%\documentclass{book}
%\usepackage[pdftex]{graphicx}
%\begin{document}
\chapter{Results}
%this is basically taken from Selim's ``THE LIST`` 
This chapter gives an overview about different aspects of human and monkey eye movements that we investigated into. Each section consists of a description of the methods we used and a summary of the findings. In some cases, when the data allowed and when it was feasible under the time constraints, we extended our analysis to all experiments (will be remarked).\footnote{For the Bochum data durations time stamps for saccades and fixations were not available, therefore, when durations and speed are under examination, the analysis in this section is restricted to experiments 1 and 2. Due to technical restrictions, we did not perform analysis of barness for experiments 3 and 4.}{}\footnote{All of the plots in this section have been created using function plotsome.m  \ref{ssec:./plots:plotsome}.}{} %Note that \cite{Einhaeuser2006} defined feature contrasts agnostic about the modifications. Though the difference might be negligible, we compared luminance contrast and texture contrast on the modified images, instead of the original images. 

\section{Basic eye-movement properties}
This sections reports basic eye movement properties of monkeys and humans. Probability density functions (pdf) of the fixation locations make the start.\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$^{\circ}$. The pdfs of the four experiments revealed considerable differences, so we chose not to fix them and included only experiments 1 and 2. For a thorough comparison of human and monkey fixation maps see \ref{fixmapcomp}. 
\end{minipage} }
\end{figure}

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

We looked at correlations between eye movements in humans and monkeys. 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 highly correlated and -- except for correlations of saccade duration and saccade length and saccade length and saccade speed -- there are significant differences between humans and monkeys (Kruskal-Wallis test). For fixation duration, all correlations are very small, interestingly though with reversed sign for monkeys and humans. Hence, in humans, there is a trend that with shorter timed, more narrow, and slower saccades fixations become longer. With monkeys the opposite is true: longer timed, wider, faster saccades are followed by longer saccades. 

As for saccade movements, the significance of the differences between humans and monkeys gets higher (KW) and the correlations higher, in both humans and monkeys very similarly. As was expected, saccade duration is highly related to saccade length. Interestingly, the faster a saccade the wider it becomes and the longer it takes the faster it becomes (related to the former). 

\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}{cc}
fixation duration and saccade length \\
\input{fixationdurationsaccadelength.tex} & \input{saccadespeedsaccadelength.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 30 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 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade speed and saccade length } \\
 {} & monkeys & humans \\
{   } correlations  &  0.9494  &  0.9363  \\ 
{   } p-values  &  0.0000  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.3084 } \\ 
\end{tabular}
% median  161.0435 ,  112.9491 
% std 115.4573 ,  120.3972 
\caption{Correlations of eye movements}
%description of figure
Corresponds to fig. \ref{alleyemovements}. KW means the Krukal-Wallis test, correlations and p-values refer to the Spearman 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 human and monkey distributions are significantly different (KW). 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. As can be clearly seen, monkeys fixate more with an increasing ordinate and less with an increasing abscissa. This leads to the specific form of the probability density function (\ref{pdfs}) and the \textit{Next fixation} plot (\ref{nextfixation}). 

\begin{singlespacing}  
\begin{table}[!htb]
\label{eccentricitytable}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{lcc}
\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}
\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 (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}
\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}
\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}
\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}
\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 
\begin{tabular}{lcc}
\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 
\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). See fig. \ref{eccentricitysaccadelength} for the corresponding plots. 
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing

\begin{figure}[!htbp]
\label{eccentricitysaccadelength}
\centering
\fbox{ \begin{minipage}{\textwidth}
\begin{tabular}{cc}
\input{abscissaeccentricitysaccadelength.tex} & \input{ordinateeccentricitysaccadelength.tex} \\
\input{abscissaeccentricitysaccadespeed.tex} & \input{ordinateeccentricitysaccadespeed.tex} \\
\input{abscissaeccentricitysaccadeduration.tex} & \input{ordinateeccentricitysaccadeduration.tex} \\
\input{abscissaeccentricityfixationduration.tex} & \input{ordinateeccentricityfixationduration.tex} \\
\end{tabular}
\caption{Eccentricity and eye movements}
Correlation of eccentricity and eye movements. Refer to table \ref{eccentricitytable} for correlations of other eye movements with eccentricity.  
\end{minipage} }
\end{figure}

\section{Statistics of saccade targets}
%on ``THE LIST`` this was called ``Next Fixation Statistics``
This section characterizes saccades with respect to the properties of the respective target location. 

\begin{figure}[!htb]
\label{nextfixation}
\centering
\fbox{ \begin{minipage}{\textwidth}
\begin{tabular}{cc}
monkeys & humans \\
\input{nextfixmonkeys.tex} & \input{nextfixhumans.tex} \\ % are file names are misnomer?
\end{tabular}
\caption{\textit{Next fixation} statistics for humans and monkeys}
%description of figure
All saccades, as defined by magnitude and directions plotted with respect to the center of a coordinate system of double the size an image. All points are averaged (means). 
\end{minipage} }
\end{figure}

