ライフサイエンスコーパス: differential equation

1 corporating uncertainty through a stochastic differential equation.

2 ity levels from the corresponding stochastic differential equation.

3 n mathematics as a linear, parabolic partial-differential equation.

4 single variable problem of a diffusion-only differential equation.

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

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

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

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

9 ternatives consisting of up to 1000 ordinary differential equations.

10 which are typically studied through ordinary differential equations.

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

12 ten modeled using reaction-diffusion partial differential equations.

13 ulations are understood as coupled nonlinear differential equations.

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

15 atistical approaches and systems of ordinary differential equations.

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

17 thways successfully without solving ordinary differential equations.

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

19 itably modelled by stiff systems of ordinary differential equations.

20 oscopic state variables as an alternative to differential equations.

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

22 e.g., chemical reaction networks, stochastic differential equations.

23 the CYP1A biomarker, the model uses ordinary differential equations.

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

25 rk to tackle this difficulty using impulsive differential equations.

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

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

28 are classically modeled by means of ordinary differential equations.

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

30 perfectly mixed, and represented by ordinary differential equations.

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

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

33 systems are typically modelled by nonlinear differential equations.

34 implemented as systems of nonlinear ordinary differential equations.

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

36 ing 15 interacting reactions and 26 ordinary differential equations.

37 for a population of newts using a system of differential equations.

38 s the discretization and solution of partial differential equations.

39 tional algorithms based on discretization of differential equations.

40 gures the demonstrated problem into ordinary differential equations.

41 l as a system of coupled stochastic ordinary differential equations.

42 d the dynamics of T cell density via partial differential equations.

43 , expressed in terms of a system of ordinary differential equations.

44 tiotemporal dynamical evolution from partial differential equations.

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

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

47 outperforms its truncated rival and a delay differential equation alternative in recapitulating obse

48 [Formula: see text])-in a system of ordinary differential equations analogous to the Susceptible-Expo

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

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

51 nsists of a large system of coupled ordinary differential equations and algebraic equations.

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

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

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

55 We construct a model based on delay differential equations and parameterize and validate the

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

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

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

59 ow that an instance with 156 parameters, 144 differential equations, and 1,704 experimental data poin

60 problems with up to 2,352 parameters, 2,304 differential equations, and 20,352 data points in less t

61 atory mediators is described through partial differential equations, and immune cells (neutrophils an

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

63 matching approach has been proposed to solve differential equations approximately.

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

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

66 machine) that, when its non-linear ordinary differential equations are integrated numerically, shows

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

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

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

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

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

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

73 hey often involve highly nonlinear and stiff differential equations as well as many experimental data

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

75 The system of differential equations associated with the proposed cons

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

77 We limit our analysis to nonlinear differential equation based inference methods.

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

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

80 r competition using a system of two ordinary differential equations based on the Lotka-Volterra model

81 We used a differential-equation based poliovirus transmission and

82 In this work, we present an ODE (Ordinary Differential Equation)-based model of the expression of

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

84 An ordinary differential equation-based mathematical model was devel

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

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

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

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

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

90 networks is produced by a system of partial differential equations coupling landscape evolution dyna

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

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

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

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

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

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

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

98 l model, in the form of a system of ordinary differential equations, describing dynamics of platinum-

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

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

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

102 In our Ordinary Differential Equation examples the crossing of infinity

103 A stochastic differential equation for supersaturation predicts that

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

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

106 potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free C

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

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

109 ltine and Rawlings (HR), is a combination of differential equations for traditional deterministic mod

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

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

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

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

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

115 ily of methods for solving continuum partial differential equations has shown promise in realizing pa

116 the need for solving complex single-molecule differential equations has the potential to address some

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

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

119 rvation laws, which are expressed as partial differential equations in space and time.

120 aplace Approximation with Stochastic Partial Differential Equation, INLA-SPDE) is used to predict the

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

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

123 thm that incorporates the system of ordinary differential equations into the neural networks.

