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mathmlben

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Visualization for goldstandard

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="normal upper Phi colon script upper O Subscript upper M Superscript left-parenthesis m double-struck right-parenthesis Baseline times script upper L left-parenthesis script upper S Subscript n Baseline script upper S Subscript m Baseline right-parenthesis right-arrow script upper L left-parenthesis script upper S Subscript n Baseline comma script upper S Subscript m Baseline right-parenthesis colon left-parenthesis f comma upper A right-parenthesis right-arrow from bar f upper A"> <semantics> <mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="56" data-semantic-children="0,1,52,31,55" data-semantic-content="1,31"> <mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-id="0" data-semantic-parent="56">Φ <!-- Φ --> </mi> <mo data-semantic-type="punctuation" data-semantic-role="unknown" data-semantic-id="1" data-semantic-parent="56" data-semantic-operator="punctuated">:</mo> <mrow data-semantic-type="relseq" data-semantic-role="arrow" data-semantic-id="52" data-semantic-children="51,48" data-semantic-content="20" data-semantic-parent="56"> <mrow data-semantic-type="infixop" data-semantic-role="unknown" data-semantic-id="51" data-semantic-children="9,50" data-semantic-content="10" data-semantic-parent="52"> <msubsup data-semantic-type="subsup" data-semantic-role="latinletter" data-semantic-id="9" data-semantic-children="2,3,7" data-semantic-parent="51" data-semantic-collapsed="(9 (8 2 3) 7)"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="script" data-semantic-id="2" data-semantic-parent="9">O</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="3" data-semantic-parent="9">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="7" data-semantic-children="5" data-semantic-content="4,6" data-semantic-parent="9"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="4" data-semantic-parent="7" data-semantic-operator="fenced">(</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="5" data-semantic-parent="7">m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="double-struck" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-font="double-struck" data-semantic-id="6" data-semantic-parent="7" data-semantic-operator="fenced">)</mo> </mrow> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo data-semantic-type="operator" data-semantic-role="unknown" data-semantic-id="10" data-semantic-parent="51" data-semantic-operator="infixop,×">× <!-- × --> </mo> </mrow> <mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="50" data-semantic-children="11,42" data-semantic-content="49,11" data-semantic-parent="51"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="script" data-semantic-id="11" data-semantic-parent="50" data-semantic-operator="appl">L</mi> </mrow> </mrow> <mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="49" data-semantic-parent="50" data-semantic-added="true" data-semantic-operator="appl"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="42" data-semantic-children="41" data-semantic-content="12,19" data-semantic-parent="50"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="12" data-semantic-parent="42" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="41" data-semantic-children="15,18" data-semantic-content="40" data-semantic-parent="42"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="15" data-semantic-children="13,14" data-semantic-parent="41"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="script" data-semantic-id="13" data-semantic-parent="15">S</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="14" data-semantic-parent="15">n</mi> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="40" data-semantic-parent="41" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="18" data-semantic-children="16,17" data-semantic-parent="41"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="script" data-semantic-id="16" data-semantic-parent="18">S</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="17" data-semantic-parent="18">m</mi> </mrow> </msub> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="19" data-semantic-parent="42" data-semantic-operator="fenced">)</mo> </mrow> </mrow> </mrow> <mo stretchy="false" data-semantic-type="relation" data-semantic-role="arrow" data-semantic-id="20" data-semantic-parent="52" data-semantic-operator="relseq,→"><!-- → --> </mo> <mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="48" data-semantic-children="21,44" data-semantic-content="47,21" data-semantic-parent="52"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="script" data-semantic-id="21" data-semantic-parent="48" data-semantic-operator="appl">L</mi> </mrow> </mrow> <mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="47" data-semantic-parent="48" data-semantic-added="true" data-semantic-operator="appl"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="44" data-semantic-children="43" data-semantic-content="22,30" data-semantic-parent="48"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="22" data-semantic-parent="44" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="43" data-semantic-children="25,26,29" data-semantic-content="26" data-semantic-parent="44"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="25" data-semantic-children="23,24" data-semantic-parent="43"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="script" data-semantic-id="23" data-semantic-parent="25">S</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="24" data-semantic-parent="25">n</mi> </mrow> </msub> <mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="26" data-semantic-parent="43" data-semantic-operator="punctuated">,</mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="29" data-semantic-children="27,28" data-semantic-parent="43"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="script" data-semantic-id="27" data-semantic-parent="29">S</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="28" data-semantic-parent="29">m</mi> </mrow> </msub> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="30" data-semantic-parent="44" data-semantic-operator="fenced">)</mo> </mrow> </mrow> </mrow> <mo data-semantic-type="punctuation" data-semantic-role="unknown" data-semantic-id="31" data-semantic-parent="56" data-semantic-operator="punctuated">:</mo> <mrow data-semantic-type="relseq" data-semantic-role="arrow" data-semantic-id="55" data-semantic-children="46,54" data-semantic-content="37" data-semantic-parent="56"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="46" data-semantic-children="45" data-semantic-content="32,36" data-semantic-parent="55"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="32" data-semantic-parent="46" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="45" data-semantic-children="33,34,35" data-semantic-content="34" data-semantic-parent="46"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="33" data-semantic-parent="45">f</mi> <mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="34" data-semantic-parent="45" data-semantic-operator="punctuated">,</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="35" data-semantic-parent="45">A</mi> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="36" data-semantic-parent="46" data-semantic-operator="fenced">)</mo> </mrow> <mo stretchy="false" data-semantic-type="relation" data-semantic-role="arrow" data-semantic-id="37" data-semantic-parent="55" data-semantic-operator="relseq,↦"><!-- ↦ --> </mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="54" data-semantic-children="38,39" data-semantic-content="53" data-semantic-parent="55"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="38" data-semantic-parent="54">f</mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="53" data-semantic-parent="54" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="39" data-semantic-parent="54">A</mi> </mrow> </mrow> </mrow> <annotation encoding="application/x-tex">\Phi :{\mathcal {O}}_{M}^{(m\mathbb {)} }\mathbb {\times } {\mathcal {L}}({\mathcal {S}}_{n}{\mathcal {S}}_{m})\rightarrow {\mathcal {L}}({\mathcal {S}}_{n},{\mathcal {S}}_{m}):(f,A)\mapsto fA</annotation> </semantics> </math>