## General

Display information for equation id:math.266692.18 on revision:266692

* Page found: Graphical models for protein structure (eq math.266692.18)

(force rerendering)

Occurrences on the following pages:

Hash: a67a983fc61162252125a99921aa5a29

TeX (original user input):

f(\Theta=D) = \frac{1}{Z} \exp\left\{-\frac{1}{2}(D-\mu)^T\Sigma^{-1}(D-\mu)\right\}


TeX (checked):

f(\Theta =D)={\frac {1}{Z}}\exp \left\{-{\frac {1}{2}}(D-\mu )^{T}\Sigma ^{-1}(D-\mu )\right\}


### LaTeXML (experimental; uses MathML) rendering

MathML (6.999 KB / 1.313 KB) :

${\displaystyle f(\Theta=D)={\frac{1}{Z}}\exp\left\{-{\frac{1}{2}}(D-\mu)^{T}% \Sigma^{{-1}}(D-\mu)\right\}}$
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle f(\Theta=D)={\frac{1}{Z}}\exp\left\{-{\frac{1}{2}}(D-\mu)^{T}%&#10;\Sigma^{{-1}}(D-\mu)\right\}}" display="inline">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1b">
<mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">f</mi>
<mrow id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
<mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">(</mo>
<mi mathvariant="normal" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">Θ</mi>
<mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">=</mo>
<mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">D</mi>
<mo stretchy="false" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">)</mo>
</mrow>
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
<mfrac id="p1.1.m1.1.8a" xref="p1.1.m1.1.8.cmml">
<mn id="p1.1.m1.1.8.2" xref="p1.1.m1.1.8.2.cmml">1</mn>
<mi id="p1.1.m1.1.8.3" xref="p1.1.m1.1.8.3.cmml">Z</mi>
</mfrac>
</mstyle>
<mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">exp</mi>
<mrow id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">
<mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">{</mo>
<mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">-</mo>
<mstyle displaystyle="true" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
<mfrac id="p1.1.m1.1.12a" xref="p1.1.m1.1.12.cmml">
<mn id="p1.1.m1.1.12.2" xref="p1.1.m1.1.12.2.cmml">1</mn>
<mn id="p1.1.m1.1.12.3" xref="p1.1.m1.1.12.3.cmml">2</mn>
</mfrac>
</mstyle>
<msup id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">
<mrow id="p1.1.m1.1.27.2" xref="p1.1.m1.1.27.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">(</mo>
<mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">D</mi>
<mo id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">-</mo>
<mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">μ</mi>
<mo stretchy="false" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">)</mo>
</mrow>
<mi id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">T</mi>
</msup>
<msup id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">
<mi mathvariant="normal" id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">Σ</mi>
<mrow id="p1.1.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">
<mo id="p1.1.m1.1.20.1.1" xref="p1.1.m1.1.20.1.1.cmml">-</mo>
<mn id="p1.1.m1.1.20.1.2" xref="p1.1.m1.1.20.1.2.cmml">1</mn>
</mrow>
</msup>
<mrow id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">
<mo stretchy="false" id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">(</mo>
<mi id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">D</mi>
<mo id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">-</mo>
<mi id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">μ</mi>
<mo stretchy="false" id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">)</mo>
</mrow>
<mo id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">}</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1c">
<cerror id="p1.1.m1.1d">
<csymbol cd="ambiguous" id="p1.1.m1.1e">fragments</csymbol>
<csymbol cd="unknown" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">f</csymbol>
<cerror id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">
<csymbol cd="ambiguous" id="p1.1.m1.1.18a.cmml" xref="p1.1.m1.1.18">fragments</csymbol>
<ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">(</ci>
<csymbol cd="unknown" id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">Θ</csymbol>
<eq id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
<csymbol cd="unknown" id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">D</csymbol>
<ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">)</ci>
</cerror>
<eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
<apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
<divide id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8"/>
<cn type="integer" id="p1.1.m1.1.8.2.cmml" xref="p1.1.m1.1.8.2">1</cn>
<ci id="p1.1.m1.1.8.3.cmml" xref="p1.1.m1.1.8.3">𝑍</ci>
</apply>
<exp id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9"/>
<cerror id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">
<csymbol cd="ambiguous" id="p1.1.m1.1.29a.cmml" xref="p1.1.m1.1.29">fragments</csymbol>
<ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">{</ci>
<minus id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
<apply id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
<divide id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12"/>
<cn type="integer" id="p1.1.m1.1.12.2.cmml" xref="p1.1.m1.1.12.2">1</cn>
<cn type="integer" id="p1.1.m1.1.12.3.cmml" xref="p1.1.m1.1.12.3">2</cn>
</apply>
<apply id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">
<csymbol cd="ambiguous" id="p1.1.m1.1.27.1.cmml" xref="p1.1.m1.1.27">superscript</csymbol>
<cerror id="p1.1.m1.1.27.2.cmml" xref="p1.1.m1.1.27.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.27.2a.cmml" xref="p1.1.m1.1.27.2">fragments</csymbol>
<ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">(</ci>
<csymbol cd="unknown" id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">D</csymbol>
<minus id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15"/>
<csymbol cd="unknown" id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">μ</csymbol>
<ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">)</ci>
</cerror>
<ci id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">𝑇</ci>
</apply>
<apply id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">
<csymbol cd="ambiguous" id="p1.1.m1.1.28.1.cmml" xref="p1.1.m1.1.28">superscript</csymbol>
<ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">Σ</ci>
<apply id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">
<minus id="p1.1.m1.1.20.1.1.cmml" xref="p1.1.m1.1.20.1.1"/>
<cn type="integer" id="p1.1.m1.1.20.1.2.cmml" xref="p1.1.m1.1.20.1.2">1</cn>
</apply>
</apply>
<cerror id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">
<csymbol cd="ambiguous" id="p1.1.m1.1.20a.cmml" xref="p1.1.m1.1.20">fragments</csymbol>
<ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">(</ci>
<csymbol cd="unknown" id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">D</csymbol>
<minus id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23"/>
<csymbol cd="unknown" id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">μ</csymbol>
<ci id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">)</ci>
</cerror>
<ci id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">}</ci>
</cerror>
</cerror>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle f(\Theta=D)={\frac{1}{Z}}\exp\left\{-{\frac{1}{2}}(D-\mu)^{T}%
\Sigma^{{-1}}(D-\mu)\right\}}</annotation>
</semantics>
[/itex]