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

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

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

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

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

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

130 metry theory through Lokta-Volterra ordinary differential equations (LVODE) into an R-based computing

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

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

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

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

135 Here, we used an ordinary differential equation model for CML, which explicitly in

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

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

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

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

140 An ordinary differential equation model is developed and the antibio

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

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

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

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

145 We constructed an ordinary differential equation model of SHR and SCR in the QC and

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

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

148 d an agent-based model (ABM) and an ordinary differential equation model of tumor regression after ad

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

150 ks the position of individuals and a partial differential equation model that describes locust densit

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

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

153 ved in efficacy, here we develop an ordinary differential equation model that predicts bacterial grow

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

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

156 We also developed an ordinary differential equation model which is the Kolmogorov forw

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

158 mic trends more effectively than an ordinary differential equation model with generalized mass action

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

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

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

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

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

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

165 Here, we used a differential equations model of the signalling network t

166 circadian pattern of DNA replication, and a differential equations model that describes time-depende

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

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

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

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

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

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

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

174 Continuous differential equation models do not recapitulate this ph

175 Differential equation models have also been used to mode

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

177 Delay-differential equation models include lags but no variati

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

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

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

181 trophy and typical Alzheimer's disease using differential equation models.

182 tures intracellular dynamics through partial differential equation models.

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

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

185 blem appear in the form of nonlinear partial differential equations (NPDEs) against the conservation

186 rection of Smoluchowski's 1918 full Ordinary Differential Equation (ODE) approach to the PBM is anoth

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

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

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

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

191 Using a nonlinear ordinary differential equation (ODE) model that accounts for acti

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

193 In fact, commonly used ordinary differential equation (ODE) models of genetic circuits a

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

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

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

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

198 Most models of viral infections use ordinary differential equations (ODE) that reproduce the average

199 ults to solutions from a continuum, ordinary differential equations (ODE)-based model.

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

201 lutions of renovated boundary layer ordinary differential equations (ODEs) are attained by a proficie

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

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

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

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

206 Ordinary differential equations (ODEs) with polynomial derivative

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

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

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

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

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

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

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

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

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

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

217 gle S4 segment using the Langevin stochastic differential equation or the behavior of a population of

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

219 er of candidate models, including parametric differential equations or their corresponding non-parame

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

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

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

223 Reaction-diffusion partial differential equation (PDE) models have been only occasi

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

225 of the governing reaction-diffusion partial differential equation (PDE).

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

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

228 The partial differential equations (PDEs) are derived using the exte

229 The numerical solution of partial differential equations (PDEs) is challenging because of

230 Therefore, fitted ordinary differential equations provide a basis for single-trial

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

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

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

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

235 such as solving a linear system or solving a differential equation require a large number of computin

236 tz diffusion dynamics, which is a stochastic differential equation (SDE).

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

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

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

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

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

242 ameters embedded within a system of ordinary differential equations, similar to the well-known suscep

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

244 ferential expression analysis with in silico differential equation simulations to yield accurate, qua

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

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

247 e of cell-cycle-phase times, and an ordinary differential equation system to capture single-cell prot

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

249 ntionally, plant clock models have comprised differential equation systems based on Michaelis-Menten

250 ffExPy proposed ensembles of several minimal differential equation systems for each differentially ex

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

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

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

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

255 The ordinary differential equations that define this model were numer

256 We thereby obtain differential equations that describe how nonlinearity ca

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

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

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

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

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

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

263 causal models-state space models based upon differential equations-that can be used to distinguish s

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

265 uum limit of this model is a system of Delay Differential Equations, the analysis of which reveals cl

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

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

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

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

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

271 e multivariable problem of kinetic-diffusive differential equations to a single variable problem of a

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

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

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

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

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

277 nonlinear system of enzymatic functions and differential equations to mathematically model molecular

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

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

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

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

282 ion framework that enables us to compare the differential equation version with an agent-based versio

283 A mathematical model with one ordinary differential equation was used to estimate translation (

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

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

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

287 Ordinary differential equations were applied to describe the subs

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

289 ient description of the dynamics in terms of differential equations which capture the statistics of t

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

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

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

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

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

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

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

297 as an optimal control problem for stochastic differential equations with jumps.

298 t the system-level lead to a set of ordinary differential equations with many unknown parameters that

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

300 ical processes are often modeled by ordinary differential equations with unknown parameters.