HOUSE_OVERSIGHT_013689.jpg
1.84 MB
Extraction Summary
15
People
1
Organizations
1
Locations
0
Events
3
Relationships
2
Quotes
Document Information
Type:
Scientific manuscript / academic paper
File Size:
1.84 MB
Summary
This document is page 189 of a scientific manuscript regarding applied nonlinear mathematics, specifically focusing on dynamical systems and computational discoveries. It reviews the history of the field, citing works by Van der Pol, Hodgkin-Huxley, and others regarding neuronal dynamics and oscillators. The document includes a House Oversight Committee stamp, suggesting it was part of evidence gathered during an investigation, likely related to Jeffrey Epstein's funding of or interest in theoretical science/mathematics (specifically citing 'Mandell', likely Arnold Mandell).
People (15)
| Name | Role | Context |
|---|---|---|
| Herr | Medical Student / Researcher |
Conducted thesis research with Van der Pol in 1926.
|
| Van der Pol | Radio Engineer / Researcher |
Collaborated with Herr; known for Van der Pol equations.
|
| Rinzel | Researcher |
Cited for 1985 work on Hodgkin-Huxley type equations.
|
| Carpenter | Researcher |
Cited for 1979 work on neuronal dynamics.
|
| Aihara | Researcher |
Cited for 1984 work.
|
| Chay | Researcher |
Cited for 1985 work with Rinzel.
|
| Magoun | Researcher |
Cited for 1954 work on brain stem evoked EEG.
|
| Nicolis | Researcher |
Cited for 1986 work.
|
| Selz | Researcher |
Cited for 1992 and 1993 work with Mandell.
|
| Mandell | Researcher |
Cited for 1992 and 1993 work with Selz. (Likely Arnold Mandell, a scientist associated with Epstein).
|
| Levinson | Researcher |
Cited for 1949 analog computer studies.
|
| Mary Cartwright | Mathematician |
Cambridge mathematician cited for 1945 work.
|
| Joe Littlewood | Mathematician |
Cambridge mathematician cited for 1945 work.
|
| McMurran, S. | Researcher |
Cited for 1999 work.
|
| Tattersal, J. | Researcher |
Cited for 1999 work.
|
Organizations (1)
| Name | Type | Context |
|---|---|---|
| Cambridge |
University associated with mathematicians Cartwright and Littlewood.
|
Locations (1)
| Location | Context |
|---|---|
|
Location of mathematicians mentioned.
|
Relationships (3)
Herr, in his thesis research with the 'radio engineer', Van der Pol
Cambridge mathematicians, Mary Cartwright and Joe Littlewood
Key Quotes (2)
"Modern Applied Dynamical Systems Emerged from Accidental Computational Discoveries"Source
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Quote #1
"unanticipated results of analog and digital computer experiments were responsible for most if not all of the discoveries underlying the current era’s revolution in applied nonlinear mathematics"Source
HOUSE_OVERSIGHT_013689.jpg
Quote #2
Full Extracted Text
Complete text extracted from the document (2,220 characters)
unanticipated results of analog and digital computer experiments were responsible
for most if not all of the discoveries underlying the current era’s revolution in applied
nonlinear mathematics
for most if not all of the discoveries underlying the current era’s revolution in applied
nonlinear mathematics
Modern Applied Dynamical Systems Emerged from Accidental
Computational Discoveries
Computational Discoveries
A medical student named Herr, in his thesis research with the “radio
engineer”, Van der Pol (1926), was simulating cardiac electrophysiology with an
analog device which permitted real time, exploration of a full range of parameter
values long before there were fast enough digital processors to do so. Studying the
behavior of equations of a periodically, pace maker, driven, nonlinear triode
oscillator, Herr found orbital points that appeared to belong to two different periods
simultaneously thus violating the uniqueness of solutions of differential equation
theory. The Van der Pol relaxation oscillator equations, with their slow buildup and
sudden discharge of membrane potential are good models for the slow-fast
processes of repolarization and depolarization of Hodgkin-Huxley type equations
(Rinzel, 1985). Periodically driven, nonlinear differential equations of the Van der
Pol type are generally applicable to the multiplicity of dynamical regimes of neuronal
dynamics (Carpenter, 1979; Aihara et al, 1984; Chay and Rinzel, 1985) and, with
periodic and aperiodic driving and noise, can be made relevant to particular
mammalian neuronal subsystems in the context of clinically relevant global
electrophysiological phenomena such as Magoun’s (1954) brain stem evoked EEG
and behavioral arousal (Nicolis, 1986; Selz and Mandell, 1992; Mandell and Selz,
1993).
engineer”, Van der Pol (1926), was simulating cardiac electrophysiology with an
analog device which permitted real time, exploration of a full range of parameter
values long before there were fast enough digital processors to do so. Studying the
behavior of equations of a periodically, pace maker, driven, nonlinear triode
oscillator, Herr found orbital points that appeared to belong to two different periods
simultaneously thus violating the uniqueness of solutions of differential equation
theory. The Van der Pol relaxation oscillator equations, with their slow buildup and
sudden discharge of membrane potential are good models for the slow-fast
processes of repolarization and depolarization of Hodgkin-Huxley type equations
(Rinzel, 1985). Periodically driven, nonlinear differential equations of the Van der
Pol type are generally applicable to the multiplicity of dynamical regimes of neuronal
dynamics (Carpenter, 1979; Aihara et al, 1984; Chay and Rinzel, 1985) and, with
periodic and aperiodic driving and noise, can be made relevant to particular
mammalian neuronal subsystems in the context of clinically relevant global
electrophysiological phenomena such as Magoun’s (1954) brain stem evoked EEG
and behavioral arousal (Nicolis, 1986; Selz and Mandell, 1992; Mandell and Selz,
1993).
In the early 1940’s, using the pre-publication results of similar analog
computer studies (Levinson, 1949), the Cambridge mathematicians, Mary
Cartwright and Joe Littlewood (1945; McMurran, S., Tattersal, J.,1999) used
geometric methods to prove that the highly nonlinear, periodically driven Van der
Pol equations, depending upon one or two changing parameters, generated fixed
point (“homeostatic”), periodic (“cyclic”), subharmonic (“period doubling”),
quasiperiodic (“multiply periodic”), intermittent (“bursting”) and “deterministically
computer studies (Levinson, 1949), the Cambridge mathematicians, Mary
Cartwright and Joe Littlewood (1945; McMurran, S., Tattersal, J.,1999) used
geometric methods to prove that the highly nonlinear, periodically driven Van der
Pol equations, depending upon one or two changing parameters, generated fixed
point (“homeostatic”), periodic (“cyclic”), subharmonic (“period doubling”),
quasiperiodic (“multiply periodic”), intermittent (“bursting”) and “deterministically
189
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