ライフサイエンスコーパス: differential equation

1 ity levels from the corresponding stochastic differential equation.

2 corporating uncertainty through a stochastic differential equation.

3 tiotemporal dynamical evolution from partial differential equations.

4 raction terms in a system of partial integro-differential equations.

5 thways successfully without solving ordinary differential equations.

6 any system that can be described by ordinary differential equations.

7 itably modelled by stiff systems of ordinary differential equations.

8 oscopic state variables as an alternative to differential equations.

9 it as a set of nonlinear coupled stochastic differential equations.

10 literature and defined as a set of ordinary differential equations.

11 pathways, and are based on simple non-linear differential equations.

12 and built a kinetic model based on ordinary differential equations.

13 or model them with patchy models by ordinary differential equations.

14 perfectly mixed, and represented by ordinary differential equations.

15 nt the FIM in terms of solutions of ordinary differential equations.

16 licable, because they hold for any system of differential equations.

17 systems are typically modelled by nonlinear differential equations.

18 implemented as systems of nonlinear ordinary differential equations.

19 lar (multicellular) events by using ordinary differential equations.

20 mics of root apical meristems, using Partial Differential Equations.

21 tate Markov jump process driving a system of differential equations.

22 ormation matrix to solving a set of ordinary differential equations.

23 , and I ended up numerically solving partial differential equations.

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

25 model is represented by a system of partial differential equations.

26 simulating an exponentially large number of differential equations.

27 en genes as a system of first-order ordinary differential equations.

28 ulting in a set of 6 minimally parameterized differential equations.

29 ct of cancer development through a system of differential equations.

30 ternatives consisting of up to 1000 ordinary differential equations.

31 which are typically studied through ordinary differential equations.

32 oupled two-phase two-layer system of partial differential equations.

33 ten modeled using reaction-diffusion partial differential equations.

34 circumvents the need for solving 12th order differential equations.

35 atistical approaches and systems of ordinary differential equations.

36 notypic formation as a cohesive system using differential equations, a different approach-systems map

37 is proposed to solve the temporal auxiliary differential equations (ADEs) with a high degree of effi

38 Differential equation and computational models were used

39 erface with support for arbitrary functions, differential equation and kinetic system integration, an

40 VCell provides a number of ordinary differential equation and stochastic numerical solvers f

41 tical models are generally based on ordinary differential equations and become intractable when consi

42 t and approximate solutions of the continuum differential equations and compare to kinetic Monte Carl

43 SM, interactions are represented by ordinary differential equations and compared across conditions th

44 e cortisol dynamics using nonlinear ordinary differential equations and estimated the kinetic paramet

45 using data simulated with nonlinear ordinary differential equations and known cyclic network topologi

46 the calculations such as the solving of the differential equations and of the associated sensitivity

47 id computational model comprised of ordinary differential equations and stochastic simulation.

48 Computations are presented using ordinary differential equations and stochastic spatial simulation

49 e group selection model by solving a partial differential equation, and that it is mathematically imp

50 ) equilibrium of a linear system of ordinary differential equations, and (ii) deterministic data.

51 model by designing and solving the system of differential equations, and obtaining computationally pr

52 Although partial differential equations are available to describe the spa

53 design and advanced numerical integration of differential equations are developed.

54 Both Petri nets and differential equations are important modeling tools for

55 be used even in cases where models based on differential equations are not applicable, for example,

56 The simultaneous first-order ordinary-differential equations are solved numerically for the co

57 The simultaneous first-order ordinary-differential equations are solved numerically for the re

58 only five state variables linked by integral-differential equations are sufficient to describe the on

59 ptions and hypotheses formulated as ordinary differential equations) are separated from the experimen

60 In this article, we show that the partial differential equations arising from classical elastic mo

61 unctional response, we here analyze a set of differential equations as well as simulations employing

62 The system of differential equations associated with the proposed cons

63 e and time, whereas existing models based on differential equations average over space and consequent

64 niques of these models can be classified as "differential equation based" (DE) or "agent based" (AB).

