(***********************************************************************

                    Mathematica-Compatible Notebook

This notebook can be used on any computer system with Mathematica 4.0,
MathReader 4.0, or any compatible application. The data for the notebook 
starts with the line containing stars above.

To get the notebook into a Mathematica-compatible application, do one of 
the following:

* Save the data starting with the line of stars above into a file
  with a name ending in .nb, then open the file inside the application;

* Copy the data starting with the line of stars above to the
  clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be
sent directly in email or through ftp in text mode.  Newlines can be
CR, LF or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing the 
word CacheID, otherwise Mathematica-compatible applications may try to 
use invalid cache data.

For more information on notebooks and Mathematica-compatible 
applications, contact Wolfram Research:
  web: http://www.wolfram.com
  email: info@wolfram.com
  phone: +1-217-398-0700 (U.S.)

Notebook reader applications are available free of charge from 
Wolfram Research.
***********************************************************************)

(*CacheID: 232*)


(*NotebookFileLineBreakTest
NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[    177360,       6125]*)
(*NotebookOutlinePosition[    178111,       6151]*)
(*  CellTagsIndexPosition[    178067,       6147]*)
(*WindowFrame->Normal*)



Notebook[{
Cell["\<\
Section 2.
Application 1: The evolution of worker reproduction\
\>", "Title",
  TextAlignment->Left,
  FontFamily->"Arial",
  FontSize->40,
  FontWeight->"Bold",
  FontSlant->"Italic",
  FontColor->RGBColor[0.500008, 0, 0.500008],
  Background->GrayLevel[1]],

Cell[TextData[{
  "Accompanying paper: \nFrank, S.A. 1995a. Mutual policing and repression of \
competition in the evolution of cooperative groups. ",
  StyleBox["Nature ",
    FontSlant->"Italic"],
  "377: 520-522."
}], "Text",
  FontSize->16],

Cell[CellGroupData[{

Cell["Purpose :", "Section",
  FontSize->25],

Cell[TextData[{
  "Many papers in the social insect literature have pointed out that since \
workers are related more to sons than to nephews, any worker should gain from \
producing male offspring. But how many workers should breed within a colony? \
Clearly, a rare laying worker within a colony would be at an advantage \
relative to a nonlaying one, but what if all workers took on a reproductive \
role? In that case, the colony would perish as a result of a dearth of \
foragers. Here we will derive the ESS probability for a worker to switch to a \
reproductive role, using the model of Frank (1995, 1996) as a basis. To \
simplify the matter we will only model the evolution of worker reproduction \
under queenless condition.\nFrank's  model (1995, 1996) was not specifically \
formulated to solve the worker reproduction problem (in fact worker \
reproduction is not even mentioned in the paper), instead it is framed around \
the more general concept of a ",
  StyleBox["tragedy of the commons",
    FontSlant->"Italic"],
  ". The reasoning is as follows. Any individual in the group will maximise \
its success relative to others by reproducing more (or with higher \
probability) than average. But since all individuals are selected to do this, \
it will eventually cause all individuals in the group to reproduce at a \
higher rate than can be sustained, hence the ",
  StyleBox["\"tragedy of the commons\"",
    FontSlant->"Italic"],
  ". Frank then analyses two situations. The first (",
  StyleBox["\"self restraint model\"",
    FontSlant->"Italic"],
  ", Ratnieks sometimes uses the terms ",
  StyleBox["\"self policing\"",
    FontSlant->"Italic"],
  ") is where individuals can control their own probability to breed but can \
not control the behaviour of others. The second (",
  StyleBox["\"policing model\"",
    FontSlant->"Italic"],
  ") is where individuals also have the possibility to prevent others from \
breeding.\nIn terms of our worker reproduction problem, this corresponds to \
the situations where workers can either (1) control their own probability to \
become a reproductive worker, but not influence the fate of others, or (2) \
also inhibit others from becoming reproductive workers."
}], "Text",
  FontSize->16]
}, Open  ]],

Cell[CellGroupData[{

Cell["Assumptions :", "Section",
  FontSize->25],

Cell["\<\
Throughout Frank assumes that the optimum for the group is to have very few \
reproductive individuals, and that group efficiency is a linear decreasing \
function of the proportion of selfish (i.e. breeding) individuals in the \
group. This may be quite reasonable for the worker reproduction problem, \
since a few workers are enough to produce all the male eggs and mainly \
foragers are needed to rear these into adults.\
\>", "Text",
  FontSize->16]
}, Open  ]],

Cell[CellGroupData[{

Cell["2.1 Self-restraint model", "Section",
  FontSize->25],

Cell["\<\
Parameters:
y = probability with which a focal individual takes on a breeding role
z = average probability with which individuals start to breed within the \
colony 
g = genotype of a focal individual\
\>", "Text",
  FontSize->18],

Cell["\<\
Step 1: Write individual reproductive success w as a function of your own \
breeding probability (y) and the average probability with which individuals \
breed in the colony (z)\
\>", "Definition",
  FontSize->16],

Cell["Frank (1995) uses the equation ", "Text",
  FontSize->14],

Cell[BoxData[
    \(\(w = \((y/z)\)*\((1 - z)\);\)\)], "Input"],

Cell["\<\
because the chance that any reared egg is yours is y/z, but the chance that \
it will be reared into adulthood is 1-z (with z=1 there are no foragers, so \
that no eggs can be reared). If you find this equation hard to understand you \
could think of absolute fitness w as being the product of relative individual \
success and group productivity, with relative individual success given by \
y/z, and group (colony) productivity given by 1-z (i.e. the total number of \
males reared over the colony's lifetime).\
\>", "Text",
  FontSize->14],

Cell["\<\
Step 2: analyse when the regression of fitness on genotype is positive\
\>", "Definition",
  FontSize->16],

Cell["\<\
A higher probability of becoming a reproductive worker is favoured when\
\>", "Text",
  FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(\(dwdg\)\(=\)\(FullSimplify[
        Dt[w, g] /. {Dt[z, g] -> r, Dt[y, g] -> 1, Dt[k, g] \[Rule] 0, 
            y -> z}]\)\(\ \ \ \ \ \)\)\)], "Input"],

