# LaTeX2HTML 2019.2 (Released June 5, 2019)
# Associate images original text with physical files.


$key = q/%latex2htmlidmarker273ref{eq:linear};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.68ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img51.svg"
 ALT="% latex2html id marker 273
$\ref{eq:linear}$">|; 

$key = q/(k,r,bar{{tau}});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img62.svg"
 ALT="$(k, r, \bar{ {\tau} } )$">|; 

$key = q/1-p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.13ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img66.svg"
 ALT="$1-p$">|; 

$key = q/H;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.77ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img76.svg"
 ALT="$H$">|; 

$key = q/P(bar{{tau}})=krslash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img58.svg"
 ALT="$P( \bar{ {\tau} } ) = k r /4$">|; 

$key = q/P({tau});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img56.svg"
 ALT="$P( {\tau} )$">|; 

$key = q/P^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.05ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img63.svg"
 ALT="$P^i$">|; 

$key = q/Q(-infty)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img52.svg"
 ALT="$Q(- \infty ) = 0$">|; 

$key = q/Q(infty)=k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img53.svg"
 ALT="$Q(\infty ) = k$">|; 

$key = q/Q({tau});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img43.svg"
 ALT="$Q( {\tau} )$">|; 

$key = q/bar{{tau}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.50ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img41.svg"
 ALT="$\bar{ {\tau} } $">|; 

$key = q/beta_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img73.svg"
 ALT="$\beta_0$">|; 

$key = q/beta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img74.svg"
 ALT="$\beta_1$">|; 

$key = q/dQ({tau})slashd{tau};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img54.svg"
 ALT="$d Q( {\tau} ) / d {\tau} $">|; 

$key = q/df(t)slashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img34.svg"
 ALT="$df(t)/dt$">|; 

$key = q/displaystyle-infty.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.74ex; vertical-align: -0.29ex; " SRC="|."$dir".q|img12.svg"
 ALT="$\displaystyle - \infty .$">|; 

$key = q/displaystyle0,mbox{and};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img7.svg"
 ALT="$\displaystyle 0 , \mbox{ and }$">|; 

$key = q/displaystyle1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.13ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img21.svg"
 ALT="$\displaystyle 1 ,$">|; 

$key = q/displaystyle1,mbox{and};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img13.svg"
 ALT="$\displaystyle 1 , \mbox{ and }$">|; 

$key = q/displaystyle1-f(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img14.svg"
 ALT="$\displaystyle 1 - f(t),$">|; 

$key = q/displaystyle1-f(t)=1slash[1+exp(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img30.svg"
 ALT="$\displaystyle 1- f(t) = 1/[ 1 + \exp(t)]$">|; 

$key = q/displaystyle1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.68ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img33.svg"
 ALT="$\displaystyle 1.$">|; 

$key = q/displaystyle1slash4,mbox{and}{df(pminfty)overdt}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.08ex; vertical-align: -1.69ex; " SRC="|."$dir".q|img37.svg"
 ALT="$\displaystyle 1/4 , \mbox { and }
{d f ( \pm \infty ) \over dt} = 0 .$">|; 

$key = q/displaystyleH(p)equiv-plogp-(1-p)log(1-p).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img77.svg"
 ALT="$\displaystyle H(p) \equiv - p \log p - (1 - p) \log (1 - p) .$">|; 

$key = q/displaystyleP({tau})equiv{dQ({tau})overd{tau}}={krover{exp[r({tau}-bar{{tau}})slash2]+exp[-r({tau}-bar{{tau}})slash2]}^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.66ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img57.svg"
 ALT="$\displaystyle P( {\tau} ) \equiv
{d Q( {\tau} ) \over d {\tau} } =
{k r \over \...
... ( {\tau} - \bar{ {\tau} } )/2] + \exp[-r ( {\tau} - \bar{ {\tau} } )/2]\}^2} .$">|; 

$key = q/displaystyleQ(bar{{tau}})equivkslash2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img45.svg"
 ALT="$\displaystyle Q( \bar{ {\tau} } ) \equiv k / 2 .$">|; 

$key = q/displaystyleQ({tau})={kover1+exp[-r({tau}-bar{{tau}})]}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.53ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img55.svg"
 ALT="$\displaystyle Q( {\tau} ) = {k \over 1 + \exp[-r ( {\tau} - \bar{ {\tau} } )]} .$">|; 

$key = q/displaystylebeta_0+beta_1x.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img72.svg"
 ALT="$\displaystyle \beta_0 + \beta_1 x .$">|; 

