Optimal Schedules of Light Exposure for Rapidly Correcting Circadian Misalignment
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{"title"=>"Optimal Schedules of Light Exposure for Rapidly Correcting Circadian Misalignment", "type"=>"journal", "authors"=>[{"first_name"=>"Kirill", "last_name"=>"Serkh", "scopus_author_id"=>"55836257800"}, {"first_name"=>"Daniel B.", "last_name"=>"Forger", "scopus_author_id"=>"6602414425"}], "year"=>2014, "source"=>"PLoS Computational Biology", "identifiers"=>{"doi"=>"10.1371/journal.pcbi.1003523", "scopus"=>"2-s2.0-84901359165", "isbn"=>"9550111016", "sgr"=>"84901359165", "pmid"=>"24722195", "issn"=>"15537358", "pui"=>"373162974"}, "id"=>"5d5dd099-0993-31d6-8553-52dbb8328f46", "abstract"=>"Author Summary When our body's internal timekeeping system becomes misaligned with the time of day in the outside world, many negative effects can be felt, including decreased performance, improper sleep, and jet lag. When misalignment is prolonged, it can also lead to serious medical conditions, including cancer, cardiovascular disease, and possibly even late-onset diabetes. Rapid readjustment of our internal daily (circadian) clock by properly timed exposure to light, which is the strongest signal to our internal circadian clock, is therefore important to the large proportion of the population which suffers from misalignment, including transmeridian travelers, shift workers, and individuals with circadian disorders. Here we develop a methodology to determine schedules of light exposure which may shift the human circadian clock in the minimum time. By calculating thousands of schedules, we show how the human circadian pacemaker is predicted to be capable of shifting much more rapidly than previously thought, simply by adjusting the timing of the beginning and end of each day. Schedules are summarized into general principles of optimal shifting, which can be applied without knowledge of the schedules themselves.", "link"=>"http://www.mendeley.com/research/optimal-schedules-light-exposure-rapidly-correcting-circadian-misalignment", "reader_count"=>54, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>4, "Librarian"=>1, "Student > Doctoral Student"=>4, "Researcher"=>10, "Student > Ph. D. Student"=>16, "Student > Postgraduate"=>2, "Student > Master"=>4, "Other"=>6, "Student > Bachelor"=>2, "Lecturer"=>1, "Professor"=>4}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>4, "Librarian"=>1, "Student > Doctoral Student"=>4, "Researcher"=>10, "Student > Ph. D. Student"=>16, "Student > Postgraduate"=>2, "Student > Master"=>4, "Other"=>6, "Student > Bachelor"=>2, "Lecturer"=>1, "Professor"=>4}, "reader_count_by_subject_area"=>{"Agricultural and Biological Sciences"=>17, "Arts and Humanities"=>1, "Chemistry"=>2, "Computer Science"=>2, "Engineering"=>4, "Environmental Science"=>1, "Biochemistry, Genetics and Molecular Biology"=>3, "Mathematics"=>3, "Medicine and Dentistry"=>11, "Neuroscience"=>1, "Sports and Recreations"=>1, "Physics and Astronomy"=>2, "Psychology"=>5, "Social Sciences"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>11}, "Social Sciences"=>{"Social Sciences"=>1}, "Sports and Recreations"=>{"Sports and Recreations"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>2}, "Psychology"=>{"Psychology"=>5}, "Mathematics"=>{"Mathematics"=>3}, "Environmental Science"=>{"Environmental Science"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>1}, "Engineering"=>{"Engineering"=>4}, "Chemistry"=>{"Chemistry"=>2}, "Neuroscience"=>{"Neuroscience"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>17}, "Computer Science"=>{"Computer Science"=>2}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>3}}, "reader_count_by_country"=>{"Canada"=>1, "United States"=>2, "Australia"=>2, "France"=>1, "Portugal"=>1, "Spain"=>1}, "group_count"=>2}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1459782"], "description"=>"<p>Predicted core body temperature minima (CBTmin, magenta triangles) are plotted against the pattern of optimal exposure to bright light (200 lux–10,000 lux, yellow), moderate light (100 lux, white), and darkness (0 lux, black). Predicted CBTmin under noisy light levels (See supplemental <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523.s001\" target=\"_blank\">figure S1</a>), with circadian period randomly sampled from an experimentally measured distribution <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523-Czeisler2\" target=\"_blank\">[18]</a>, is plotted for 20 hypothetical subjects (blue circles). The timing of entrained CBTmin in the new time zone is indicated by the dotted line. Circadian amplitude at CBTmin is indicated by the brightness of the markers, with white corresponding to zero amplitude. The subjects are initially entrained to a 16∶8 LD-cycle in moderate light. At day 0 the schedule shift occurs. Optimal schedules are grouped in rows by maximum admissible bright light level (yellow), and in columns by effected phase shift. Figures (<b>A</b>), (<b>B</b>), (<b>C</b>) use a maximum light level of 10,000 lux; (<b>D</b>), (<b>E</b>), (<b>F</b>) use 1000 lux; (<b>G</b>), (<b>H</b>), (<b>I</b>) use 500 lux; (<b>J</b>), (<b>K</b>), (<b>L</b>) use 200 lux; (<b>M</b>), (<b>N</b>), (<b>O</b>) use 100 lux. Figures (<b>A</b>), (<b>D</b>), (<b>G</b>), (<b>J</b>), (<b>M</b>) are optimal schedules for an 8-hour delay; (<b>B</b>), (<b>E</b>), (<b>H</b>), (<b>K</b>), (<b>N</b>) a 12-hour shift; (<b>C</b>), (<b>F</b>), (<b>I</b>), (<b>L</b>), (<b>O</b>) an 8-hour advance.