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Feed Sideward Understanding Biological Rhythms

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Feed Sideward Understanding Biological Rhythms

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    1. Jim Holte University of Minnesota 1 1/15/02 Feed Sideward Understanding Biological Rhythms Jim Holte 1/15/2002

    2. Jim Holte University of Minnesota 2 1/15/02 Sessions Session 1 - Feed Sideward Concepts and Examples, 1/15 Session 2 Feed Sideward Applications to Biological & Biomedical Systems, 1/31 Session 3 Chronobiology, 2/12 Franz Hallberg and Germaine Cornalissen

    3. Jim Holte University of Minnesota 3 1/15/02 Feed Sideward Terms Simple Example Feed Back Reinvesting dividends Feed Foreward Setting money aside Feed Sideward Moving money to another account

    4. Jim Holte University of Minnesota 4 1/15/02 Introduction Feed Sideward is a coupling that shifts resources from one subsystem to another Feed Sideward #1 feeds values of other variables into the specified variable Feed Sideward #2 feeds changes of parameters into the specified variable. (time varying parameters) Feed Sideward #3 feeds changes of topology by switch operations (switched systems) Tool for global analysis especially useful for biological systems

    5. Jim Holte University of Minnesota 5 1/15/02 Phase Space Laws of the physical world Ordinary differential equations Visualization of Solutions Understanding

    6. Jim Holte University of Minnesota 6 1/15/02 Phase Space The Lotka-Volterra Equations for Predator-Prey Systems H' = b*H - a*H*P P' = -d*P + c*H*P H = prey abundance, P = predator Set the parameters b = 2 growth coefficient of prey d = 1 growth coefficient of predators a = 1 rate of capture of prey per predator per unit time c = 1 rate of "conversion" of prey to predators per unit time per predator.

    7. Jim Holte University of Minnesota 7 1/15/02 Phase Space

    8. Jim Holte University of Minnesota 8 1/15/02 Coupled Oscillators Model x and y represent the "phases of two oscillators. Think of x and y: angular positions of two "particles" moving around the unit circle a1 = 0 x has constant angular rate a2 = 0 y has constant angular rate. Coupling when a1 or a2 non-zero

    9. Jim Holte University of Minnesota 9 1/15/02 Example Uncoupled Oscillators

    10. Jim Holte University of Minnesota 10 1/15/02 Example Coupled Oscillators

    11. Jim Holte University of Minnesota 11 1/15/02 Phase Resetting

    12. Jim Holte University of Minnesota 12 1/15/02 Example Phase Resetting

    13. Jim Holte University of Minnesota 13 1/15/02 Oscillator Entrainment

    14. Jim Holte University of Minnesota 14 1/15/02 Oscillator Entrainment Example

    15. Jim Holte University of Minnesota 15 1/15/02 Singularities

    16. Jim Holte University of Minnesota 16 1/15/02 Example - Singularities

    17. Jim Holte University of Minnesota 17 1/15/02 Feed Sideward Terms Simple Example Feed Back Reinvesting dividends Feed Foreward Setting money aside Feed Sideward Moving money to another account

    18. Jim Holte University of Minnesota 18 1/15/02 Feed Sideward Example

    19. Jim Holte University of Minnesota 19 1/15/02 Summary Feed Sideward is a coupling that shifts resources from one subsystem to another Feed Sideward #1 feeds values of other variables into the specified variable Feed Sideward #2 feeds changes of parameters into the specified variable. (time varying parameters) Feed Sideward #3 feeds changes of topology by switch operations (switched systems) Tool for global analysis especially useful for biological systems

    20. Jim Holte University of Minnesota 20 1/15/02 Next Session Session 1 - Feed Sideward Concepts and Examples, 1/15 Session 2 Feed Sideward Applications to Biological & Biomedical Systems, 1/31 Session 3 Chronobiology, 2/12 Franz Hallberg and Germaine Cornelissen

    21. Jim Holte University of Minnesota 21 1/15/02 Backup

    22. Jim Holte University of Minnesota 22 1/15/02 Feed Sideward - Topics (60 min) Session 1 (14 slides) Background Concepts & Examples Phase Space (1 slide) Singularities (2 slides) * Coupled Oscillators (2 slides) Phase Resetting (2 slides) * Oscillator Entrainment (1 slide) Feed Sideward as modulation (3 slides) ** Summary (1 slide)

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