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Determining moment of waking up

From our measurements we've got information about the respiration during your sleep. Out of this information, we get a globel line of of the sleepphase during the night. Out of these line, we've to determine what's the best moment to wake someone between a given interval. The best moment to wake someone is just after the REM-sleep. So this is the first or second nREM-sleep stage. (see literature, add reference). In our algorithm are developed two methods which can determine which moment you've to wake someone. The first method is looking to the slope of the line. During REM-sleep, the respiration is at his highest point. So we can detect the end of the REM-phase with a declining line. (slope is negative) Another method is looking to position relative to the mean of the line. With this method, we can detect a 'good' moment when the line is under the mean of the whole night. But the mean is probably a too low value, so we've to increase the value with a factor of the variation.

However, during the REM-sleep, the respiration variates a lot (see literature, add referece), so we've to be sure that a declining line, or the position below the mean, is realy the end of the REM-sleep, and not just the variation during the REM-sleep. This can be done by detecting two or three times a declining line over two/three frames. (two/three frames is around 8/12 minutes).

In the comming days, we will test both methods before we chose the best one. Another option is to combinate the two methods. So we could call it a good moment of waking up when the line is declining and when the line is under the mean + variationfactor.

Room Brightness Control

function that calculates the brightness of sunlight based on the date/time

 to-report light[day time]
   let psi   51.4408                ;; lat. ehv
   let Gsc   1367                   ;; w/m2 solar constant
   let LC    (15 * 1 - 5.4778) / 15 ;; timezone corrected longitude
   let c     0.21                   ;; fraction of extraterrestrial sunlight that reaches
                                     ; the surface (clear weather
 
   ;; most of the following formulas are from wikipedia, they need to be verified and sourced.
   let Ext   Gsc * (1 + 0.034 * cos(360 / 365 * (day - 2))) ;; day
   let theta 360 * (day - 1) / 365.242
   let d     23.45 * sin(360 * (day + 10) / 365)
   let eqt   0.258 * cos(theta) - 7.416 * sin(theta) - 3.648 * cos(2 * theta) - 9.228 * sin(2 * theta)
   let w     time + eqt / 60 - LC
   let as    asin(cos((w - 12) / 24 * 360) * cos(psi) * cos(d) + sin(psi) * sin(d))
   let Edv   Ext * exp(- c / sin(as)) * sin(90 - as) * (max list 0 as) / as
   report Edv * 93;;lm/w http://physics.ucsd.edu/~tmurphy/papers/lumens-per-watt.pdf
 end

Temperature Control

simple model to calculate the room temperature

 globals [T
          k
          h
          Tr
          Ti
          dT]
 
 to setup
   Clear-all
   set T  T0;; input starting temperature
   set k  -0.03
   set h  0.02
   set Tr 50
   set Ti 12
   set dT 0
   reset-ticks
 end
 
 to Go
     ifelse Heater;; Heater = true when the heater is on
     [set dT h * (Tr - T)] [set dT 0]
     set T T + k * (T - Ti) + dT
     tick
 end