</p>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "systems biology", "Theoretical biology", "Control engineering", "schedules", "re-entrainment", "12", "shifts"], "article_id"=>995245, "categories"=>["Biological Sciences"], "users"=>["Kirill Serkh", "Daniel B. Forger"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003523.g003", "stats"=>{"downloads"=>0, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Optimal_schedules_for_re_entrainment_to_8_and_12_hour_shifts_of_the_LD_cycle_/995245", "title"=>"Optimal schedules for re-entrainment to 8 and 12 hour shifts of the LD-cycle.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-10 03:55:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/1459780"], "description"=>"<p>Circadian phase is plotted in degrees, with 0° corresponding to entrained CBTmin (before the schedule shift occurs), while amplitude is measured on the radius. A 6 hour advance would be indicated by a shift to 90°, a 12 hour shift to 180°, and a 6 hour delay to 270°. The sleep/dark region is indicated by the shaded regions on the PARMs. The timing of entrained CBTmin in the new time zone is indicated by the dotted line. Figures (<b>A</b>)–(<b>G</b>) correspond directly to <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi-1003523-g001\" target=\"_blank\">figures 1A–1G</a>, with each subplot displaying the process re-entrainment under one of the six schedules considered in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi-1003523-g001\" target=\"_blank\">figure 1</a>. The phase and amplitude of predicted CBTmin (magenta triangles) are plotted in a one-to-one correspondence with the markers of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi-1003523-g001\" target=\"_blank\">figure 1</a>. In other words, the markers and lines of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi-1003523-g001\" target=\"_blank\">figure 1</a> are simply re-plotted here in phase-amplitude space. As in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi-1003523-g001\" target=\"_blank\">figure 1</a>, re-entrainment is plotted for 4 days before the schedule shift and for 14 days after.</p>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "systems biology", "Theoretical biology", "Control engineering", "phase-amplitude", "resetting", "maps", "corresponding"], "article_id"=>995244, "categories"=>["Biological Sciences"], "users"=>["Kirill Serkh", "Daniel B. Forger"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003523.g002", "stats"=>{"downloads"=>1, "page_views"=>20, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Polar_phase_amplitude_resetting_maps_corresponding_to_figure_1_/995244", "title"=>"Polar phase-amplitude resetting maps corresponding to figure 1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-10 03:55:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/1459790"], "description"=>"<p>The number of days required to achieve re-entrainment (both complete and partial) are recorded for each of the seven schedules presented in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi-1003523-g001\" target=\"_blank\">figure 1</a>. The number of days does not include the first day on which re-entrainment occurs (i.e. if re-entrainment occurs on the third day then the number of days required is two). This way if the subject starts out re-entrained the number of days required is zero. Complete re-entrainment is said to occur when CBTmin falls within approximately one hour of the exactly entrained time (the dotted line in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi-1003523-g001\" target=\"_blank\">figure 1</a>). Partial re-entrainment is said to occur when CBTmin falls within the sleep/dark region of the destination time zone.</p>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "systems biology", "Theoretical biology", "Control engineering", "re-entrainment", "schedules", "presented"], "article_id"=>995253, "categories"=>["Biological Sciences"], "users"=>["Kirill Serkh", "Daniel B. Forger"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003523.t001", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Times_to_re_entrainment_under_the_schedules_presented_in_figure_1_/995253", "title"=>"Times to re-entrainment under the schedules presented in figure 1.