameter estimates optimization approach starkly contrasts traditional shooting methods state variables model parameters kept distinct system state computed afresh iteration stepwise optimization nlp formulation uses mfa modeling framework wiechert et al 1 amenable incorporation model equations nlp nlp constraints consist balances either elementary metabolite units emus cumomers formulation steadystate isotopicallynonstationary mfa instmfa problems may solved nlp instmfa case ordinary differential equation ode system describing labeling dynamics transcribed system algebraic constraints nlp using collocation largescale nlp may solved efficiently using nlp solver implemented aml implementation used reduced gradient solver conopt implemented general algebraic modeling system gams nlp framework particularly advantageous instmfa scaling well large networks many free parameters robust convergence properties compared shooting methods compute system state sensitivities iteration additionally nlp approach supports use tandemms data steadystate instmfa cumomer framework used assembled software eiflux written python gams uses nlp approach supports steadystate instmfa demonstrate effectiveness nlp formulation several examples including genomescale instmfa model highlight scalability robustness approach addition typical instmfa applications expect framework associated software eiflux particularly useful applying instmfa complex mfa models developed eukaryotes eg algae cocultures multiple cell types