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Inverse Problems are Detective Problems

Inverse Problems are Detective Problems. Inverse Problems are Difficult Inverse Problems are usually ill posed. Inverse Problems require a world of data. Channels are Selective. Different Types of Channels use Different Types of Ions for Different Information.

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Inverse Problems are Detective Problems

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  1. Inverse Problems are Detective Problems

  2. Inverse Problems are Difficult Inverse Problems are usually ill posed.

  3. Inverse Problems require a world of data

  4. Channels are Selective Different Types of Channels use Different Types of Ionsfor Different Information

  5. For Modelers and Mathematicians:This is reverse engineering! Central Problem How does the channel control Selectivity? Inverse Problem for Selectivity Badly posed, many answers are possible,simultaneously over and under determined with noise and systematic error Core Math Problem has actually been solved using methods for the Inverse Problem of a Blast Furnace Burger, Eisenberg and Engl (2007) SIAM J Applied Math 67: 960-989

  6. Modelers and Mathematicians:this is reverse engineering How does theChannel control Selectivity? Inverse ProblemsMany answers are possible Central Issue Which answer is right? Burger, Eisenberg and Engl (2007) SIAM J Applied Math 67: 960-989

  7. How does theChannel control Selectivity? Inverse Problems: many answers possible Central Issue Which answer is right? Key is ALWAYS Large Amount of Data from Many different Conditions Burger, Eisenberg and Engl (2007) SIAM J Applied Math 67: 960-989

  8. Goal: Understand Selectivity well enough toFit Large Amounts of Data from many solutions and concentrationsand to Make a Calcium Channel Atomic Scale Macro Scale

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