\section{Basic eye-movement properties}
This sections reports basic eye movement properties of monkeys and humans. A good start are probability density functions (pdf) of the fixation locations.\footnote{Done using function fixationprob.m \ref{ssec:.:fixationprob}.}{} 

\begin{figure}[!htb]
\label{pdfs}
\centering
\fbox{ \begin{minipage}{\textwidth}
\begin{tabular}{cc}
humans & monkeys \\
\input{humanpdf.tex} & \input{monkeypdf.tex} \\
\end{tabular}
\caption{Probability Distributions of Fixated Locations}
%description of figure
Probability distributions of fixated locations on the images for humans and monkeys convoluted with a Gaussian of half width at full maximum of 1$^{\circ}$. Included are all four experiments, i.e. 58545 human saccades and 3949 monkey saccades. 
\end{minipage} }
\end{figure}


Figure \ref{pdfs} describes the probability distribution of fixated locations on the images for humans and monkeys. As will be demonstrated in fig. \ref{XYMovement}, the shift along x/y-axes indicates a possible systematic difference between monkeys and humans. % discussion: difference in eccentricity in pdfs between monkeys and humans due to missing/existant fixation crosses before trials

We looked at correlations between fixation durations and saccade speed, saccade duration and saccade speed, saccade duration and saccade length, fixation duration and saccade duration, and fixation duration and saccade length, in monkeys and humans. See fig. \ref{alleyemovements}.\footnote{Using function specialplot.m \ref{ssec:./plots:specialplot}.}{}\footnote{As a convention throughout this thesis, humans are blue and monkeys are red. When the humans and monkeys in Bochum were plotted with extra graphs together with humans and monkeys from Osnabr\"uck and Montana, they were colored cyan and magenta, respectively. Error bars are the standard error of the bins as given by $\sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}$. }{} As can be seen from the figure and read from table \ref{alleyemovementstable}, several eye movements are highly significant and correlated. In humans, the faster, the wider, and the longer in time the saccades are, the shorter the fixation durations. This was not found in monkeys. The Kruskal-Wallis test allows to reject the null hypotheses (equality of humans and monkeys) only in the case of saccade speed and saccade length, but becomes insignificant for the saccade duration. In humans and monkeys, saccade durations become longer with increasing saccade speed and saccade length (more in humans then in monkeys). Here significant differences between humans and monkeys were found in both cases. 

\begin{figure}[!htb]
\label{alleyemovements}
\centering
\fbox{ \begin{minipage}{\textwidth}
\begin{tabular}{cc}
fixation duration and saccade speed & saccade duration and saccade speed \\
\input{fixationdurationsaccadespeed.tex} & \input{saccadedurationsaccadespeed.tex}
\end{tabular}
\begin{tabular}{cc}
saccade duration and saccade length & fixation duration and saccade duration \\
\input{saccadedurationsaccadelength.tex} & \input{fixationdurationsaccadeduration.tex}
\end{tabular}
\begin{tabular}{c}
fixation duration and saccade length \\
\input{fixationdurationsaccadelength.tex}
\end{tabular}
\caption{Correlations of eye movements}
%description of figure
Eye movement properties plotted as function of each other. Fixation duration refers to the saccade target. Bin size was 20 over X and Y dimensions.\footnote{plotted using function specialplot(2) \ref{ssec:./plots:specialplot} which relies on function histcnew \ref{ssec:.:histcnew}. }{} Statistics see table \ref{alleyemovementstable}. 
\end{minipage} }
\end{figure}

