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The Algebra of Open and Interconnected Systems [article]

Brendan Fong
2016 arXiv   pre-print
To illustrate these principles, the second part of this thesis details applications to linear time-invariant dynamical systems and passive linear networks.  ...  The first part of this thesis develops the theory of hypergraph categories. In particular, we introduce the tools of decorated cospans and corelations.  ...  In this thesis, we study an algebraic structure called a hypergraph category, and argue that this is the relevant algebraic structure for modelling interconnection of open systems.  ... 
arXiv:1609.05382v1 fatcat:rxuhgb2ub5c67otn5ij2y7g6iq

Constrained probability

Jan C. Willems
2012 2012 IEEE International Symposium on Information Theory Proceedings  
A stochastic system is defined as a probability triple. Models often require a coarse event sigma-algebra.  ...  The SCD-SISTA research of the KU Leuven is supported by the projects.  ...  INTRODUCTION By an 'open' system we mean a model that explicitly incorporates the influence of the environment, but as an unmodeled feature. Open systems can be interconnected with other systems.  ... 
doi:10.1109/isit.2012.6283011 dblp:conf/isit/Willems12 fatcat:pubmu4dea5ftzeshhtgcgsqx3m

LTI Stochastic Processes: a Behavioral Perspective [article]

Giacomo Baggio, Rodolphe Sepulchre
2017 arXiv   pre-print
This paper revisits the definition of linear time-invariant (LTI) stochastic process within a behavioral systems framework.  ...  Building on [Willems, 2013], we derive a canonical representation of an LTI stochastic process and a physically grounded notion of interconnection between independent stochastic processes.  ...  In this setting, a theory of open systems is de facto a theory of interconnected systems.  ... 
arXiv:1704.02154v1 fatcat:rqza7p4qqffjfiuoylrqnjljdq

Quantum behaviors and networks

Matthew R. James, John Gough
2008 2008 47th IEEE Conference on Decision and Control  
A simple framework for modeling open quantum systems and networks of such systems is described; this framework provides tools for determining quantum behaviors.  ...  This evolution is determined by parameters that specify the internal energy of the system, and any interfaces to other systems or fields.  ...  The authors wish to thank Ian Petersen and Jochen Trumpf for helpful discussions.  ... 
doi:10.1109/cdc.2008.4738928 dblp:conf/cdc/JamesG08 fatcat:ojk56pgz6zcalhqhga4apnpgum

Camouflaging electrical $1$-networks as graphs

Gabriel Kron
1962 Quarterly of Applied Mathematics  
The latter also were endowed with variable connectedness ("tearing and interconnecting"), in order to allow all possible types of network manipulations and operations.  ...  This paper points out that the proper stage of an electrically excited e, i, z system is not a graph, nor a planar polyhedron, but a 1-network,-a configuration that contains branches only and no nodes,  ...  algebraic peculiarities of the superimposed electrical e, i, z system.  ... 
doi:10.1090/qam/148347 fatcat:xcteywu52vbhdnok5kfhe3kbgm

Open Stochastic Systems

Jan C. Willems
2013 IEEE Transactions on Automatic Control  
laws of a system from the laws of the environment?  ...  B is called the behavior of the deterministic system.  ...  Assume that the interconnection Σ 1 ∧ Σ 2 is a classical random vector. Sampling ; the mean and covariance of Σ 1 ∧ Σ 2 . Assume that the covariance is nonsingular.  ... 
doi:10.1109/tac.2012.2210836 fatcat:cnq5ee2ikffozpxtlyjspsykay

Open stochastic systems

Jan C. Willems
2011 IEEE Conference on Decision and Control and European Control Conference  
laws of a system from the laws of the environment?  ...  B is called the behavior of the deterministic system.  ...  Assume that the interconnection Σ 1 ∧ Σ 2 is a classical random vector. Sampling ; the mean and covariance of Σ 1 ∧ Σ 2 . Assume that the covariance is nonsingular.  ... 
doi:10.1109/cdc.2011.6160329 dblp:conf/cdc/Willems11 fatcat:knh6rv4garfcnl2gluyagqhspi

Specification architecture

K.J. Turner, G. Scollo
1997 Computer networks and ISDN systems  
The editors also extend their thanks to the reviewers for their careful reading of the papers. The advice and involvement of H. Rudin, a senior editor of the journal, was much appreciated.  ...  Acknowledgements The guest editors are grateful to the contributors for their enthusiasm in elaborating the topic of this special issue.  ...  The papers deal with mes- sage switching, ODP (Open Distributed Processing [6]), OS1 (Open Systems Interconnection [3]), multi- media communication and telephony.  ... 
doi:10.1016/s0169-7552(96)00124-9 fatcat:3nu2a45g3ncl3pkarlrg2oqmty

