ライフサイエンスコーパス: ordinary differential equation

1 been almost exclusively modelled by using an ordinary differential equation.

2 ng back to the lungs is calculated from this ordinary differential equation.

3 We model the HDX with a system of ordinary differential equations.

4 ons between genes as a system of first-order ordinary differential equations.

5 ining FBA with regulatory Boolean logic, and ordinary differential equations.

6 models of biochemical systems defined using ordinary differential equations.

7 teractions cannot be directly implemented as ordinary differential equations.

8 ed using analytical solutions to a system of ordinary differential equations.

9 of the model are described by a system of 50 ordinary differential equations.

10 tions that are translated by Cellerator into ordinary differential equations.

11 hich are typically represented as systems of ordinary differential equations.

12 on throughout the tumor volume via a pair of ordinary differential equations.

13 no longer satisfy the uniqueness theorem for ordinary differential equations.

14 urrent alternatives consisting of up to 1000 ordinary differential equations.

15 cations, which are typically studied through ordinary differential equations.

16 using statistical approaches and systems of ordinary differential equations.

17 dicted pathways successfully without solving ordinary differential equations.

18 also to any system that can be described by ordinary differential equations.

19 are inevitably modelled by stiff systems of ordinary differential equations.

20 l biology literature and defined as a set of ordinary differential equations.

21 e pathway and built a kinetic model based on ordinary differential equations.

22 species or model them with patchy models by ordinary differential equations.

23 assumed perfectly mixed, and represented by ordinary differential equations.

24 o represent the FIM in terms of solutions of ordinary differential equations.

25 c models implemented as systems of nonlinear ordinary differential equations.

26 xtracellular (multicellular) events by using ordinary differential equations.

27 isher information matrix to solving a set of ordinary differential equations.

28 VCell provides a number of ordinary differential equation and stochastic numerical

29 se theoretical models are generally based on ordinary differential equations and become intractable w

30 In CDSM, interactions are represented by ordinary differential equations and compared across cond

31 odeled the cortisol dynamics using nonlinear ordinary differential equations and estimated the kineti

32 ifferential equations, including subcellular ordinary differential equations and extracellular reacti

33 squares formulation that handles systems of ordinary differential equations and is implemented in Ma

34 valuated using data simulated with nonlinear ordinary differential equations and known cyclic network

35 ed a hybrid computational model comprised of ordinary differential equations and stochastic simulatio

36 Computations are presented using ordinary differential equations and stochastic spatial s

37 molecular mechanisms into sets of nonlinear ordinary differential equations and use standard analyti

38 suming (i) equilibrium of a linear system of ordinary differential equations, and (ii) deterministic

39 These ordinary differential equations are numerically solved b

40 The simultaneous first-order ordinary-differential equations are solved numerically f

41 The simultaneous first-order ordinary-differential equations are solved numerically f

42 ive assumptions and hypotheses formulated as ordinary differential equations) are separated from the

43 thematical model that is used to derive this ordinary differential equation assumes that the partial

44 Ordinary Differential Equation-based (ODE) models are us

45 An ordinary differential equation-based mathematical model

46 re studied using numerical simulations of an ordinary differential equation-based multi-compartment m

47 Deterministic models based on ordinary differential equations can capture essential re

48 ions and compare them to the solution of the ordinary differential equations described above.

49 ion kinetics have been limited to systems of ordinary differential equations describing spatially ave

50 , it is found that equilibrium properties of ordinary differential equations describing the dynamics

51 ycolytic metabolism with a system of coupled ordinary differential equations describing the individua

52 transduction pathways traditionally employs ordinary differential equations, deterministic models ba

53 In our Ordinary Differential Equation examples the crossing of

54 When the ordinary differential equation for the [Ca(2+)] in a res

55 essible to analysis by reduction to a set of ordinary differential equations for the amplitudes of sh

56 When these equations are coupled to ordinary differential equations for the bulk cytosolic a

57 sulting probability densities are coupled to ordinary differential equations for the bulk myoplasmic

58 This projection yields a system of ordinary differential equations for the spatio-temporal

59 The model is described by twelve ordinary differential equations for the time rate of cha

60 Instead, we derive and solve the systems of ordinary differential equations for the two lower-order

61 isting of low-dimensional systems of coupled ordinary differential equations, from these more complex

62 odule to reduce the generated mechanisms, an ordinary differential equations generator and solver to

63 we modeled the integrin signaling network as ordinary differential equations in multiple compartments

64 f-magnitude speedups relative to a CPU-based ordinary differential equation integrator.

