dorsal/arxiv
View SchemaSleep as the solution to an optimization problem
| Authors | Emmanuel Tannenbaum |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0601008 |
| URL | https://arxiv.org/abs/q-bio/0601008 |
Abstract
This paper develops a highly simplified model with which to analyze the phenomenon of sleep. Motivated by Crick's suggestion that sleep is the brain's way of ``taking out the trash,'' a suggestion that is supported by emerging evidence, we consider the problem of the filling and emptying of a tank. At any given time, the tank may take in external resource, or fill, if resource is available at that time, or it may empty. The filling phases correspond to information input from the environment, or input of some material in general, while the emptying phases correspond to the processing of the resource. Given a resource-availablility profile over some time interval $ T $, we develop a canonical algorithm for determining the fill-empty profile that produces the maximum quantity of processed resource at the end of the time interval. From this algorithm, it readily follows that for a periodically oscillating resource-availability profile, the optimal fill-empty strategy is given by a fill period when resource is available, followed by an empty period when resource is not. This cycling behavior is analogous to the wake-sleep cycles in organismal life, where the generally nocturnal sleep phase is a period where the information collected from the day's activities may be processed. The sleep cycle is then a mechanism for the organism to process a maximal amount of information over a daily cycle. Our model can exhibit phenomena analogous to ``microsleeps,'' and other behavior associated with breakdown in sleep patterns.
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"abstract": "This paper develops a highly simplified model with which to analyze the\nphenomenon of sleep. Motivated by Crick\u0027s suggestion that sleep is the brain\u0027s\nway of ``taking out the trash,\u0027\u0027 a suggestion that is supported by emerging\nevidence, we consider the problem of the filling and emptying of a tank. At any\ngiven time, the tank may take in external resource, or fill, if resource is\navailable at that time, or it may empty. The filling phases correspond to\ninformation input from the environment, or input of some material in general,\nwhile the emptying phases correspond to the processing of the resource. Given a\nresource-availablility profile over some time interval $ T $, we develop a\ncanonical algorithm for determining the fill-empty profile that produces the\nmaximum quantity of processed resource at the end of the time interval. From\nthis algorithm, it readily follows that for a periodically oscillating\nresource-availability profile, the optimal fill-empty strategy is given by a\nfill period when resource is available, followed by an empty period when\nresource is not. This cycling behavior is analogous to the wake-sleep cycles in\norganismal life, where the generally nocturnal sleep phase is a period where\nthe information collected from the day\u0027s activities may be processed. The sleep\ncycle is then a mechanism for the organism to process a maximal amount of\ninformation over a daily cycle. Our model can exhibit phenomena analogous to\n``microsleeps,\u0027\u0027 and other behavior associated with breakdown in sleep\npatterns.",
"arxiv_id": "q-bio/0601008",
"authors": [
"Emmanuel Tannenbaum"
],
"categories": [
"q-bio.NC"
],
"title": "Sleep as the solution to an optimization problem",
"url": "https://arxiv.org/abs/q-bio/0601008"
},
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