# Interpretable exact linear reductions via positivity

@inproceedings{Pogudin2021InterpretableEL, title={Interpretable exact linear reductions via positivity}, author={Gleb Pogudin and Xingjian Zhang}, booktitle={CMSB}, year={2021} }

Kinetic models of biochemical systems used in the modern literature often contain hundreds or even thousands of variables. While these models are convenient for detailed simulations, their size is often an obstacle to deriving mechanistic insights. One way to address this issue is to perform an exact model reduction by finding a self-consistent lower-dimensional projection of the corresponding dynamical system. Recently, a new algorithm CLUE [16] has been designed and implemented, which allows…

## One Citation

### On Realizing Differential-Algebraic Equations by Rational Dynamical Systems

- MathematicsISSAC
- 2022

Real-world phenomena can often be conveniently described by dynamical systems (that is, ODE systems in the state-space form). However, if one observes the state of the system only partially, the…

## References

SHOWING 1-10 OF 20 REFERENCES

### CLUE: Exact maximal reduction of kinetic models by constrained lumping of differential equations

- Computer ScienceBioinform.
- 2021

This work presents CLUE, an algorithm for exact model reduction of systems of polynomial differential equations by constrained linear lumping that computes the smallest dimensional reduction as a linear mapping of the state space such that the reduced model preserves the dynamics of user-specified linear combinations of the original variables.

### Maximal aggregation of polynomial dynamical systems

- Computer ScienceProceedings of the National Academy of Sciences
- 2017

An aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion).

### Exact model reduction of combinatorial reaction networks

- BiologyBMC Systems Biology
- 2008

This work provides techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization and discusses a new modeling approach that allows the direct generation of exactly reduced model structures.

### Efficient modeling, simulation and coarse-graining of biological complexity with NFsim

- BiologyNature Methods
- 2011

The Network-Free Stochastic Simulator (NFsim) is introduced, a general- Purpose modeling platform that overcomes the combinatorial nature of molecular interactions and enables researchers to simulate many biological systems that were previously inaccessible to general-purpose software.

### Internal coarse-graining of molecular systems

- Computer ScienceProceedings of the National Academy of Sciences
- 2009

This work presents a formal (and automated) method for constructing a coarse-grained and self-consistent dynamical system aimed at molecular patterns that are distinguishable by the dynamics of the original system as posited by the rules.

### ERODE: A Tool for the Evaluation and Reduction of Ordinary Differential Equations

- Computer ScienceTACAS
- 2017

ERODE supports two recently introduced, complementary, equivalence relations over ODE variables: forward differential equivalence yields a self-consistent aggregate system where each ODE gives the cumulative dynamics of the sum of the original variables in the respective equivalence class.

### Simplification of Mathematical Models of Chemical Reaction Systems.

- ChemistryChemical reviews
- 1998

The simulation, monitoring, and control of a complex chemical process benefit from the derivation of accurate and reliable reduced models tailored to particular process modeling tasks.

### Signaling through receptors and scaffolds: independent interactions reduce combinatorial complexity.

- BiologyBiophysical journal
- 2005

This analysis dissects a highly branched network into interacting pathways originated by protein complexes assembled on different sites of receptors and scaffolds and specifies when the temporal dynamics of any given microstate can be expressed using the product of the relative concentrations of individual sites.

### Approximation of Large-Scale Dynamical Systems

- Computer ScienceAdvances in Design and Control
- 2005

This paper presents SVD-Krylov Methods and Case Studies, a monograph on model reduction using Krylov methods for linear dynamical systems, and some examples of such reduction schemes.

### Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language

- Computer ScienceISSAC
- 2017

We introduce two new packages, Nemo and Hecke, written in the Julia programming language for computer algebra and number theory. We demonstrate that high performance generic algorithms can be…