SVG (15.165 KB / 5.809 KB) :

### SVG (MathML can be enabled via browser plugin) rendering

MathML (1.925 KB / 551 B) :

${\displaystyle f(\Theta =D)={\frac {1}{Z}}\exp \left\{-{\frac {1}{2}}(D-\mu )^{T}\Sigma ^{-1}(D-\mu )\right\}}$
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle f(\Theta =D)={\frac {1}{Z}}\exp \left\{-{\frac {1}{2}}(D-\mu )^{T}\Sigma ^{-1}(D-\mu )\right\}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">&#x0398;<!-- Θ --></mi>
<mo>=</mo>
<mi>D</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<mi>Z</mi>
</mfrac>
</mrow>
<mi>exp</mi>
<mo>&#x2061;<!-- ⁡ --></mo>
<mrow>
<mo>{</mo>
<mrow>
<mo>&#x2212;<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo stretchy="false">(</mo>
<mi>D</mi>
<mo>&#x2212;<!-- − --></mo>
<mi>&#x03BC;<!-- μ --></mi>
<msup>
<mo stretchy="false">)</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>T</mi>
</mrow>
</msup>
<msup>
<mi mathvariant="normal">&#x03A3;<!-- Σ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2212;<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
<mo stretchy="false">(</mo>
<mi>D</mi>
<mo>&#x2212;<!-- − --></mo>
<mi>&#x03BC;<!-- μ --></mi>
<mo stretchy="false">)</mo>
</mrow>
<mo>}</mo>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle f(\Theta =D)={\frac {1}{Z}}\exp \left\{-{\frac {1}{2}}(D-\mu )^{T}\Sigma ^{-1}(D-\mu )\right\}}</annotation>
</semantics>
[/itex]


SVG (12.783 KB / 5.427 KB) :

In Maple:

In Mathematica:

## Similar pages

Calculated based on the variables occurring on the entire Graphical models for protein structure page

## Identifiers

• ${\displaystyle f}$
• ${\displaystyle \Theta }$
• ${\displaystyle D}$
• ${\displaystyle Z}$
• ${\displaystyle D}$
• ${\displaystyle \mu }$
• ${\displaystyle T}$
• ${\displaystyle \Sigma }$
• ${\displaystyle D}$
• ${\displaystyle \mu }$

### MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results