Cell[BoxData[
    \(\(-\(\(\(-1\) + r + z\)\/z\)\)\)], "Output"]
}, Open  ]],

Cell["is greater than zero.", "Text",
  FontSize->14],

Cell["\<\
Note that, as in the hawk-dove game, the costs and benefits of becoming a \
reproductive worker again depend on what everyone else does in the colony. \
E.g., the personal benefit of becoming a reproductive worker (D[w,y]=(1-z)/z) \
is very large if everyone else decides not to reproduce ((1-z)/z then \
approaches plus infinity), but tends towards zero as more workers become \
reproductive. Similarly, the personal cost of a high average level of worker \
reproduction (D[w,z]) depends on the reproductive decisions of all other \
workers in the colony. However, while in the hawk-dove game it would still \
have been possible to write down costs and benefits straight away, this would \
have been very challenging in this case. 
The derivative dz/zg (D[z,g]), mentioned by Frank (1995) to equal \
relatedness, deserves some explanation. Before we had relatedness to be the \
slope of partner phenotype on actor genotype, but in this case z is the \
average phenotype of any worker in the colony, including the actor itself. \
That is, suppose you would have a colony with only one worker. In that case z \
would be equal to y, and dz/zg would equal 1. Therefore, dz/zg is not just \
pairwise genetic relatedness, but average relatedness to any individual in \
the group, including self (Frank 1996). Formally, with group size N, 
r = (1/N) + r'.(N-1)/N , 
where r' is pairwise genetic relatedness (see also Q&A question 6).\
\>", "Text",
  FontSize->14],

Cell["Step 3: Solve to yield the ESS", "Definition",
  FontSize->16],

Cell["\<\
Near the ESS, the selection equation above should equal 0, so that the ESS is \
given by  \
\>", "Text",
  FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
    \(ESS = FullSimplify[Solve[dwdg == 0, z]]\)], "Input"],

Cell[BoxData[
    \({{z \[Rule] 1 - r}}\)], "Output"]
}, Open  ]],

Cell[TextData[{
  StyleBox["Conclusion:",
    FontSize->18,
    FontWeight->"Bold"],
  "\nThe ESS probability with which workers should start to breed = 1-r\n\
E.g., 25% of all workers should start laying male eggs when their mother \
queen is singly mated, 50% when she is doubly mated, etc...  (assuming a \
linear cost function)\nIf you find it hard to understand why 25% reproductive \
workers is the ESS with single mating, then it is also possible to look at \
the problem from a classical inclusive fitness angle :\nAt the ESS the\n\t\
Selfish direct fitness benefits due to own male production (r = 0.5) =\n\t\t\
0.25 \t\t(chance of becoming a reproductive worker)\n\t\t* (1-0.25)\t(chance \
that any egg laid can be reared into an adult) \n\t\t* 0.5\t\t(relatedness to \
sons)\n\t\t= 3/32\n\t\n\tInclusive fitness costs due to reduced production of \
nephews (r = 0.375) =\n\t\t0.25\t\t(25% fewer nephews are reared into adults)\
\n\t\t* 0.375\t\t(relatedness to nephews)\n\t\t= 3/32  \n\nTherefore, at the \
ESS the selfish benefits of worker laying exactly balance the inclusive \
fitness costs due to reduced nephew production, which is what had to be \
shown. Simple inclusive fitness arguments are often useful for interpreting \
results in intuitive ways. However, simple IF analysis is often unreliable \
for more complex problems. In fact, for asymmetrical games, a direct fitness \
perspective is the only correct way to handle the problem. "
}], "Text",
  FontSize->14]
}, Closed]],

Cell[CellGroupData[{

Cell["2.2 Social policing model", "Section",
  FontSize->25],

Cell[CellGroupData[{

Cell["2.2.1 ANALYTICAL SOLUTION", "Subsection",
  FontSize->19],

Cell["\<\
Parameters:
y = probability with which a focal individual takes on a breeding role
z = average probability with which individuals start breeding within the \
group 
p = individual investment in a policing trait that inhibits others to breed
P = average individual investment in policing within the group 
b = focal individual's genotype as the breeding locus
\[Pi] = focal individual's genotype at the policing locus
c = individual cost of policing\
\>", "Text",
  FontSize->18],

Cell["\<\
Step 1: write individual reproductive success w as a function of individual \
(yB) and average (zB) breeding probability and individual (yP) and average \
(zP) investment in policing \
\>", "Definition",
  FontSize->16],

Cell["\<\
Many different equations are possible, depending on assumptions, but this is \
the equation that Frank used (I am not entirely convinced that it is \
appropriate for the worker reproduction problem, but let's use it anyway):\
\>", "Text",
  FontSize->14],

Cell[BoxData[{
    \( (*\ Relative\ Individual\ success\ *) \n\(Ind = 
        P - c*p + \((1 - P)\)*y/z;\)\n\n (*\ Group\ success\ *) \), "\n", 
    \(\(Grp = 1 - \((1 - P)\) z;\)\n\n (*\ 
      Direct\ fitness\ of\ a\ focal\ individual\ *) \), "\n", 
    \(\(w = Ind*Grp;\)\)}], "Input"],

Cell["\<\
Step 2: analyse when the regression of  fitness on genotype is positive\
\>", "Definition",
  FontSize->16],

Cell["\<\
We now have 2 equations: one specifying selection for breeding, the other \
specifying selection for policing, i.e. we are analysing a 2-locus model. But \
since each of the selection equations is dependent on each other, they will \
need to be simultaneously maximised to provide the joint ESS. \
\>", "Text",
  FontSize->14],

Cell["\<\
This is the equation that says when more workers should  reproduce :\
\>", "Text",
  FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
    \(dWdb[r_, c_, z_, 
        p_] = \((D[w, y] + D[w, z]*r)\) /. {y \[Rule] z, 
          P \[Rule] p}\)], "Input"],

Cell[BoxData[
    \(\(\((1 - p)\)\ \((1 - \((1 - p)\)\ z)\)\)\/z + 
      r\ \((\((\(-1\) + p)\)\ \((1 - 
                  c\ p)\) - \(\((1 - p)\)\ \((1 - \((1 - p)\)\ \
z)\)\)\/z)\)\)], "Output"]
}, Open  ]],

Cell["\<\
where D[w,y] is the benefit of breeding and -D[w,z] is the cost of having \
other workers breed in the colony\
\>", "Text",
  FontSize->14],

Cell["\<\
(we assume that the breeding and policing locus are not linked, so that dP/db \
and dp/db can both be set to zero)\
\>", "Text",
  FontSize->14],

Cell["\<\
This is the equation that says when workers should inhibit others from \
reproducing (police) :\
\>", "Text",
  FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
    \(dWd\[Pi][r_, c_, z_, 
        p_] = \((D[w, p] + D[w, P]*r)\) /. {y \[Rule] z, 
          P \[Rule] p}\)], "Input"],

Cell[BoxData[
    \(\((1 - c\ p)\)\ r\ z - c\ \((1 - \((1 - p)\)\ z)\)\)], "Output"]
}, Open  ]],

