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diff --git a/docs/diffusion/stable_diffusion/model/autoencoder.html b/docs/diffusion/stable_diffusion/model/autoencoder.html
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                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
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                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
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                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
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diff --git a/docs/diffusion/stable_diffusion/model/index.html b/docs/diffusion/stable_diffusion/model/index.html
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-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/diffusion/stable_diffusion/model/unet.html b/docs/diffusion/stable_diffusion/model/unet.html
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-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
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@@ -52,10 +52,6 @@
                 <a class="parent" href="index.html">model</a>
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                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/diffusion/stable_diffusion/sampler/ddim.html b/docs/diffusion/stable_diffusion/sampler/ddim.html
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@@ -52,10 +52,6 @@
                 <a class="parent" href="index.html">sampler</a>
             </p>
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-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
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                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
@@ -133,7 +129,7 @@ <h2>DDIM Sampler</h2>
 H400000v40H845.2724
 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
-M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25783em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.05077em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord"><span class="delimsizing size4">)</span></span></span></span><span style="top:-2.9119384999999998em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqh" style=""><span class="mord sqrt" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2580465em;"><span class="svg-align" style="top:-3.8em;"><span class="pstrut" style="height:3.8em;"></span><span class="mord" style="padding-left:1em"><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-left:-0.0037em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32808571428571426em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.20252142857142857em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.291765em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqw" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.2180465em;"><span class="pstrut" style="height:3.8em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.8800000000000001em"><svg height="1.8800000000000001em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1944" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M983 90
+M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25783em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="mord coloredeq eqo" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqo" style="">(</span><span class="mord coloredeq eqo" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose coloredeq eqo" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.05077em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord"><span class="delimsizing size4">)</span></span></span></span><span style="top:-2.9119384999999998em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqh" style=""><span class="mord sqrt" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2580465em;"><span class="svg-align" style="top:-3.8em;"><span class="pstrut" style="height:3.8em;"></span><span class="mord" style="padding-left:1em"><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-left:-0.0037em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32808571428571426em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.20252142857142857em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.291765em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqw" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.2180465em;"><span class="pstrut" style="height:3.8em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.8800000000000001em"><svg height="1.8800000000000001em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1944" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M983 90
 l0 -0
 c4,-6.7,10,-10,18,-10 H400000v40
 H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7
@@ -142,7 +138,7 @@ <h2>DDIM Sampler</h2>
 c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722
 c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5
 c53.7,-170.3,84.5,-266.8,92.5,-289.5z
-M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5819535em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span><span style="top:-1.1899850000000005em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqw" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mord coloredeq eqs" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.2200149999999996em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>where <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68066em;vertical-align:-0.2501em;"></span><span class="mord coloredeq eqs" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span></span></span></span></span> is random noise, <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqbi" style=""><span class="mord mathnormal" style="margin-right:0.1132em">τ</span></span></span></span></span></span> is a subsequence of <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqy" style=""><span class="mopen" style="">[</span><span class="mord" style="">1</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="">2</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner" style="">…</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.13889em">T</span><span class="mclose" style="">]</span></span></span></span></span></span> of length <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqbo" style=""><span class="mord mathnormal" style="margin-right:0.05764em">S</span></span></span></span></span></span>, and <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.04em;vertical-align:-1.2110725000000002em;"></span><span class="mord coloredeq eqc" style=""><span class="mord" style=""><span class="mord coloredeq eqw" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqbh" style="margin-right:0.03588em">η</span></span><span class="mord sqrt" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8289274999999998em;"><span class="svg-align" style="top:-5em;"><span class="pstrut" style="height:5em;"></span><span class="mord" style="padding-left:1em"><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3262049999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord" style=""><span class="mord coloredeq eqv" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.0037em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6817649999999995em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord" style=""><span class="mord coloredeq eqr" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-left:-0.0037em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32808571428571426em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.20252142857142857em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.291765em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9361em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.7889275em;"><span class="pstrut" style="height:5em;"></span><span class="hide-tail" style="min-width:1.02em;height:3.08em"><svg height="3.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 3240" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M473,2793
+M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5819535em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord coloredeq eqo" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqo" style="">(</span><span class="mord coloredeq eqo" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose coloredeq eqo" style="">)</span></span></span></span></span><span style="top:-1.1899850000000005em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqw" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mord coloredeq eqs" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.2200149999999996em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>where <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68066em;vertical-align:-0.2501em;"></span><span class="mord coloredeq eqs" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span></span></span></span></span> is random noise, <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqbi" style=""><span class="mord mathnormal" style="margin-right:0.1132em">τ</span></span></span></span></span></span> is a subsequence of <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqy" style=""><span class="mopen" style="">[</span><span class="mord" style="">1</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="">2</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner" style="">…</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.13889em">T</span><span class="mclose" style="">]</span></span></span></span></span></span> of length <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqbo" style=""><span class="mord mathnormal" style="margin-right:0.05764em">S</span></span></span></span></span></span>, and <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.04em;vertical-align:-1.2110725000000002em;"></span><span class="mord coloredeq eqc" style=""><span class="mord" style=""><span class="mord coloredeq eqw" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqbh" style="margin-right:0.03588em">η</span></span><span class="mord sqrt" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8289274999999998em;"><span class="svg-align" style="top:-5em;"><span class="pstrut" style="height:5em;"></span><span class="mord" style="padding-left:1em"><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3262049999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord" style=""><span class="mord coloredeq eqv" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.0037em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6817649999999995em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord" style=""><span class="mord coloredeq eqr" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-left:-0.0037em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32808571428571426em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.20252142857142857em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.291765em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9361em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.7889275em;"><span class="pstrut" style="height:5em;"></span><span class="hide-tail" style="min-width:1.02em;height:3.08em"><svg height="3.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 3240" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M473,2793
 c339.3,-1799.3,509.3,-2700,510,-2702 l0 -0
 c3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7
 s-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9
@@ -538,7 +534,7 @@ <h3>Sample <span ><span class="katex"><span aria-hidden="true" class="katex-html
             <div class='section-link'>
                 <a href='#section-23'>#</a>
             </div>
-            <p>Get <span ><strong style="">Error</strong></span> </p>
+            <p>Get <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0001em;vertical-align:-0.2501em;"></span><span class="mord coloredeq eqo" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span> </p>
 
