scholarly journals Metabolic regulation inferred from Jacobian and Hessian matrices of metabolic functions

2021 ◽  
Author(s):  
Thomas Naegele
Keyword(s):  
Quantitative Analysis ◽  
Regulatory Networks ◽  
Metabolic Regulation ◽  
Reaction Network ◽  
Sucrose Hydrolysis ◽  
Essential Information ◽  
Partial Derivatives ◽  
Metabolic Functions ◽  
Metabolite Concentrations ◽  
Derivatives Of

Quantitative analysis of experimental metabolic data is frequently challenged by non-intuitive, complex patterns which emerge from regulatory networks. Quantitative output of metabolic regulation can be summarised by metabolic functions which comprise information about dynamics of metabolite concentrations. They reflect the sum of biochemical reactions which affect a metabolite concentration. Derivatives of metabolic functions provide essential information about system dynamics. The Jacobian matrix of a reaction network summarises first-order partial derivatives of metabolic functions with respect to metabolite concentrations while Hessian matrices summarise second-order partial derivatives. Here, a simple model of invertase-driven sucrose hydrolysis is simulated and both Jacobian and Hessian matrices of metabolic functions are derived for quantitative analysis of kinetic regulation of sucrose metabolism. Based on previous experimental observations, metabolite dynamics are quantitatively explained in context of underlying metabolic functions. Their potential regulatory role during plant cold acclimation is derived from Jacobian and Hessian matrices.

Quantitative Analysis for SF6 and its Compositions in GIS

2012 ◽  
Vol 562-564 ◽  
pp. 1336-1339
Author(s):  
Hai Lun Wang ◽  
Jian Wei Shen
Keyword(s):  
Neural Network ◽  
Particle Swarm Optimization ◽  
Quantitative Analysis ◽  
Fault Diagnosis ◽  
Traditional Method ◽  
Particle Swarm ◽  
Prediction Errors ◽  
Swarm Optimization ◽  
Training Analysis ◽  
Derivatives Of

In this paper, a method for GIS equipment fault diagnosis by the analysis of volume fractions of the derivatives of SF6 gas inside GIS equipment is presented. For the method, based on the differential spectra method, a neural network model and the particle swarm optimization are used for training analysis of infrared spectra, to realize the quantitative analysis of specific derivatives. The experimental results show that the prediction errors obtained by particle swarm optimization training are markedly superior to prediction errors obtained using the traditional method.

Partial Derivatives of the Lambert Problem

2014 ◽  
Author(s):  
Nitin Arora ◽  
Ryan P. Russell ◽  
Nathan J. Strange
Keyword(s):  
Partial Derivatives ◽  
Lambert Problem ◽  
Derivatives Of

Perturbation theory and finite Markov chains

1968 ◽  
Vol 5 (2) ◽  
pp. 401-413 ◽  
Author(s):  
Paul J. Schweitzer
Keyword(s):  
Perturbation Theory ◽  
Markov Chain ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Fundamental Matrix ◽  
Transition Probabilities ◽  
Semi Group ◽  
Partial Derivatives ◽  
Finite Markov Chains ◽  
Derivatives Of

A perturbation formalism is presented which shows how the stationary distribution and fundamental matrix of a Markov chain containing a single irreducible set of states change as the transition probabilities vary. Expressions are given for the partial derivatives of the stationary distribution and fundamental matrix with respect to the transition probabilities. Semi-group properties of the generators of transformations from one Markov chain to another are investigated. It is shown that a perturbation formalism exists in the multiple subchain case if and only if the change in the transition probabilities does not alter the number of, or intermix the various subchains. The formalism is presented when this condition is satisfied.

scholarly journals ON A NONLOCAL PROBLEM FOR PARTIAL DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE

2020 ◽  
Vol 8 (2) ◽  
pp. 24-39
Author(s):  
V. Gorodetskiy ◽  
R. Kolisnyk ◽  
O. Martynyuk
Keyword(s):  
Cauchy Problem ◽  
Fundamental Solution ◽  
Parabolic Type ◽  
Generalized Functions ◽  
Initial Condition ◽  
Partial Derivatives ◽  
Time Problem ◽  
The Cauchy Problem ◽  
Space Of Generalized Functions ◽  
Derivatives Of

Spaces of $S$ type, introduced by I.Gelfand and G.Shilov, as well as spaces of type $S'$, topologically conjugate with them, are natural sets of the initial data of the Cauchy problem for broad classes of equations with partial derivatives of finite and infinite orders, in which the solutions are integer functions over spatial variables. Functions from spaces of $S$ type on the real axis together with all their derivatives at $|x|\to \infty$ decrease faster than $\exp\{-a|x|^{1/\alpha}\}$, $\alpha > 0$, $a > 0$, $x\in \mathbb{R}$. The paper investigates a nonlocal multipoint by time problem for equations with partial derivatives of parabolic type in the case when the initial condition is given in a certain space of generalized functions of the ultradistribution type ($S'$ type). Moreover, results close to the Cauchy problem known in theory for such equations with an initial condition in the corresponding spaces of generalized functions of $S'$ type were obtained. The properties of the fundamental solution of a nonlocal multipoint by time problem are investigated, the correct solvability of the problem is proved, the image of the solution in the form of a convolution of the fundamental solution with the initial generalized function, which is an element of the space of generalized functions of $S'$ type.

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