In fig. \ref{nextfixation} all saccades are plotted with respect to the origin.\footnote{function nextfixation.m \ref{ssec:.:nextfixation}.}{} Fewer saccades lead to a slightly clustered image in monkeys. Human saccades show a tendency towards moving more horizontally than vertically and more upwards than downwards as compared to monkeys. 

\begin{table}[!htbp]
	\label{marginalxy}
\fbox{ \begin{minipage}{\textwidth}
	\begin{tabular}{cc}
		\begin{tabular}{lcc}
			\multicolumn{3}{c}{ increase of x- and y-movement } \\
			 {} & monkeys & humans \\
			{   } correlations  &  0.1622  &  0.2463  \\ 
			{   } p-values  &  0.0000  &  0.0000  \\ 
			KW & \multicolumn{2}{c}{ p= 0.0802 } \\ 
			slope\footnote{\textsc{Matlab} function robustfit}{} & 0.1162 & 0.1105 \\ 
			% median  84.5000 ,  47.0000 
			% std 101.8333 ,  87.4388 
		\end{tabular} &
		\begin{minipage}{4cm}
			\center{      absolute ordinate and abscissa movement} \\
			\input{xyradius.tex}
		\end{minipage} \\
	\end{tabular}
	\begin{tabular}{lcclcc}
		& \multicolumn{5}{c} {  } \\        
		& \multicolumn{5}{c} { marginal probabilities of movements on ordinate and abscissa } \\
		& \multicolumn{2}{c} { abscissa movements } & & \multicolumn{2}{c} { ordinate movements } \\
		& monkeys & humans & & monkeys & humans\\
		right & 0.4789 & 0.5012 & up & 0.5090 & 0.4756 \\
		left & 0.5183 & 0.4941 & down & 0.4865 & 0.5168 \\
		none & 0.0028 & 0.0047 & none & 0.0045 & 0.0077 \\
	\end{tabular}
	\caption{Correlation of absolute ordinate and abscissa movement}
The figure plots absolute movement on the x-axis against absolute movement of the y-axis and the table right to it correlations of x/y and a Kruskal-Wallis test of the two lines. The table below lists the marginal probabilities of eye movements along the four main directions. 
	\end{minipage} }
\end{table}

In order to understand correlations of feature effects and eye movement, we needed a different concept of controls. Controls were defined as feature contrast on an image at fixation points by the same participant on different images. However, as can be seen exemplarily in fig. \ref{eccentricitysaccadelength}, many eye movements change with eccentricity (cf. table \ref{eccentricitytable}). Therefore, taking the usual definition of controls, we will have biased correlations, e.g. we would erroneously find that short fixations have increased influences of feature contrasts. This would be wrong, as short saccades are more in the center. \cite{Tatler2006} correlated saccade length and feature contrasts and controls were defined by saccade length. We defined controls straightforwardly as average feature contrast over all images. We argue that this removes central biases at fixation points, and with large data sizes, false alarms and misses get averaged out (which can be deduced from the standard errors in the figure). As can be seen in fig. \ref{eccentricitysaccadelength}, saccade length and eccentricity are related, but our definition removes all bias instead of only some parts of it as by Tatler et al.'s  definition. Tables \ref{eyemovementlctable}, \ref{eyemovementtctable}, and \ref{eyemovementbarnesstable} show the effect sizes of features for different eye movements according to this definition.\footnote{restricted to Osnabr\"uck/Montana. 30 bin edges on the abscissa}{} The tables show corresponding correlations and p-values. Our definition of controls had a considerable impact on effect sizes, but we hold that thorough examination with different controls will reveal that our correlations give a correct picture of the interrelations. 

\begin{figure}[!hbtp]
\label{eyemovementfeatures}
\centering
\fbox{ \begin{minipage}{\textwidth}\begin{tabular}{cccc}
& saccade duration & saccade length & fixation duration \\
\begin{rotate}{90} luminance contrast \end{rotate} & \input{saccadedurationlc.tex} & \input{saccadelengthlc.tex} & \input{fixationdurationlc.tex} \\
\begin{rotate}{90} texture contrast \end{rotate} & \input{saccadedurationtc.tex} & \input{saccadelengthtc.tex} & \input{fixationdurationtc.tex} \\
\begin{rotate}{90} {           barness } \end{rotate} & \input{saccadedurationbarness.tex} & \input{saccadelengthbarness.tex} & \input{fixationdurationbarness.tex} \\
\end{tabular}
\caption{Effect sizes of image features for eye movements}
The idea was to get all feature values at saccade targets and take the median actuals. For this purpose it was practical to redefine controls. We read out controls from averages feature maps based on the locations of fixations. Effect sizes were were calculated as actual feature contrast - control feature contrast over control feature contrast. See also tables \ref{eyemovementlctable}, \ref{eyemovementtctable}, and \ref{eyemovementbarnesstable}. 
\end{minipage} }
\end{figure}

