# LaTeX2HTML 2002 (1.67)# Associate images original text with physical files.$key = q/{figure*}tabular{{cccc}{par{{psfig{figure=slashafsslashcsslashuserslashvyassslasth=200pt}{Port80&Port6346&Port9898&Port43726tabular{{par{{{{figure*};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="1332" HEIGHT="270" BORDER="0" SRC="|."$dir".q|img84.png" ALT="\begin{figure*}\begin{tabular}{cccc}\par\psfig{figure=/afs/cs/user/vyass/Fall05......Port 80 &amp; Port 6346 &amp; Port 9898 &amp; Port 43726 \\\\\end{tabular}\par\end{figure*}">|; $key = q/lambda_1,ldots,lambda_m;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="77" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img51.png" ALT="$ \lambda_1,\ldots, \lambda_m$">|; $key = q/delta_k(t);MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img32.png" ALT="$ \delta_k(t)$">|; $key = q/frac{|R|^2}{|S|^2};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="37" HEIGHT="43" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img24.png" ALT="$ \frac{\Vert R\Vert^2}{\Vert S\Vert^2}$">|; $key = q/t;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="10" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img60.png" ALT="$ t$">|; $key = q/D_{H+S};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="48" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img74.png" ALT="$ D_{H+S}$">|; $key = q/kapproxk';MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="47" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img18.png" ALT="$ k \approx k'$">|; $key = q/O(mkN^2);MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="73" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img48.png" ALT="$ O(mkN^2)$">|; $key = q/D_{W};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img70.png" ALT="$ D_{W}$">|; $key = q/D_{F+S};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="46" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img3.png" ALT="$ D_{F+S}$">|; $key = q/D_{F+H};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="49" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img73.png" ALT="$ D_{F+H}$">|; $key = q/{figure}tabular{{cc}{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05st_port_1214_week2.eps,width=200pt}{Port80&Port1214tabular{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="656" HEIGHT="270" BORDER="0" SRC="|."$dir".q|img86.png" ALT="\begin{figure}\begin{tabular}{cc}\psfig{figure=/afs/cs/user/vyass/Fall05/IMC_CA......4_week2.eps,width=200pt}\\\\Port 80 &amp; Port 1214 \\\\\end{tabular}\end{figure}">|; $key = q/k;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img10.png" ALT="$ k$">|; $key = q/X;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img1.png" ALT="$ X$">|; $key = q/{figure*}tabular{{cccc}{psfig{figure=slashafsslashcsslashuserslashvyassslashFallhVolumePorts&ScanTargetPorts&P2PPorts&RandomPortstabular{{{{figure*};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="1331" HEIGHT="275" BORDER="0" SRC="|."$dir".q|img80.png" ALT="\begin{figure*}\begin{tabular}{cccc}\psfig{figure=/afs/cs/user/vyass/Fall05/......can Target Ports &amp; P2P Ports &amp; Random Ports \\\\\end{tabular}\end{figure*}">|; $key = q/{figure}{centerline{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05slfs_udp_fourier_cameraready.eps,width=175pt,height=150pt}}{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="279" HEIGHT="240" BORDER="0" SRC="|."$dir".q|img67.png" ALT="\begin{figure}\centerline{\psfig{figure=/afs/cs/user/vyass/Fall05/IMC_CAMERA_R......ON/cdfs_udp_fourier_cameraready.eps,width=175pt,height=150pt}}\end{figure}">|; $key = q/Ntimesk;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="47" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img9.png" ALT="$ N \times k$">|; $key = q/0^{th};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img62.png" ALT="$ 0^{th}$">|; $key = q/alphaN;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="29" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img15.png" ALT="$ \alpha N$">|; $key = q/dtimesN;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="46" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img49.png" ALT="$ d \times N$">|; $key = q/m=30;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="55" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img27.png" ALT="$ m=30$">|; $key = q/D_H;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="29" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img72.png" ALT="$ D_H$">|; $key = q/S;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img21.png" ALT="$ S$">|; $key = q/bm{varphi}_j;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img43.png" ALT="$ \bm{\varphi }_j$">|; $key = q/lambda_t;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="19" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img55.png" ALT="$ \lambda_t$">|; $key = q/mtimesk'+|D|;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="93" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img12.png" ALT="$ m \times k' + \vert D\vert $">|; $key = q/d=kN;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="57" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img47.png" ALT="$ d=kN$">|; $key = q/|D|;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img13.png" ALT="$ \vert D\vert$">|; $key = q/tneqk;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="40" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img33.png" ALT="$ t \neq k$">|; $key = q/{figure}{centerline{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05sltionaries_tcp_camera_ready.eps,width=175pt,height=150pt}}{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="279" HEIGHT="240" BORDER="0" SRC="|."$dir".q|img77.png" ALT="\begin{figure}\centerline{\psfig{figure=/afs/cs/user/vyass/Fall05/IMC_CAMERA_R......ct_dictionaries_tcp_camera_ready.eps,width=175pt,height=150pt}}\end{figure}">|; $key = q/{figure}tabular{{cc}{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05ses_80_imag.eps,width=200pt}{Realpart&Imaginaryparttabular{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="656" HEIGHT="269" BORDER="0" SRC="|."$dir".q|img81.png" ALT="\begin{figure}\begin{tabular}{cc}\psfig{figure=/afs/cs/user/vyass/Fall05/I......,width=200pt}\\\\Real part &amp; Imaginary part \\\\\end{tabular}\end{figure}">|; $key = q/bm{P}_t;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img57.png" ALT="$ \bm{P}_t$">|; $key = q/%latex2htmlidmarker2598setcounter{footnote}{3}fnsymbol{footnote};AAT/;$cached_env_img{$key} = q|<IMG WIDTH="6" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img7.png" ALT="% latex2html id marker 2598\setcounter{footnote}{3}\fnsymbol{footnote}">|; $key = q/{figure}tabular{{cc}{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05s00pt,height=200pt}{Port25slashTCP&Port4662slashTCPtabular{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="657" HEIGHT="338" BORDER="0" SRC="|."$dir".q|img63.png" ALT="\begin{figure}\begin{tabular}{cc}\psfig{figure=/afs/cs/user/vyass/Fall05/I......eight=200pt}\\\\Port 25/TCP &amp; Port 4662/TCP \\\\\end{tabular}\end{figure}">|; $key = q/displaystyleX(t)=frac{1}{100}sum_{k=0}^{99}hatX(k)cosBig(frac{pik(t+frac12)}{100}Big);MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="265" HEIGHT="65" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img37.png" ALT="$\displaystyle X(t) = \frac{1}{100} \sum_{k=0}^{99} \hat X(k)\cos\Big(\frac{\pi k(t+\frac12)}{100}\Big)$">|; $key = q/-f;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="26" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img65.png" ALT="$ -f$">|; $key = q/bm{r}_0=bm{v};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="50" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img53.png" ALT="$ \bm{r}_0 = \bm{v}$">|; $key = q/hatX(k);MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="40" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img38.png" ALT="$ \hat X(k)$">|; $key = q/bm{v};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img50.png" ALT="$ \bm{v}$">|; $key = q/{figure}{centerline{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05sles_cdf_30_tcp_camera_ready.eps,width=175pt,height=150pt}}{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="279" HEIGHT="240" BORDER="0" SRC="|."$dir".q|img75.png" ALT="\begin{figure}\centerline{\psfig{figure=/afs/cs/user/vyass/Fall05/IMC_CAMERA_R......ionaries_cdf_30_tcp_camera_ready.eps,width=175pt,height=150pt}}\end{figure}">|; $key = q/d;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img42.png" ALT="$ d$">|; $key = q/R=S-C_s;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="86" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img23.png" ALT="$ R = S - C_s $">|; $key = q/displaystyleX(t)=3cosBig(frac{pi8(t+frac12)}{100}Big)-5delta_{10}(t)+15delta_{20}(t);MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="321" HEIGHT="58" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img35.png" ALT="$\displaystyle X(t) = 3 \cos\Big(\frac{\pi 8(t + \frac12)}{100}\Big) - 5 \delta_{10}(t) + 15\delta_{20}(t)$">|; $key = q/t=k;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="40" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img34.png" ALT="$ t = k$">|; $key = q/{figure}{centerline{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05sltionaries_udp_camera_ready.eps,width=175pt,height=150pt}}{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="279" HEIGHT="240" BORDER="0" SRC="|."