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 TRANSACTIONS AS SET OPERATIONS

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

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

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

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

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.” n-tuples behave badly, e.g., <a, b>  <a, c> = <a, a>

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

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

Logical Data Physical Data Transaction Types 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 L P

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

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

Information Access Strategies Adapt Query to Data Adapt Data to Query

Information Access Strategies Adapt Query to Data Adapt Data to Query