Cell["\<\
(we again assume that the breeding and policing locus are not linked,so that \
dz/d\[Pi] and dy/d\[Pi] can be set to zero)\
\>", "Text",
  FontSize->14],

Cell["Step 3: Joint maximisation to provide the joint ESS", "Definition",
  FontSize->16],

Cell["\<\
Joint maximisation of these 2 equations is difficult, but as a first start \
let us check when a policing trait can invade from a sitation where all \
individuals are reproducing with optimum probability (breeding \
probability=1-r, see Section 2.1 above). For this, set the probability of \
breeding (z*=0) to 1-r and the level of policing p* to 0 in the selection \
equation for policing, and see when an increase in policing is favoured.
As it turns out, this is when \
\>", "Text",
  FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
    \(dWd\[Pi][r, c, 1 - r, 0] > 0\)], "Input"],

Cell[BoxData[
    \(\(-c\)\ r + \((1 - r)\)\ r > 0\)], "Output"]
}, Open  ]],

Cell["i.e. when c < 1-r. ", "Text",
  FontSize->14],

Cell[TextData[{
  StyleBox["Conclusion :",
    FontSize->18,
    FontWeight->"Bold"],
  "\nWhen the cost of policing c < 1-r, policing is favoured. Otherwise, the \
self restraint and no policing optimum will be reached (Section 2.1). Below \
it is checked graphically that whenever policing invades it will also tend to \
be maximally favoured. This can best be done using field plots.\nThe \
intuitive explanation for this result is that unrestrained breeding will \
reduce the net group output by a fraction 1-r, whereas policing can restore \
group output at a cost c (the cost of policing). If policing can restore \
group efficiency (i.e. resolve the ",
  StyleBox["tragedy of the commons",
    FontSlant->"Italic"],
  ") at a lesser cost, it will be favoured. Low relatedness will cause large \
costs due to excessive, unrestrained breeding, and is therefore conducive to \
the evolution of social policing (Frank 1995). \nWith respect to worker \
reproduction this means that if policing occurs in queenless condition (e.g. \
workers that force other workers to work rather than to reproduce) it will \
cause fewer workers to reproduce than is predicted by the self restraint \
model (Section 2.1). For example, less than 25% of the workers for single \
mating or less than 50% for double mating, perhaps just a few (which is the \
colony optimum)."
}], "Text",
  FontSize->14]
}, Closed]],

Cell[CellGroupData[{

Cell["2.2.2 GRAPHICAL SOLUTION", "Subsection",
  FontSize->19],

Cell["\<\
As in section 1.2, we can also check graphically how an ESS may be reached.\
\>", "Text",
  FontSize->14],

Cell[BoxData[{
    \( (*\ 
      load\ the\ PlotField\ package\ to\ enable\ you\ to\ draw\ field\ plots\ \
and\ the\ ImplicitPlot\ package\ to\ allow\ you\ to\ make\ plots\ of\ the\ \
equilibrium\ lines\ *) \[IndentingNewLine]<< 
      Graphics`PlotField`\), "\[IndentingNewLine]", 
    \(<< Graphics`ImplicitPlot`\)}], "Input"],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Case 1 : c > 1-r \n(r=c=0.75)",
  FontSize->17]], "Subsubsection"],

Cell[BoxData[
    \(\(\(\(rex = 0.75\) \)\(;\)\(\(cex = 
        0.75\) \)\(;\)\(\ \ \ \ \ \ \)\( (*\ 
      Some\ example\ values\ for\ r\ and\ c\ *) \)\)\)], "Input"],

Cell[BoxData[
    \(\(fieldplot = 
        PlotVectorField[{dWd\[Pi][rex, cex, z, p], \ 
            dWdb[rex, cex, z, p]}, \n\ \ \ \ \ \ \ \ \ \ \ \ \ {p, \ 0, \ 
            1}, \ {z, \ 0, \ 1}, PlotPoints -> 17];\)\)], "Input"],

Cell[BoxData[
    \(\(equillines = 
        ImplicitPlot[{dWd\[Pi][rex, cex, z, p] \[Equal] 0, \ 
            dWdb[rex, cex, z, p] \[Equal] 0}, {p, 0, 1}, {z, 0, 1}, 
          PlotStyle \[Rule] {RGBColor[0, 0, 1], RGBColor[1, 0, 0]}, 
          DisplayFunction \[Rule] Identity];\)\)], "Input"],

Cell[BoxData[
    \(\(\(ESS = 
        Graphics[{\[IndentingNewLine]{RGBColor[1, 0, 0], 
              Disk[{0, 1 - rex}, 0.02]}, \[IndentingNewLine]{RGBColor[1, 0, 
                0], Text["\<ESS\>", {0.07, 
                  1 - rex - 
                    0.04}]}, \[IndentingNewLine]}];\)\(\ \ \ \ \ \)\)\)], \
"Input"],

