Live mathematical reference

Mathematical compendium

A live index of the equations in published articles. Each entry leads to its article, equation guide, and the terms explained there. New or edited published articles appear automatically.

1815 equations across 1477 symbols.

W_{\max} = k_B T \ln 2

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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x^\ast = y^\ast = 252

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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x+y=B

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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y - x = 224

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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(n-1)/n

1 published occurrence

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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\Delta F = \alpha \ln\!\left(\frac{C}{C_0}\right)

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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\dot{x}_i = x_i\big(f_i(x) - \phi(x)\big)

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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\hat{f} = \frac{\sum_{i} (P_2(i) - P_1(i))\,(P_4(i) - P_1(i))}{\sum_{i} (P_3(i) - P_1(i))\,(P_4(i) - P_1(i))}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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\operatorname{Var}(\Delta p) = \frac{p(1-p)}{2N_e}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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\phi(x) = \sum_i x_i f_i(x)

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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2.3\times10^{13}

1 published occurrence

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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2(n-1)/n

1 published occurrence

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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4.096\ \mu s \times 2^{\text{timeout}}

1 published occurrence

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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D_{\mathrm{KL}}(p \,\|\, q) = \sum_i p_i \log_2(p_i/q_i)

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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E_{\text{inference}} = P_{\text{active}} \cdot t_{\text{active}}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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E(i,j)

1 published occurrence

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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f_i(x) = \sum_j x_j\, U(i,j)

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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I \times BW_{\text{peak memory}}

1 published occurrence

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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I = \frac{\text{FLOPs performed}}{\text{bytes moved}}, \qquad P_{\text{achievable}} = \min\left(P_{\text{peak compute}},\; I \times BW_{\text{peak memory}}\right)

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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P_{\text{avg}} = d \cdot P_{\text{active}} + (1-d) \cdot P_{\text{sleep}}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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