Author	Strogatz, Steven H. author
Title	The Mathematical Structure of the Human Sleep-Wake Cycle [electronic resource] / by Steven H. Strogatz
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1986
Connect to	http://dx.doi.org/10.1007/978-3-642-46589-5
Descript	VIII, 239 p. online resource

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 funcยญ 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

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 Weverโs Noninteractive Model -- 5.3 Kronauerโs XY Model: Coupled Van der Pol Oscillators -- 5.4 Conceptual Model of Borbely -- 5.5 Winfreeโs 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

1. Mathematics
2. Probabilities
3. Biomathematics
4. Statistics
5. Mathematics
6. Probability Theory and Stochastic Processes
7. Mathematical and Computational Biology
8. Statistics for Life Sciences
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