         </div>
         <div class='code'>
@@ -578,7 +574,7 @@ <h3>Sample <span ><span class="katex"><span aria-hidden="true" class="katex-html
             <div class='section-link'>
                 <a href='#section-26'>#</a>
             </div>
-            <h3>Sample <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.722325em;vertical-align:-0.291765em;"></span><span class="mord coloredeq eqx" style=""><span class="mord" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32808571428571426em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.20252142857142857em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.291765em;"><span></span></span></span></span></span></span></span></span></span></span></span> given <span ><strong style="">Error</strong></span></h3>
+            <h3>Sample <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.722325em;vertical-align:-0.291765em;"></span><span class="mord coloredeq eqx" style=""><span class="mord" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32808571428571426em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.20252142857142857em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.291765em;"><span></span></span></span></span></span></span></span></span></span></span></span> given <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.0001em;vertical-align:-0.2501em;"></span><span class="mord coloredeq eqo" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span></h3>
 
         </div>
         <div class='code'>
@@ -673,7 +669,7 @@ <h3>Sample <span ><span class="katex"><span aria-hidden="true" class="katex-html
 H400000v40H845.2724
 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
-M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25783em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.05077em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></span> </p>
+M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25783em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="mord coloredeq eqo" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqo" style="">(</span><span class="mord coloredeq eqo" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose coloredeq eqo" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.05077em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></span> </p>
 
         </div>
         <div class='code'>
@@ -694,7 +690,7 @@ <h3>Sample <span ><span class="katex"><span aria-hidden="true" class="katex-html
 c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722
 c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5
 c53.7,-170.3,84.5,-266.8,92.5,-289.5z
-M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5819535em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span></span> </p>
+M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5819535em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord coloredeq eqo" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqo" style="">(</span><span class="mord coloredeq eqo" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose coloredeq eqo" style="">)</span></span></span></span></span></span></span></span> </p>
 
