The Mathematical Structure of the Human Sleep-Wake Cycle

ISBN-13: 9783540171768 / Angielski / Miękka / 1986 / 239 str.

Steven H. Strogatz

Opis

Over the past three years I have grown accustomed to the puzzled look which appears on people's faces when they hear that I am a mathematician who studies sleep. They wonder, but are usually too polite to ask, what does mathematics have to do with sleep? Instead they ask the questions that fascinate us all: Why do we have to sleep? How much sleep do we really need? Why do we dream? These questions usually spark a lively discussion leading to the exchange of anecdotes, last night's dreams, and other personal information. But they are questions about the func- tion of sleep and, interesting as they are, I shall have little more to say about them here. The questions that have concerned me deal instead with the timing of sleep. For those of us on a regular schedule, questions of timing may seem vacuous. We go to bed at night and get up in the morning, going through a cycle of sleeping and waking every 24 hours. Yet to a large extent, the cycle is imposed by the world around us.

Spis treści

1. Introduction.- 1.1 Beyond Time.- 1.2 The Rosetta Stone.- 1.3 Overview.- 2. Experimental Background.- 2.1 Phenomena and Terminology.- 2.2 History of Free-Run Studies.- 3. Data Bank.- 3.1 Subject 1.- 3.2 Subject 2.- 3.3 Subject 3.- 3.4 Subject 4.- 3.5 Subject 5.- 3.6 Subject 6.- 3.7 Subject 7.- 3.8 Subject 8.- 3.9 Subject 9.- 3.10 Subject 10.- 3.11 Subject 11.- 3.12 Subject 12.- 3.13 Subject 13.- 3.14 Subject 14.- 3.15 Subject 15.- 3.16 Subject 16.- 3.17 Subject 17.- 3.18 Subject 18.- 3.19 Subject 19.- 3.20 Subject 20.- 3.21 Subject 21.- 3.22 Subject 22.- 4. Patterns.- 4.1 Durations Vary with Circadian Phase of Sleep Onset.- 4.2 Sleep Length and Prior Wake Length.- 4.3 Timing of Wake-Up.- 4.4 Timing of Sleep Onset.- 4.5 Wake-Maintenance Zones.- 4.6 Estimating Circadian Parameters from Sleep Data Alone.- 4.7 Phase-Trapping.- 4.8 Slow Changes in Sleep-Wake Cycle Length.- 4.9 Miscellany and Missing Patterns.- 4.10 Napping and Split Sleep.- 4.11 Summary: The Basic Patterns of Internal Desynchrony.- 5. Theoretical Background.- 5.1 Conceptual Model of Aschoff and Wever.- 5.2 Wever’s Noninteractive Model.- 5.3 Kronauer’s XY Model: Coupled Van der Pol Oscillators.- 5.4 Conceptual Model of Borbely.- 5.5 Winfree’s Half-Model.- 5.6 Gated Pacemaker of Daan, Beersma, and Borbely.- 5.7 Other Approaches.- 6. Analysis of Models.- 6.1 Introduction.- 6.2 BEATS Model.- 6.3 PHASE Model.- 6.4 XY Model of Kronauer et al..- 6.5 Model of Daan et al..- 7. Simulations.- 7.1 Transition from Synchrony to Desynchrony.- 7.2 Napping and Split Sleep Simulations.- 7.3 A Representative Simulation of Internal Desynchrony.- 7.4 Overall Performance During Desynchrony.- 7.5 Summary and Discussion.- 8. Epilogue.- 8.1 Contributions.- 8.2 Directions for Future Research.- References.- Index of Authors.

O autorze

Steven Strogatz, geboren 1959, promovierte an der Harvard University in Mathematik. Heute lehrt er als Professor für angewandte Mathematik an der Cornell University. Er ist einer der weltweit meistzitierten Mathematiker und erhielt eine Auszeichnung für sein Lebenswerk für mathematische Kommunikation. Für die New York Times schrieb er die populäre Kolumne "The Elements of Math", auf der dieses Buch basiert.