managing data mathematically

MANAGINGDATA

MATHEMATICALLY

MANAGINGDATA

MATHEMATICALLY

DATA AS A MATHEMATICAL OBJECT

MANAGINGDATA

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

• 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– 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

Visual Summary

E-DATA

M-DATA

Specification

Execution

Brains

Logical Enterprise

MachinePhysical

Disjoint Environments

Mathematical View

Specification

Execution

Brains

Logical Enterprise

MachinePhysical

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

managing data mathematically

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