$dir".q|img78.png" ALT="\begin{figure}\centerline{\psfig{figure=/afs/cs/user/vyass/Fall05/IMC_CAMERA_R......ct_dictionaries_udp_camera_ready.eps,width=175pt,height=150pt}}\end{figure}">|; $key = q/N;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img8.png" ALT="$ N$">|; $key = q/O(mdN);MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img46.png" ALT="$ O(mdN)$">|; $key = q/NlogN;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="59" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img68.png" ALT="$ N\log N$">|; $key = q/{figure}tabular{{cc}{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05s_1214_imag.eps,width=200pt}{RealPart&ImaginaryParttabular{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="656" HEIGHT="269" BORDER="0" SRC="|."$dir".q|img82.png" ALT="\begin{figure}\begin{tabular}{cc}\psfig{figure=/afs/cs/user/vyass/Fall05/IMC......,width=200pt}\\\\Real Part &amp; Imaginary Part \\\\\end{tabular}\end{figure}">|; $key = q/t<m;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="45" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img61.png" ALT="$ t &lt; m$">|; $key = q/{figure}tabular{{cc}{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05sal{X{.overtheredundantdictionary{{calD}{.&tabular{{{{figure};MSF=1.6;FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="794" HEIGHT="360" BORDER="0" SRC="|."$dir".q|img36.png" ALT="\begin{figure}\begin{tabular}{cc}\psfig{figure=/afs/cs/user/vyass/Fall05/IMC......over the redundant dictionary ${\cal D}$. &amp; \\\\\end{tabular}\end{figure}">|; $key = q/{calD};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img40.png" ALT="$ {\cal D}$">|; $key = q/displaystyleX(t)=3cosBig(frac{pi8(t+frac12)}{100}Big)-5delta_{10}(t)+15delta_{20}(t).;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="325" HEIGHT="58" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img41.png" ALT="$\displaystyle X(t) = 3 \cos\Big(\frac{\pi 8(t + \frac12)}{100}\Big) - 5 \delta_{10}(t) + 15\delta_{20}(t).$">|; $key = q/db4;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="27" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img2.png" ALT="$ db4$">|; $key = q/D_{F+H+S};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="67" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img4.png" ALT="$ D_{F+H+S}$">|; $key = q/(mk'+alphaN)slash(Nk);MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="131" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img17.png" ALT="$ ( mk' + \alpha N )/(N k )$">|; $key = q/m;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img11.png" ALT="$ m$">|; $key = q/mslashN;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="40" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img20.png" ALT="$ m/N$">|; $key = q/f;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="14" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img64.png" ALT="$ f$">|; $key = q/X(t);MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img39.png" ALT="$ X(t)$">|; $key = q/{figure}tabular{{cc}{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05ss_invcdf.eps,width=200pt}{HighVolumePorts&P2PPortstabular{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="657" HEIGHT="280" BORDER="0" SRC="|."$dir".q|img83.png" ALT="\begin{figure}\begin{tabular}{cc}\psfig{figure=/afs/cs/user/vyass/Fall05/IMC......dth=200pt}\\\\High Volume Ports&amp; P2P Ports \\\\\end{tabular}\end{figure}">|; $key = q/alphallk;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="48" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img19.png" ALT="$ \alpha \ll k$">|; $key = q/bm{Phi};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img44.png" ALT="$ \bm{\Phi}$">|; $key = q/168times12=2016;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="116" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img87.png" ALT="$ 168 \times 12 = 2016$">|; $key = q/N+{rmpolylog}(d);MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="109" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img45.png" ALT="$ N + {\rm polylog}(d)$">|; $key = q/displaystylebm{r}_t=bm{v}-bm{P}_t,bm{v}.;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="102" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img59.png" ALT="$\displaystyle \bm{r}_t = \bm{v} - \bm{P}_t   \bm{v}.$">|; $key = q/{figure}{centerline{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05slslashsnmp_sn1ca32ck4-gigabitethernet4-0.eps,width=200pt}}{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="319" HEIGHT="250" BORDER="0" SRC="|."