UNPKG

mathmlben

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Visualization for goldstandard

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="upper S equals minus upper T integral d Superscript p plus 1 Baseline sigma StartRoot negative zeta EndRoot left-bracket e Superscript minus beta upper U Baseline one-half zeta Superscript a b Baseline left-parenthesis upper G Subscript b a Baseline minus script upper F Subscript b a Baseline right-parenthesis minus left-parenthesis p minus 1 right-parenthesis right-bracket"> <semantics> <mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="75" data-semantic-children="0,74" data-semantic-content="1"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="0" data-semantic-parent="75">S</mi> <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="1" data-semantic-parent="75" data-semantic-operator="relseq,=">=</mo> <mrow data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="74" data-semantic-children="73" data-semantic-content="2" data-semantic-parent="75"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="2" data-semantic-parent="74" data-semantic-operator="prefixop,−"><!-- − --> </mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="73" data-semantic-children="3,71" data-semantic-content="72" data-semantic-parent="74"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="3" data-semantic-parent="73">T</mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="72" data-semantic-parent="73" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="integral" data-semantic-role="integral" data-semantic-id="71" data-semantic-children="4,69,70" data-semantic-content="4" data-semantic-parent="73"> <mo data-semantic-type="largeop" data-semantic-role="integral" data-semantic-id="4" data-semantic-parent="71" data-semantic-operator="integral"><!-- ∫ --> </mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="69" data-semantic-children="10,11,15,65" data-semantic-content="66,67,68" data-semantic-parent="71"> <msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="10" data-semantic-children="5,9" data-semantic-parent="69"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="5" data-semantic-parent="10">d</mi> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="9" data-semantic-children="6,8" data-semantic-content="7" data-semantic-parent="10"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="6" data-semantic-parent="9">p</mi> <mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="7" data-semantic-parent="9" data-semantic-operator="infixop,+">+</mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="8" data-semantic-parent="9">1</mn> </mrow> </msup> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="66" data-semantic-parent="69" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="11" data-semantic-parent="69">σ <!-- σ --> </mi> <mspace width="thinmathspace"/> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="67" data-semantic-parent="69" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt data-semantic-type="sqrt" data-semantic-role="unknown" data-semantic-id="15" data-semantic-children="14" data-semantic-parent="69"> <mrow data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="14" data-semantic-children="13" data-semantic-content="12" data-semantic-parent="15"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="12" data-semantic-parent="14" data-semantic-operator="prefixop,−"><!-- − --> </mo> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="13" data-semantic-parent="14">ζ <!-- ζ --> </mi> </mrow> </msqrt> </mrow> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="68" data-semantic-parent="69" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="65" data-semantic-children="64" data-semantic-content="16,57" data-semantic-parent="69"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="16" data-semantic-parent="65" data-semantic-operator="fenced">[</mo> </mrow> </mrow> <mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="64" data-semantic-children="63,59" data-semantic-content="51" data-semantic-parent="65"> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="63" data-semantic-children="24,27,33,50" data-semantic-content="60,61,62" data-semantic-parent="64"> <msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="24" data-semantic-children="17,23" data-semantic-parent="63"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="17" data-semantic-parent="24">e</mi> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="23" data-semantic-children="22" data-semantic-content="18" data-semantic-parent="24"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="18" data-semantic-parent="23" data-semantic-operator="prefixop,−"><!-- − --> </mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="22" data-semantic-children="19,20" data-semantic-content="21" data-semantic-parent="23"> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="19" data-semantic-parent="22">β <!-- β --> </mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="21" data-semantic-parent="22" 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="20" data-semantic-parent="22">U</mi> </mrow> </mrow> </msup> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="60" data-semantic-parent="63" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="vulgar" data-semantic-id="27" data-semantic-children="25,26" data-semantic-parent="63"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="25" data-semantic-parent="27">1</mn> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="26" data-semantic-parent="27">2</mn> </mfrac> </mrow> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="61" data-semantic-parent="63" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <msup data-semantic-type="superscript" data-semantic-role="greekletter" data-semantic-id="33" data-semantic-children="28,32" data-semantic-parent="63"> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="28" data-semantic-parent="33">ζ <!-- ζ --> </mi> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="32" data-semantic-children="29,30" data-semantic-content="31" data-semantic-parent="33"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="29" data-semantic-parent="32">a</mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="31" data-semantic-parent="32" 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="30" data-semantic-parent="32">b</mi> </mrow> </msup> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="62" data-semantic-parent="63" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="50" data-semantic-children="48" data-semantic-content="34,49" data-semantic-parent="63"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="34" data-semantic-parent="50" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="48" data-semantic-children="40,47" data-semantic-content="41" data-semantic-parent="50"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="40" data-semantic-children="35,39" data-semantic-parent="48"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="35" data-semantic-parent="40">G</mi> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="39" data-semantic-children="36,37" data-semantic-content="38" data-semantic-parent="40"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="36" data-semantic-parent="39">b</mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="38" data-semantic-parent="39" 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="37" data-semantic-parent="39">a</mi> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="41" data-semantic-parent="48" data-semantic-operator="infixop,−"><!-- − --> </mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="47" data-semantic-children="42,46" data-semantic-parent="48"> <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="42" data-semantic-parent="47">F</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="46" data-semantic-children="43,44" data-semantic-content="45" data-semantic-parent="47"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="43" data-semantic-parent="46">b</mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="45" data-semantic-parent="46" 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="44" data-semantic-parent="46">a</mi> </mrow> </msub> </mrow> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="49" data-semantic-parent="50" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="51" data-semantic-parent="64" data-semantic-operator="infixop,−"><!-- − --> </mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="59" data-semantic-children="58" data-semantic-content="52,56" data-semantic-parent="64"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="52" data-semantic-parent="59" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="58" data-semantic-children="53,55" data-semantic-content="54" data-semantic-parent="59"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="53" data-semantic-parent="58">p</mi> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="54" data-semantic-parent="58" data-semantic-operator="infixop,−"><!-- − --> </mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="55" data-semantic-parent="58">1</mn> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="56" data-semantic-parent="59" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="57" data-semantic-parent="65" data-semantic-operator="fenced">]</mo> </mrow> </mrow> </mrow> </mrow> <mrow data-semantic-type="empty" data-semantic-role="unknown" data-semantic-id="70" data-semantic-parent="71"/></mrow> </mrow> </mrow> </mrow> <annotation encoding="application/x-tex">S=-T\int d^{p+1}\sigma \,{\sqrt {-\zeta }}{\Bigl [}e^{-\beta U}{\frac {1}{2}}\zeta ^{ab}\left(G_{ba}-{\mathcal {F}}_{ba}\right)-(p-1){\Bigr ]}</annotation> </semantics> </math>