master equation models

USAGE SUMMARY

The phrase "master equation models" is correct and usable in written English.
It can be used in contexts related to mathematical modeling, physics, or systems theory where one discusses models based on master equations. Example: "The research focused on developing master equation models to better understand the dynamics of the system."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

5 human-written examples

As is thoroughly discussed in [5] establishing the connection between master equation models and mean field equations involves two limit procedures.

The Journal of Mathematical Neuroscience

MSMs are discrete-time master equation models which describe a biomolecule's conformational and energy landscape as a set of distinct structures and the short transitions between them.

Wikipedia

Fine-scale modeling of genetic regulatory networks using stochastic master equation models entails a huge computational complexity and Karim et al. [ 5] presents a computationally inexpensive way to generate the steady state distributions for stochastic master equation models.

BMC Genomics

For macroscopic KMC this table contains processes and input parameters similar to those in rate equation and master equation models.

Chemical Reviews

Since the likelihood of revisiting a site decreases with the number of nearest neighbors, more H2 is formed for surfaces with a higher coordination number, although still less than predicted by the rate equation and master equation models.

Chemical Reviews

Human-verified similar examples from authoritative sources

Similar Expressions

54 human-written examples

Asumming the reaction system is in well-stirred condition with a fixed volume, we can introduce the master equation model, also known as "chemical master equation (CME)" in the biochemical modeling field [ 26], which describe the time evolution of the state probability using a set of ordinary differential equations.

BMC Systems Biology

Section 2 describes the chemical master equation model of a gene regulatory network and its approximation by a chemical Langevin equation.

EURASIP Journal on Advances in Signal Processing

The results were compared to a master equation model.

Chemical Reviews

In the master equation model, all CO molecules appear to be converted almost immediately to methanol, while in the rate equation model the conversion occurs much later.

Chemical Reviews

A reasonable agreement with ice observations was obtained, better than for the master equation model, and this agreement improved with the lateral interactions switched on.

Chemical Reviews

The relative occupancy of the different configurations was calculated using a Master equation model, with transitions between configurations carried out by the binding of the enzyme RP, to a single domain or two adjacent domains.

BMC Systems Biology

Expert writing Tips

Best practice

When describing a specific application of "master equation models", specify the type of system being modeled (e.g., chemical, biological, physical) to provide context for the reader.

Common error

Avoid using "master equation models" as a blanket term without specifying the context or type of system. This can lead to confusion and a lack of clarity in scientific writing.

Linguistic Context

The phrase "master equation models" functions as a noun phrase, specifically identifying a category of mathematical models. As indicated by Ludwig, it's a correct and usable term. Examples show its use in describing models in biomolecular dynamics and genetic regulatory networks.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Ludwig's WRAP-UP

The phrase "master equation models" is a grammatically correct noun phrase primarily used in scientific contexts to describe a specific class of mathematical models used to simulate stochastic processes. Ludwig AI confirms its usability. The phrase appears mainly in scientific publications, and related terms include "chemical master equation models" and "stochastic master equation models". When writing about "master equation models", it's important to specify the type of system to which they are applied for clarity.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

chemical master equation models

Specifies the type of master equation models used, focusing on chemical systems.

stochastic master equation models

Highlights the stochastic nature of the master equation models, emphasizing randomness.

kinetic master equation models

Indicates that the master equation models are used in kinetic studies.

master equation approach

Focuses on the general method rather than specific models.

rate equation models

Emphasizes the rate equations as a form of modeling.

kinetic models

Broader term for models describing kinetics, not specific to master equations.

mathematical models

General term that includes "master equation models" but is far less specific.

computational models

Highlights the computational aspect of the modeling.

statistical models

Focuses on the statistical characteristics of the models.

simulation models

Describes models used for simulation purposes.

FAQs

How are "master equation models" used in scientific research?

"Master equation models" are used to describe the time evolution of a system's probability distribution, particularly in stochastic systems. They find applications in various fields, including chemical kinetics, population dynamics, and neuroscience.

What are the advantages of using "master equation models" compared to other modeling approaches?

"Master equation models" can capture the stochastic nature of systems, which deterministic models may overlook. This is particularly important when dealing with small populations or when fluctuations play a significant role. Furthermore, they can be linked to microscopic Markov models.

What is the difference between "master equation models" and "rate equation models"?

"Master equation models" describe the probability of being in a certain state at a certain time. "Rate equation models", on the other hand, describe the rate of change of the average population size. Master equations are typically used to model stochastic systems, while rate equations are often used to model deterministic systems.

How do you solve "master equation models"?

Solving "master equation models" can be done analytically for simple systems or numerically using techniques like the Gillespie algorithm or finite state projection. The complexity of the solution depends on the dimensionality of the state space and the nature of the transition rates.