mathmlben
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Visualization for goldstandard
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text/mathml
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="upper A Subscript k Baseline left-parenthesis n right-parenthesis equals sigma-summation Underscript 1 less-than h less-than-or-equal-to k left-parenthesis h comma k right-parenthesis equals 1 Endscripts normal e Superscript pi normal i f left-parenthesis h comma k right-parenthesis minus left-parenthesis 2 pi normal i n h slash k right-parenthesis">
<semantics>
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<msub data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-id="2" data-semantic-children="0,1" data-semantic-parent="64">
<mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="0" data-semantic-parent="2" data-semantic-operator="appl">A</mi>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="1" data-semantic-parent="2">k</mi>
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</msub>
<mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="63" data-semantic-parent="64" data-semantic-added="true" data-semantic-operator="appl"></mo>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="3" data-semantic-parent="61" data-semantic-operator="fenced">(</mo>
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="4" data-semantic-parent="61">n</mi>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="5" data-semantic-parent="61" data-semantic-operator="fenced">)</mo>
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</mrow>
<mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="6" data-semantic-parent="65" data-semantic-operator="relseq,=">=</mo>
<mrow data-semantic-type="bigop" data-semantic-role="sum" data-semantic-id="62" data-semantic-children="25,60" data-semantic-content="7" data-semantic-parent="65">
<munder data-semantic-type="limlower" data-semantic-role="sum" data-semantic-id="25" data-semantic-children="7,24" data-semantic-parent="62">
<mo data-semantic-type="largeop" data-semantic-role="sum" data-semantic-id="7" data-semantic-parent="25" data-semantic-operator="bigop">∑
<!-- ∑ -->
</mo>
<mrow class="MJX-TeXAtom-ORD" data-semantic-type="multirel" data-semantic-role="unknown" data-semantic-id="24" data-semantic-children="8,10,23,19" data-semantic-content="9,11,18" data-semantic-parent="25">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="8" data-semantic-parent="24">1</mn>
<mo data-semantic-type="relation" data-semantic-role="inequality" data-semantic-id="9" data-semantic-parent="24" data-semantic-operator="multirel"><</mo>
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="10" data-semantic-parent="24">h</mi>
<mo data-semantic-type="relation" data-semantic-role="inequality" data-semantic-id="11" data-semantic-parent="24" data-semantic-operator="multirel">≤
<!-- ≤ -->
</mo>
<mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="23" data-semantic-children="12,21" data-semantic-content="22,12" data-semantic-parent="24">
<mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="12" data-semantic-parent="23" data-semantic-operator="appl">k</mi>
<mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="22" data-semantic-parent="23" data-semantic-added="true" data-semantic-operator="appl"></mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="21" data-semantic-children="20" data-semantic-content="13,17" data-semantic-parent="23">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="13" data-semantic-parent="21" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="20" data-semantic-children="14,15,16" data-semantic-content="15" data-semantic-parent="21">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="14" data-semantic-parent="20">h</mi>
<mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="15" data-semantic-parent="20" data-semantic-operator="punctuated">,</mo>
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="16" data-semantic-parent="20">k</mi>
</mrow>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="17" data-semantic-parent="21" data-semantic-operator="fenced">)</mo>
</mrow>
</mrow>
<mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="18" data-semantic-parent="24" data-semantic-operator="multirel">=</mo>
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="19" data-semantic-parent="24">1</mn>
</mrow>
</munder>
<mrow class="MJX-TeXAtom-ORD">
<msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="60" data-semantic-children="26,59" data-semantic-parent="62">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="26" data-semantic-parent="60">e</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="59" data-semantic-children="58,53" data-semantic-content="35" data-semantic-parent="60">
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="58" data-semantic-children="27,28,55" data-semantic-content="56,57" data-semantic-parent="59">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="27" data-semantic-parent="58">π
<!-- π -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="56" data-semantic-parent="58" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="28" data-semantic-parent="58">i</mi>
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="57" data-semantic-parent="58" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="29" data-semantic-parent="55" data-semantic-operator="appl">f</mi>
<mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="54" data-semantic-parent="55" data-semantic-added="true" data-semantic-operator="appl"></mo>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="30" data-semantic-parent="46" data-semantic-operator="fenced">(</mo>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="31" data-semantic-parent="45">h</mi>
<mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="32" 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="33" data-semantic-parent="45">k</mi>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="34" data-semantic-parent="46" data-semantic-operator="fenced">)</mo>
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<mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="35" data-semantic-parent="59" data-semantic-operator="infixop,−">−
<!-- − -->
</mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="53" data-semantic-children="52" data-semantic-content="36,44" data-semantic-parent="59">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="36" data-semantic-parent="53" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="division" data-semantic-id="52" data-semantic-children="51,43" data-semantic-content="42" data-semantic-parent="53">
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="51" data-semantic-children="37,38,39,40,41" data-semantic-content="47,48,49,50" data-semantic-parent="52">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="37" data-semantic-parent="51">2</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="47" data-semantic-parent="51" 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="38" data-semantic-parent="51">π
<!-- π -->
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="48" data-semantic-parent="51" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="39" data-semantic-parent="51">i</mi>
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="49" data-semantic-parent="51" 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="40" data-semantic-parent="51">n</mi>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="50" data-semantic-parent="51" 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="41" data-semantic-parent="51">h</mi>
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<mo data-semantic-type="operator" data-semantic-role="division" data-semantic-id="42" data-semantic-parent="52" data-semantic-operator="infixop,/">/</mo>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="43" data-semantic-parent="52">k</mi>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="44" data-semantic-parent="53" data-semantic-operator="fenced">)</mo>
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<annotation encoding="application/x-tex">A_{k}(n)=\sum _{1<h\leq k(h,k)=1}{\mathrm {e} ^{\pi \mathrm {i} f(h,k)-(2\pi \mathrm {i} nh/k)}}</annotation>
</semantics>
</math>