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- Martin Golubitsky, Ian Stewart, Andrei Török
- SIAM J. Applied Dynamical Systems
- 2005

A coupled cell system is a network of dynamical systems, or " cells, " coupled together. The architecture of a coupled cell network is a graph that indicates how cells are coupled and which cells are equivalent. Stewart, Golubitsky, and Pivato presented a framework for coupled cell systems that permits a classification of robust synchrony in terms of… (More)

A formal theory of symmetries of networks of coupled dynamical systems, stated in terms of the group of permutations of the nodes that preserve the network topology, has existed for some time. Global network symmetries impose strong constraints on the corresponding dynamical systems, which affect equilibria, periodic states, heteroclinic cycles, and even… (More)

- Ian Stewart, Martin Golubitsky, Marcus Pivato
- SIAM J. Applied Dynamical Systems
- 2003

A coupled cell system is a network of dynamical systems, or 'cells', coupled together. Such systems can be represented schematically by a directed graph whose nodes correspond to cells and whose edges represent couplings. A symmetry of a coupled cell system is a permutation of the cells that preserves all internal dynamics and all couplings. Symmetry can… (More)

- S C Robins, I Stewart, +9 authors M Placzek
- Nature communications
- 2013

Emerging evidence suggests that new cells, including neurons, can be generated within the adult hypothalamus, suggesting the existence of a local neural stem/progenitor cell niche. Here, we identify α-tanycytes as key components of a hypothalamic niche in the adult mouse. Long-term lineage tracing in vivo using a GLAST::CreER(T2) conditional driver… (More)

- J. J. Collins, Ian Stewart
- Biological Cybernetics
- 1993

The general, model-independent features of different networks of six symmetrically coupled nonlinear oscillators are investigated. These networks are considered as possible models for locomotor central pattern generators (CPGs) in insects. Numerical experiments with a specific oscillator network model are briefly described. It is shown that some generic… (More)

- J. J. Collins, Ian Stewart
- Biological Cybernetics
- 1994

In this paper, a general approach for studying rings of coupled biological oscillators is presented. This approach, which is group-theoretic in nature, is based on the finding that symmetric ring networks of coupled non-linear oscillators possess generic patterns of phaselocked oscillations. The associated analysis is independent of the mathematical details… (More)

Coupled cell systems are systems of ODEs, defined by 'admissible' vector fields, associated with a network whose nodes represent variables and whose edges specify couplings between nodes. It is known that non-isomorphic networks can correspond to the same space of admissible vector fields. Such networks are said to be 'ODE-equivalent'. We prove that two… (More)

- Martin Golubitsky, Matthew Nicol, Ian Stewart
- J. Nonlinear Science
- 2004

We discuss several examples of synchronous dynamical phenomena in coupled cell networks that are unexpected from symmetry considerations, but are natural using a theory developed by Stewart, Golubitsky, and Pivato. In particular we demonstrate patterns of synchrony in networks with small numbers of cells and in lattices (and periodic arrays) of cells that… (More)

- William E. McClintock, Nicholas M. Schneider, +6 authors Justin Deighan
- 2014

The Imaging Ultraviolet Spectrograph (IUVS) is one of nine science instruments aboard the Mars Atmosphere and Volatile and EvolutioN (MAVEN) spacecraft. MAVEN, launched in November 18, 2013 and arriving at Mars in September 2014, is designed to explore the planet's upper atmosphere and ionosphere and examine their interaction with the solar wind and solar… (More)

- Cheryl L Wright, Ian D Stewart
- The American journal of surgical pathology
- 2003

Defects in the mismatch repair (MMR) genes hMLH1 and hMSH2 have been found in 10% to 20% of sporadic colorectal carcinomas and also many cases of hereditary nonpolyposis colorectal cancer syndrome. Patients with these tumors have an improved prognosis and may show greater sensitivity to chemotherapy. We examined 458 resected colorectal carcinomas from 430… (More)