$key = q/displaystyleexp(t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img28.svg"
 ALT="$\displaystyle \exp(t) .$">|; 

$key = q/displaystylef(-t);;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img31.svg"
 ALT="$\displaystyle f(-t) ;$">|; 

$key = q/displaystylef(0)=1slash2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img4.svg"
 ALT="$\displaystyle f(0) = 1/2.$">|; 

$key = q/displaystylef(t)+f(-t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img32.svg"
 ALT="$\displaystyle f(t) + f(-t)$">|; 

$key = q/displaystylef(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img10.svg"
 ALT="$\displaystyle f(t),$">|; 

$key = q/displaystylef(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img5.svg"
 ALT="$\displaystyle f(t)$">|; 

$key = q/displaystylef(t)={exp(t)over1+exp(t)}={1over1+exp(-t)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.66ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img29.svg"
 ALT="$\displaystyle f(t) = {\exp(t) \over 1 + \exp(t)} = {1 \over 1 + \exp(-t)} .$">|; 

$key = q/displaystylef(t)equivQ({tau})slashk,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img42.svg"
 ALT="$\displaystyle f(t) \equiv Q( {\tau} )/k ,$">|; 

$key = q/displaystyleinfty.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img15.svg"
 ALT="$\displaystyle \infty .$">|; 

$key = q/displaystyleleft[{1overf(t)}+{1over1-f(t)}right]df(t)slashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.98ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img19.svg"
 ALT="$\displaystyle \left [ {1 \over f(t)} + {1 \over 1-f(t)} \right ] df(t)/dt$">|; 

$key = q/displaystylelogf(t)-log[1-f(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img23.svg"
 ALT="$\displaystyle \log f(t) - \log [1-f(t)]$">|; 

$key = q/displaystylelogleft[{f(t)over1-f(t)}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.98ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img25.svg"
 ALT="$\displaystyle \log \left [ {f(t) \over 1-f(t)} \right ]$">|; 

$key = q/displaystylelogleft[{p(x)over1-p(x)}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.98ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img71.svg"
 ALT="$\displaystyle \log \left [ {p(x) \over 1-p(x)} \right ]$">|; 

$key = q/displaystylembox{as}t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.62ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img11.svg"
 ALT="$\displaystyle \mbox{ as } t$">|; 

$key = q/displaystylembox{logit}(p)equivlogleft({pover1-p}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.98ex; vertical-align: -2.42ex; " SRC="|."$dir".q|img69.svg"
 ALT="$\displaystyle \mbox{logit}(p) \equiv \log \left ( {p \over 1-p} \right ) .$">|; 

$key = q/displaystylemin_{k,r,bar{{tau}}}sum_ileft{P^i~log[P^i~slash~P({tau}^i)]right}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.01ex; vertical-align: -2.60ex; " SRC="|."$dir".q|img61.svg"
 ALT="$\displaystyle \min_{k, r, \bar{ {\tau} } } \sum_i \left \{ P^i&nbsp; \log [ P^i&nbsp;/&nbsp; P( {\tau} ^i ) ]\right \} .$">|; 

$key = q/displaystyler-(rslashk)Q({tau}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img49.svg"
 ALT="$\displaystyle r - (r/k) Q( {\tau} ) .$">|; 

$key = q/displaystyler[1-Q({tau})slashk]Q({tau});;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img47.svg"
 ALT="$\displaystyle r [1-Q( {\tau} )/k] Q( {\tau} ) ;$">|; 

$key = q/displaystylet,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.07ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img24.svg"
 ALT="$\displaystyle t ,$">|; 

$key = q/displaystylet,mbox{and};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img26.svg"
 ALT="$\displaystyle t , \mbox{ and }$">|; 

$key = q/displaystyletequivr({tau}-bar{{tau}}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img38.svg"
 ALT="$\displaystyle t \equiv r ( {\tau} - \bar{ {\tau} } ) ,$">|; 

$key = q/displaystyle{dH(p)overdp}=-mbox{logit}(p).<comment_mark>4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.53ex; vertical-align: -2.14ex; " SRC="|."$dir".q|img80.svg"
 ALT="$\displaystyle {d H(p) \over dp} = - \mbox{logit}(p).
% dH(p)/dp = -log(p) - 1 + log(1-p) + (1-p)/(1-p) = log[(1-p)/p] = -log[p/(1-p)]
$">|; 

