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.

1676 equations across 1477 symbols.

Δzˉ=Cov⁡s(wi,zi)wˉ+Es[wi Δzi]wˉ\Delta \bar z = \frac{\operatorname{Cov}_s(w_i, z_i)}{\bar w} + \frac{\mathbb{E}_s[w_i \, \Delta z_i]}{\bar w}

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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dzˉdt∣selection=β Var⁡s(z)\frac{d\bar z}{dt}\Big|_{\text{selection}} = \beta \, \operatorname{Var}_s(z)

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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PF(+W)PR(−W)=exp⁡ ⁣(W−ΔFkBT)\frac{P_{\mathrm F}(+W)}{P_{\mathrm R}(-W)} = \exp\!\left(\frac{W - \Delta F}{k_{\mathrm{B}} T}\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^+z0.95p^(1−p^)n≤ε\hat{p} + z_{0.95}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \le \varepsilon

1 published occurrence

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This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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⟨e−βW⟩=e−βΔF,β=1kBT\left\langle e^{-\beta W} \right\rangle = e^{-\beta \Delta F}, \qquad \beta = \frac{1}{k_{\mathrm{B}} T}

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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Var⁡(Sel)=σ2∑isi2(zi−zˉ)2,Ne=1HHI\operatorname{Var}(\mathrm{Sel}) = \sigma^2 \sum_i s_i^2 (z_i - \bar z)^2, \qquad N_e = \frac{1}{\mathrm{HHI}}

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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ρt=ρh+(ρm−ρh) st,ρm<ρh\rho_t = \rho_h + (\rho_m - \rho_h)\, s_t, \qquad \rho_m < \rho_h

1 published occurrence

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This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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harm(scope)  =  p(misuse)⋅blast_radius(scope)\text{harm}(\text{scope}) \;=\; p(\text{misuse}) \cdot \text{blast\_radius}(\text{scope})

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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