Cell["\<\
Now display the whole lot together (field plot, equilibrium lines, ESS). 
As you can see, with c > 1-r, the system tends to the self restraint optimum \
with the ESS probability to become a reproductive worker = 1-r = 0.25 and no \
policing :\
\>", "Text",
  FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
    \(Show[{fieldplot, equillines, ESS}, AspectRatio -> 1, Frame -> True, 
      PlotRange -> {{0, 1}, {0, 1}}, 
      FrameLabel -> {"\<Policing\>", "\<Breeding prob.\>"}]\)], "Input"],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: 1 
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10  scalefont  setfont
% Scaling calculations
0 1 0 1 [
[.2 -0.0125 -9 -9 ]
[.2 -0.0125 9 0 ]
[.4 -0.0125 -9 -9 ]
[.4 -0.0125 9 0 ]
[.6 -0.0125 -9 -9 ]
[.6 -0.0125 9 0 ]
[.8 -0.0125 -9 -9 ]
[.8 -0.0125 9 0 ]
[1 -0.0125 -3 -9 ]
[1 -0.0125 3 0 ]
[ 0 0 -0.125 0 ]
[.5 -0.0125 -26 -21.5625 ]
[.5 -0.0125 26 -9 ]
[-0.0125 .2 -18 -4.5 ]
[-0.0125 .2 0 4.5 ]
[-0.0125 .4 -18 -4.5 ]
[-0.0125 .4 0 4.5 ]
[-0.0125 .6 -18 -4.5 ]
[-0.0125 .6 0 4.5 ]
[-0.0125 .8 -18 -4.5 ]
[-0.0125 .8 0 4.5 ]
[-0.0125 1 -6 -4.5 ]
[-0.0125 1 0 4.5 ]
[ 0 0 -0.125 0 ]
[-0.01875 .5 -30.5625 -44 ]
[-0.01875 .5 -18 44 ]
[ 0 1 .125 0 ]
[ 1 0 .125 0 ]
[ 0 0 0 0 ]
[ 1 1 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.2 0 m
.2 .00625 L
s
[(0.2)] .2 -0.0125 0 1 Mshowa
.4 0 m
.4 .00625 L
s
[(0.4)] .4 -0.0125 0 1 Mshowa
.6 0 m
.6 .00625 L
s
[(0.6)] .6 -0.0125 0 1 Mshowa
.8 0 m
.8 .00625 L
s
[(0.8)] .8 -0.0125 0 1 Mshowa
1 0 m
1 .00625 L
s
[(1)] 1 -0.0125 0 1 Mshowa
.125 Mabswid
.05 0 m
.05 .00375 L
s
.1 0 m
.1 .00375 L
s
.15 0 m
.15 .00375 L
s
.25 0 m
.25 .00375 L
s
.3 0 m
.3 .00375 L
s
.35 0 m
.35 .00375 L
s
.45 0 m
.45 .00375 L
s
.5 0 m
.5 .00375 L
s
.55 0 m
.55 .00375 L
s
.65 0 m
.65 .00375 L
s
.7 0 m
.7 .00375 L
s
.75 0 m
.75 .00375 L
s
.85 0 m
.85 .00375 L
s
.9 0 m
.9 .00375 L
s
.95 0 m
.95 .00375 L
s
.25 Mabswid
0 0 m
1 0 L
s
gsave
.5 -0.0125 -87 -25.5625 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 20.5625 translate 1 -1 scale
63.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(Policing) show
111.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 .2 m
.00625 .2 L
s
[(0.2)] -0.0125 .2 1 0 Mshowa
0 .4 m
.00625 .4 L
s
[(0.4)] -0.0125 .4 1 0 Mshowa
0 .6 m
.00625 .6 L
s
[(0.6)] -0.0125 .6 1 0 Mshowa
0 .8 m
.00625 .8 L
s
[(0.8)] -0.0125 .8 1 0 Mshowa
0 1 m
.00625 1 L
s
[(1)] -0.0125 1 1 0 Mshowa
.125 Mabswid
0 .05 m
.00375 .05 L
s
0 .1 m
.00375 .1 L
s
0 .15 m
.00375 .15 L
s
0 .25 m
.00375 .25 L
s
0 .3 m
.00375 .3 L
s
0 .35 m
.00375 .35 L
s
0 .45 m
.00375 .45 L
s
0 .5 m
.00375 .5 L
s
0 .55 m
.00375 .55 L
s
0 .65 m
.00375 .65 L
s
0 .7 m
.00375 .7 L
s
0 .75 m
.00375 .75 L
s
0 .85 m
.00375 .85 L
s
0 .9 m
.00375 .9 L
s
0 .95 m
.00375 .95 L
s
.25 Mabswid
0 0 m
0 1 L
s
gsave
-0.01875 .5 -129.281 -10.2813 Mabsadd m
1 1 Mabs scale
currentpoint translate
105 10.2813 translate
90 rotate
-105 -10.2813 translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 20.5625 translate 1 -1 scale
63.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(Breeding) show
117.000 12.813 moveto
(prob) show
141.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(.) show
147.000 12.813 moveto
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 .99375 m
0 1 L
s
.2 .99375 m
.2 1 L
s
.4 .99375 m
.4 1 L
s
.6 .99375 m
.6 1 L
s
.8 .99375 m
.8 1 L
s
.125 Mabswid
.05 .99625 m
.05 1 L
s
.1 .99625 m
.1 1 L
s
.15 .99625 m
.15 1 L
s
.25 .99625 m
.25 1 L
s
.3 .99625 m
.3 1 L
s
.35 .99625 m
.35 1 L
s
.45 .99625 m
.45 1 L
s
.5 .99625 m
.5 1 L
s
.55 .99625 m
.55 1 L
s
.65 .99625 m
.65 1 L
s
.7 .99625 m
.7 1 L
s
.75 .99625 m
.75 1 L
s
.85 .99625 m
.85 1 L
s
.9 .99625 m
.9 1 L
s
.95 .99625 m
.95 1 L
s
.25 Mabswid
0 1 m
1 1 L
s
.99375 0 m
1 0 L
s
.99375 .2 m
1 .2 L
s
.99375 .4 m
1 .4 L
s
.99375 .6 m
1 .6 L
s
.99375 .8 m
1 .8 L
s
.125 Mabswid
.99625 .05 m
1 .05 L
s
.99625 .1 m
1 .1 L
s
.99625 .15 m
1 .15 L
s
.99625 .25 m
1 .25 L
s
.99625 .3 m
1 .3 L
s
.99625 .35 m
1 .35 L
s
.99625 .45 m
1 .45 L
s
.99625 .5 m
1 .5 L
s
.99625 .55 m
1 .55 L
s
.99625 .65 m
1 .65 L
s
.99625 .7 m
1 .7 L
s
.99625 .75 m
1 .75 L
s
.99625 .85 m
1 .85 L
s
.99625 .9 m
1 .9 L
s
.99625 .95 m
1 .95 L
s
.25 Mabswid
1 0 m
1 1 L
s
0 0 m
1 0 L
1 1 L
0 1 L
closepath
clip
newpath
% Start of user PostScript
/mathtops {
gsave
MBeginOrig
moveto
MEndOrig
currentpoint
grestore
} bind def
/MAtocoords {
mathtops 4 2 roll mathtops
4 copy pop pop
3 -1 roll sub
/arry exch def
exch sub
/arrx exch def
arrx dup mul
arry dup mul
add sqrt
/arrl exch def
translate
} bind def
/MAarrowhead1 {
gsave
MAtocoords
arrl 0. eq
{ 0 0 Mdot }
{
[ arrx arrl div
arry arrl div
-1 arry mul arrl div
arrx arrl div
0 0 ]
concat
-0.02 0.005 moveto 0 0 lineto
-0.02 -0.005 lineto fill
-0.02 0.005 moveto 0 0 lineto
-0.02 -0.005 lineto
-0.02 0.005 lineto stroke
} ifelse
grestore
} def
% End of user PostScript
.0001 w
0 .0625 m
0 0 rlineto s
% Start of user PostScript
