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Rϵ,δ(g)=max⁡{M:F1,…,FM are disjoint,pϵ(Fk)≥1−δ for every k}R_{\epsilon,\delta}(g)= \max\left\{M:\begin{array}{l} F_1,\ldots,F_M\ \text{are disjoint},\\ p_{\epsilon}(F_k)\geq1-\delta\ \text{for every }k \end{array}\right\}

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Now define Rϵ,δ(g)=max⁡{M:F1,…,FM are disjoint,pϵ(Fk)≥1−δ for every k}R_{\epsilon,\delta}(g)= \max\left\{M:\begin{array}{l} F_1,\ldots,F_M\ \text{are disjoint},\\ p_{\epsilon}(F_k)\geq1-\delta\ \text{for every }k \end{array}\right\}. subject to 1-δ\delta>pblind(ϵ)p_{\mathrm{blind}}(\epsilon) and to a fixed rule for which fragment partitions are admissible. The displayed g records the physical parameter of interest; under the Haar-average convention the resulting scalar is independent of its coordinate label. A worst-case definition would retain explicit dependence until the infimum is taken.

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Rϵ,δR_{\epsilon,\delta}

Symbol R_epsilon,delta

ReR_epsilon,delta is the quantity selected or evaluated by the optimization written on the right.

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pϵp_{\epsilon}

Symbol p_epsilon

pep_epsilon appears in the objective or constraint used by the optimization on the right.

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Published contexts (1)

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Rϵ,δ(g)=max⁡{M:F1,…,FM are disjoint,pϵ(Fk)≥1−δ for every k},R_{\epsilon,\delta}(g)= \max\left\{M:\begin{array}{l} F_1,\ldots,F_M\ \text{are disjoint},\\ p_{\epsilon}(F_k)\geq1-\delta\ \text{for every }k \end{array}\right\},

Equation 55 · Evolutionary Physics

A Reference Frame Becomes Classical by Publishing Its Orientation

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

Now define Rϵ,δ(g)=max⁡{M:F1,…,FM are disjoint,pϵ(Fk)≥1−δ for every k}R_{\epsilon,\delta}(g)= \max\left\{M:\begin{array}{l} F_1,\ldots,F_M\ \text{are disjoint},\\ p_{\epsilon}(F_k)\geq1-\delta\ \text{for every }k \end{array}\right\}. subject to 1-δ\delta>pblind(ϵ)p_{\mathrm{blind}}(\epsilon) and to a fixed rule for which fragment partitions are admissible. The displayed g records the physical parameter of interest; under the Haar-average convention the resulting scalar is independent of its coordinate label. A worst-case definition would retain explicit dependence until the infimum is taken.

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