65 We show that a simple model of differential equations based on chemical kinetics accura

66 We used a differential-equation based poliovirus transmission and

67 Ordinary Differential Equation-based (ODE) models are useful when

68 th dynamic Bayesian network analysis, called Differential Equation-based Local Dynamic Bayesian Netwo

69 An ordinary differential equation-based mathematical model was devel

70 We used a differential equation-based model to characterize the dy

71 We used a differential equation-based model to simulate the dynami

72 a rule-based model into a reduced system of differential equations by exploiting the granularity at

73 e response, which can be modeled by a single differential equation, can by itself rapidly clear small

74 We show that a differential equation captures the details of the tempor

75 A set of first order, partial differential equations comprise the model and were solve

76 a system of partial differential and integro-differential equations containing a flux term to represe

77 te a system of biologically meaningful delay differential equations (DDEs) into functional mapping, a

78 se laws typically take the form of nonlinear differential equations depending on parameters; dynamica

79 modeled by a pair of first order, non-linear differential equations, derived from the Lotka-Volterra

80 A set of coupled first-order differential equations describes the exponential growth

81 Parameters derived from partial differential equation describing the process of gradient

82 ere exists an analytical solution of partial differential equations describing mass transfer in ACE.

83 ound that equilibrium properties of ordinary differential equations describing the dynamics in local

84 We propose a set of differential equations describing the dynamics of: (1) a

85 zig formalism is an effective tool to derive differential equations describing the evolution of a sma

86 metabolism with a system of coupled ordinary differential equations describing the individual metabol

87 a potential-like function using a stochastic differential equation description (Langevin/Fokker-Planc

88 be simulated using either the VCell partial differential equations deterministic solvers or the Smol

89 tion pathways traditionally employs ordinary differential equations, deterministic models based on th

90 r model using a displacement integro-partial differential equation (DiPDE) population density model.

91 whose behaviour is described by a system of differential equations driven by a latent stochastic pro

92 In our Ordinary Differential Equation examples the crossing of infinity

93 A stochastic differential equation for supersaturation predicts that

94 we reduce the problem to a single nonlinear differential equation for the luminal radius.

95 el has three components: a transient partial differential equation for the simultaneous diffusion and

96 This model is expanded into differential equations for five-site NMR chemical exchan

97 We introduce a system of differential equations for plasmid transfer in well-mixe

98 ramework based on reaction-diffusion partial differential equations for studying the dynamics of crim

99 we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse

100 consider a spatio-temporal model of partial differential equations for the NF-kappaB pathway, where

101 we derive and solve the systems of ordinary differential equations for the two lower-order moments o

102 ugh the use of mathematical models by way of differential equations, for example, reaction-diffusion

103 We developed a differential equation framework of cyst growth and emplo

104 tion from standard text files, conversion to differential equations, generating stand-alone Python so

105 reduce the generated mechanisms, an ordinary differential equations generator and solver to solve the

106 the framework of a nonlinear integro-partial differential equation governing biofluids flow in fractu

107 olutions for a system of n+1 coupled partial differential equations governing biomolecular mass trans

108 l approaches to cellular mechanisms based on differential equations, graph models, and other techniqu

109 hogonal dynamics equation which is a partial differential equation in a high dimensional space.

110 fast approximation of numerical solutions of differential equations in general.

111 d the integrin signaling network as ordinary differential equations in multiple compartments, and cel

112 e parsed by Pycellerator and translated into differential equations in Python, and Python code is aut

113 odel consists of a coupled system of partial differential equations in the partially healed region, w

114 de speedups relative to a CPU-based ordinary differential equation integrator.

115 space of a parameterized system of ordinary differential equations into regions for which the system

116 Modeling of dynamical systems using ordinary differential equations is a popular approach in the fiel

117 Modeling of dynamical systems using ordinary differential equations is a popular approach in the fiel

118 A system of nonlinear transient partial differential equations is solved numerically using cell-

119 l cast as a system of numerically integrated differential equations is the simplified, irreversible V

120 representing mycelia as a system of partial differential equations is used to simulate combat betwee

121 d model, posed as a set of nonlinear partial differential equations, is a continuous treatment of the

122 Because our model comprises only 17 ordinary differential equations, its computational cost is orders

123 The ordinary differential equation model also included blood pressure

124 only be described by such a complex partial differential equation model and not by ordinary differen