\begin{singlespacing}  
\begin{table}[!htbp]
\label{eyemovementlctable}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade duration } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0740  &  -0.1737  \\ 
{   } p-values  &  0.0001  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  0.0185 ,  1.2211 
% std 0.8841 ,  0.9384 
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade speed } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0254  &  -0.1581  \\ 
{   } p-values  &  0.1776  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  0.0159 ,  1.2223 
% std 0.8814 ,  0.9396 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade length } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0534  &  -0.1810  \\ 
{   } p-values  &  0.0044  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  0.0149 ,  1.2224 
% std 0.8817 ,  0.9397 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ fixation duration } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0378  &  0.1153  \\ 
{   } p-values  &  0.0358  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  0.0140 ,  1.2197 
% std 0.8864 ,  0.9364 
\caption{Influence of luminance contrast on eye movements}
These effect sizes, corresponding to fig. \ref{eyemovementfeatures}, were computed according to the re-definition of controls (see above). Medians of effect sizes of luminance contrast were 0.015 (std=0.88) for monkeys and 1.22 (0.94) for humans. 
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing

%%%%%%%%%%%%%%% barness
\begin{singlespacing}  
\begin{table}[!htbp]
\label{eyemovementbarnesstable}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade duration } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0418  &  -0.0245  \\ 
{   } p-values  &  0.0293  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.7006 } \\ 
\end{tabular}
% median  0.0318 ,  0.0132 
% std 0.5203 ,  0.4365 
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade speed } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0404  &  -0.0164  \\ 
{   } p-values  &  0.0336  &  0.0006  \\ 
KW & \multicolumn{2}{c}{ p= 0.2404 } \\ 
\end{tabular}
% median  0.0321 ,  0.0132 
% std 0.5197 ,  0.4363 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade length } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0462  &  -0.0230  \\ 
{   } p-values  &  0.0144  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0846 } \\ 
\end{tabular}
% median  0.0316 ,  0.0128 
% std 0.5195 ,  0.4356 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ fixation duration } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0502  &  0.0137  \\ 
{   } p-values  &  0.0055  &  0.0036  \\ 
KW & \multicolumn{2}{c}{ p= 1.0000 } \\ 
\end{tabular}
% median  0.0346 ,  0.0117 
% std 0.5222 ,  0.4386 
\caption{Influence of barness on eye movements}
These effect sizes, corresponding to fig. \ref{eyemovementfeatures}, were computed according to the re-definition of controls (see above). Medians of effect sizes of barness were 0.032 (std=0.52) for monkeys and 0.013 (0.44) for humans. 
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing



\begin{singlespacing}  
\begin{table}[!htbp]
\label{eyemovementtctable}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade duration } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0717  &  -0.0945  \\ 
{   } p-values  &  0.0003  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0118 } \\ 
\end{tabular}
% median  -0.0715 ,  0.0872 
% std 0.9484 ,  0.9489 
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade speed } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0265  &  -0.0969  \\ 
{   } p-values  &  0.1776  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0002 } \\ 
\end{tabular}
% median  -0.0704 ,  0.0879 
% std 0.9401 ,  0.9471 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade length } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0445  &  -0.1099  \\ 
{   } p-values  &  0.0221  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0073 } \\ 
\end{tabular}
% median  -0.0705 ,  0.0877 
% std 0.9476 ,  0.9480 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ fixation duration } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0715  &  0.0436  \\ 
{   } p-values  &  0.0001  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  -0.0681 ,  0.0858 
% std 0.9223 ,  0.9441 
\caption{Influence of texture contrast on eye movements}
 Effect sizes for texture contrast, corresponding to fig. \ref{eyemovementfeatures}.
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing

The Kruskal-Wallis test finds $p \leq 0.05$ for all features but barness. All Spearman correlations of eye movements with features are significant except for saccade speed and texture contrast in humans. However, the absolute values of correlations tend to be around 0.05 and are hardly visible in the plots. % distussion: While we expected that eye movements correlate positively with features contrasts, what we found is that the correlation is only marginal and sometimes negative. 

%discussion: more refined definition of controls needed for nextfixation!

\section{Time variance}
This section is dedicated to show feature contrasts and eye movement properties as functions of time, or rather as a function of number of fixation. 

