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MANAGING DATA MATHEMATICALLY

MANAGING DATA MATHEMATICALLY. MANAGING DATA MATHEMATICALLY. DATA AS A MATHEMATICAL OBJECT. MANAGING DATA MATHEMATICALLY. - THEORETICAL FOUNDATIONS. - PRACTICAL APPLICATIONS. PREVIEW. THEORETICAL FOUNDATIONS EXTENTIONS TO SET THEORY DATA AS A MATHEMATICAL OBJECT

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MANAGING DATA MATHEMATICALLY

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  1. MANAGINGDATAMATHEMATICALLY

  2. MANAGINGDATAMATHEMATICALLY DATA AS A MATHEMATICAL OBJECT

  3. MANAGINGDATAMATHEMATICALLY - THEORETICAL FOUNDATIONS - PRACTICAL APPLICATIONS

  4. PREVIEW • THEORETICAL FOUNDATIONS • EXTENTIONS TO SET THEORY • DATA AS A MATHEMATICAL OBJECT • TRANSACTIONS AS SET OPERATIONS

  5. PREVIEW • PRACTICAL APPLICATIONS • ADAPT TRANSACTION TO DATA • ADAPT DATA TO TRANSACTION • LIVE DEMONSTRATION • ADAPTIVE DATA RESTRUCTURING • ON 1, 2, 4, 8, & 10 GB OF RAW DATA

  6. ARPA - 1965 • DATA MANAGEABLE MATHEMATICALLY? • MATHEMATICAL IDENTITY FOR DATA • MATHEMATICAL EXPRESSION FOR DATA BEHAVIOR CONCOMP RESEARCH PROJECT • MATHEMATICALLY SOUND SYSTEMS

  7. Identifying Characteristics of Data • Content • Represented Relationships • Structure • Form of Representation • Behavior • Response to Manipulation

  8. Identifying Characteristics of Data • Content • Represented Relationships • Structure • Form of Representation • Behavior • Response to Manipulation

  9. n-tuples behave badly, e.g., <a, b>  <a, c> = <a, a> Two Remarks on Set Theory[Th. Skolem, Math. Scand. 5 (1957), 40-46] 2. The ordered n-tuples as sets “ But in literature I have found no answer to the general question how to define the ordered n-tuple as a set.” In conclusion: “I shall not pursue these considerations here, but only emphasize that it is still a problem how the ordered n-typle can be defined in the most suitable way.”

  10. XST Definition of n-tuple <a, b, c> = { a1, b2, c3} <x, b, y> = { x1, b2, y3} <a, b, c>  <x, b, y> = {b2}

  11. Working Definitions • Data A Representation of Relationships • Data Transaction Any Transformation of Data from One State to Another

  12. L L L P P P P L • Logical Data • Representations friendly to humans • Used to specify enterprise transactions • Physical Data • Representations friendly to machines • Used to support execution of enterprise transactions • Transaction Types • Logical Data to Logical Data • Logical Data to Physical Data • Physical Data to Physical Data • Physical Data to Logical Data

  13. Visual Summary E-DATA Logical Enterprise Specification Brains Execution Bytes M-DATA Physical Machine Disjoint Environments

  14. Mathematical View Logical Enterprise f L2 L1 b a Specification Brains Execution Bytes P2 P1 F Physical Machine XST: f (L1) = b ( F ( a ( L1) ) ) = L2

  15. Information Access Strategies • Adapt Query to Data • Adapt Data to Query

  16. Information Access Strategies • Adapt Query to Data • Adapt Data to Query

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