2015
Observability and Controllability of Nonlinear Networks: The Role of Symmetry
Whalen A, Brennan S, Sauer T, Schiff S. Observability and Controllability of Nonlinear Networks: The Role of Symmetry. Physical Review X 2015, 5: 011005. PMID: 30443436, PMCID: PMC6234006, DOI: 10.1103/physrevx.5.011005.Peer-Reviewed Original ResearchNonlinear networksMathematical modelPresence of symmetryComplex nonlinear networksRole of symmetryNetworked systemsExplicit symmetryLinear networkSuch subspacesPresent theoryRotational symmetryStructural controllabilityObservabilityReal systemComplex networksSymmetryControllabilityObserver modelNonlinear measuresSuch networksSubspaceModel behaviorNetwork observationsNetworkModel
2009
The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics
Cressman J, Ullah G, Ziburkus J, Schiff S, Barreto E. The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics. Journal Of Computational Neuroscience 2009, 26: 159-170. PMID: 19169801, PMCID: PMC2704057, DOI: 10.1007/s10827-008-0132-4.Peer-Reviewed Original ResearchConceptsSingle neuron dynamicsDetailed bifurcation analysisLarge amplitude oscillationsExtracellular ion concentration dynamicsMathematical modelBifurcation analysisDynamical mechanismIon concentration dynamicsNeuron dynamicsReasonable approximationFull modelCompanion paperDynamicsImportant fundamental processesConcentration dynamics
2004
Electric Field Control of Seizure Propagation: From Theory to Experiment
Richardson K, Schiff S, Gluckman B. Electric Field Control of Seizure Propagation: From Theory to Experiment. AIP Conference Proceedings 2004, 742: 185-196. DOI: 10.1063/1.1846476.Peer-Reviewed Original ResearchMathematical modelSpeed of propagationMathematical solutionElectric fieldElectric field controlEpileptic seizure propagationSuch electric fieldsField controlHigh enough valuesEnough valuesPropagationWavesActivity wavesDimensional networkSolutionModelFieldTheoryLower threshold valueNetworkThreshold valueSpeedParameters