*2.5. Model Selection*

Within MCLUST framework, selection for the number of clusters can be achieved through the use of the Bayesian information criterion (BIC). Given a random sample of *n* independent *d*-vectors *y* = (*y*1, ..., *yn*) drawn from (4) and (9) with some value of *G*, the BIC for this *G*-component mixture model is given by:

$$BIC\_G = 2l\_O(\blackdot{\Theta}; \mathfrak{y}) - \nu\_G \log(n),\tag{21}$$

where Θˆ is the MLE for model parameters, *lO* is the observed likelihood as in (5) or (10), and *νG* is the number of independent parameters to be estimated. In the most simplistic case, we allow the mean and covariance of each component to vary freely—this is the case we will focus on in this paper. Therefore, for a *G*-component mixture model, we have *νG* = (*G* − 1) + *Gd* + *Gd*(*d* − 1)/2. For comparison purpose, in this paper, we will compare MCLUST-ME results to MCLUST results with the same number of components.


**5. Summary**

In the western and eastern industrial countries, the number of sleep disturbed subjects increased over the time. Undiagnosed and untreated, sleep disorders caused on one hand often by subjective suffering among those affected individuals and on the other hand, due to decreased attention and increased daytime fatigue or daytime sleepiness, to an increased risk of accidents in road traffic and workplace (e.g. Peter et al. 1995, Gerdesmeyer et al. 1997, Randerath et al. 1997, 1998, Büttner et al. 2000a/b).

Sleep Apnea syndromes are common disorders. 1-5% of the population is affected by it (men are about ten times more affected than women). In particular, patients with OSAS suffer in addition to their symptoms often also on a multitude of sequelae, including excessive daytime sleepiness (Büttner et al. 2004e), vigilance decrease (Büttner et al. 2003b, 2004c) and memory disorders (Büttner et al. 2003c/d).

These performance restrictions or impairments affect the affected subjects, both professionally and in their ability to drive motor vehicles (Findley et al. 1988a/b, 1989b, 1990, 1991, 1995, Mitler et al. In 1988, Cassel et al. 1991a/b, 1993, 1996 , ATS 1994, Gerdesmeyer et al. 1997, Krieger et al. 1997, Randerath et al. 1997, 1998, 2000, Weeß 1997, Weeß et al. 1998a/b, Büttner et al. 2000a/b, Büttner 2001). Consequences of this reduced performance are therefore often accidents or nearly accidents by falling asleep at the wheel. However, other cognitive and mental functions and the quality of life can be affected by sleep disorders (Sleep Apnea Syndrome, Insomnia and/or Narcolepsy).

In summary therefore, can be said that sleep disorders and/or sleep diseases are complex disorders which human beings can affect in his totality and in his whole personality. It can therefore affect all physical, mental and spiritual processes. It can lead to lower physical and mental performances; reduce vigilance, impaired attention and concentration. It can affect the quality of life, reduce, limit and/or prevent social contacts and competencies skills, and cause in other psychiatric5, neurological6 and organic7 diseases.

A detailed sleep diagnostics and possibly therapy of previously known sleep disorders and/or sleep diseases is therefore essential to prevent complications and comorbidities, to prevent treatment resistance with respect to other physical and mental diseases and to provide effective medical treatment.


2.1.3. Effect of Carbohydrate Amount

Several studies have directly compared varying amounts of CHO ingested before exercise, either showing no differences in substrate oxidation with varying amounts of pre-exercise CHO [5,52–54], or differences throughout all [55] or portions [56,57] of the exercise bout. When pooling a number of studies together, there is a weak positive relationship between the amount of CHO ingested and RER during subsequent exercise, while differences in RER between CHO-fed and fasted-state exercise increase as the amount of CHO ingested is increased (Figure 5).

**Figure 4.** Substrate oxidation in relation to exercise intensity for studies comparing overnight-fasted and CHO-fed exercise with normal muscle glycogen levels (**A**,**B**), exercise undertaken with high (471 ± 208 mmol kg−1 dry mass) and low (232 ± 112 mmol kg−1 dry mass) muscle glycogen levels (**C**,**D**), and following high (82 ± 10) and low (36 ± 9) glycemic index meals (**E**,**F**). Shaded areas represent 95% confidence intervals. Data were obtained by pooling results from 103 studies (see supplementary files for references).