%% eye movement correlations
\begin{singlespacing}  
\begin{table}[!htb]
\label{alleyemovementstable}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ fixation duration and saccade speed } \\
 {} & monkeys & humans \\
{   } correlations  &  0.0162  &  -0.0211  \\ 
{   } p-values  &  0.4108  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  4.4874 ,  2.9617 
% std 2.1792 ,  1.7323 
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade duration and saccade speed } \\
 {} & monkeys & humans \\
{   } correlations  &  0.8195  &  0.8437  \\ 
{   } p-values  &  0.0000  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0140 } \\ 
\end{tabular}
% median  4.4874 ,  2.9617 
% std 2.1792 ,  1.7323 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade duration and saccade length } \\
 {} & monkeys & humans \\
{   } correlations  &  0.9159  &  0.9418  \\ 
{   } p-values  &  0.0000  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.3823 } \\ 
\end{tabular}
% median  161.0435 ,  112.9690 
% std 115.4573 ,  120.3982 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ fixation duration and saccade duration } \\
 {} & monkeys & humans \\
{   } correlations  &  0.0833  &  -0.0368  \\ 
{   } p-values  &  0.0000  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0070 } \\ 
\end{tabular}
% median  35.0000 ,  36.0000 
% std 10.3678 ,  16.5700 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ fixation duration and saccade length } \\
 {} & monkeys & humans \\
{   } correlations  &  0.0290  &  -0.0323  \\ 
{   } p-values  &  0.1423  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  161.0435 ,  112.9690 
% std 115.4573 ,  120.3982 
\caption{Correlations of eye movements}
%description of figure
Corresponds to fig. \ref{alleyemovements}. Signed-test means the Wilcoxon signed rank test for zero median.\footnote{Function signrank from \textsc{Matlab} statistics toolbox.}{} Correlations and p-values refer to the Pearson product-moment correlation coefficient, which is obtained by dividing the covariance of the two variables by the product of their standard deviations.\footnote{\textsc{Matlab} function corrcoef}{} Medians and standard deviations of the eye movements follow: 
\begin{tabular}{lcc}
& monkeys & humans \\
fixation duration & 192 (78.9897) & 228 (141.5190) \\
saccade length & 161.0435 (115.4573) & 112.9690 (120.3982) \\
saccade speed & 4.4874 (2.1792) & 2.9617 (1.7323) \\
saccade duration & 35 (10.3678 & 36 (16.5700) \\
\end{tabular}
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing


A commonly stated effect is the effect of eccentricity. We wanted to know, what it means exactly and what it extends to. Table \ref{eccentricitytable} is a short overview about eye movements and the corresponding effect of eccentricity in humans and monkeys. Table \ref{eccentricitytable} shows that in humans, fixations become shorter and saccades speed up with increasing eccentricity. In monkeys saccade duration and saccade length increase with eccentricity on both x- and y-axes. As for saccade length in humans, it increases only on the ordinate with eccentricity. 

\begin{singlespacing}  
\begin{table}[!htb]
\label{eccentricitytable}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade length (ordinate)} \\
 {} & monkeys & humans \\
{   } correlations  &  0.0974  &  0.0197  \\ 
{   } p-values  &  0.0000  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0002 } \\ 
\end{tabular}
% median  161.0435 ,  112.9690 
% std 115.4573 ,  120.3982 
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade speed (ordinate) } \\
 {} & monkeys & humans \\
{   } correlations  &  0.1042  &  0.4688  \\ 
{   } p-values  &  0.6124  &  0.0241  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\
\end{tabular}
% median  4.4874 ,  2.9617 
% std 2.1792 ,  1.7323 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade duration (ordinate) } \\
 {} & monkeys & humans \\
{   } correlations  &  0.0793  &  0.0332  \\ 
{   } p-values  &  0.0000  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  35.0000 ,  36.0000 
% std 10.3678 ,  16.5700 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ fixation duration (ordinate) } \\
 {} & monkeys & humans \\
{   } correlations  &  0.1145  &  0.0154  \\ 
{   } p-values  &  0.0000  &  0.0007  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  192.0000 ,  228.0000 
% std 78.9897 ,  141.5190 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade length (abscissa) } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0317  &  0.0264  \\ 
{   } p-values  &  0.0747  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  161.0435 ,  112.9690 
% std 115.4573 ,  120.3982 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade speed (abscissa) } \\
 {} & monkeys & humans \\
{   } correlations  &  0.0477  &  0.1042  \\ 
{   } p-values  &  0.0105  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  4.4874 ,  2.9617 
% std 2.1792 ,  1.7323 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade duration (abscissa) } \\
 {} & monkeys & humans \\
{   } correlations  &  0.0225  &  0.0985  \\ 
{   } p-values  &  0.2305  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  35.0000 ,  36.0000 
% std 10.3678 ,  16.5700 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ fixation duration (abscissa) } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.1302  &  -0.0021  \\ 
{   } p-values  &  0.0000  &  0.6394  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  192.0000 ,  228.0000 
% std 78.9897 ,  141.5190 
\caption{Effects of eccentricity on eye movements}
%description of figure
Here, except for fixation duration, the figures show correlations of eye movements and eccentric saccade target position (as opposed to eccentric position at saccade begin). For saccade length, this allows a comparison of the controls in \cite{Tatler2006} to our different controls. This includes only experiments 1 and 2. For saccade length refer to fig. \ref{eccentricitysaccadelength}.  
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing
