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Morphisms of reaction networks that couple structure to function

Luca Cardelli
2014 BMC Systems Biology  
Conclusions: Structural similarity between reaction networks can be revealed by network morphisms, elucidating mechanistic and functional aspects of complex networks in terms of simpler networks.  ...  Results: We define morphisms (mappings) between reaction networks that establish structural connections between them.  ...  Attila Csikász-Nagy provided deep insights on cell cycle switches and other biological networks.  ... 
doi:10.1186/1752-0509-8-84 pmid:25128194 pmcid:PMC4236760 fatcat:dgnrlepd5bdw3owcuisf4mlfcy

Open Markov Processes and Reaction Networks [article]

Blake S. Pollard
2017 arXiv   pre-print
We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation.  ...  Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into  ...  Given an function f : S → S ′ , there is a function F (f ) : F (S) → F (S ′ ) that maps a reaction network on S to a reaction network on S ′ .  ... 
arXiv:1709.09743v2 fatcat:oryvrwxqvvg4nextwgimzi7mxe

A recipe for black box functors [article]

Brendan Fong, Maru Sarazola
2018 arXiv   pre-print
semantics that describes the properties of each network that can be observed externally, by composition, while discarding the internal structure.  ...  We then argue that the category of decorating data is a good setting in which to construct any hypergraph functor, giving a new construction of Baez and Pollard's black box functor for reaction networks  ...  Concentrations and flows require different Frobenius structures to describe how they transform under coupling of reaction networks: we set concentrations equal, and add their flows.  ... 
arXiv:1812.03601v1 fatcat:w2pivxeekffmdhxcmlabvibhzq

Network Models from Petri Nets with Catalysts [article]

John C. Baez, John Foley, Joe Moeller
2019 arXiv   pre-print
This network model maps any list of catalysts from the chosen set to the category whose morphisms are all the processes enabled by this list of catalysts.  ...  Here we show how to combine them using the concept of a "catalyst": an entity that is neither destroyed nor created by any process it engages in.  ...  JB also thanks the Centre for Quantum Technologies, where some of this work was done.  ... 
arXiv:1904.03550v3 fatcat:ukz26w76bndzfg2tzifoxeact4

Network Models from Petri Nets with Catalysts

John C. Baez, John Foley, Joe Moeller
2019 Compositionality  
This network model maps any list of catalysts from the chosen set to the category whose morphisms are all the processes enabled by this list of catalysts.  ...  Here we show how to combine them using the concept of a 'catalyst': an entity that is neither destroyed nor created by any process it engages in.  ...  JB also thanks the Centre for Quantum Technologies, where some of this work was done.  ... 
doi:10.32408/compositionality-1-4 fatcat:5psadggdq5cghbpruzoer45id4

What is Applied Category Theory? [article]

Tai-Danae Bradley
2018 arXiv   pre-print
(functorial semantics and compositionality), two constructions (monoidal categories and decorated cospans) and two examples (chemical reaction networks and natural language processing) within the field  ...  This is a collection of introductory, expository notes on applied category theory, inspired by the 2018 Applied Category Theory Workshop, and in these notes we take a leisurely stroll through two themes  ...  reaction networks is also being used to model ATP coupling!  ... 
arXiv:1809.05923v2 fatcat:b4gwk5ywh5ddlfpcxxbzoovpge

Cognitive Topology Mapping based on HumanComputer Interaction

Meng Shimin, Cheng Rengui, Liu Yonglin
2013 Journal of Internet Technology and Secured Transaction  
Preliminary results of this study confirmed that Cognitive coupling is feasible way to Brain imaging of cognitive information.  ...  We tried to use the coupling cognitive research framework in a word memory. Assuming the brain state of English word to the existence of complex networks, explore the network activity model of word.  ...  We're trying to get the word cognitive network specific topology with coupling, get the word complex network of brain activity patterns.  ... 
doi:10.20533/jitst.2046.3723.2013.0017 fatcat:imtgf3tzcbejpgni7ebzjja5z4

Abstract hierarchical graph transformation

GIORGIO BUSATTO, HANS-JÖRG KREOWSKI, SABINE KUSKE
2005 Mathematical Structures in Computer Science  
Received In this paper, we introduce a new hierarchical graph model to structure large graphs into small components by distributing the nodes (and edges likewise) into a hierarchy of packages.  ...  In contrast to other known approaches, we do not fix the type of underlying graphs.  ...  Related Work Hierarchical graphs appear in the computer science literature often as a means to model complex networks of objects with additional structure on top of them.  ... 
doi:10.1017/s0960129505004846 fatcat:ogdvbiujojdohm7rkj7hj6vtza

