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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="h left-parenthesis epsilon comma script l semicolon r right-parenthesis equals left-parenthesis StartFraction 2 Over pi tau EndFraction StartFraction upper A left-parenthesis epsilon comma script l right-parenthesis Over 1 minus e Superscript minus 2 pi slash tau Baseline EndFraction right-parenthesis Superscript one-half Baseline upper G Subscript script l Baseline left-parenthesis negative 1 slash tau comma tau r right-parenthesis"> <semantics> <mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="75" data-semantic-children="72,74" data-semantic-content="10"> <mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="72" data-semantic-children="0,9" data-semantic-content="71,0" data-semantic-parent="75"> <mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="0" data-semantic-parent="72" data-semantic-operator="appl">h</mi> <mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="71" data-semantic-parent="72" data-semantic-added="true" data-semantic-operator="appl"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="9" data-semantic-children="7" data-semantic-content="1,8" data-semantic-parent="72"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="1" data-semantic-parent="9" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="7" data-semantic-children="2,3,4,5,6" data-semantic-content="3,5" data-semantic-parent="9"> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="2" data-semantic-parent="7">ϵ <!-- ϵ --> </mi> <mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="3" data-semantic-parent="7" data-semantic-operator="punctuated">,</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="script" data-semantic-id="4" data-semantic-parent="7"><!-- ℓ --> </mi> <mo data-semantic-type="punctuation" data-semantic-role="unknown" data-semantic-id="5" data-semantic-parent="7" data-semantic-operator="punctuated">;</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="6" data-semantic-parent="7">r</mi> </mrow> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="8" data-semantic-parent="9" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="10" data-semantic-parent="75" data-semantic-operator="relseq,=">=</mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="74" data-semantic-children="50,70" data-semantic-content="73" data-semantic-parent="75"> <msup data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-id="50" data-semantic-children="46,49" data-semantic-parent="74"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="46" data-semantic-children="44" data-semantic-content="11,45" data-semantic-parent="50"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="11" data-semantic-parent="46" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="44" data-semantic-children="17,42" data-semantic-content="43" data-semantic-parent="46"> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="17" data-semantic-children="12,16" data-semantic-parent="44"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="12" data-semantic-parent="17">2</mn> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="16" data-semantic-children="13,14" data-semantic-content="15" data-semantic-parent="17"> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="13" data-semantic-parent="16">π <!-- π --> </mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="15" data-semantic-parent="16" 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="14" data-semantic-parent="16">τ <!-- τ --> </mi> </mrow> </mfrac> </mrow> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="43" data-semantic-parent="44" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="42" data-semantic-children="27,41" data-semantic-parent="44"> <mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="27" data-semantic-children="18,25" data-semantic-content="26,18" data-semantic-parent="42"> <mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="18" data-semantic-parent="27" data-semantic-operator="appl">A</mi> <mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="26" data-semantic-parent="27" data-semantic-added="true" data-semantic-operator="appl"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="25" data-semantic-children="24" data-semantic-content="19,23" data-semantic-parent="27"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="19" data-semantic-parent="25" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="24" data-semantic-children="20,21,22" data-semantic-content="21" data-semantic-parent="25"> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="20" data-semantic-parent="24">ϵ <!-- ϵ --> </mi> <mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="21" data-semantic-parent="24" data-semantic-operator="punctuated">,</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="script" data-semantic-id="22" data-semantic-parent="24"><!-- ℓ --> </mi> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="23" data-semantic-parent="25" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="41" data-semantic-children="28,40" data-semantic-content="29" data-semantic-parent="42"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="28" data-semantic-parent="41">1</mn> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="29" data-semantic-parent="41" data-semantic-operator="infixop,−"><!-- − --> </mo> <msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="40" data-semantic-children="30,39" data-semantic-parent="41"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="30" data-semantic-parent="40">e</mi> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="division" data-semantic-id="39" data-semantic-children="38,35" data-semantic-content="34" data-semantic-parent="40"> <mrow data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="38" data-semantic-children="37" data-semantic-content="31" data-semantic-parent="39"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="31" data-semantic-parent="38" data-semantic-operator="prefixop,−"><!-- − --> </mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="37" data-semantic-children="32,33" data-semantic-content="36" data-semantic-parent="38"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="32" data-semantic-parent="37">2</mn> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="36" data-semantic-parent="37" 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="33" data-semantic-parent="37">π <!-- π --> </mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo data-semantic-type="operator" data-semantic-role="division" data-semantic-id="34" data-semantic-parent="39" data-semantic-operator="infixop,/">/</mo> </mrow> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="35" data-semantic-parent="39">τ <!-- τ --> </mi> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="45" data-semantic-parent="46" data-semantic-operator="fenced">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="vulgar" data-semantic-id="49" data-semantic-children="47,48" data-semantic-parent="50"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="47" data-semantic-parent="49">1</mn> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="48" data-semantic-parent="49">2</mn> </mfrac> </mrow> </msup> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="73" data-semantic-parent="74" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="70" data-semantic-children="53,68" data-semantic-content="69,51" data-semantic-parent="74"> <msub data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-id="53" data-semantic-children="51,52" data-semantic-parent="70"> <mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="51" data-semantic-parent="53" data-semantic-operator="appl">G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="script" data-semantic-id="52" data-semantic-parent="53"><!-- ℓ --> </mi> </mrow> </msub> <mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="69" data-semantic-parent="70" data-semantic-added="true" data-semantic-operator="appl"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="68" data-semantic-children="66" data-semantic-content="54,67" data-semantic-parent="70"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="54" data-semantic-parent="68" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="66" data-semantic-children="63,59,65" data-semantic-content="59" data-semantic-parent="68"> <mrow data-semantic-type="infixop" data-semantic-role="division" data-semantic-id="63" data-semantic-children="62,58" data-semantic-content="57" data-semantic-parent="66"> <mrow data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="62" data-semantic-children="56" data-semantic-content="55" data-semantic-parent="63"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="55" data-semantic-parent="62" data-semantic-operator="prefixop,−"><!-- − --> </mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="56" data-semantic-parent="62">1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo data-semantic-type="operator" data-semantic-role="division" data-semantic-id="57" data-semantic-parent="63" data-semantic-operator="infixop,/">/</mo> </mrow> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="58" data-semantic-parent="63">τ <!-- τ --> </mi> </mrow> <mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="59" data-semantic-parent="66" data-semantic-operator="punctuated">,</mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="65" data-semantic-children="60,61" data-semantic-content="64" data-semantic-parent="66"> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="60" data-semantic-parent="65">τ <!-- τ --> </mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="64" data-semantic-parent="65" 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="61" data-semantic-parent="65">r</mi> </mrow> </mrow> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="67" data-semantic-parent="68" data-semantic-operator="fenced">)</mo> </mrow> </mrow> </mrow> </mrow> <annotation encoding="application/x-tex">h\left(\epsilon ,\ell ;r\right)=\left({\frac {2}{\pi \tau }}{\frac {A(\epsilon ,\ell )}{1-e^{-2\pi /\tau }}}\right)^{\frac {1}{2}}G_{\ell }\left(-1/\tau ,\tau r\right)</annotation> </semantics> </math>