65 parameter space of a parameterized system of ordinary differential equations into regions for which t

66 s/deterministic model, expressed as a set of ordinary differential equations, into a discrete/stochas

67 It is found that the solution of the ordinary differential equation is very different from th

68 Modeling of dynamical systems using ordinary differential equations is a popular approach in

69 Modeling of dynamical systems using ordinary differential equations is a popular approach in

70 Because our model comprises only 17 ordinary differential equations, its computational cost

71 The ordinary differential equation model also included blood

72 This ordinary differential equation model could be fit to bot

73 In this paper we present a simple ordinary differential equation model for wound healing i

74 e single-cell level, a mechanistic nonlinear ordinary differential equation model is used to calculat

75 s in combination with a previously validated ordinary differential equation model of apoptosis to sim

76 We consider a three-dimensional ordinary differential equation model of inflammation con

77 We developed an ordinary differential equation model of the infectious p

78 We here present a simple ordinary differential equation model of the intrahost im

79 We formulate a deterministic nonlinear ordinary differential equation model of the sterol regul

80 matory phase in more detail, we developed an ordinary differential equation model that accounts for t

81 In doing so, we derive an ordinary differential equation model that explores how t

82 tions of one or more cytokines to develop an ordinary differential equation model that includes the e

83 We developed an ordinary differential equation model to describe this be

84 in part on principal component analysis, an ordinary differential equation model was constructed, co

85 sed on the evolution of CML according to our ordinary differential equation model.

86 mouse hepatocytes with interaction graph and ordinary differential equation modeling, we identify and

87 We use stochastic and ordinary-differential-equation modeling frameworks to ex

88 The underlying system of ordinary differential equations, modelling the host-para

89 is based on the notion that all mechanistic ordinary differential equation models can be coupled wit

90 of rapid rebinding and show that well-mixed ordinary differential equation models can use this proba

91 this work we developed a series of nonlinear ordinary differential equation models that are direct re

92 article, a new hybrid algorithm integrating ordinary differential equation models with dynamic Bayes

93 ro bioluminescence experiments and in silico ordinary differential equation models, and will lead to

94 rtial differential equation model and not by ordinary differential equation models.

95 autonomous oscillations in yeast, we analyze ordinary differential equations models of large populati

96 ction networks): it builds dynamic (based on ordinary differential equation) models, which can be use

97 structed computationally by use of a coupled ordinary differential equation network (CODE) in a 2D la

98 Further reducing a 106-node ordinary differential equations network encompassing the

99 n (ASR) that identifies links among nodes of ordinary differential equation networks, given a small s

100 nd sensitivity analysis of large and complex ordinary differential equation (ODE) based models.

101 We built an ordinary differential equation (ODE) model describing pa

102 An ordinary differential equation (ODE) model further suppo

103 onte Carlo (MCMC) method for the sampling of ordinary differential equation (ode) model parameters.

104 ts are negligible and we modify the standard ordinary differential equation (ODE) model to accommodat

105 We previously developed a nonlinear ordinary differential equation (ODE) model to explain th

106 Finally, in the special case of linear ordinary differential equation (ODE) models, we explore

107 with cancer were developed with the help of ordinary differential equation (ODE) models.

108 pecific tool for building compartmentalized, ordinary differential equation (ODE) models.

109 differential equation models, and especially ordinary differential equation (ODE) models.

110 r the identification of links among nodes of ordinary differential equation (ODE) networks, given a s

111 C signal is cast explicitly as a first-order ordinary differential equation (ODE) with total titrant

112 Using ordinary differential equation (ODE)-based modeling, we

113 Two mathematical models, a system of ordinary differential equations (ODE) and a continuous-t

114 s reactions deterministically as a system of ordinary differential equations (ODE) and uses a Monte C

115 inty upon the estimation of parameters in an ordinary differential equations (ODE) model of a cell si

116 mic model, expressed in terms of a system of ordinary differential equations (ODE), developed by Stil

117 sentimental dynamics described by a group of ordinary differential equations (ODE).