0 0.0625 -0.0133561 0.123556 MAarrowhead1
% End of user PostScript
0 .125 m
0 0 rlineto s
% Start of user PostScript
0 0.125 -0.011448 0.145352 MAarrowhead1
% End of user PostScript
0 .1875 m
0 0 rlineto s
% Start of user PostScript
0 0.1875 -0.00954004 0.194284 MAarrowhead1
% End of user PostScript
0 .25 m
0 0 rlineto s
% Start of user PostScript
0 0.25 -0.00763203 0.25 MAarrowhead1
% End of user PostScript
0 .3125 m
0 0 rlineto s
% Start of user PostScript
0 0.3125 -0.00572402 0.30843 MAarrowhead1
% End of user PostScript
0 .375 m
0 0 rlineto s
% Start of user PostScript
0 0.375 -0.00381602 0.368216 MAarrowhead1
% End of user PostScript
0 .4375 m
0 0 rlineto s
% Start of user PostScript
0 0.4375 -0.00190801 0.428778 MAarrowhead1
% End of user PostScript
0 .5 m
0 .48982 L
s
% Start of user PostScript
0 0.5 0 0.489824 MAarrowhead1
% End of user PostScript
0 .5625 m
.00191 .55119 L
s
% Start of user PostScript
0 0.5625 0.00190801 0.551193 MAarrowhead1
% End of user PostScript
0 .625 m
.00382 .61279 L
s
% Start of user PostScript
0 0.625 0.00381602 0.612789 MAarrowhead1
% End of user PostScript
0 .6875 m
.00572 .67455 L
s
% Start of user PostScript
0 0.6875 0.00572402 0.674549 MAarrowhead1
% End of user PostScript
0 .75 m
.00763 .73643 L
s
% Start of user PostScript
0 0.75 0.00763203 0.736432 MAarrowhead1
% End of user PostScript
0 .8125 m
.00954 .79841 L
s
% Start of user PostScript
0 0.8125 0.00954004 0.79841 MAarrowhead1
% End of user PostScript
0 .875 m
.01145 .86046 L
s
% Start of user PostScript
0 0.875 0.011448 0.860463 MAarrowhead1
% End of user PostScript
0 .9375 m
.01336 .92258 L
s
% Start of user PostScript
0 0.9375 0.0133561 0.922575 MAarrowhead1
% End of user PostScript
0 1 m
.01526 .98474 L
s
% Start of user PostScript
0 1. 0.0152641 0.984736 MAarrowhead1
% End of user PostScript
.0625 .0625 m
.04904 .12071 L
s
% Start of user PostScript
0.0625 0.0625 0.0490396 0.120709 MAarrowhead1
% End of user PostScript
.0625 .125 m
.05084 .14505 L
s
% Start of user PostScript
0.0625 0.125 0.0508433 0.145049 MAarrowhead1
% End of user PostScript
.0625 .1875 m
.05265 .19483 L
s
% Start of user PostScript
0.0625 0.1875 0.0526469 0.194829 MAarrowhead1
% End of user PostScript
.0625 .25 m
.05445 .25097 L
s
% Start of user PostScript
0.0625 0.25 0.0544506 0.250969 MAarrowhead1
% End of user PostScript
.0625 .3125 m
.05625 .30965 L
s
% Start of user PostScript
0.0625 0.3125 0.0562543 0.309653 MAarrowhead1
% End of user PostScript
.0625 .375 m
.05806 .36961 L
s
% Start of user PostScript
0.0625 0.375 0.0580579 0.369609 MAarrowhead1
% End of user PostScript
.0625 .4375 m
.05986 .43029 L
s
% Start of user PostScript
0.0625 0.4375 0.0598616 0.430292 MAarrowhead1
% End of user PostScript
.0625 .5 m
.06167 .49143 L
s
% Start of user PostScript
0.0625 0.5 0.0616652 0.491429 MAarrowhead1
% End of user PostScript
.0625 .5625 m
.06347 .55287 L
s
% Start of user PostScript
0.0625 0.5625 0.0634689 0.552869 MAarrowhead1
% End of user PostScript
.0625 .625 m
.06527 .61452 L
s
% Start of user PostScript
0.0625 0.625 0.0652726 0.614521 MAarrowhead1
% End of user PostScript
.0625 .6875 m
.06708 .67633 L
s
% Start of user PostScript
0.0625 0.6875 0.0670762 0.676327 MAarrowhead1
% End of user PostScript
.0625 .75 m
.06888 .73825 L
s
% Start of user PostScript
0.0625 0.75 0.0688799 0.738249 MAarrowhead1
% End of user PostScript
.0625 .8125 m
.07068 .80026 L
s
% Start of user PostScript
0.0625 0.8125 0.0706836 0.80026 MAarrowhead1
% End of user PostScript
.0625 .875 m
.07249 .86234 L
s
% Start of user PostScript
0.0625 0.875 0.0724872 0.86234 MAarrowhead1
% End of user PostScript
.0625 .9375 m
.07429 .92448 L
s
% Start of user PostScript
0.0625 0.9375 0.0742909 0.924477 MAarrowhead1
% End of user PostScript
.0625 1 m
.07609 .98666 L
s
% Start of user PostScript
0.0625 1. 0.0760946 0.986659 MAarrowhead1
% End of user PostScript
.125 .0625 m
.11144 .11773 L
s
% Start of user PostScript
0.125 0.0625 0.111435 0.117733 MAarrowhead1
% End of user PostScript
.125 .125 m
.11313 .14462 L
s
% Start of user PostScript
0.125 0.125 0.113135 0.144617 MAarrowhead1
% End of user PostScript
.125 .1875 m
.11483 .19524 L
s
% Start of user PostScript
0.125 0.1875 0.114834 0.195245 MAarrowhead1
% End of user PostScript
.125 .25 m
.11653 .25181 L
s
% Start of user PostScript
0.125 0.25 0.116533 0.251809 MAarrowhead1
% End of user PostScript
.125 .3125 m
.11823 .31075 L
s
% Start of user PostScript
0.125 0.3125 0.118233 0.310747 MAarrowhead1
% End of user PostScript
.125 .375 m
.11993 .37087 L
s
% Start of user PostScript
0.125 0.375 0.119932 0.370873 MAarrowhead1
% End of user PostScript
.125 .4375 m
.12163 .43168 L
s
% Start of user PostScript
0.125 0.4375 0.121631 0.431677 MAarrowhead1
% End of user PostScript
.125 .5 m
.12333 .4929 L
s
% Start of user PostScript
0.125 0.5 0.12333 0.492905 MAarrowhead1
% End of user PostScript
.125 .5625 m
.12503 .55442 L
s
% Start of user PostScript
