“…Motivation: The Systems Biology Markup Language (SBML) is currently supported by >230 software tools, among which 160 support numerical integration of ordinary differential equation (ODE) models. …”
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“…The accuracy of the parameter estimates is refined by iteratively increasing the accuracy of numerical integration using the model structure. As a case study, we applied our framework to four gene circuit models with complex dynamics based on three synthetic datasets and one time series microarray data set. …”
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“…The drawback of the MAJ model is that numerical integration must be used to estimate the resulting ACPDvD. …”
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“…The use of ensemble kinetics and numerical integration unraveled how the antibiotic targets molecular motions within the ribosome-EF-G complex.…”
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“…A mode shape formulation is used for the cantilever dynamics that allows the generalized mass to be the actual mass at the first resonant frequency, removing the need for numerical integration in the design process. Results are presented in the form of physical insight from the model structure and also numerical evaluations of the model to provide trends in dynamic EMCF with actuator design parameters. …”
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“…Even greater accuracy is achieved with fitting the raw data directly by numerical integration of the rate equations rather than using analytically derived equations. …”
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“…In the presence of gravity or other external fields, liquid surface curvature deviates from a spherical shape and the surface configuration can be found by numerical integration of the Young–Laplace equation and the typical initial point for integration is the apex of the interface. …”
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“…In any case the problem of evaluating an option price can be considered as a numerical integration problem. For the purposes of modelling and complexity reduction, one should make the distinction between the model nominal dimension and its effective dimension. …”
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“…Beginning in 2013, the Merz research group addressed this cost with the introduction of a novel sampling methodology termed “Movable Type” (MT). Using numerical integration methods, the MT method reduces the computational expense for energy state sampling by independently calculating each atomic partition function from an initial molecular conformation in order to estimate the molecular free energy using ensembles of the atomic partition functions. …”
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“…The ingredients of the new algorithm include the definition of the mass operator, the equations for the Hamiltonian flow, the (approximate) numerical integration of the evolution equations, and finally, the Metropolis–Hastings acceptance rule. …”
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“…The integrals can be evaluated using numerical integration methods, but it requires a large computational cost in some cases, so an efficient algorithm plays an important role in solving the physics problems. …”
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“…We addressed the neuronal signatures of the numerical integration using an EEG technique tagged at the frequency of visual stimulation. …”
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“…Furthermore, the numerical integration of the flow allows the calculation of the total volume per breath (tidal volume), which clinicians use to identify trauma or lung capacity in the patient. …”
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“…Employing high-order numerical integration and fitting to burst statistics we enable efficient quantitative parameter estimation and discriminate models that assume noise in different reactions at the receptor level. …”
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“…Our implementation generates efficient code for the numerical integration of neuronal states and for the propagation of synaptic events on GPUs, making use of their massively parallel arithmetic capabilities. …”
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“…Start values for numerical integration were taken from measured data and analytical solutions of the differential growth equation. …”
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“…CONCLUSIONS: The knowledge of closed-form solutions allows to illustrate the differences between the different absorption models and minimizes the errors of numerical integration.…”
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“…These models utilise analytical approximations and numerical integration called Integrated Nested Laplace Approximations (INLA). …”
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“…To validate these decodings, we simulated affect processing by numerical integration of the true temporal sequence of neurally decoded derivatives for each subject and demonstrated that these decodings generate significantly less (p < 0.05) group-level simulation error than integration based upon decoded derivatives sampled uniformly randomly from the true temporal sequence. …”
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“…We propose a hybrid physics-informed machine learning approach that simulates dynamical responses by directly implementing numerical integration of principle-based governing equations through recurrent neural networks. …”
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