[freehaven-cvs] a few more fixes

[arma@seul.org (Roger Dingledine)]

Update of /home/freehaven/cvsroot/doc/mixmaster-vs-reliable
In directory moria.mit.edu:/home2/arma/work/freehaven/doc/mixmaster-vs-reliable

Modified Files:
	mixvreliable.tex 
Log Message:
a few more fixes
figure 1 -> Figure 1
quantile -> quartile
and some minor grammar issues


Index: mixvreliable.tex
===================================================================
RCS file: /home/freehaven/cvsroot/doc/mixmaster-vs-reliable/mixvreliable.tex,v
retrieving revision 1.25
retrieving revision 1.26
diff -u -d -r1.25 -r1.26
--- mixvreliable.tex	1 Jul 2004 00:11:40 -0000	1.25
+++ mixvreliable.tex	1 Jul 2004 00:19:20 -0000	1.26
@@ -139,7 +139,7 @@
 
 Mixmaster is represented in the generalized mix model proposed by
 D\'iaz and Serjantov~\cite{DS03} as shown in
-figure~\ref{fig-mm}. In this model, the mix is represented at the time of
+Figure~\ref{fig-mm}. In this model, the mix is represented at the time of
 flushing. The function $P(n)$ represents the probability of a message
 of being flushed by the mix, as a function of the number $n$ of
 messages in the pool. Note that $P(n)=s/n$.
@@ -372,8 +372,8 @@
 level of $0.01$, the null hypothesis gets rejected (Chi-value=$826 208$)!
 % END (Evelyne)
 
-In the left part of figure~\ref{arr-day} we show the number of messages arrived to
-the mix per hour. The right part of figure~\ref{arr-day} shows
+In the left part of Figure~\ref{arr-day} we show the number of messages arrived to
+the mix per hour. The right part of Figure~\ref{arr-day} shows
 the evolution of the arrivals per day. We can observe that the traffic
 arrived to the mix during the first month is much heavier than in the
 following three months. This shows that the input traffic pattern that
@@ -429,7 +429,7 @@
 anonymity value. In this section we show the results obtained in our
 simulation. 
 
-In figure~\ref{3d-sen} we show the correlation between the recipient anonymity
+In Figure~\ref{3d-sen} we show the correlation between the recipient anonymity
 and the delay for every message. Figure~\ref{3d-sen} shows the
 same for sender anonymity. 
 
@@ -454,28 +454,28 @@
 In order to study the behavior of the mix under different traffic loads,
 we have plotted values of delay and anonymity obtained in the simulation 
 for the rounds with few arrivals (low traffic), intermediate number of 
-arrivals (medium traffic) and many arrivals (high traffic).
+arrivals (medium traffic), and many arrivals (high traffic).
 
-We have selected the low, medium and high traffic taking into account 
+We have selected the low, medium, and high traffic taking into account 
 the data statistics of the arrival process:
 \begin{description}
 \item[Low traffic:] all rounds where the number of arrivals was 
-between the first and third quantile ($1 \leq$\ data $\leq\ 17$); 
+between the first and third quartile ($1 \leq$\ data $\leq\ 17$); 
 hence $50$ percent of the rounds
 are denoted as normal traffic.
 \item[Medium traffic:] all rounds where the number of arrivals was greater
-than the third quantile but lower than the outlier bound ($17 <$\ data $\leq\ 41$).
+than the third quartile but lower than the outlier bound ($17 <$\ data $\leq\ 41$).
 \item[High traffic:] all rounds with outlier values for the incoming
 messages (data $> 41$).
 \end{description}
 
-In figure~\ref{del-mm} we show the minutes of delay of every message
+In Figure~\ref{del-mm} we show the minutes of delay of every message
 (the x-axis indicates the evolution in time). 
 We can see that the delay only takes high values when the traffic 
 is low. The fact that some messages appear as having a delay close 
 to zero in the low traffic figure is due to the fact that we have more 
 samples, so there are messages that arrive just before the flushing and 
-are forwarded immediately. In figure~\ref{an-mm} we show the recipient 
+are forwarded immediately. In Figure~\ref{an-mm} we show the recipient 
 anonymity of every message (the sender anonymity presents very similar
 characteristics). We can see that as the traffic increases, the anonymity 
 provided to the messages takes higher values. No matter how low the
@@ -515,7 +515,7 @@
 it delays it a predetermined amount of time (picked from an exponential
 distribution) and then forwards it. We represent a star, '*', per message.
 
-In figure~\ref{rel-sen} we present the sender and recipient anonymity
+In Figure~\ref{rel-sen} we present the sender and recipient anonymity
 provided by Reliable 
 for the real stream of inputs we have considered.
 We can see that the
@@ -962,7 +962,7 @@
 \caption{\small The matching exponential cumulative density function } \label{evie2}   
 \end{center}
 
-How can we then calculate the probabilities of the delay times? To make this clear, let us look at figure~\ref{evie1} and suppose 
+How can we then calculate the probabilities of the delay times? To make this clear, let us look at Figure~\ref{evie1} and suppose 
 that we only have three arrival times prior to \emph{out}. We have thus three possible delays $d_1 > d_2 > d_3$. Let us now 
 assume for simplicity reasons that $d_1=3$ hours, $d_2=2$ hours and $d_3=1$ hour. 
 The variable delay is continuous and can theoretically take every value in the interval $[0,3]$. However, we know that 
@@ -974,7 +974,7 @@
 P(D = d_3) &\approx& P(0 < D \leq d_3) = \mathrm{\ dark\ surface}\ .  
 \end{eqnarray*}  
 In this way one can clearly see that the biggest surface corresponds to the most probable delay! This is straightforward for
-more than three delays. For computation we make use of the cumulative distribution function (cdf) which is graphed in figure~\ref{evie2}. 
+more than three delays. For computation we make use of the cumulative distribution function (cdf) which is graphed in Figure~\ref{evie2}. 
 Cumulative probabilities are listed in tables and known in statistical software. For reasons of simplicity we put the mean
 of the exponential to be $1$ hour (easy parameterization):
 \begin{eqnarray*}
@@ -983,7 +983,7 @@
 P(D = d_3) &\approx& F(d_3) = 0.6321\ .  
 \end{eqnarray*}  
 In our little example, the message corresponds most likely with the one that entered the mix $1$ hour before \emph{out}.
-You can also clearly see this on figure~\ref{evie1}. In practical applications however, many possible delays will occur so that
+You can also clearly see this on Figure~\ref{evie1}. In practical applications however, many possible delays will occur so that
 visual inspections will not be efficient and calculations have to made and compared.
 % END ADDITION EVELYNE
 

***********************************************************************
To unsubscribe, send an e-mail to majordomo@seul.org with
unsubscribe freehaven-cvs       in the body. http://freehaven.net/