\begin{singlespacing}  
\begin{figure}[!htb]
\label{XYMovement}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{cc}
\input{OrdinateMovement.tex} & \input{AbscissaMovement.tex}
\end{tabular}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ experiments 1 and 2 on abscissa } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0416  &  0.1323  \\ 
{   } p-values  &  0.0188  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.5203 } \\ 
% median  90.0000 ,  64.0000 
% std 102.5593 ,  114.9615 
\end{tabular}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ Bochum SS on abscissa} \\
 {} & monkeys & humans \\
{   } correlations  &  -0.1230  &  -0.0507  \\ 
{   } p-values  &  0.0054  &  0.2730  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
% median  5.0000 ,  90.0000 
% std 112.3016 ,  121.0107 
\end{tabular}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ Bochum BS on abscissa } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.1360  &  -0.0483  \\ 
{   } p-values  &  0.0016  &  0.2599  \\ 
KW & \multicolumn{2}{c}{ p= 0.0005 } \\
\end{tabular}
% median  44.0000 ,  70.5000 
% std 57.9822 ,  96.0051 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ experiments 1 and 2 on ordinate } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0696  &  0.0818  \\ 
{   } p-values  &  0.0001  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  84.0000 ,  46.0000 
% std 101.2458 ,  87.5609 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ Bochum SS on ordinate } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.1351  &  -0.0760  \\ 
{   } p-values  &  0.0022  &  0.1000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0026 } \\ 
\end{tabular}
% median  12.0000 ,  62.0000 
% std 89.9109 ,  89.1035 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ Bochum BS on ordinate } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.1360  &  -0.0727  \\ 
{   } p-values  &  0.0016  &  0.0899  \\ 
KW & \multicolumn{2}{c}{ p= 0.2866 } \\ 
\end{tabular}
% median  59.0000 ,  45.0000 
% std 56.9517 ,  74.4895 
\caption{Movements on the axes over time}
Absolute lengths of movements on the ordinate and abscissa over fixations (enumerated by their occurrence in the trial).  \textit{Correlations} refers to the coefficients when the eye movements were compared to fixation numbers. 
\end{minipage} }
\end{figure}
\end{singlespacing}  % double line spacing

Figure \ref{XYMovement} shows means between participants and images of absolute differences of x and y coordinates between fixations. You can see that in the Montana/Osnabr\"uck comparison, humans have elevated movements along the abscissa, while monkeys' movements are elevated along the ordinate. In the Bochum Experiment, human movements are more agile, while monkeys generally did not move that much comparatively, however, this difference in agility is more emphasized for movements along the x-axis and reduced, respectively, for movements along the y-axis. 

\begin{figure}[!htb]
\label{basicfunctionsoftime}
\centering
\fbox{ \begin{minipage}{\textwidth}\begin{tabular}{cc}
\input{fixationdurations.tex} & \input{saccadedurations.tex}
\end{tabular}
\begin{tabular}{cc}
\input{saccadelengths.tex} & \input{saccadespeed.tex} 
\end{tabular}
\caption{Eye movements over time}
Statistics see \ref{eyemovementtable}. We want to remind that human fixations that end after trial end are cut off. 
\end{minipage} }
\end{figure}

Figure \ref{basicfunctionsoftime} shows the four basic eye movements over fixations. While at the last fixations, humans slowed down with respect to the saccade speed\footnote{As for time, the unit are milliseconds, for lengths, units are Euclidean distances in pixels. Saccade speed was defined as Euclidean distance in pixels per milliseconds.}{} monkeys become faster. We see in all four plots after the 12th--14th fixation a sudden change in humans, while there is no such radical change in monkey eye movements. This seems to be a cognitive effect. Interestingly, while in humans, saccade speed increases over time, saccade durations decrease, and saccade lengths first increase, peak around the 8th fixation, and decrease, in monkeys the indication thereof is only faintly visible. Generally can be said that monkeys make slightly faster, longer, longer lasting saccades than humans and fixate shorter than humans. Correlations and statistical significance are given in table \ref{eyemovementtable}. % discussion: 1) cognitive strategies noticeable in humans, but not in monkeys? 2)last sentence -- artefact of definitions? No! Definitions are ok! 

\begin{singlespacing}  
\begin{table}[!htb]
\label{eyemovementtable}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ fixation durations } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.1762  &  -0.0269  \\ 
{   } p-values  &  0.0000  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.1013 } \\ 
\end{tabular}
% median  192.0000 ,  228.0000 
% std 78.9897 ,  141.5190 
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade durations } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.1048  &  0.1467  \\ 
{   } p-values  &  0.0000  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0009 } \\ 
\end{tabular}
% median  35.0000 ,  36.0000 
% std 10.3678 ,  16.5700 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade lengths } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0583  &  0.1631  \\ 
{   } p-values  &  0.0018  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0006 } \\ 
\end{tabular}
% median  161.0435 ,  112.9690 
% std 115.4573 ,  120.3982 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade speed } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0162  &  0.1684  \\ 
{   } p-values  &  0.3836  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0001 } \\ 
\end{tabular}
% median  4.4874 ,  2.9617 
% std 2.1792 ,  1.7323 
\caption{Eye movements over time}
Figure see \ref{basicfunctionsoftime}. 
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing


\begin{singlespacing}  
\begin{table}[!htb]
\label{featurecontrastovertimetable}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ luminance contrast } \\
 {} & monkeys & humans \\
{   } correlations  &  0.0571  &  -0.0364  \\ 
{   } p-values  &  0.0009  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  0.0255 ,  1.2579 
% std 1.0195 ,  1.1532 
\begin{tabular}{lcc}
\multicolumn{3}{c}{ barness } \\
 {} & monkeys & humans \\
{   } correlations  &  0.0529  &  0.0551  \\ 
{   } p-values  &  0.0023  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0237 } \\ 
\end{tabular}
% median  0.0111 ,  -0.0304 
% std 0.6542 ,  0.5853 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ texture contrast } \\
 {} & monkeys & humans \\
{   } correlations  &  0.0629  &  -0.0356  \\ 
{   } p-values  &  0.0004  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0195 } \\
\end{tabular}
% median  -0.0678 ,  0.0901 
% std 0.9496 ,  0.9765 
\caption{Feature contrast over time}
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing

\begin{figure}[!htb]
\label{featurecontrastovertime}
\centering
\fbox{ \begin{minipage}{\textwidth}
\begin{tabular}{ccc}
\input{luminancecontrastovertime.tex} & \input{barnessovertime.tex} & \input{texturecontrastovertime.tex}
\end{tabular}
\caption{Feature contrast over time}
Correlation of normalized feature contrasts with time according to the re-definition of controls. The abscissa shows fixation numbers (by occurrence in trial). 
\end{minipage} }
\end{figure}

\begin{singlespacing}  
\begin{figure}[!htbp]
	\label{eccentricityovertimetable}
	\centering
	\fbox{ \begin{minipage} {\textwidth}
		\begin{tabular}{cc}
			\begin{tabular}{lcc}
				\multicolumn{3}{c}{ Eccentricity and fixation numbers } \\
				 {} & monkeys & humans \\
				{   } correlations  &  0.1118  &  0.1643  \\ 
				{   } p-values  &  0.0000  &  0.0000  \\ 
				KW & \multicolumn{2}{c}{ p= 0.0237 } \\ 
			\end{tabular} &
			\begin{minipage}{6cm}
				\input{eccentricityovertime.tex}
			\end{minipage} \\
		\end{tabular}
		\caption{Eccentricity over time}
	\end{minipage} }
\end{figure}
\end{singlespacing}  % double line spacing

Figure \ref{eccentricityovertimetable} shows that fixations in humans and in monkeys become more eccenric towards the end of the trial. Monkeys second fixations tend to be more central than their predecessor but then the trend towards eccentricity sets in. In humans the last fixation comes back to the center a little (again we can speculate about a cognitive effect of trial end). 


\section{Features at fixation points}
%classical actual vs control, effect size, Frank's analysis


\begin{figure}[!htb]
\label{actualvscontrolfig}
\centering
\fbox{ \begin{minipage}{\textwidth}
	\begin{tabular}{cc}
		Osnabr\"uck & Montana \\
		\hline
		\multicolumn{2}{c}{luminance contrast} \\
		\input{acluminancehumans.tex} & \input{acluminancemonkeys.tex} \\
		\hline
		\multicolumn{2}{c}{texture contrast} \\
		\input{actexturehumans.tex} & \input{actexturemonkeys.tex} \\
		\hline
		\multicolumn{2}{c}{barness} \\
		\input{acbarnesshumans.tex} & \input{acbarnessmonkeys.tex}  \\
	\end{tabular}
	\caption{Feature contrasts at fixation points versus controls}
The scatterplots depict median contrast on actual and control fixation. Points in the upper bisector indicate an elevation of feature contrast at fixations. Compare fig. \ref{actualvscontroltable}. In yellow green and magenta are points representing Disco, Clark, and Tang, respectively. 
\end{minipage} }
\end{figure}



In fig. \ref{actualvscontrolfig} you find scatterplots for luminace contrast, texture contrast, and barness (from top to bottom) for humans (left) and monkeys (right). Table \ref{actualvscontroltable} shows the corresponding effect sizes and the percentage of points in upper sector. Points in the upper bisector show elevation of feature values compared to controls. Effect sizes are defined as $\frac{\mu (actual-control)}{\mu (control)}$. Quite unexpectedly, by measure of effect size and elevation at fixation points, luminance contrast and texture contrast for humans exceed those of monkeys. Only for barness, we found comparatively higher elevation at fixation points in monkeys, however, also here, the effect size is lower than for humans. 

\cite{Lierhaus}, comparing with \cite{ReinagelZador} had concluded there was a considerable increase of the influence of luminance contrast in monkeys (ignoring however effects of image category). \cite{Einhaeuser2006} had reported similar degrees of influence for both luminance contrast and texture contrasts in monkeys and humans, which we confirmed in our calculations. Note that effect sizes in \ref{actualvscontroltable} depend highly on the size of the Gaussian that is convolved with the fixation map for the computation of feature values. 