0.125 0.5625 0.12503 0.554415 MAarrowhead1
% End of user PostScript
.125 .625 m
.12673 .61612 L
s
% Start of user PostScript
0.125 0.625 0.126729 0.616124 MAarrowhead1
% End of user PostScript
.125 .6875 m
.12843 .67798 L
s
% Start of user PostScript
0.125 0.6875 0.128428 0.677976 MAarrowhead1
% End of user PostScript
.125 .75 m
.13013 .73994 L
s
% Start of user PostScript
0.125 0.75 0.130128 0.739937 MAarrowhead1
% End of user PostScript
.125 .8125 m
.13183 .80198 L
s
% Start of user PostScript
0.125 0.8125 0.131827 0.80198 MAarrowhead1
% End of user PostScript
.125 .875 m
.13353 .86409 L
s
% Start of user PostScript
0.125 0.875 0.133526 0.864089 MAarrowhead1
% End of user PostScript
.125 .9375 m
.13523 .92625 L
s
% Start of user PostScript
0.125 0.9375 0.135226 0.926249 MAarrowhead1
% End of user PostScript
.125 1 m
.13693 .98845 L
s
% Start of user PostScript
0.125 1. 0.136925 0.988453 MAarrowhead1
% End of user PostScript
.1875 .0625 m
.17383 .11463 L
s
% Start of user PostScript
0.1875 0.0625 0.173831 0.114627 MAarrowhead1
% End of user PostScript
.1875 .125 m
.17543 .14406 L
s
% Start of user PostScript
0.1875 0.125 0.175426 0.144055 MAarrowhead1
% End of user PostScript
.1875 .1875 m
.17702 .19553 L
s
% Start of user PostScript
0.1875 0.1875 0.177021 0.195531 MAarrowhead1
% End of user PostScript
.1875 .25 m
.17862 .25252 L
s
% Start of user PostScript
0.1875 0.25 0.178616 0.252519 MAarrowhead1
% End of user PostScript
.1875 .3125 m
.18021 .31171 L
s
% Start of user PostScript
0.1875 0.3125 0.180211 0.311712 MAarrowhead1
% End of user PostScript
.1875 .375 m
.18181 .37201 L
s
% Start of user PostScript
0.1875 0.375 0.181806 0.372007 MAarrowhead1
% End of user PostScript
.1875 .4375 m
.1834 .43293 L
s
% Start of user PostScript
0.1875 0.4375 0.183401 0.432932 MAarrowhead1
% End of user PostScript
.1875 .5 m
.185 .49425 L
s
% Start of user PostScript
0.1875 0.5 0.184996 0.494251 MAarrowhead1
% End of user PostScript
.1875 .5625 m
.18659 .55583 L
s
% Start of user PostScript
0.1875 0.5625 0.186591 0.555832 MAarrowhead1
% End of user PostScript
.1875 .625 m
.18819 .6176 L
s
% Start of user PostScript
0.1875 0.625 0.188186 0.617598 MAarrowhead1
% End of user PostScript
.1875 .6875 m
.18978 .6795 L
s
% Start of user PostScript
0.1875 0.6875 0.189781 0.679496 MAarrowhead1
% End of user PostScript
.1875 .75 m
.19138 .7415 L
s
% Start of user PostScript
0.1875 0.75 0.191376 0.741495 MAarrowhead1
% End of user PostScript
.1875 .8125 m
.19297 .80357 L
s
% Start of user PostScript
0.1875 0.8125 0.192971 0.803571 MAarrowhead1
% End of user PostScript
.1875 .875 m
.19457 .86571 L
s
% Start of user PostScript
0.1875 0.875 0.194566 0.865708 MAarrowhead1
% End of user PostScript
.1875 .9375 m
.19616 .92789 L
s
% Start of user PostScript
0.1875 0.9375 0.196161 0.927893 MAarrowhead1
% End of user PostScript
.1875 1 m
.19776 .99012 L
s
% Start of user PostScript
0.1875 1. 0.197756 0.990117 MAarrowhead1
% End of user PostScript
.25 .0625 m
.23623 .11139 L
s
% Start of user PostScript
0.25 0.0625 0.236227 0.111393 MAarrowhead1
% End of user PostScript
.25 .125 m
.23772 .14336 L
s
% Start of user PostScript
0.25 0.125 0.237717 0.143365 MAarrowhead1
% End of user PostScript
.25 .1875 m
.23921 .19569 L
s
% Start of user PostScript
0.25 0.1875 0.239208 0.195689 MAarrowhead1
% End of user PostScript
.25 .25 m
.2407 .2531 L
s
% Start of user PostScript
0.25 0.25 0.240698 0.253101 MAarrowhead1
% End of user PostScript
.25 .3125 m
.24219 .31255 L
s
% Start of user PostScript
0.25 0.3125 0.242189 0.312548 MAarrowhead1
% End of user PostScript
.25 .375 m
.24368 .37301 L
s
% Start of user PostScript
0.25 0.375 0.24368 0.373012 MAarrowhead1
% End of user PostScript
.25 .4375 m
.24517 .43406 L
s
% Start of user PostScript
0.25 0.4375 0.24517 0.434059 MAarrowhead1
% End of user PostScript
.25 .5 m
.24666 .49547 L
s
% Start of user PostScript
0.25 0.5 0.246661 0.495468 MAarrowhead1
% End of user PostScript
.25 .5625 m
.24815 .55712 L
s
% Start of user PostScript
0.25 0.5625 0.248152 0.55712 MAarrowhead1
% End of user PostScript
.25 .625 m
.24964 .61894 L
s
% Start of user PostScript
0.25 0.625 0.249642 0.618942 MAarrowhead1
% End of user PostScript
.25 .6875 m
.25113 .68089 L
s
% Start of user PostScript
0.25 0.6875 0.251133 0.680887 MAarrowhead1
% End of user PostScript
.25 .75 m
.25262 .74292 L
s
% Start of user PostScript
0.25 0.75 0.252624 0.742924 MAarrowhead1
% End of user PostScript
.25 .8125 m
.25411 .80503 L
s
% Start of user PostScript
0.25 0.8125 0.254114 0.805033 MAarrowhead1
% End of user PostScript
.25 .875 m
.2556 .8672 L
s
% Start of user PostScript
0.25 0.875 0.255605 0.867198 MAarrowhead1
% End of user PostScript
.25 .9375 m
.2571 .92941 L
s
% Start of user PostScript
0.25 0.9375 0.257095 0.929407 MAarrowhead1
% End of user PostScript
.25 1 m
.25859 .99165 L
s
% Start of user PostScript
0.25 1. 0.258586 0.991652 MAarrowhead1