$dir".q|img88.png" ALT="\begin{figure}\centerline{\psfig{figure=/afs/cs/user/vyass/Fall05/IMC_CAMERA_REA......C_RESULTS/SNMP/snmp_sn1ca32ck4-gigabitethernet4-0.eps,width=200pt} }\end{figure}">|; $key = q/{figure}{centerline{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05slAug03slashIMC_RESULTSslashtrendanalysis.eps,width=150pt}}{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="238" HEIGHT="199" BORDER="0" SRC="|."$dir".q|img85.png" ALT="\begin{figure}\centerline{\psfig{figure=/afs/cs/user/vyass/Fall05/IMC_CAMERA_READY_Aug03/IMC_RESULTS/trendanalysis.eps,width=150pt}}\end{figure}">|; $key = q/bm{r}_m;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="25" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img52.png" ALT="$ \bm{r}_m$">|; $key = q/k';MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img14.png" ALT="$ k'$">|; $key = q/L_2;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="22" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img26.png" ALT="$ L_2$">|; $key = q/%latex2htmlidmarker2597setcounter{footnote}{4}fnsymbol{footnote};AAT/;$cached_env_img{$key} = q|<IMG WIDTH="5" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img6.png" ALT="% latex2html id marker 2597\setcounter{footnote}{4}\fnsymbol{footnote}">|; $key = q/|cdot|;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img25.png" ALT="$ \Vert \cdot \Vert$">|; $key = q/N=168;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="64" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img28.png" ALT="$ N=168$">|; $key = q/alpha;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img16.png" ALT="$ \alpha$">|; $key = q/D_{F};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="28" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img69.png" ALT="$ D_{F}$">|; $key = q/operatorname{span}{}{bm{varphi}_lambda:lambda_1,ldots,lambda_t};MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="155" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img58.png" ALT="$ \operatorname{span}{\}{ \bm{\varphi }_\lambda : \lambda_1,\ldots,\lambda_t \}$">|; $key = q/%latex2htmlidmarker2596setcounter{footnote}{2}fnsymbol{footnote};AAT/;$cached_env_img{$key} = q|<IMG WIDTH="6" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img5.png" ALT="% latex2html id marker 2596\setcounter{footnote}{2}\fnsymbol{footnote}">|; $key = q/{figure}{centerline{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05slfs_tcp_fourier_cameraready.eps,width=175pt,height=150pt}}{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="279" HEIGHT="240" BORDER="0" SRC="|."$dir".q|img66.png" ALT="\begin{figure}\centerline{\psfig{figure=/afs/cs/user/vyass/Fall05/IMC_CAMERA_R......ON/cdfs_tcp_fourier_cameraready.eps,width=175pt,height=150pt}}\end{figure}">|; $key = q/60slash10timesX=6X;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="121" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img29.png" ALT="$ 60/10\times X = 6 X $">|; $key = q/x;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img79.png" ALT="$ x$">|; $key = q/displaystylelambda_t={rmargmax}_{j}leftvert{leftlangle{bm{r}_{t-1}},{bm{varphi}_j}rightrangle}rightvert.;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="198" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img56.png" ALT="$\displaystyle \lambda_t  =  {\rm argmax}_{j} \\left\vert {\left\langle { \bm{r}_{t-1} }, { \bm{\varphi }_j } \right\rangle } \right\vert .$">|; $key = q/t=1;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="39" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="|."$dir".q|img54.png" ALT="$ t = 1$">|; $key = q/C_s;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="22" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img22.png" ALT="$ C_s$">|; $key = q/k=0,ldots,N-1;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="119" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img31.png" ALT="$ k = 0, \ldots, N-1$">|; $key = q/D_S;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="26" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img71.png" ALT="$ D_S$">|; $key = q/{figure}{centerline{psfig{figure=slashafsslashcsslashuserslashvyassslashFall05sles_cdf_30_udp_camera_ready.eps,width=175pt,height=150pt}}{{{{figure};FSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="279" HEIGHT="240" BORDER="0" SRC="|."$dir".q|img76.png" ALT="\begin{figure}\centerline{\psfig{figure=/afs/cs/user/vyass/Fall05/IMC_CAMERA_R......ionaries_cdf_30_udp_camera_ready.eps,width=175pt,height=150pt}}\end{figure}">|; $key = q/displaystyle{calD}=Bigg{cosBig(frac{pik(t+frac12)}{N}Big)Bigg}bigcupBigg{delta_k(t)Bigg},;MSF=1.6;AAT/;$cached_env_img{$key} = q|<IMG WIDTH="265" HEIGHT="63" ALIGN="MIDDLE" BORDER="0" SRC="|."$dir".q|img30.png" ALT="$\displaystyle {\cal D} = \Bigg\{ \cos\Big(\frac{\pi k(t + \frac12)}{N}\Big)\Bigg\}\bigcup \Bigg\{\delta_k(t)\Bigg\} ,$">|; 1;