Feature effects differed for humans less than for monkeys, which is surely an artifact of the different set of images for the three monkeys.  E.g. for luminance contrast we obtained mean values of 0.4495 with standard deviations of 0.0642, for monkeys the mean was 0.1917, the standard deviation 0.1876. The maximum effect size of luminance contrast for monkeys (Clark at 0.3786) is however still well below all but three human participants who in turn exceeded highly Disco (at 0.1931) and Tang (at 0.0034). Figure \ref{actualvscontrolfig} and \ref{actualvscontroltable} differentiate therefore between the image sets of the three monkeys. Clark is on level with humans with respect to influence of luminance and texture contrasts than are the other two monkeys. Tang's values are extremely low for both luminance contrast and texture contrast, while humans show on his images an increase. Disco's values are midway between Tang and Clark for these two contrasts. 

% this is for discussion!! Expected stupid monkeys, found stupid humans? Differences not clear! Monkeys don't understand pictures? cf. Einhaeuser2006. Show image illustrations. Differences in images, e.g. categories (Alper, 2006)? Surprising higher influence of feature contrasts in humans. However, the Bochum experiments are not that clear-cut as to this point. 
% for humans in LC and TC, characteristic distribution on the scatterplot. However monkeys -- don't they recognize a scene. To what extend are the experimental settings ecologically valid for monkeys?

\begin{singlespacing}  % line spacing 1
\begin{table}[!htbp]
\label{actualvscontroltable}
\centering
\fbox{ \begin{minipage} {\textwidth}\begin{center}
\begin{tabular}{lcc}
\hline
{ } & \multicolumn{2}{c}{Osnabr\"uck/Montana} \\
\textbf{} & humans & monkeys \\
\hline
LC \\
{  } elevation & 0.90 (0.8904, 0.8771, 0.9261) & 0.69 (0.8900, 0.6800, 0.5000) \\
{  } effect size & 0.43 (0.3924, 0.3400, 0.5748) & 0.20 (0.3786, 0.1931, 0.0034)\\
\hline
TC \\
{  } elevation &  0.84 (0.8189, 0.7774, 0.9106) &  0.67 (0.8400, 0.6500, 0.5300) \\
{  } effect size &  0.23 (0.1642, 0.1570, 0.3682) &  0.08 (0.1496, 0.0762, 0.0052)  \\
\hline
barness & \\
{  } elevation &  0.58 (0.5950, 0.5465, 0.6069) & 0.65 (0.6900, 0.6700, 0.6000) \\
{  } effect size & 0.07 (0.0787, 0.0363, 0.0831) & 0.10 0.1485, 0.0873, 0.0802)  \\
 \hline
\end{tabular}
\caption{Influences of feature contrasts}
\end{center}
Percentage of points in the upper bisector and effect sizes in humans and monkeys for luminance contrast (LC), texture contrast (TC), and barness. In brackets are percent of points in upper bisector and effect size for the image sets of Disco, Clark, and Tang, respectively. (cf. fig. \ref{actualvscontrolfig})
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing

\begin{figure}[!htb]
\label{condfeatures}
\centering
\fbox{ \begin{minipage}{\textwidth}\begin{tabular}{ccc}
\multicolumn{3}{c}{ Osnabr\"uck  and Montana } \\
\input{conditionallc.tex} & \input{conditionaltc.tex} & \input{conditionalbarness.tex}  \\
\end{tabular}
\caption{Conditional probability of fixations at feature contrasts}
The red and blue lines show feature distributions at fixations for monkeys and humans in experiments 1 and 2. The straight horizontal line shows the baseline over all images (as per equalized histogram). The error bars show standard errors within the bins. 
\end{minipage} }
\end{figure}

Fig. \ref{condfeatures} shows conditional probabilities for humans and monkeys for luminance contrast, texture contrast and barness, respectively. In monkeys, in the case of luminance contrast and texture contrast, saliency of low extrema is increased and decreased for high extrema as compared to humans. This is not the case with barness, where monkeys look more at high extrema. 

\begin{singlespacing}  
\begin{table}[!htb]
\label{condfeaturestable}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ luminance contrast } \\
 {} & monkeys & humans \\
entropy & 4.14 & 4.03 \\
correlations  &   \multicolumn{2}{c}{  r=08701, p=0.0000 } \\ 
signed-test & \multicolumn{2}{c}{  0, p= 0.9702 } \\ 
kstest & \multicolumn{2}{c}{ 0, p=0.7710 } \\
\end{tabular}
% median  0.0185 ,  1.2211 
% std 0.8841 ,  0.9384 
\begin{tabular}{lcc}
\multicolumn{3}{c}{ texture contrast } \\
 {} & monkeys & humans \\
entropy & 4.12 & 4.06 \\
correlations  &   \multicolumn{2}{c}{  r=0.7496, p=0.0001 } \\ 
signed-test & \multicolumn{2}{c}{  0, p= 0.6274 } \\ 
kstest & \multicolumn{2}{c}{ 0, p=0.7710 } \\
\end{tabular}
% median  0.0159 ,  1.2223 
% std 0.8814 ,  0.9396 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ barness } \\
 {} & monkeys & humans \\
entropy & 4.07 & 4.22 \\
correlations  &  \multicolumn{2}{c} {  r= 0.8369, p=0.0000 }  \\ 
{   } p-values  &  0.0931  &  0.0661  \\ 
signed-test & \multicolumn{2}{c}{  0, p= 0.6012 } \\ 
kstest & \multicolumn{2}{c}{ 0, p=0.2753 } \\
\end{tabular}
% median  0.0149 ,  1.2224 
% std 0.8817 ,  0.9397 
\caption{Conditional probability of fixations at feature contrasts}
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing

Joint feature probabilities, computed as in \cite{Schumann}, again showed emphasized saliencies for low feature contrasts in monkeys as compared to humans. It remains to be investigated, whether the joint saliencies of features add differently in humans and monkeys. It can be questioned, however, whether it is correct to presume the statistical independence of feature contrasts as presumed in this calculation (cf. \cite{Parkhurst2004}). 

\begin{figure}[htbp]
\label{jointprobabilities}
\fbox{ \begin{minipage}{\textwidth}
\begin{tabular}{cc}
monkeys & humans \\
\input{jointprobTCLCmonkeys.tex} & \input{jointprobTCLChumans.tex} \\
\input{jointprobbarnessLCmonkeys.tex} & \input{jointprobbarnessLChumans.tex} \\
\input{jointprobbarnessTCmonkeys.tex} & \input{jointprobbarnessTChumans.tex} \\
\end{tabular}
\caption{Joint probabilities of the image features}
\end{minipage} }
\end{figure}

\begin{table}[htbp]
\fbox{ \begin{minipage}{\textwidth}
\begin{tabular}{lcccccc}
& monkeys & humans & monkeys & humans & monkeys & humans \\
& \multicolumn{2}{c} { LC/TC } & \multicolumn{2}{c} { barness/LC } & \multicolumn{2}{c} { barness/TC } \\
$I(X;Y)$ & 0.1601 & 0.0970 & 0.2127 & 0.3534 & 0.2010 & 0.2531 \\
$r$ & 0.5483 & 0.9432 & 0.5416 & 0.4324  & 0.3857 & 0.4188 \\
ks-test & \multicolumn{2}{c}{ 1, p=1.3340e-08 } & \multicolumn{2}{c}{ 1, p=1.1264e-04 } & \multicolumn{2}{c}{ 1, p=1.1264e-04 } \\
signed-test & \multicolumn{2}{c}{ 1, p=0.0082 } & \multicolumn{2}{c}{ 0, p=0.3789 } & \multicolumn{2}{c}{ 0, p=0.0977 } \\
\end{tabular}
\label{jointprobabilitiestable}
\caption{Joint probabilities of the image features}
Calculated on 30 bins. 
\end{minipage} }
\end{table}

\section{Comparison of fixation maps}
\label{fixmapcomp}

\begin{figure}[htbp]
\label{correlations}
\fbox{ \begin{minipage}{\textwidth}
\begin{tabular}{c}
\input{bootstrap.tex} 
\end{tabular}
\caption{Bootstrap comparison of fixation maps}
Each point represents significance values of Pearson product-moment
correlations of fixation maps on the same images of a particular human participant's to those of an
other human participant (abscissa) and significances of each monkey's fixations to
human fixations (ordinate). Tang is magenta, Disco is green, Clark is yellow. 
\end{minipage} }
\end{figure}

% bootstrapping thing that I presented at the tea-time
Visual observation confirmed that the centers of gravity of fixation points of monkeys are more off-center than are humans'. However this is most probably caused by lacking inter-trial fixation crosses for monkeys. Bootstrap comparisons further indicated that monkey and human fixations differed a lot as compared to a baseline. Monkey fixation maps and human fixation maps on same images were very similar to the baseline of correlations of two random human participant fixation maps. 

% now the modified bootstrap sampling: ...
We refined this latter investigation to include fixation maps normalized by mean fixation maps of participants on all images (corrected for multiple comparisons) and came to the same conclusion. The scatter plot of significance values from this comparison is fig. \ref{correlations}. It can also be clearly seen that Tang is far more different from humans than the other two (Tang (magenta) differs also much more from the other two monkeys, than they differ among themselves, by the way). Clark and Disco are different from humans to a similar extend. 

\section{Divergence}
Lacking inter-trial fixation crosses for monkeys let us expect an overall higher divergence of fixation locations, as compared to humans, which should be emphasized in the beginning of trials (cf. \cite{Tatler2006}). 

Figure \ref{divergence} plots divergence (ordinate) over fixation numbers (abscissa). Divergence was defined as median inter-subject Euclidean distances of tuples of X/Y coordinates, fixation duration/saccade length, luminance contrast effect/texture contrast effect, respectively. Note that for the Montana data we had to rely on only 38 common images.  

Our expectation was confirmed. We see that humans are much more similar among each other according to their fixation maps than monkeys. For monkeys divergence stayed on the same level, where humans systematically increased over time. 