**Figure 5.** Substrate oxidation in relation to amount of carbohydrate (CHO) consumed before exercise, as absolute RER value during exercise (**A**) and difference in RER between fed and fasted-state exercise (**B**). Shaded areas represent 95% confidence intervals. Data were obtained by pooling results from 76 studies (see supplementary files for references).

**Figure 6.** Substrate oxidation in relation to the time food was consumed before exercise, as absolute RER value during exercise (**A**) and difference in RER between CHO-fed and fasted-state exercise (**B**). Shaded areas represent 95% confidence intervals. Data were obtained by pooling results from 76 studies (see supplementary files for references).

**Figure 7.** Relationship between AMPKα2 activity during exercise (measured as fold-change from pre-exercise resting levels to immediately post-exercise) and carbohydrate (CHO) intake before exercise including (**A**) and excluding (**B**) studies that tested in the overnight-fasted state. HIIT: high-intensity interval training. Shaded areas represent 95% confidence intervals. Data were obtained by pooling results from 22 studies (see supplementary files for references), which included 265 participants (6.0% female), 25.1 ± 2.8 years, VO2max 52.9 ± 11.0 mL kg−1 min−1.

#### 2.1.4. Effect of Pre-Exercise Meal Timing

The amount of time before exercise food is consumed is another factor that can influence metabolism and substrate oxidation, and studies have undertaken exercise in the fed state between 5 [58] and 240 min [59,60] post-prandial. Although direct comparisons of the influence of meal-timing are limited, no differences in substrate oxidation were found when the same meals were ingested 15, 45, or 75 min [61] and 30, 60, or 90 min [62] before exercise. When consumed within 4 h of exercise, the amount of time prior to exercise does not have a meaningful impact on substrate oxidation (Figure 6).

## 2.1.5. Summary and Future Directions

During submaximal steady-state exercise, fat oxidation is generally higher in the overnight-fasted compared with CHO-fed state.  However, as exercise intensity increases the difference in fat oxidation between CHO-fed and fasted-state exercise diminishes. Fat oxidation is also higher when undertaking exercise with low, compared with normal muscle glycogen levels, with the di fferences maintained across varying exercise intensities but diminishing as the duration of exercise extends. While the amount of time before exercise food is consumed does not meaningfully influence substrate oxidation, greater amounts of CHO in the pre-exercise meal leads to greater di fferences in substrate oxidation between fed and fasted-state exercise. These findings are most applicable to moderately-trained males, who made up ~87% of study participants. Substrate metabolism may di ffer between males and females [63], with di fferences further a ffected by the female menstrual cycle [64] and the use of oral contraceptives [65]. Additionally, sedentary populations typically show no di fferences in post-exercise glucose, insulin, or FFAs between fasted and fed conditions [66], which is in contrast with trained athletes [67–69] who also show a greater capacity for fat oxidation compared with untrained or recreationally active populations [70].

Despite fasted-state training being performed by a large number of endurance athletes [15], there are potential negative implications from its use. Particularly for athletes doing a high volume of training, exercising in the overnight-fasted state could more likely lead to a negative energy balance, which can be associated with hormonal and immune dysfunction [71]. As a method of providing energy intake while still allowing higher levels of fat oxidation, future studies should examine the effects of a protein-rich breakfast on fat oxidation during exercise, in direct comparison with exercise following a CHO-rich breakfast and in the overnight-fasted state. As this approach is currently utilized by few endurance athletes [16], it could be a useful tool for those who want to increase fat burning without incurring a large caloric deficit. The influence of various pre-exercise meals on gut comfort should also be investigated, as a large number of athletes perform fasted-state training to avoid gut discomfort [15]. Exercise-induced gastrointestinal distress is beyond the scope of this review but has been reviewed elsewhere [72,73].