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-04-10 03:55:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/1459808", "https://ndownloader.figshare.com/files/1459809", "https://ndownloader.figshare.com/files/1459810", "https://ndownloader.figshare.com/files/1459811", "https://ndownloader.figshare.com/files/1459812", "https://ndownloader.figshare.com/files/1459813", "https://ndownloader.figshare.com/files/1459814", "https://ndownloader.figshare.com/files/1459815", "https://ndownloader.figshare.com/files/1459816", "https://ndownloader.figshare.com/files/1459817", "https://ndownloader.figshare.com/files/1459818", "https://ndownloader.figshare.com/files/1459819", "https://ndownloader.figshare.com/files/1459820", "https://ndownloader.figshare.com/files/1459821", "https://ndownloader.figshare.com/files/1459822", "https://ndownloader.figshare.com/files/1459823", "https://ndownloader.figshare.com/files/1459824"], "description"=>"<div><p>Jet lag arises from a misalignment of circadian biological timing with the timing of human activity, and is caused by rapid transmeridian travel. Jet lag's symptoms, such as depressed cognitive alertness, also arise from work and social schedules misaligned with the timing of the circadian clock. Using experimentally validated mathematical models, we develop a new methodology to find mathematically optimal schedules of light exposure and avoidance for rapidly re-entraining the human circadian system. In simulations, our schedules are found to significantly outperform other recently proposed schedules. Moreover, our schedules appear to be significantly more robust to both noise in light and to inter-individual variations in endogenous circadian period than other proposed schedules. By comparing the optimal schedules for thousands of different situations, and by using general mathematical arguments, we are also able to translate our findings into general principles of optimal circadian re-entrainment. These principles include: 1) a class of schedules where circadian amplitude is only slightly perturbed, optimal for dim light and for small shifts 2) another class of schedules where shifting occurs along the shortest path in phase-space, optimal for bright light and for large shifts 3) the determination that short light pulses are less effective than sustained light if the goal is to re-entrain quickly, and 4) the determination that length of daytime should be significantly shorter when delaying the clock than when advancing it.</p></div>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "systems biology", "Theoretical biology", "Control engineering", "schedules", "correcting", "circadian"], "article_id"=>995267, "categories"=>["Biological Sciences"], "users"=>["Kirill Serkh", "Daniel B. Forger"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003523.s001", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s002", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s003", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s004", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s005", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s006", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s007", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s008", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s009", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s010", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s011", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s012", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s013", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s014", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s015", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s016", "https://dx.doi.org/10.1371/journal.pcbi.1003523.s017"], "stats"=>{"downloads"=>4, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Optimal_Schedules_of_Light_Exposure_for_Rapidly_Correcting_Circadian_Misalignment_/995267", "title"=>"Optimal Schedules of Light Exposure for Rapidly Correcting Circadian Misalignment", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2014-04-10 03:55:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/1459789"], "description"=>"<p>The top plot shows the entraining stimulus (LD-cycle) to the oscillator, plotted on a log scale, shifted by hours at time 0. The light level increases from 100 lux before time 0 to ( = 10,000 lux) after time 0. In this case ( = 7 hours) is positive, so the schedule is advanced. The middle plot shows the oscillations in first coordinate of the model. The entrained oscillator before the phase shift is shown with a solid line, and the dotted line shows how the oscillator would behave were it entrained to the shifted stimulus. The solid line after time 0 shows the process of re-entrainment to the phase shift. The last plot shows the phase of the stimulus or, equivalently, of the entrained oscillator. Notice that the shift takes place when the phase of the stimulus (and therefore of the entrained oscillator) is ( = 7 hours). All significant features are labeled with the appropriate notation (See <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#s4\" target=\"_blank\">Methods</a>, or Setting up the Problem in supplemental <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523.s016\" target=\"_blank\">text S1</a>).