The second plot shows divergence of eye movements over time based on fixation duration and saccade length. We see that humans first differ very much, but then converge more, while monkeys stay on the same (comparatively lower) level of divergence. 

The third plot shows divergence of effect sizes for humans and monkeys over time. We see that in monkeys the divergence of effect sizes is generally higher, while it increases in humans. 


\begin{singlespacing}  
\begin{figure}[!htpb]
\label{divergence}
%\begin{rotate}{1} 
\fbox{ \begin{minipage}{\textwidth}
\begin{tabular}{ccc}
Fixation maps & Eye movements & Feature effects \\
\input{intersubeucliddist.tex} & \input{intersubeucliddisteyemovements.tex} & \input{intersubeucliddistfeatureeffects.tex} \\
\end{tabular}
\caption{Divergence over time}
Divergence of fixation locations, eye movements, and effect sizes of features. The X-axes give fixation number, the y-axes divergence by a metric of median inter-subject Euclidean distance. Eye movements were fixation duration and saccade length. Effect sizes refer to redefined controls. The second and third figure only represents experiments 1 and 2. In the first figure, humans from Osnabr\"uck are blue, Montana monkeys are red. As for Bochum small condition, humans are cyan, monkeys magenta. In the big big screen condition, humans are green and monkeys yellow. Compare statistics in table \ref{divergencetable}. \\
\end{minipage} }
\end{figure}


\begin{table}[!htpb]
\label{divergencetable}
\fbox{ \begin{minipage}{\textwidth}
\scriptsize
\begin{tabular}{lcccccc}
\multicolumn{7}{c}{ divergence of fixation locations } \\
	 {} & monkeys & humans & monkeysSS & humansSS & monkeysBS & monkeysBS \\
	median  & 273.3697 &  240.4071 &  339.7094 &  329.4333 &  228.7352 &  230.3894  \\ 
	std  & 20.0616 &  66.2950 &  106.2013 &  51.3139 &  43.9180 &  39.2206  \\ 
	correlations(t) &  0.2309  &  0.9020  &  -0.4952  &  0.3485  &  0.4357  &  0.6995  \\ 
	{   } p-values &  0.4271  &  0.0000  &  0.0101  &  0.1216  &  0.0622  &  0.0037  \\ 
	correlations & \multicolumn{2}{c}{ 0.3412 } & \multicolumn{2}{c}{ 0.1218 } & \multicolumn{2}{c}{ 0.0920 } \\ 
	{   } p-values & \multicolumn{2}{c}{ 0.2325 } & \multicolumn{2}{c}{ 0.5988 } & \multicolumn{2}{c}{ 0.7443 } \\ 
	signed-test & \multicolumn{2}{c}{ 1 , p= 0.0017 } & \multicolumn{2}{c}{ 1 , p= 0.0325 } & \multicolumn{2}{c}{ 0 , p= 0.8469 } \\ 
	\\
\end{tabular}
\vfill
\begin{tabular}{lr}
	\begin{tabular}{lcc}
		\multicolumn{3}{c}{ divergence of eye movements } \\
		 {} & monkeys & humans \\
		median  & 163.9469 &  181.0036 \\ 
		std & 13.4151 &  19.4164 \\ 
		correlations(t) &  0.1054  &  -0.1586  \\ 
		{   } p-values &  0.7444  &  0.6224  \\ 
		correlations & \multicolumn{2}{c}{ 0.1662 } \\ 
		{   } p-values & \multicolumn{2}{c}{ 0.6057 } \\ 
		signed-test & \multicolumn{2}{c}{ 1 , p= 0.0161 } \\ 
		\\
	\end{tabular}
	\begin{tabular}{lcc}
		\multicolumn{3}{c}{ divergence of features } \\
		 {} & monkeys & humans \\
		median & 1.0725 &  0.6956  \\ 
		std & 0.1034 &  0.1720  \\ 
		correlations(t) &  -0.0182  &  0.9306  \\ 
		{   } p-values &  0.9507  &  0.0000  \\ 
		correlations & \multicolumn{2}{c}{ 0.0612 } \\ {   } p-values & \multicolumn{2}{c}{ 0.8354 } \\
		signed-test & \multicolumn{2}{c}{ 1 , p= 0.0001 } \\ 
		\\
	\end{tabular}
\end{tabular}
\normalsize
\caption{Divergence of subjects over time}
Statistics corresponding to the figures. \textit{Correlations(t)} refers to correlation coefficients when looking at each line as a time series and the line below gives the matching p-values. \textit{Correlations} below compares humans and monkeys, respectively for the two through maximally four cases. Correlations are the Pearson product-moment correlation coefficient, the signed-test refers to the Wilcoxon signed rank test for zero median. 
\end{minipage} }
%\end{rotate}
\end{table}
\end{singlespacing}  



% discussion: w�lfel, ekenel, feature weighted mahalanobis distance: improved robustness for gaussian classifiers

%mutual information is symmetric and non-negative

%\end{document}