118 Networks of coupled ordinary differential equations (ODEs) are the natural l

119 nd commonly described by Lotka-Volterra-type ordinary differential equations (ODEs) for continuous po

120 When coupled to ordinary differential equations (ODEs) for the bulk myop

121 Next, we derived ordinary differential equations (ODEs) from the data rel

122 In particular, the use of sets of nonlinear ordinary differential equations (ODEs) has been proposed

123 stochastic differential equations (SDEs) and ordinary differential equations (ODEs) that addresses th

124 The ordinary differential equations (ODEs) that describe the

125 We used ordinary differential equations (ODEs) to describe the t

126 Ordinary differential equations (ODEs) with polynomial d

127 ethods of modelling biochemical pathways are ordinary differential equations (ODEs), and logical/grap

128 thematical model, in the form of a system of ordinary differential equations (ODEs), governing cancer

129 ese approaches with detailed models based on ordinary differential equations (ODEs).

130 for creating and simulating models that use ordinary differential equations (ODEs).

131 represented by systems of coupled non-linear ordinary differential equations (ODEs).

132 iii) solving the non-linear stiff systems of ordinary differential equations (ODEs); (iv) bifurcation

133 tical model, in the form of a system of five ordinary differential equations, of the core of this con

134 of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm

135 Unlike previous models that are based on ordinary differential equations, our mathematical model

136 cient than population-based methods based on ordinary differential equations, partial differential eq

137 A local projection onto a system of ordinary differential equations predicts the consequence

138 Mechanistic models based on ordinary differential equations provide powerful and acc

139 stem, we have integrated a set of structured ordinary differential equations quantifying T7 replicati

140 teristic extensively for dynamic networks of ordinary differential equations ranging up to 30 interac

141 ractions, we have constructed a system of 29 ordinary differential equations representing different p

142 he partial differential equation, and so the ordinary differential equation should not be used if an

143 Our approach uses ordinary differential equations, solved implicitly and n

144 MANTIS wraps a C/C++ ordinary-differential equations system and Runge-Kutta s

145 tions that are translated by Cellerator into ordinary differential equations that are numerically sol

146 The model is composed of ordinary differential equations that connect the molecul

147 The ordinary differential equations that define this model w

148 nts can be calculated by solving a system of ordinary differential equations that depend only on the

149 system are characterized by four non-linear, ordinary differential equations that describe rates of c

150 model takes the form of a set of nonlinear, ordinary differential equations that describe the change

151 developed that solves a system of algebraic-ordinary differential equations that describe the phenom

152 el of the infection described by six coupled ordinary differential equations that describe the time c

153 We cast the master equation in terms of ordinary differential equations that describe the time e

154 is a four-dimensional, non-linear system of ordinary differential equations that describes the dynam

155 s a result, techniques that are based on the ordinary differential equation to calculate the mixed-ve

156 We have used a system of coupled ordinary differential equations to analyze the regulator

157 mpartmentalized model of RVF and the related ordinary differential equations to assess disease spread

158 a and formulated a compartmental model using ordinary differential equations to investigate how the c

159 We use a system of ordinary differential equations to investigate the separ

160 this protein, we introduced a new system of ordinary differential equations to model regulatory netw

161 We develop a system of ordinary differential equations to model the dynamics of

162 Here, using simple ordinary differential equations to represent phosphoryla

163 In this paper, we construct a model of ordinary differential equations to study the dynamics of

164 A system of ordinary differential equations was used to calculate pr

165 Ordinary differential equations were applied to describe

166 Mechanistic and semimechanistic ordinary differential equations were developed to descri

167 cancer cells in the body, using a system of ordinary differential equations which gives rates of cha

168 on the space of solutions to the associated ordinary differential equations which no longer satisfy

169 terms of coupled non-homogeneous first-order ordinary differential equations, which have a dynamic re

170 dynamic biological phenomena as solutions to ordinary differential equations, which, when parameters

171 , the model is constructed as a system of 10 ordinary differential equations with 27 parameters chara

172 Using a system of ordinary differential equations with a pair approximatio