% End of user PostScript
.3125 .0625 m
.29862 .10803 L
s
% Start of user PostScript
0.3125 0.0625 0.298622 0.108029 MAarrowhead1
% End of user PostScript
.3125 .125 m
.30001 .14254 L
s
% Start of user PostScript
0.3125 0.125 0.300009 0.142545 MAarrowhead1
% End of user PostScript
.3125 .1875 m
.30139 .19572 L
s
% Start of user PostScript
0.3125 0.1875 0.301395 0.195717 MAarrowhead1
% End of user PostScript
.3125 .25 m
.30278 .25355 L
s
% Start of user PostScript
0.3125 0.25 0.302781 0.253553 MAarrowhead1
% End of user PostScript
.3125 .3125 m
.30417 .31325 L
s
% Start of user PostScript
0.3125 0.3125 0.304167 0.313254 MAarrowhead1
% End of user PostScript
.3125 .375 m
.30555 .37389 L
s
% Start of user PostScript
0.3125 0.375 0.305554 0.373889 MAarrowhead1
% End of user PostScript
.3125 .4375 m
.30694 .43506 L
s
% Start of user PostScript
0.3125 0.4375 0.30694 0.435056 MAarrowhead1
% End of user PostScript
.3125 .5 m
.30833 .49656 L
s
% Start of user PostScript
0.3125 0.5 0.308326 0.496557 MAarrowhead1
% End of user PostScript
.3125 .5625 m
.30971 .55828 L
s
% Start of user PostScript
0.3125 0.5625 0.309713 0.558279 MAarrowhead1
% End of user PostScript
.3125 .625 m
.3111 .62016 L
s
% Start of user PostScript
0.3125 0.625 0.311099 0.620157 MAarrowhead1
% End of user PostScript
.3125 .6875 m
.31249 .68215 L
s
% Start of user PostScript
0.3125 0.6875 0.312485 0.682149 MAarrowhead1
% End of user PostScript
.3125 .75 m
.31387 .74422 L
s
% Start of user PostScript
0.3125 0.75 0.313871 0.744225 MAarrowhead1
% End of user PostScript
.3125 .8125 m
.31526 .80637 L
s
% Start of user PostScript
0.3125 0.8125 0.315258 0.806366 MAarrowhead1
% End of user PostScript
.3125 .875 m
.31664 .86856 L
s
% Start of user PostScript
0.3125 0.875 0.316644 0.868558 MAarrowhead1
% End of user PostScript
.3125 .9375 m
.31803 .93079 L
s
% Start of user PostScript
0.3125 0.9375 0.31803 0.930792 MAarrowhead1
% End of user PostScript
.3125 1 m
.31942 .99306 L
s
% Start of user PostScript
0.3125 1. 0.319417 0.993059 MAarrowhead1
% End of user PostScript
.375 .0625 m
.36102 .10454 L
s
% Start of user PostScript
0.375 0.0625 0.361018 0.104536 MAarrowhead1
% End of user PostScript
.375 .125 m
.3623 .1416 L
s
% Start of user PostScript
0.375 0.125 0.3623 0.141596 MAarrowhead1
% End of user PostScript
.375 .1875 m
.36358 .19562 L
s
% Start of user PostScript
0.375 0.1875 0.363582 0.195616 MAarrowhead1
% End of user PostScript
.375 .25 m
.36486 .25388 L
s
% Start of user PostScript
0.375 0.25 0.364864 0.253876 MAarrowhead1
% End of user PostScript
.375 .3125 m
.36615 .31383 L
s
% Start of user PostScript
0.375 0.3125 0.366146 0.313832 MAarrowhead1
% End of user PostScript
.375 .375 m
.36743 .37464 L
s
% Start of user PostScript
0.375 0.375 0.367428 0.374636 MAarrowhead1
% End of user PostScript
.375 .4375 m
.36871 .43592 L
s
% Start of user PostScript
0.375 0.4375 0.36871 0.435924 MAarrowhead1
% End of user PostScript
.375 .5 m
.36999 .49752 L
s
% Start of user PostScript
0.375 0.5 0.369991 0.497516 MAarrowhead1
% End of user PostScript
.375 .5625 m
.37127 .55931 L
s
% Start of user PostScript
0.375 0.5625 0.371273 0.559309 MAarrowhead1
% End of user PostScript
.375 .625 m
.37256 .62124 L
s
% Start of user PostScript
0.375 0.625 0.372555 0.621244 MAarrowhead1
% End of user PostScript
.375 .6875 m
.37384 .68328 L
s
% Start of user PostScript
0.375 0.6875 0.373837 0.683281 MAarrowhead1
% End of user PostScript
.375 .75 m
.37512 .7454 L
s
% Start of user PostScript
0.375 0.75 0.375119 0.745396 MAarrowhead1
% End of user PostScript
.375 .8125 m
.3764 .80757 L
s
% Start of user PostScript
0.375 0.8125 0.376401 0.807569 MAarrowhead1
% End of user PostScript
.375 .875 m
.37768 .86979 L
s
% Start of user PostScript
0.375 0.875 0.377683 0.86979 MAarrowhead1
% End of user PostScript
.375 .9375 m
.37897 .93205 L
s
% Start of user PostScript
0.375 0.9375 0.378965 0.932048 MAarrowhead1
% End of user PostScript
.375 1 m
.38025 .99434 L
s
% Start of user PostScript
0.375 1. 0.380247 0.994336 MAarrowhead1
% End of user PostScript
.4375 .0625 m
.42341 .10091 L
s
% Start of user PostScript
0.4375 0.0625 0.423414 0.100914 MAarrowhead1
% End of user PostScript
.4375 .125 m
.42459 .14052 L
s
% Start of user PostScript
0.4375 0.125 0.424591 0.140517 MAarrowhead1
% End of user PostScript
.4375 .1875 m
.42577 .19539 L
s
% Start of user PostScript
0.4375 0.1875 0.425769 0.195385 MAarrowhead1
% End of user PostScript
.4375 .25 m
.42695 .25407 L
s
% Start of user PostScript
0.4375 0.25 0.426946 0.254069 MAarrowhead1
% End of user PostScript
.4375 .3125 m
.42812 .31428 L
s
% Start of user PostScript
0.4375 0.3125 0.428124 0.31428 MAarrowhead1
% End of user PostScript
.4375 .375 m
.4293 .37525 L
s
% Start of user PostScript
0.4375 0.375 0.429302 0.375253 MAarrowhead1
% End of user PostScript
.4375 .4375 m
.43048 .43666 L
s
% Start of user PostScript
0.4375 0.4375 0.430479 0.436663 MAarrowhead1