$key = q/displaystyle{dQ({tau})overd{tau}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.08ex; vertical-align: -1.69ex; " SRC="|."$dir".q|img46.svg"
 ALT="$\displaystyle {d Q( {\tau} ) \over d {\tau} }$">|; 

$key = q/displaystyle{dQ({tau})overd{tau}}slashQ({tau});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.08ex; vertical-align: -1.69ex; " SRC="|."$dir".q|img48.svg"
 ALT="$\displaystyle {d Q( {\tau} ) \over d {\tau} } / Q( {\tau} )$">|; 

$key = q/displaystyle{df(0)overdt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.08ex; vertical-align: -1.69ex; " SRC="|."$dir".q|img36.svg"
 ALT="$\displaystyle {d f (0) \over dt}$">|; 

$key = q/displaystyle{df(t)overdt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.08ex; vertical-align: -1.69ex; " SRC="|."$dir".q|img8.svg"
 ALT="$\displaystyle {d f(t) \over dt}$">|; 

$key = q/displaystyle{df(t)overdt}=f(t)[1-f(t)].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.08ex; vertical-align: -1.69ex; " SRC="|."$dir".q|img17.svg"
 ALT="$\displaystyle {d f(t) \over dt}= f(t) [1-f(t)] .$">|; 

$key = q/displaystyle{df(t)overdt}>0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.08ex; vertical-align: -1.69ex; " SRC="|."$dir".q|img3.svg"
 ALT="$\displaystyle {d f(t) \over dt}&gt; 0.$">|; 

$key = q/displaystyle{df(t)overdt}proptof(t)[1-f(t)].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.08ex; vertical-align: -1.69ex; " SRC="|."$dir".q|img16.svg"
 ALT="$\displaystyle {d f(t) \over dt}\propto f(t) [1-f(t)] .$">|; 

$key = q/displaystyle{doverdt}{logf(t)-log[1-f(t)]};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.95ex; vertical-align: -1.69ex; " SRC="|."$dir".q|img22.svg"
 ALT="$\displaystyle {d \over dt} \{ \log f(t) - \log [1-f(t)] \}$">|; 

$key = q/displaystyle{exp(-t)over[1+exp(-t)]^2}={1over[exp(tslash2)+exp(-tslash2)]^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.66ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img35.svg"
 ALT="$\displaystyle { \exp(-t) \over [ 1 + \exp(-t) ]^2 }
= {1 \over [ \exp(t/2) + \exp(-t/2) ]^2} ,$">|; 

$key = q/displaystyle{f(t)over1-f(t)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 5.66ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img27.svg"
 ALT="$\displaystyle {f(t) \over 1-f(t)}$">|; 

$key = q/f(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img1.svg"
 ALT="$f(t)$">|; 

$key = q/f(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img18.svg"
 ALT="$f(x)$">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.71ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img60.svg"
 ALT="$i$">|; 

$key = q/k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img44.svg"
 ALT="$k$">|; 

$key = q/log(2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img78.svg"
 ALT="$\log(2)$">|; 

$key = q/mbox{logit};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img70.svg"
 ALT="$\mbox{logit}$">|; 

$key = q/p(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img68.svg"
 ALT="$p(x)$">|; 

$key = q/p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.64ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img65.svg"
 ALT="$p$">|; 

$key = q/p=frac{1}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.90ex; vertical-align: -0.90ex; " SRC="|."$dir".q|img79.svg"
 ALT="$p=\frac{1}{2}$">|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img40.svg"
 ALT="$r$">|; 

$key = q/rslashk;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img50.svg"
 ALT="$r/k$">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.62ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img2.svg"
 ALT="$t$">|; 

$key = q/tequivbeta_0+beta_1x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img75.svg"
 ALT="$t \equiv \beta_0 + \beta_1 x$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.03ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img20.svg"
 ALT="$\textstyle =$">|; 

$key = q/textstylepropto;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img9.svg"
 ALT="$\textstyle \propto$">|; 

$key = q/textstylerightarrow;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.04ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img6.svg"
 ALT="$\textstyle \rightarrow$">|; 

$key = q/x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img67.svg"
 ALT="$x$">|; 

$key = q/{P^i,{tau}^i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.63ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img59.svg"
 ALT="$\{P^i , {\tau} ^i \}$">|; 

$key = q/{tau};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img39.svg"
 ALT="${\tau} $">|; 

$key = q/{tau}^i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.05ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img64.svg"
 ALT="${\tau} ^i$">|; 

1;