</p>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "systems biology", "Theoretical biology", "Control engineering", "re-entrainment", "jewett-forger-kronauer"], "article_id"=>995252, "categories"=>["Biological Sciences"], "users"=>["Kirill Serkh", "Daniel B. Forger"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003523.g008", "stats"=>{"downloads"=>0, "page_views"=>41, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_process_of_re_entrainment_to_a_phase_shift_of_the_Jewett_Forger_Kronauer_Model_/995252", "title"=>"The process of re-entrainment to a phase shift of the Jewett-Forger-Kronauer Model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-10 03:55:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/1459786"], "description"=>"<p>The format is exactly the same as <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi-1003523-g004\" target=\"_blank\">figure 4</a>. Days −2 and −1 may be used as a legend associating a unique hue to each phase of the oscillator. Brightness is then used to represent amplitude, with white corresponding to zero amplitude <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523-Winfree3\" target=\"_blank\">[37]</a>. The exact coloring, based on the state of the model variables, is shown in supplemental <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523.s003\" target=\"_blank\">figure S3</a>. Figure (<b>A</b>) shows the predicted phase and amplitude under the optimal schedules for resetting the clock when 10,000 lux light is available; (<b>B</b>) 1000 lux; (<b>C</b>) 500 lux; (<b>D</b>) 200 lux; (<b>E</b>) 100 lux.</p>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "systems biology", "Theoretical biology", "Control engineering", "optimal", "circadian", "amplitude"], "article_id"=>995249, "categories"=>["Biological Sciences"], "users"=>["Kirill Serkh", "Daniel B. Forger"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003523.g005", "stats"=>{"downloads"=>1, "page_views"=>18, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Predicted_optimal_circadian_phase_and_amplitude_for_all_phase_shifts_/995249", "title"=>"Predicted optimal circadian phase and amplitude for all phase shifts.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-10 03:55:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/1459783"], "description"=>"<p>This plot shows the pattern of bright light (200 lux–10,000 lux, yellow), background light (100 lux, white), and darkness (0 lux, black) under which the clock is optimally reset from the corresponding initial phase. If a vertical line is drawn on the plot, then the pattern of light and dark along this vertical line is the optimal schedule for resetting the clock from the corresponding initial phase. Figure (<b>A</b>) shows the optimal schedules for resetting the clock when 10,000 lux light is available; (<b>B</b>) 1000 lux; (<b>C</b>) 500 lux; (<b>D</b>) 200 lux; (<b>E</b>) 100 lux.</p>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "systems biology", "Theoretical biology", "Control engineering", "schedules"], "article_id"=>995246, "categories"=>["Biological Sciences"], "users"=>["Kirill Serkh", "Daniel B. Forger"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003523.g004", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Optimal_schedules_for_all_phase_shifts_/995246", "title"=>"Optimal schedules for all phase shifts.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-10 03:55:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/1459779"], "description"=>"<p>Predicted circadian phase, indicated by simulated core body temperature minima (CBTmin, magenta triangles), is plotted against the pattern of exposure to bright light (10,000 lux, yellow), moderate light (100 lux, white), dim light (5 lux, gray), and darkness (0 lux, black). Predicted CBTmin under noisy light levels (See supplemental <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523.s001\" target=\"_blank\">figure S1</a>), with circadian period randomly sampled from an experimentally measured distribution <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523-Czeisler2\" target=\"_blank\">[18]</a>, is plotted for 20 hypothetical subjects (blue circles). Circadian amplitude at CBTmin is indicated by the brightness of the markers, with white corresponding to zero amplitude. The timing of entrained CBTmin in the new time zone is indicated by the dotted line. The subjects are initially entrained to a 16∶8 LD-cycle in moderate light. At day 0 the schedule shift occurs. The six schedules are compared are: (<b>A</b>) The abruptly shifted LD-cycle; also called a slam shift. (<b>B</b>) Times of light exposure and avoidance in the new time zone are prescribed to quicken re-entrainment. Phase delays of 1 hour/day are assumed. Based on the recommendations proposed by R. Sack (See Supplementary Appendix of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523-Sack1\" target=\"_blank\">[49]</a>.) (<b>C</b>) Times of light exposure and avoidance are prescribed, with an assumed phase delay of 2 hours/day. Based on the recommendations proposed by J. Waterhouse et.al. (See Table 2 of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523-Waterhouse1\" target=\"_blank\">[50]</a>.) (<b>D</b>) The sleep/dark region is gradually delayed, with 2 hours of bright light before bed and 2 hours of light avoidance after wake. Assumed delay of 2 hours/day. Based on the recommendations proposed by C. Eastman et.al. in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523-Eastman1\" target=\"_blank\">[51]</a>. (<b>E</b>) A PRC is used to place a series of 5 hour light stimuli, in a background of dim light, in order to produce a large delay. The timings are refined using a model <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523-Jewett2\" target=\"_blank\">[16]</a>. Proposed by D. Dean et.al. (See <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523.s001\" target=\"_blank\">Figure