Index of papers in PLOS Comp. Biol. that mention
• differential equation
Jorge G. T. Zañudo, Réka Albert
 Supporting Information Translating the logical network models into ordinary differential equation models, and intervention target validation for the ordinary differential equation models. Supporting Information Validation of the intervention targets in Table 1 for the T -LGL leukemia differential equation network model and single interventions from control sets with more than one node in Table 1 for the T -LGL leukemia differential equation network model. Supporting Information Validation of the stable motif control intervention targets in Table 2 for the helper T cell differential equation network model. The control targets transcend the logical modeling framework To address this, we translate the studied Boolean network models into ordinary differential equation (ODE) models using the method described by Wittmann et al.
differential equation is mentioned in 6 sentences in this paper.
Topics mentioned in this paper:
Matthew Hartfield, Samuel Alizon
 Comparing pathogen growth against death rate If there are two strains spreading concurrently, the deterministic rate of change of immunity, y, and the second strain x2, is given by the following set of differential equations: Comparing pathogen growth against death rate This can be seen by forming dxz / dy as before, and after substituting either (p2 —> (p2 c or 02 —> az/c, one sees that each transformation results in the same rescaled differential equation (Section 3 of 81 Text): Model outline Our analytical approach involves using a set of deterministic differential equations to ascertain pathogen spread in a stochastic birth-death process, where an infection (or immune cell) can only either die or produce 1 offspring. Model outline By dividing Equation 1 by Equation 2, we obtain a differential equation for x1 as a function of y: Model outline This differential equation is straightforward to solve (Section 1 of 81 Text), and yields the following function for x1(y): Supporting Information In-depth mathematical analyses of the differential equations used, and how to derive the emergence probability if affected by immune growth (Equation 10 in the main text).
differential equation is mentioned in 6 sentences in this paper.
Topics mentioned in this paper:
Lorenza A. D’Alessandro, Regina Samaga, Tim Maiwald, Seong-Hwan Rho, Sandra Bonefas, Andreas Raue, Nao Iwamoto, Alexandra Kienast, Katharina Waldow, Rene Meyer, Marcel Schilling, Jens Timmer, Steffen Klamt, Ursula Klingmüller
 Abstract By combining time-resolved quantitative experimental data generated in primary mouse hepatocytes with interaction graph and ordinary differential equation modeling, we identify and experimentally validate a network structure that represents the experimental data best and indicates specific crosstalk mechanisms. Experimental Prediction of Ordinary differential equation (ODE) modeling utilizes the entire information of the time resolved data. Introduction To analyze the impact of crosstalk and feedback regulation, dynamic modeling approaches using coupled ordinary differential equations (ODEs) are most suited and allow quantitative insights [24, 35—38]. Ordinary differential equation model selection Ordinary differential equation model selection Ordinary differential equation modeling Ordinary differential equation modeling
differential equation is mentioned in 5 sentences in this paper.
Topics mentioned in this paper:
Alejandro Torres-Sánchez, Jesús Gómez-Gardeñes, Fernando Falo
 Abstract This framework allows us to formulate the essential dynamical ingredients of the genetic circuit of a single cyanobacterium into a set of differential equations describing the time evolution of the concentrations of the relevant molecular products. Methods (16) is a set of stochastic differential equations (SDE) so its numerical integration requires generating a statistical representative trajectory for a discrete set of time-values. Regulatory equations In this section we translate the genetic circuit previously described into a set of differential equations , for Which we follow the derivation in [46—48]. Regulatory equations Finally we introduce the differential equations governing cyanobacterial reaction to nitrogen deprivation. Strains of cyanobacteria. Heterocyst patterns We used a Runge-Kutta method for the numerical integration of stochastic differential equations
differential equation is mentioned in 5 sentences in this paper.
Topics mentioned in this paper:
Rodrigo Cilla, Vinodh Mechery, Beatriz Hernandez de Madrid, Steven Del Signore, Ivan Dotu, Victor Hatini
 Adherens Junction Segmentation The time needed to travel from each point x E Voronoi(v) to the verteX v is found as the solution to the partial differential equation : with boundary condition T (v) = O. Adherens Junction Segmentation This equation is a well known partial differential equation known as the Eikonal equation. Introduction [15, 16] have built a Partial Differential Equation framework to filter image noise, segment cell nuclei, locate the cell membrane and model the evolution of cell shapes to track the cells. Introduction A 2D simplification of the 3D Partial Differential Equation framework introduced in [15] has been reported in [22].
differential equation is mentioned in 4 sentences in this paper.
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