125 This ordinary differential equation model could be fit to both inflamm

126 Based on a stochastic differential equation model for a single genetic regulat

127 le acceleration and recruitment by forming a differential equation model for ATP mediated calcium-cel

128 of this study was to develop and validate a differential equation model for energy balance during pr

129 In this paper we present a simple ordinary differential equation model for wound healing in which a

130 We formulate a simple partial differential equation model in an effort to qualitativel

131 The methods are based on fitting a differential equation model incorporating the processes

132 A partial differential equation model is developed to understand t

133 cell level, a mechanistic nonlinear ordinary differential equation model is used to calculate the tra

134 In this article, we construct a partial differential equation model of a single colonic crypt th

135 ination with a previously validated ordinary differential equation model of apoptosis to simulate the

136 se experimental data, we developed a partial differential equation model of MYOF effects on cancer ce

137 Here, we show that a simple differential equation model of normalization explains th

138 ate an individual-based model and an integro-differential equation model of reversible phenotypic evo

139 We developed an ordinary differential equation model of the infectious process th

140 We here present a simple ordinary differential equation model of the intrahost immune resp

141 formulate a deterministic nonlinear ordinary differential equation model of the sterol regulatory ele

142 ase in more detail, we developed an ordinary differential equation model that accounts for two system

143 one or more cytokines to develop an ordinary differential equation model that includes the effect of

144 We used a partial differential equation model that postulates three morpho

145 formulated a minimal one-dimensional partial differential equation model that reproduced the range of

146 and validate a computational energy balance differential equation model to determine individual EI d

147 on principal component analysis, an ordinary differential equation model was constructed, consisting

148 We combine a mechanistic differential equation model with a nonparametric statist

149 n the development of a Monod-equation based, differential equation model, which produces computer sim

150 In the differential equation model, which treats virus and cell

151 iological systems is by creating a nonlinear differential equation model, which usually contains many

152 re for mixed-effects modeling with a partial differential equation model.

153 e evolution of CML according to our ordinary differential equation model.

154 xperimental data, resulting in a logic-based differential equation model.

155 We first derived a partial differential equations model of gas exchange on a small

156 First, we derive a differential equations model of midgut resizing and show

157 The resulting nonlinear differential equations model the biological outcome, in

158 In this article, we formulate a partial-differential-equation model to describe the interaction

159 For the second stage, a differential-equation model was formulated and solved nu

160 We also derived an integro-differential equation modeling a second, dynamic phase i

161 atocytes with interaction graph and ordinary differential equation modeling, we identify and experime

162 We use stochastic and ordinary-differential-equation modeling frameworks to examine var

163 In this review we present several differential equation models and assess their relative s

164 on the notion that all mechanistic ordinary differential equation models can be coupled with a laten

165 rebinding and show that well-mixed ordinary differential equation models can use this probability to

166 Continuous differential equation models do not recapitulate this ph

167 evaluate potentially vast sets of candidate differential equation models in light of experimental an

168 Delay-differential equation models include lags but no variati

169 estimates of transfer rates from mass-action differential equation models of plasmid population biolo

170 we developed a series of nonlinear ordinary differential equation models that are direct representat

171 a new hybrid algorithm integrating ordinary differential equation models with dynamic Bayesian netwo

172 We examine Boolean models, delay differential equation models, and especially ordinary di

173 inescence experiments and in silico ordinary differential equation models, and will lead to a better

174 Using partial differential equation models, new information can be gai

175 ferential equation model and not by ordinary differential equation models.

176 tures intracellular dynamics through partial differential equation models.

177 s oscillations in yeast, we analyze ordinary differential equations models of large populations of ce

178 We therefore propose two differential-equation models of dengue fever (DF) with d

179 works): it builds dynamic (based on ordinary differential equation) models, which can be used for mec

180 hat identifies links among nodes of ordinary differential equation networks, given a small set of obs

181 ivity analysis of large and complex ordinary differential equation (ODE) based models.

182 We built an ordinary differential equation (ODE) model describing pathway act

183 An ordinary differential equation (ODE) model further supported the

184 o (MCMC) method for the sampling of ordinary differential equation (ode) model parameters.

185 gligible and we modify the standard ordinary differential equation (ODE) model to accommodate age-of-

186 We previously developed a nonlinear ordinary differential equation (ODE) model to explain the dynamic

187 ally, in the special case of linear ordinary differential equation (ODE) models, we explore how wrong

188 cer were developed with the help of ordinary differential equation (ODE) models.