S1</a>:E1 in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523-Dean1\" target=\"_blank\">[9]</a>.) (<b>F</b>) Our optimal schedule for complete re-entrainment in minimum time. A model <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523-Jewett2\" target=\"_blank\">[16]</a> is used to compute the mathematically optimal schedule of light exposure (See <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#s4\" target=\"_blank\">Methods</a>) which resets the model in the least possible amount of time. (<b>G</b>) Our optimal schedule for partial re-entrainment in minimum time, designed to place CBTmin at the beginning of the sleep/dark region as quickly as possible (See Designing schedules for Partial Reentrainment in supplemental <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523.s016\" target=\"_blank\">text S1</a>).</p>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "systems biology", "Theoretical biology", "Control engineering", "schedules", "12-hour", "light-dark"], "article_id"=>995242, "categories"=>["Biological Sciences"], "users"=>["Kirill Serkh", "Daniel B. Forger"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003523.g001", "stats"=>{"downloads"=>3, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_schedules_for_a_12_hour_shift_of_the_light_dark_cycle_/995242", "title"=>"Comparison of schedules for a 12-hour shift of the light-dark cycle.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-10 03:55:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/1459788"], "description"=>"<p>The top plot shows the entraining stimulus (LD-cycle) and the leftmost plot, the entrained limit cycle corresponding to this stimulus. Here pink corresponds to day and black to night. The middle plot shows the oscillations in the first coordinate of the entrained limit cycle. The last plot shows the phase of periodic stimulus or, equivalently, of the entrained oscillator. All significant features are labeled with the appropriate notation (See <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#s4\" target=\"_blank\">Methods</a>, or Notation in supplemental <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523.s016\" target=\"_blank\">text S1</a>).</p>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "systems biology", "Theoretical biology", "Control engineering", "corresponding", "jewett-forger-kronauer"], "article_id"=>995251, "categories"=>["Biological Sciences"], "users"=>["Kirill Serkh", "Daniel B. Forger"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003523.g007", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Entraining_stimulus_and_corresponding_limit_cycle_of_the_Jewett_Forger_Kronauer_model_/995251", "title"=>"Entraining stimulus and corresponding limit cycle of the Jewett-Forger-Kronauer model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-10 03:55:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/1459787"], "description"=>"<p>We simulated the PRCs to all possible one-pulse stimuli for a variety of different light levels. For each light level, two stimuli were selected: the one producing the greatest advance and the one producing the greatest delay. The model was kept in total darkness before the stimulus was administered. Resulting phase shifts were measured using the concept of isochrons <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi.1003523-Winfree2\" target=\"_blank\">[22]</a>. On the right the optimal advancing stimuli (top) and optimal delaying stimuli (bottom) are plotted for each light level. The bars indicate both the duration (bar length) and phase (midpoint) of the light stimuli relative to the timing of CBTmin (solid magenta vertical line). On the left the PRCs corresponding to each optimal stimulus length are plotted. On each PRC, the optimal phase maximizing the shift is marked by a circle (filled for advances and unfilled for delays). The PRCs corresponding to optimal advancing stimuli are drawn using solid lines, and ones corresponding to optimal delaying stimuli, using dashed lines. We found that, for low light levels and smaller shifts, the daily light exposures observed in the optimal schedules (See <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi-1003523-g004\" target=\"_blank\">figures 4</a> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003523#pcbi-1003523-g005\" target=\"_blank\">5</a>) matched the optimal one-pulse stimuli very closely. In particular, we find that the optimal advancing stimuli are much longer than the optimal delaying stimuli.</p>", "links"=>[], "tags"=>["Computational biology", "neuroscience", "systems biology", "Theoretical biology", "Control engineering", "one-pulse", "stimuli"], "article_id"=>995250, "categories"=>["Biological Sciences"], "users"=>["Kirill Serkh", "Daniel B. Forger"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003523.g006", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Optimal_one_pulse_stimuli_to_advance_or_delay_the_clock_/995250", "title"=>"Optimal one-pulse stimuli to advance or delay the clock.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-04-10 03:55:26"}

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Relative Metric

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