         </div>
         <div class='code'>
@@ -790,7 +786,7 @@ <h3>Sample <span ><span class="katex"><span aria-hidden="true" class="katex-html
 H400000v40H845.2724
 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
-M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25783em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.05077em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord"><span class="delimsizing size4">)</span></span></span></span><span style="top:-2.9119384999999998em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqh" style=""><span class="mord sqrt" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2580465em;"><span class="svg-align" style="top:-3.8em;"><span class="pstrut" style="height:3.8em;"></span><span class="mord" style="padding-left:1em"><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-left:-0.0037em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32808571428571426em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.20252142857142857em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.291765em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqw" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.2180465em;"><span class="pstrut" style="height:3.8em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.8800000000000001em"><svg height="1.8800000000000001em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1944" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M983 90
+M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.25783em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="mord coloredeq eqo" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqo" style="">(</span><span class="mord coloredeq eqo" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose coloredeq eqo" style="">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.05077em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord"><span class="delimsizing size4">)</span></span></span></span><span style="top:-2.9119384999999998em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqh" style=""><span class="mord sqrt" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2580465em;"><span class="svg-align" style="top:-3.8em;"><span class="pstrut" style="height:3.8em;"></span><span class="mord" style="padding-left:1em"><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-left:-0.0037em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32808571428571426em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.20252142857142857em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.291765em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqw" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.2180465em;"><span class="pstrut" style="height:3.8em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.8800000000000001em"><svg height="1.8800000000000001em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1944" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M983 90
 l0 -0
 c4,-6.7,10,-10,18,-10 H400000v40
 H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7
@@ -799,7 +795,7 @@ <h3>Sample <span ><span class="katex"><span aria-hidden="true" class="katex-html
 c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722
 c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5
 c53.7,-170.3,84.5,-266.8,92.5,-289.5z
-M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5819535em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span><span style="top:-1.1899850000000005em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqw" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mord coloredeq eqs" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.2200149999999996em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p> </p>
+M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5819535em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord coloredeq eqo" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">θ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqo" style="">(</span><span class="mord coloredeq eqo" style=""><span class="mord coloredeq eqba" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mclose coloredeq eqo" style="">)</span></span></span></span></span><span style="top:-1.1899850000000005em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqw" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span><span class="mord coloredeq eqs" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqbc" style="">ϵ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbf" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbi" style="margin-right:0.1132em">τ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbr" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.2200149999999996em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p> </p>
 