189 ool for building compartmentalized, ordinary differential equation (ODE) models.

190 ial equation models, and especially ordinary differential equation (ODE) models.

191 ntification of links among nodes of ordinary differential equation (ODE) networks, given a small set

192 is cast explicitly as a first-order ordinary differential equation (ODE) with total titrant concentra

193 Using ordinary differential equation (ODE)-based modeling, we show that

194 wo mathematical models, a system of ordinary differential equations (ODE) and a continuous-time Marko

195 the estimation of parameters in an ordinary differential equations (ODE) model of a cell signalling

196 al dynamics described by a group of ordinary differential equations (ODE).

197 Networks of coupled ordinary differential equations (ODEs) are the natural language f

198 ly described by Lotka-Volterra-type ordinary differential equations (ODEs) for continuous population

199 Next, we derived ordinary differential equations (ODEs) from the data relating the

200 cular, the use of sets of nonlinear ordinary differential equations (ODEs) has been proposed to model

201 The ordinary differential equations (ODEs) that describe the degradat

202 We used ordinary differential equations (ODEs) to describe the transcript

203 Ordinary differential equations (ODEs) with polynomial derivative

204 ed by systems of coupled non-linear ordinary differential equations (ODEs).

205 aches with detailed models based on ordinary differential equations (ODEs).

206 ting and simulating models that use ordinary differential equations (ODEs).

207 meshes and solvers for ordinary and partial differential equations (ODEs/PDEs).

208 attice IBM leads to a single partial integro-differential equation of the same form as proposed by Sh

209 scriptions to a model in terms of stochastic differential equations of Langevin type, which we use to

210 alleles, p(i),i=1,...,k, satisfy a system of differential equations of the form (1.2).

211 nuum mechanical model and associated partial differential equations of the GC model have remained lac

212 ed a previously developed model that employs differential equations of the main biochemical interacti

213 el, in the form of a system of five ordinary differential equations, of the core of this control syst

214 (in this case an advection-diffusion partial differential equation on a growing domain) which describ

215 plications of various definitions, we solved differential equations on the basis of mass balance prin

216 k-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provide

217 on ordinary differential equations, partial differential equations, or the Gillespie stochastic simu

218 s assay of the HIV protease, analyzed by the differential-equation oriented software package DYNAFIT.

219 e previous models that are based on ordinary differential equations, our mathematical model takes int

220 n population-based methods based on ordinary differential equations, partial differential equations,

221 The solution to the diffusion partial differential equation (PDE) that mimics the evolutionary

222 model converges to the solution of a partial differential equation (PDE).

223 Partial differential equations (PDE) were built to model a radia

224 This model couples macroscale partial differential equations posed over the tissue to microsca

225 Mechanistic models based on ordinary differential equations provide powerful and accurate mea

226 have integrated a set of structured ordinary differential equations quantifying T7 replication and an

227 extensively for dynamic networks of ordinary differential equations ranging up to 30 interacting node

228 we have constructed a system of 29 ordinary differential equations representing different phenotypes

229 s macroparasite model, which comprises three differential equations representing the host, attached p

230 The model, based on a system of differential equations, represents a useful tool to anal

231 Although the Lamm partial differential equation rigorously predicts the evolution

232 Stochastic Differential Equations (SDE) are often used to model the

233 he first model, posed as a set of stochastic differential equations (SDE), we propose that a simple b

234 We describe a system of stochastic differential equations (SDEs) which model the interactio

235 ntified using models described by stochastic differential equations (SDEs).

