| --- |
| title: "House Oversight: Estate Documents (Nov 12) (HOUSE_OVERSIGHT_013689)" |
| source: "House Oversight: Estate Documents (Nov 12)" |
| sourceUrl: "https://www.justice.gov/epstein" |
| date: "2026-01-01" |
| category: "House Oversight" |
| eftaNumber: "HOUSE_OVERSIGHT_013689" |
| ocrPages: 1 |
| ocrChars: 2216 |
| ocrElapsed: 0.0 |
| parseTier: "external-legacy" |
| engine: "engine undisclosed (ep-nov-12.greg.technology mirror)" |
| externalSource: "greg-ep-nov-12" |
| externalLicense: "not granted" |
| externalCredit: "ep-nov-12.greg.technology" |
| externalUrl: "https://ep-nov-12.greg.technology" |
| --- |
| |
| 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 |
| Modern Applied Dynamical Systems Emerged from Accidental |
| 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). |
| 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 |
| 189 |
| HOUSE_OVERSIGHT_013689 |
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