         </div>
         <div class='code'>
diff --git a/docs/diffusion/stable_diffusion/sampler/ddpm.html b/docs/diffusion/stable_diffusion/sampler/ddpm.html
index 0a17e18d..3ffeb419 100644
--- a/docs/diffusion/stable_diffusion/sampler/ddpm.html
+++ b/docs/diffusion/stable_diffusion/sampler/ddpm.html
@@ -52,10 +52,6 @@
                 <a class="parent" href="index.html">sampler</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/diffusion/stable_diffusion/sampler/index.html b/docs/diffusion/stable_diffusion/sampler/index.html
index 15b475c5..161cb511 100644
--- a/docs/diffusion/stable_diffusion/sampler/index.html
+++ b/docs/diffusion/stable_diffusion/sampler/index.html
@@ -52,10 +52,6 @@
                 <a class="parent" href="index.html">sampler</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/diffusion/stable_diffusion/scripts/image_to_image.html b/docs/diffusion/stable_diffusion/scripts/image_to_image.html
index 2e9155f1..5eb66bf8 100644
--- a/docs/diffusion/stable_diffusion/scripts/image_to_image.html
+++ b/docs/diffusion/stable_diffusion/scripts/image_to_image.html
@@ -52,10 +52,6 @@
                 <a class="parent" href="index.html">scripts</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/diffusion/stable_diffusion/scripts/in_paint.html b/docs/diffusion/stable_diffusion/scripts/in_paint.html
index 9827c22d..3e0538b6 100644
--- a/docs/diffusion/stable_diffusion/scripts/in_paint.html
+++ b/docs/diffusion/stable_diffusion/scripts/in_paint.html
@@ -52,10 +52,6 @@
                 <a class="parent" href="index.html">scripts</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/diffusion/stable_diffusion/scripts/index.html b/docs/diffusion/stable_diffusion/scripts/index.html
index e3f97c31..bcdc4877 100644
--- a/docs/diffusion/stable_diffusion/scripts/index.html
+++ b/docs/diffusion/stable_diffusion/scripts/index.html
@@ -52,10 +52,6 @@
                 <a class="parent" href="index.html">scripts</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/diffusion/stable_diffusion/scripts/text_to_image.html b/docs/diffusion/stable_diffusion/scripts/text_to_image.html
index c41557dc..96c74b10 100644
--- a/docs/diffusion/stable_diffusion/scripts/text_to_image.html
+++ b/docs/diffusion/stable_diffusion/scripts/text_to_image.html
@@ -52,10 +52,6 @@
                 <a class="parent" href="index.html">scripts</a>
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--- a/docs/transformers/xl/readme.html
+++ b/docs/transformers/xl/readme.html
@@ -51,10 +51,6 @@
                 <a class="parent" href="index.html">xl</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
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diff --git a/docs/transformers/xl/relative_mha.html b/docs/transformers/xl/relative_mha.html
index 9acabf7c..d5a3b9a0 100644
--- a/docs/transformers/xl/relative_mha.html
+++ b/docs/transformers/xl/relative_mha.html
@@ -51,10 +51,6 @@
                 <a class="parent" href="index.html">xl</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
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-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
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diff --git a/docs/uncertainty/evidence/experiment.html b/docs/uncertainty/evidence/experiment.html
index 15ae4c8c..bcc98f3f 100644
--- a/docs/uncertainty/evidence/experiment.html
+++ b/docs/uncertainty/evidence/experiment.html
@@ -51,10 +51,6 @@
                 <a class="parent" href="index.html">evidence</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/uncertainty/evidence/index.html b/docs/uncertainty/evidence/index.html
index 00c224ec..0d19e2a0 100644
--- a/docs/uncertainty/evidence/index.html
+++ b/docs/uncertainty/evidence/index.html
@@ -51,10 +51,6 @@
                 <a class="parent" href="index.html">evidence</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/uncertainty/evidence/readme.html b/docs/uncertainty/evidence/readme.html
index 96913440..e86681d6 100644
--- a/docs/uncertainty/evidence/readme.html
+++ b/docs/uncertainty/evidence/readme.html
@@ -51,10 +51,6 @@
                 <a class="parent" href="index.html">evidence</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/uncertainty/index.html b/docs/uncertainty/index.html
index c885d6c2..22ed3120 100644
--- a/docs/uncertainty/index.html
+++ b/docs/uncertainty/index.html
@@ -50,10 +50,6 @@
                 <a class="parent" href="index.html">uncertainty</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/uncertainty/readme.html b/docs/uncertainty/readme.html
index cba06c9c..2e6fa754 100644
--- a/docs/uncertainty/readme.html
+++ b/docs/uncertainty/readme.html
@@ -50,10 +50,6 @@
                 <a class="parent" href="index.html">uncertainty</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/unet/carvana.html b/docs/unet/carvana.html
index 83cff98e..98260be8 100644
--- a/docs/unet/carvana.html
+++ b/docs/unet/carvana.html
@@ -50,10 +50,6 @@
                 <a class="parent" href="index.html">unet</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/unet/experiment.html b/docs/unet/experiment.html
index 26cfabe3..5cc3a30b 100644
--- a/docs/unet/experiment.html
+++ b/docs/unet/experiment.html
@@ -50,10 +50,6 @@
                 <a class="parent" href="index.html">unet</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/unet/index.html b/docs/unet/index.html
index cedf9963..c4f8f0e9 100644
--- a/docs/unet/index.html
+++ b/docs/unet/index.html
@@ -50,10 +50,6 @@
                 <a class="parent" href="index.html">unet</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/utils/index.html b/docs/utils/index.html
index 3f12a5a2..c4b7a3aa 100644
--- a/docs/utils/index.html
+++ b/docs/utils/index.html
@@ -50,10 +50,6 @@
                 <a class="parent" href="index.html">utils</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/docs/utils/tokenizer.html b/docs/utils/tokenizer.html
index 286084d7..ce2a98f2 100644
--- a/docs/utils/tokenizer.html
+++ b/docs/utils/tokenizer.html
@@ -50,10 +50,6 @@
                 <a class="parent" href="index.html">utils</a>
             </p>
             <p>
-                <a href="/sponsors/labmlai" target="_blank">
-                    <img alt="Sponsor"
-                         src="https://img.shields.io/static/v1?label=Sponsor&message=%E2%9D%A4&logo=GitHub&color=%23fe8e86"
-                         style="max-width:100%;"/></a>
                 <a href="/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
                     <img alt="Github"
                          src="https://img.shields.io/github/stars/labmlai/annotated_deep_learning_paper_implementations?style=social"
diff --git a/labml_nn/diffusion/stable_diffusion/sampler/ddim.py b/labml_nn/diffusion/stable_diffusion/sampler/ddim.py
index 6e3fea21..1baee902 100644
--- a/labml_nn/diffusion/stable_diffusion/sampler/ddim.py
+++ b/labml_nn/diffusion/stable_diffusion/sampler/ddim.py
@@ -168,7 +168,7 @@ def p_sample(self, x: torch.Tensor, c: torch.Tensor, t: torch.Tensor, step: int,
         :param uncond_cond: is the conditional embedding for empty prompt $c_u$
         """
 
-        # Get $\epsilon_\theta(x_{\tau_i}}$
+        # Get $\epsilon_\theta(x_{\tau_i})$
         e_t = self.get_eps(x, t, c,
                            uncond_scale=uncond_scale,
                            uncond_cond=uncond_cond)
@@ -185,7 +185,7 @@ def get_x_prev_and_pred_x0(self, e_t: torch.Tensor, index: int, x: torch.Tensor,
                                temperature: float,
                                repeat_noise: bool):
         """
-        ### Sample $x_{\tau_{i-1}}$ given $\epsilon_\theta(x_{\tau_i}}$
+        ### Sample $x_{\tau_{i-1}}$ given $\epsilon_\theta(x_{\tau_i})$
         """
 
         # $\alpha_{\tau_i}$