## 3 Results  
Table 2 shows the parameters of preliminary simulations based on only one difference between the two simulations, in the advance shift in weekday RT relative to free day RT, of either 2.0 or 3.0 h. These simulations are called \"preliminary\" because they did not account for the phase-delaying effect of a smaller (2.0 h) advance shift. Such a smaller shift leads to a later phase of light exposure of the circadian clocks on weekdays that, in turn, leads to a delayed shift in the phase of these clocks, that, in turn, leads to a shift in weekend sleep timing at a later hour. Such a shift in weekend sleep timing is a cause of a phase difference between earlier and later weekday risers (i.e., in the present study we compared the subdivisions in accord with weekday RT, either earlier than 7:00 or later (i.e., either RT \(<\) 7 or RT \(\geq\) 7, respectively). Therefore, such real-world data on the sleep timing of lecturers having early and late weekday RTs (Table 3, left columns, and Figure 4, left) were used to correct sleep timing of the preliminary simulations (Table 2). This correction yielded a 0.7 h difference in sleep timing on free days between lecturers with RT \(<\) 7 and those with RT \(\geq\) 7 (Figure 1). The difference between M- and E-types in the position of their circadian phases (\(>\)2.0 h), as mentioned in the Introduction, translates into the difference between their sleep timing on weekends. However, the difference in weekend sleep timing appears to be smaller than 2.0 h [12,13] (i.e., on average, a 1.8 h difference was obtained in the analysis of data on sleep times of as many as 50 pairs of samples of M- and E-types reported in the literature [12]). It seems that the major cause of such a reduction in the phase difference between chronotypes in weekend sleep timing is their difference in the advance in weekday waking times relative to weekend waking times. The circadian clocks of E-types are delayed by \(\geq\)2.0 h relative to the clocks of M-types, and, in turn, these types have later weekend waking times, forcing them to advance their weekday waking times by more. Such a larger advance in weekday waking times is expected to lead to an earlier phase of light exposure of their circadian clocks on weekdays that, in turn, can lead to an advancing shift in the phase of these clocks that, in turn, can lead to a shift in their weekend sleep timing at an earlier hour. Since such an advance in weekend sleep timing led to a delay of less than 2.0 h in the sleep timing of E-types relative to the timing of M-types, the real-world data on sleep timing of lecturers of M- and E-types (Table 3, middle columns, and Figure 4, middle graphs) were used to correct sleep times of the preliminary simulations that differed only in the advance in weekday RT, i.e., either a 2.0 or 3.0 h advance in weekday RT relative to free day RT (Tables 2 and 3, upper part). This correction yielded the 1.5 h difference in sleep timing on free days between the subdivisions into M- and E-types (Table 2 and Figure 2). Figure 1: Simulations of the sleep–wake cycles of early and late risers. Simulations of the whole sequence of 10 sleep–wake cycles (**A**), and two subintervals for a weekday and a weekend, (**B**,**C**), respectively, for the participants with different weekday risetime (RT), either <7 or >=7 a.m. See Table 3 and Figure 4 (left graphs) for the comparison with sleep times self-reported by lecturers. The sequence of 10 sleep–wake cycles includes two last free days (e.g., at the end of a hypothetical vacation), the following week consisting of five weekdays and two weekends, and the first weekday of the next week (i.e., Sa-Su, Mo-Fr, Sa-Su, and Mo are the days of the week, namely, Saturday, Sunday, Monday, Tuesday, Wednesday, Thursday, Friday). _S(t)_: Alterations between buildup and decay phases of the process of sleep–wake regulation. The parameters of these buildings and decays are modulated by a sine-form function with a 24 h period (i.e., this function represents the circadian pacemaker).