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2.09 MB
Extraction Summary
12
People
5
Organizations
2
Locations
2
Events
2
Relationships
2
Quotes
Document Information
Type:
Scientific/academic text (page from a book or paper)
File Size:
2.09 MB
Summary
This document is page 83 of a scientific text, likely part of a larger collection reviewed by the House Oversight Committee regarding Jeffrey Epstein (indicated by the Bates stamp). The text discusses advanced mathematical concepts relating to dynamical systems, specifically 'generating partitions,' the 'Sinai-Ruelle-Bowen (SRB) measure,' and 'metric entropy.' It details the historical academic contributions of several prominent mathematicians, including Kolmogorov, Shannon, and Ornstein, and lists researchers from institutions like IBM, Stanford, Hebrew University, and Warwick University.
People (12)
| Name | Role | Context |
|---|---|---|
| Kolmogorov | Mathematician |
Described as the Russian father of modern dynamical systems; proved Shannon metric entropy is a quantifiable invarian...
|
| Ya Sinai | Mathematician |
Russian student/follower of Kolmogorov; SRB measure named partly after him.
|
| David Ruelle | Mathematician |
Belgian Frenchman; SRB measure named partly after him.
|
| Rufus Bowen | Mathematician |
American; SRB measure named partly after him.
|
| Claude Shannon | Scientist/Mathematician |
Referenced regarding informational entropy and Shannon metric entropy.
|
| Donald Ornstein | Mathematician |
Stanford University; won a Field's Medal for late 1960s work on Shannon metric entropy.
|
| Roy Adler | Mathematician |
Affiliated with IBM in New York.
|
| Brian Marcus | Mathematician |
Affiliated with IBM in California.
|
| Benjamin Weiss | Mathematician |
Affiliated with Hebrew University.
|
| William Parry | Mathematician |
Affiliated with Warwick University.
|
| Peter Walters | Mathematician |
Affiliated with Warwick University.
|
| Mark Pollicott | Mathematician |
Affiliated with Warwick University.
|
Organizations (5)
| Name | Type | Context |
|---|---|---|
| Stanford University | University |
Institution of Donald Ornstein.
|
| IBM | Company |
Employer of Roy Adler and Brian Marcus.
|
| Hebrew University | University |
Institution of Benjamin Weiss.
|
| Warwick University | University |
Institution of William Parry, Peter Walters, and Mark Pollicott.
|
| House Oversight Committee | Government Body |
Source of the document (implied by Bates stamp).
|
Timeline (2 events)
1956
Kolmogorov proved that the Shannon metric entropy is a quantifiable invariant of systems.
N/A
Late 1960s
Donald Ornstein's work proving Shannon metric entropy was the only invariant for a class of dynamical systems, winning him a Field's Medal.
Stanford University
Locations (2)
| Location | Context |
|---|---|
|
Location of Roy Adler (IBM).
|
|
|
Location of Brian Marcus (IBM).
|
Relationships (2)
Text refers to Sinai as one of 'Kolmogorov’s students and followers'.
Both listed under IBM.
Key Quotes (2)
"It was the above noted Russian father of modern dynamical systems, Kolmogorov, who in 1956 proved that the Shannon metric entropy is a quantifiable invariant of systems even in very complicated motion."Source
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Quote #1
"Stanford University's Donald Ornstein won a Field’s Medal (the under forty year old mathematician’s Nobel Prize) for his late 1960’s work proving that the Shannon metric entropy, HM, was the only invariant for a large class of appropriately defined, expansive (near by points separating in time) dynamical systems."Source
HOUSE_OVERSIGHT_013583.jpg
Quote #2
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