Obvious and Hidden Symmetries of Mathematical Objects

Dragan Marusic
2018 Proceedings (MDPI)  
One of the core concepts essential to understanding natural phenomena and the dynamics of social systems is the concept of "relation".  ...  Social and interconnection networks, traffic systems, chemical structures, etc. can be expressed as relational structures.  ...  Abstract: One of the core concepts essential to understanding natural phenomena and the dynamics of social systems is the concept of "relation".  ... 
doi:10.3390/proceedings2010084 fatcat:4axfck7765es7c2zwgqmurmtt4

Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams [article]

Dmitry Vagner, David I. Spivak, Eugene Lerman
2015 arXiv   pre-print
In this paper, we use the language of operads to study open dynamical systems.  ...  As an example, we use these algebras to formalize the classical problem of systems of tanks interconnected by pipes, and hence make explicit the algebraic relationships among systems at different levels  ...  The algebra we present here, that of open systems, is distinct from the algebras of relations and of propagators studied in earlier works.  ... 
arXiv:1408.1598v2 fatcat:nkghr5xf3vejfgud6yvhavdm5q

Physiological Model Creation and Sharing

Jan Silar, Jiri Kofranek
2011 European Journal for Biomedical Informatics  
Jan Šilar Conclusions: New tools will simplify model creation and interconnection. They will also improve collaboration of model developers.  ...  The editor for models written in Modelica is being developed. It will run in browser and will be interconnected with web based model repository.  ...  Acknowledgments The paper was supported by the project SVV-2011-262514 of Charles University in Prague.  ... 
doi:10.24105/ejbi.2011.07.1.10 fatcat:pluc7rrlazhrrmjeujw5sopg34

Simple Robust Controllers for Delayed Systems

M. Dlapa
2010 IFAC Proceedings Volumes  
A simple controller is derived via algebraic theory and the structured singular value, which treats uncertain time delay in both the numerator and denominator of an anisochronic system.  ...  A way for treating general delayed systems with uncertain delays in both the numerator and denominator is shown. The proposed procedure is demonstrated by an example.  ...  It is apparent that the D-K iteration has a non-zero steady state error for both 1DOF and 2DOF interconnection, which is not the case of the algebraic approach.  ... 
doi:10.3182/20100607-3-cz-4010.00067 fatcat:ny6si5lrn5dejkuyauyb7tewwm

Engineering distributed software

Jeff Kramer, Jeff Magee
2005 Proceedings of the 10th European software engineering conference held jointly with 13th ACM SIGSOFT international symposium on Foundations of software engineering - ESEC/FSE-13  
The role of structure in specifying, designing, analysing, constructing and evolving software has been the central theme of our research in Distributed Software Engineering.  ...  This structural discipline dictates formalisms and techniques that are compositional, components that are context independent and systems that can be constructed and evolved incrementally.  ...  Much of the research has been supported by the Engineering and Physical Sciences Research Council and is currently partly supported by EPSRC grant READS GR/S03270/01.  ... 
doi:10.1145/1081706.1081709 dblp:conf/sigsoft/KramerM05 fatcat:zphixjuienfsvgedtahlyx3sne

Engineering distributed software

Jeff Kramer, Jeff Magee
2005 Software engineering notes  
The role of structure in specifying, designing, analysing, constructing and evolving software has been the central theme of our research in Distributed Software Engineering.  ...  This structural discipline dictates formalisms and techniques that are compositional, components that are context independent and systems that can be constructed and evolved incrementally.  ...  Much of the research has been supported by the Engineering and Physical Sciences Research Council and is currently partly supported by EPSRC grant READS GR/S03270/01.  ... 
doi:10.1145/1095430.1081709 fatcat:qerjq63yqbbaliopvnvfwkrwla

SimuPy: A Python framework for modeling and simulating dynamical systems

Benjamin W. L. Margolis
2017 Journal of Open Source Software  
SimuPy is a framework for simulating interconnected dynamical system models and provides an open source, python-based tool that can be used in model-and system-based design and simulation workflows.  ...  The examples and tests show that the block diagram algebra and timing formulations agree with the mathematical definitions.  ... 
doi:10.21105/joss.00396 fatcat:wdmj3l3ssrfpdcbozfxwxnw7zi
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