A graphical method for reducing and relating models in systems biology

S. Gay, S. Soliman, F. Fages
2010 Bioinformatics  
Conflict of Interest: none declared.  ...  ACKNOWLEDGEMENTS We acknowledge fruitful discussions with many participants of these projects and with Christine Solnon for an enlighting talk on graph matching at our seminar.  ...  A morphism from G to G is a function µ from the nodes of G,S ∪R, to the nodes of G ,S ∪R , with µ(S) ⊆ S and µ(R) ⊆ R , such that ∀(x,y) ∈ A,(µ(x),µ(y)) ∈ A .  ... 
doi:10.1093/bioinformatics/btq388 pmid:20823324 pmcid:PMC2935413 fatcat:vsi46donjbhpdjo6jey4nqen6i

Each Role of Short-term and Long-term Memory in Neural Networks

Seisuke Yanagawa
2020 American Journal of Neural Networks and Applications  
The activity of the upper neural networks changes in response to the context structure inherent in the time series data and have both function of accepting and generating of general time series data.  ...  Based on known functions of neuroscience the neural network that performs serial parallel conversion and its inverse transformation is presented.  ...  The object and morphism that make up the source category are connected by a function to the object and morphism of the target category.  ... 
doi:10.11648/j.ajnna.20200601.12 fatcat:uh5i5nj5obda5k5dnwrwegvyde

Algebraic Representation and Modeling of Evolutionary Innovation and Adaptation in Biological Systems

Igor Balaz, Dragutin T. Mihailovic
2010 Workshop on the Synthesis and Simulation of Living Systems  
Since scope of their functioning for given environment is entirely dependant on internally given structure of the coding system they are able to evolve both new traits (evolutionary innovation) and optimize  ...  We also demonstrate that evolved networks have some properties of metabolism-like systems.  ...  We are also grateful to anonymous reviewers whose useful comments helped us to improve this manuscript.  ... 
dblp:conf/alife/BalazM10 fatcat:ddjm7p6ryjesvdeoiygoofhmsm

Efficient Switches in Biology and Computer Science

Luca Cardelli, Rosa D. Hernansaiz-Ballesteros, Neil Dalchau, Attila Csikász-Nagy, Jorg Stelling
2017 PLoS Computational Biology  
To this end, we will discuss the notion of network emulation, by which a network can, in a specific sense, impersonate the functionality of another network that is easier to analyse.  ...  But how do we precisely relate a (biochemical) network, the components of which are molecules and reactions, to a (computational) algorithm, the components of which are symbolic properties and events?  ...  Structural properties: A morphism that preserves the reactants and products of each reaction under the mapping is called a homomorphism.  ... 
doi:10.1371/journal.pcbi.1005100 pmid:28056093 pmcid:PMC5215766 fatcat:wus7bxitavdzfpdghypquijrki

Page 4393 of Mathematical Reviews Vol. , Issue 87h [page]

1987 Mathematical Reviews  
Summary: “We discuss a necessary and sufficient condition for the solvability of the Lie algebra corresponding to a class of kinetic systems of coupled first-order reactions with time-dependent rate coefficients  ...  They turn out to be inverses of each other. Finally, the structure of the Lie algebra of symmetries generated by these operators is also given.  ... 

An intermediate level of abstraction for computational systems chemistry

Jakob L. Andersen, Christoph Flamm, Daniel Merkle, Peter F. Stadler
2017 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
While quantum chemical methods can accurately predict the structures and reactivities of small molecules, they are not efficient enough to cope with large-scale reaction systems.  ...  The exploration of large chemical reaction networks is a central aspect in this endeavour.  ...  All arrows in the diagram are morphisms, i.e. functions which map vertices/edges from the graph on the arrow tail to the graph at the arrow head.  ... 
doi:10.1098/rsta.2016.0354 pmid:29133452 fatcat:xgeh7poc6jgxxdhcapu7ie2idq

A Conceptual Construction of Complexity Levels Theory in Spacetime Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics and Dynamic Systems

R. Brown, J. F. Glazebrook, I. C. Baianu
2007 Axiomathes  
structures that emerge from the latter in living systems.  ...  As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational  ...  By considering a sequence of two such reactions coupled together, QG 1 (QG 2 ; corresponding to an enzyme f coupled to a ribozyme /; one obtains a quantummolecular realization of the simplest M,R-system  ... 
doi:10.1007/s10516-007-9010-3 fatcat:246y6llurzhi5mwyofr373rxvm
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