# LaTeX2HTML 2K.1beta (1.47)
# Associate images original text with physical files.


$key = q/rho>rho_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\rho &gt; \rho_c$">|; 

$key = q/rho_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\rho_c$">|; 

$key = q/(a,b,epsilon)=(1,infty,1.5);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$(a,b,\epsilon )=(1,\infty ,1.5)$">|; 

$key = q/g=1slashrho_L-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$g = 1/\rho_L - 1$">|; 

$key = q/rho^*approx0.2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\rho^* \approx
0.2$">|; 

$key = q/2times2=4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$2
\times 2 = 4$">|; 

$key = q/Ltoinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$L
\to \infty$">|; 

$key = q/displaystylex_{t+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle x_{t+1}$">|; 

$key = q/epsilon;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\epsilon$">|; 

$key = q/{displaymath}p_downarrowsimL,expleft(frac{hatalpha}{leftlanglegrightrangle-g_0}right),{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="367" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="\begin{displaymath}
p_\downarrow \sim L   \exp\left(\frac{\hat\alpha}{\left\langle g\right\rangle - g_0} \right)  ,
\end{displaymath}">|; 

$key = q/displaystylemax{v_{{rm{des}-aepsilonxi,0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle \max \{v_{\rm des} - a \epsilon \xi, 0 \}$">|; 

$key = q/d(v);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$d(v)$">|; 

$key = q/T_{rcov}simexpbig(-L(rho-rho_*)big);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$T_{rcov} \sim \exp\big( - L(\rho - \rho_*) \big)$">|; 

$key = q/xi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\xi$">|; 

$key = q/(a,b)=(1,infty);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$(a,b) = (1,\infty )$">|; 

$key = q/displaystyletildev_t+2,bfrac{g_t-tildev_t}{2,b+v_t+tildev_t};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$\displaystyle \tilde v_t + 2 b \frac{g_t - \tilde v_t}{2   b + v_t + \tilde v_t}$">|; 

$key = q/a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$a$">|; 

$key = q/xiin[0,1];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$\xi \in [0,1]$">|; 

$key = q/g_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$g_0$">|; 

$key = q/{displaymath}p_uparrowsime^{-L,(rho-rho_c)}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="338" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="\begin{displaymath}
p_\uparrow \sim e^{- L   (\rho-\rho_c)}  .
\end{displaymath}">|; 

$key = q/rhoapprox0.205;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\rho \approx 0.205$">|; 

$key = q/tau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\tau$">|; 

$key = q/N_{jam};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$N_{jam}$">|; 

$key = q/displaystylev_{t+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$\displaystyle v_{t+1}$">|; 

$key = q/v_i=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$v_i = 0$">|; 

$key = q/vleqv_{{rm{safe};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$v \leq v_{\rm safe}$">|; 

$key = q/mathop{mathgroupsymoperatorsexp}nolimits(ANrho);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\mathop {\mathgroup \symoperators exp}\nolimits (A N \rho )$">|; 

$key = q/displaystylex_t+v_{t+1}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\displaystyle x_t + v_{t+1}  .$">|; 

$key = q/leftlanglegrightrangle=1slashrho-ell=LslashN-ell;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\left\langle g\right\rangle = 1/\rho - \ell = L/N - \ell$">|; 

$key = q/v=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$v=0$">|; 

$key = q/exp(ANrho);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$\exp(A N \rho)$">|; 

$key = q/L=Nslashrho_L;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$L = N/\rho_L$">|; 

$key = q/N=625;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$N=625$">|; 

$key = q/L;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$L$">|; 

$key = q/d(v)+vtauleqd(tildev)+g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$d(v) + v\tau \leq d (\tilde v) + g$">|; 

$key = q/rho=0.2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$\rho=0.2$">|; 

$key = q/displaystylev_{{rm{safe};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle v_{\rm safe}$">|; 

$key = q/rho=0.22;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\rho=0.22$">|; 

$key = q/(a,b,epsilon)=(1,infty,1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$(a,b,\epsilon ) = (1,\infty ,1)$">|; 

$key = q/p_uparrow;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$p_\uparrow$">|; 

$key = q/t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$t$">|; 

$key = q/(a,b,epsilon)=(0.2,0.6,1.5);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$(a,b,\epsilon )=(0.2,0.6,1.5)$">|; 

$key = q/textstyle=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\textstyle =$">|; 

$key = q/rhoapprox0.17;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\rho \approx 0.17$">|; 

$key = q/g=tildex-x-ell;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$g = \tilde x - x -
\ell$">|; 

$key = q/Tsimexpbig((rho-rho_*)^{-alpha}big);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$T \sim \exp\big( (\rho-\rho_*)^{-\alpha} \big)$">|; 

$key = q/10^9;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$10^9$">|; 

$key = q/v_{{rm{max};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$v_{\rm max}$">|; 

$key = q/v_{max}=3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$v_{max}=3$">|; 

$key = q/rho=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\rho=1$">|; 

$key = q/N_{jam}simL,(rho-rho_c);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$N_{jam} \sim L   (\rho - \rho_c)$">|; 

$key = q/displaystylev_{{rm{des};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\displaystyle v_{\rm des}$">|; 

$key = q/N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$N$">|; 

$key = q/ell;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\ell$">|; 

$key = q/x=-infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$x=-\infty$">|; 

$key = q/Tsimexpbig(-gamma,(rho-rho_*)big);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$T \sim \exp\big( - \gamma   (\rho - \rho_*) \big)$">|; 

$key = q/2times2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$2 \times 2$">|; 

$key = q/(a,b,epsilon)=(0.2,0.6,1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$(a,b, \epsilon) = (0.2,0.6,1)$">|; 

$key = q/b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$b$">|; 

$key = q/g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$g$">|; 

$key = q/p_uparrowsimexp(-N_{jam});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$p_\uparrow \sim
\exp(-N_{jam})$">|; 

$key = q/N=5000;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$N=5000$">|; 

$key = q/T_{bkdn}sim1slashL;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$T_{bkdn} \sim 1/L$">|; 

$key = q/p_downarrow;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$p_\downarrow$">|; 

$key = q/d(tildev);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$d(\tilde v)$">|; 

$key = q/rhoapprox0.21;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\rho \approx 0.21$">|; 

$key = q/A;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$A$">|; 

$key = q/displaystylemin{v_t+a,v_{{rm{safe},v_{{rm{max}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\displaystyle \min \{ v_t + a, v_{\rm safe}, v_{\rm max} \}$">|; 

$key = q/(a,b)=(0.2,0.6);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$(a,b) = (0.2,0.6)$">|; 

$key = q/hatalpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\hat\alpha$">|; 

$key = q/g=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$g=0$">|; 

$key = q/rho=0.21;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\rho=0.21$">|; 

1;