236 merical simulations of the governing partial differential equations, showing that concentration-depen

237 e applied to traditional ordinary or partial differential equation simulations as well as agent-based

238 Our approach uses ordinary differential equations, solved implicitly and numericall

239 ting capabilities of a deterministic partial differential equation solver with a popular particle-bas

240 In many stochastic partial differential equations (SPDEs) involving random coeffici

241 MANTIS wraps a C/C++ ordinary-differential equations system and Runge-Kutta solver int

242 ands out as the dispersive nonlinear partial differential equation that plays a prominent role in the

243 squares solution of simultaneous, nonlinear differential equations that account for free cortisol ap

244 nally demanding time stepping of the partial differential equations that are often used to model Ca(2

245 physical systems are described by nonlinear differential equations that are too complicated to solve

246 The model is composed of ordinary differential equations that connect the molecular functi

247 The ordinary differential equations that define this model were numer

248 We thereby obtain differential equations that describe how nonlinearity ca

249 the rate of dissociation: an analysis of the differential equations that describe the dissociation sh

250 The model is based on differential equations that describe the interactions of

251 onse, we derive a set of coupled first-order differential equations that describe the probability of

252 ast the master equation in terms of ordinary differential equations that describe the time evolution

253 method with a set of simultaneous nonlinear differential equations that described nuclear magnetic r

254 r-dimensional, non-linear system of ordinary differential equations that describes the dynamic intera

255 stem cell systems are based on deterministic differential equations that ignore the natural heterogen

256 se models are usually formulated in terms of differential equations that relate the growth rate of th

257 ped a mathematical model consisting of three differential equations that represent volumes of live oy

258 Here we show that a system of differential equations that support a subcritical Hopf b

259 y a closure ansatz to obtain a closed set of differential equations; that can become the basis for th

260 For Partial Differential Equations, the crossing of infinity may per

261 numerical solutions of the relevant partial differential equations, the effective particle model pro

262 ries of patient-specific iodine mass-balance differential equations, the solutions to which provided

263 iques from nonlinear dynamics and stochastic differential equation theories, providing a systematic f

264 model that starts from a well-known partial differential equation to describe the dithering of an at

265 examine the ability of each class of partial differential equation to support travelling wave solutio

266 alized model of RVF and the related ordinary differential equations to assess disease spread in both

267 ing approaches, we derive systems of partial differential equations to capture the evolution in space

268 roplets requires analysis by complex coupled differential equations to derive diffusion coefficients.

269 We developed a system of differential equations to describe acute liver injury du

270 c melanoma, we developed a set of stochastic differential equations to describe the dynamics of heter

271 f Ca(2+) and buffer and use these stochastic differential equations to determine the magnitude of [Ca

272 mulated a compartmental model using ordinary differential equations to investigate how the compound a

273 We use a system of ordinary differential equations to investigate the separate influ

274 tein, we introduced a new system of ordinary differential equations to model regulatory networks.

275 lving Navier-Stokes and diffusion-convection differential equations to optimize the coupling between

276 The mathematical model presented here uses differential equations to predict the effects of intrace

277 Network mapping makes use of a system of differential equations to quantify the rule by which tra

278 Here, using simple ordinary differential equations to represent phosphorylation, dep

279 ating steady states from simulating 3 x 2(n) differential equations to solving two algebraic equation

280 this paper, we construct a model of ordinary differential equations to study the dynamics of virus sh

281 A system of ordinary differential equations was used to calculate protein tur

282 By incorporating this relation in a partial differential equation, we demonstrate that this model co

283 the explicitly spatial nature of the partial differential equations, we are also able to manipulate m

284 Then, using stochastic differential equations, we assess statistical relationsh

285 From the differential equations, we derive two expressions for th

286 Ordinary differential equations were applied to describe the subs

287 Mechanistic and semimechanistic ordinary differential equations were developed to describe the ex

288 estigate the approximate dynamics of several differential equations when the solutions are restricted

289 k is supposed to be captured by a stochastic differential equation which has been a standard approach

290 presents a 13-dimensional system of delayed differential equations which predicts serum concentratio

291 We avoid the use of partial differential equations which typically appear in related

292 ives rise to 22 different classes of partial differential equation, which can include Allee kinetics

293 es, there are natural bases derived from the differential equations, which promote sparsity.

294 iological phenomena as solutions to ordinary differential equations, which, when parameters in them a

295 nty in the model topology through stochastic differential equations whose trajectories contain inform

296 A system of 16 non-linear, delay differential equations with 66 parameters is developed t

297 Using a system of ordinary differential equations with a pair approximation techniq

298 We adapted stochastic differential equations with diffusion approximation (a c

299 egulatory networks (GRN) can be described by differential equations with SUM logic which has been fou

300 blem for gene regulatory networks modeled by differential equations with unknown parameters, such as