Supporting Materials and Methods
1) The double Gaussian and double Lorentzian
In order to estimate the two dates where the highest number of performances occurs for both
thermal and cultural peak, we investigated two functions:
(i) The double Gaussian function f1(x) that is the sum of two Gaussian functions:
f1(x) = f1,1(x) + f1,2(x)
(1)
where
f1(x) = a1 · exp
−

x − b1
c1


2
+a2 · exp
−

x − b2
c2


2
(2)
(ii) The double Lorentz function f2(x) that is the sum of two Lorentzian functions:
f1(x) = f2,1(x) + f2,2(x)
(3)
where
f2(x) = c1
2
a1π
1 +
x − b1
a1/2
2 + c2
2
a2π
1 +
x − b2
a2/2
2
(4)
The functions f1 and f2 are two-peak functions and x is the number of elite performances in
a week. Resulting adjusted R2 and RMSE were gathered for both functions and the elected
function for a given percent category was the function that presented the best statistics.
2) Estimates of x01, x02, p1, p2
For each elected function in each percent category, the two peaks x01, x02 were estimated, and
the proportions p1, p2 were given by estimating the area under the curve in the interval [0, 52]
for the functions f1,1, f1,2, f2,1, f2,2. For notation convenience, we denoted i and j as the indexes
of the functions, such as when i = 1 and j = 1, fi,j referred to f1,1. Integration of the functions
was given by:
Z 52
0
fi,j(x) = Fi,j(52) − Fi,j(0)
(5)
where
F1,j(x) = −√π × aj × cj × erf
bj − x
cj

(6)
and
F2,j(x) = −2
cj × tan−1
2 (bj − x)
aj

π
(7)
where erf(x) is the error function and tan−1(x) the inverse tangent function. The proportion of
performances in the two peaks was estimated by computing the area under the curve (proportion
of Performances) of each elected model and for each PC:
Z 52
0
f1(x) =
Z 52
0
f1,1(x) +
Z 52
0
f1,2(x)
(8)
Z 52
0
f2(x) =
Z 52
0
f2,1(x) +
Z 52
0
f2,2(x)
(9)
1
And the proportions were calculated in percentages using:
p1 =
R 52
0
fi,1(x)
R 52
0
fi(x)
× 100
(10)
p2 =
R 52
0
fi,2(x)
R 52
0
fi(x)
× 100
(11)
Where i = 1 or 2, depending on the elected function f1(x) or f2(x) at each PC.
2

Environment and scheduling effects on sprint and middle distance running performances.
Haïda, Amal,Dor, Frédéric,Guillaume, Marion,Quinquis, Laurent,Marc, Andy,Marquet, Laurie-Anne,Antero-Jacquemin, Juliana,Tourny-Chollet, Claire,Desgorces, François,Berthelot, Geoffroy,Toussaint, Jean-François