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# Analytical Intel LLC Group

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# Breakaway Broadcast Live Beta V0

Time taken for breakaway rider to complete a course compared to the peloton, for a course profile given by $$h=h_0\text exp(-\beta (x-x_\text max)^2)$$ (shown schematically in inset), with $$h_0=0.02,0.025,0.03,0.035,0.04$$, $$\beta =0.5$$ and $$x_\text max=6$$. Here, $$m_\text b=1$$, $$F_0=0.028$$ and $$F_\textrmb0=0.011$$. We choose $$v_i=\sqrtF_0/\gamma =0.2$$ to give $$\ddotx(0)=0$$, so that the peloton is travelling at a constant speed

## Breakaway Broadcast Live Beta V0

Effect of valley position on breakaway success. Motion along the last 20 length units ($$\approx 10$$km) of a valley course profile given by $$h=h_0\exp \bigl (-\beta (x-x_\text min)^2\bigr )$$ with $$\text h_0=-\,0.04$$, $$\beta =0.5$$, $$m_\text b=1$$, $$\text F_\text s=0.032$$, $$F_\textb0=0.8F_\text s$$, $$p_1=0.1$$, $$a=0.5$$ and $$b=0.5$$. The solution is given by (16), (17), and (32)

Effect of peak position on breakaway success. Motion along the last 20 length units ($$\approx 10$$ km) of a hill course profile given by $$h=h_0\exp \bigl (-\beta (x-x_\text max)^2\bigr )$$ with $$h_0=0.04$$, $$\beta =0.5$$, $$x_\text max=6,10,14,18$$, and $$m_\text b=1$$, $$F_\text s=0.032$$, $$F_\textrmb0=0.8F_\text s$$, $$p_1=0.1$$, $$a=0.5$$ and $$b=0.5$$. We choose $$v_i=0.2$$ so that initially the peloton is moving at constant velocity on a flat course (given by (16) with $$\ddotx=0$$). The solution is given by (16), (17), and (32)

Effect of hill gradient on breakaway success. Motion along the last 20 length units ($$\approx 10$$ km) of a hill course profile given by $$h=h_0\exp \bigl (-\beta (x-x_\text max)^2\bigr )$$ with $$h_0=0.04$$, $$\beta =0.1,0.3,0.5,0.7$$, $$x_\text max=12$$, and $$m_\text b=1$$, $$F_\text s=0.032$$, $$\text F_\textrmb0=0.8\text F_\text s$$, $$p_1=0.1$$, $$a=0.5$$ and $$b=0.5$$. We choose $$v_i=0.2$$ so that initially the peloton is moving at constant velocity on a flat course (given by (16) with $$\ddotx=0$$). The solution is given by (16), (17), and (32)

Effect of hill height on breakaway success. Motion along the last 20 length units ($$\approx 10$$ km) of a hill course profile given by $$h=h_0\exp \big (-\beta (x-x_\text max)^2\bigr )$$ with $$h_0=0.02,0.03,0.04,0.05$$, $$\beta =0.5$$, $$x_\text max=12$$, and $$m_\text b=1$$, $$F_\text s=0.032$$, $$F_\textrmb0=0.8F_\text s$$, $$p_1=0.1$$, $$a=0.5$$ and $$b=0.5$$. We choose $$v_i=0.2$$ so that initially the peloton is moving at constant velocity on a flat course (given by (16) with $$\ddotx=0$$). The solution is given by (16), (17), and (32)

To estimate alpha diversity and beta diversity we used the breakaway v4.6 and divnet v0.34 packages, respectively [47, 48]. These approaches avoid common pitfalls from applying classical ecology indexes (i.e., Chao1, Shannon) to microbiome data, such as the influence of sequencing depth and data compositionality. 350c69d7ab