% End of user PostScript
.4375 .5 m
.43166 .49835 L
s
% Start of user PostScript
0.4375 0.5 0.431657 0.498345 MAarrowhead1
% End of user PostScript
.4375 .5625 m
.43283 .56021 L
s
% Start of user PostScript
0.4375 0.5625 0.432834 0.560209 MAarrowhead1
% End of user PostScript
.4375 .625 m
.43401 .6222 L
s
% Start of user PostScript
0.4375 0.625 0.434012 0.622201 MAarrowhead1
% End of user PostScript
.4375 .6875 m
.43519 .68428 L
s
% Start of user PostScript
0.4375 0.6875 0.43519 0.684284 MAarrowhead1
% End of user PostScript
.4375 .75 m
.43637 .74644 L
s
% Start of user PostScript
0.4375 0.75 0.436367 0.746437 MAarrowhead1
% End of user PostScript
.4375 .8125 m
.43754 .80864 L
s
% Start of user PostScript
0.4375 0.8125 0.437545 0.808644 MAarrowhead1
% End of user PostScript
.4375 .875 m
.43872 .87089 L
s
% Start of user PostScript
0.4375 0.875 0.438722 0.870892 MAarrowhead1
% End of user PostScript
.4375 .9375 m
.4399 .93317 L
s
% Start of user PostScript
0.4375 0.9375 0.4399 0.933174 MAarrowhead1
% End of user PostScript
.4375 1 m
.44108 .99548 L
s
% Start of user PostScript
0.4375 1. 0.441078 0.995483 MAarrowhead1
% End of user PostScript
.5 .0625 m
.48581 .09716 L
s
% Start of user PostScript
0.5 0.0625 0.485809 0.0971621 MAarrowhead1
% End of user PostScript
.5 .125 m
.48688 .13931 L
s
% Start of user PostScript
0.5 0.125 0.486882 0.13931 MAarrowhead1
% End of user PostScript
.5 .1875 m
.48796 .19503 L
s
% Start of user PostScript
0.5 0.1875 0.487956 0.195026 MAarrowhead1
% End of user PostScript
.5 .25 m
.48903 .25413 L
s
% Start of user PostScript
0.5 0.25 0.489029 0.254134 MAarrowhead1
% End of user PostScript
.5 .3125 m
.4901 .3146 L
s
% Start of user PostScript
0.5 0.3125 0.490102 0.314599 MAarrowhead1
% End of user PostScript
.5 .375 m
.49118 .37574 L
s
% Start of user PostScript
0.5 0.375 0.491175 0.375742 MAarrowhead1
% End of user PostScript
.5 .4375 m
.49225 .43727 L
s
% Start of user PostScript
0.5 0.4375 0.492249 0.437273 MAarrowhead1
% End of user PostScript
.5 .5 m
.49332 .49905 L
s
% Start of user PostScript
0.5 0.5 0.493322 0.499046 MAarrowhead1
% End of user PostScript
.5 .5625 m
.4944 .56098 L
s
% Start of user PostScript
0.5 0.5625 0.494395 0.560981 MAarrowhead1
% End of user PostScript
.5 .625 m
.49547 .62303 L
s
% Start of user PostScript
0.5 0.625 0.495468 0.623028 MAarrowhead1
% End of user PostScript
.5 .6875 m
.49654 .68516 L
s
% Start of user PostScript
0.5 0.6875 0.496542 0.685158 MAarrowhead1
% End of user PostScript
.5 .75 m
.49761 .74735 L
s
% Start of user PostScript
0.5 0.75 0.497615 0.74735 MAarrowhead1
% End of user PostScript
.5 .8125 m
.49869 .80959 L
s
% Start of user PostScript
0.5 0.8125 0.498688 0.809589 MAarrowhead1
% End of user PostScript
.5 .875 m
.49976 .87187 L
s
% Start of user PostScript
0.5 0.875 0.499761 0.871865 MAarrowhead1
% End of user PostScript
.5 .9375 m
.50083 .93417 L
s
% Start of user PostScript
0.5 0.9375 0.500835 0.934172 MAarrowhead1
% End of user PostScript
.5 1 m
.50191 .9965 L
s
% Start of user PostScript
0.5 1. 0.501908 0.996502 MAarrowhead1
% End of user PostScript
.5625 .0625 m
.5482 .09328 L
s
% Start of user PostScript
0.5625 0.0625 0.548205 0.0932815 MAarrowhead1
% End of user PostScript
.5625 .125 m
.54917 .13797 L
s
% Start of user PostScript
0.5625 0.125 0.549174 0.137973 MAarrowhead1
% End of user PostScript
.5625 .1875 m
.55014 .19454 L
s
% Start of user PostScript
0.5625 0.1875 0.550143 0.194537 MAarrowhead1
% End of user PostScript
.5625 .25 m
.55111 .25407 L
s
% Start of user PostScript
0.5625 0.25 0.551112 0.254069 MAarrowhead1
% End of user PostScript
.5625 .3125 m
.55208 .31479 L
s
% Start of user PostScript
0.5625 0.3125 0.55208 0.314789 MAarrowhead1
% End of user PostScript
.5625 .375 m
.55305 .3761 L
s
% Start of user PostScript
0.5625 0.375 0.553049 0.376101 MAarrowhead1
% End of user PostScript
.5625 .4375 m
.55402 .43775 L
s
% Start of user PostScript
0.5625 0.4375 0.554018 0.437753 MAarrowhead1
% End of user PostScript
.5625 .5 m
.55499 .49962 L
s
% Start of user PostScript
0.5625 0.5 0.554987 0.499617 MAarrowhead1
% End of user PostScript
.5625 .5625 m
.55596 .56162 L
s
% Start of user PostScript
0.5625 0.5625 0.555956 0.561623 MAarrowhead1
% End of user PostScript
.5625 .625 m
.55693 .62373 L
s
% Start of user PostScript
0.5625 0.625 0.556925 0.623727 MAarrowhead1
% End of user PostScript
.5625 .6875 m
.55789 .6859 L
s
% Start of user PostScript
0.5625 0.6875 0.557894 0.685903 MAarrowhead1
% End of user PostScript
.5625 .75 m
.55886 .74813 L
s
% Start of user PostScript
0.5625 0.75 0.558863 0.748133 MAarrowhead1
% End of user PostScript
.5625 .8125 m
.55983 .81041 L
s
% Start of user PostScript
0.5625 0.8125 0.559832 0.810405 MAarrowhead1
% End of user PostScript
.5625 .875 m
.5608 .87271 L
s
% Start of user PostScript
0.5625 0.875 0.560801 0.872709 MAarrowhead1
% End of user PostScript
.5625 .9375 m
.56177 .93504 L
s
% Start of user PostScript
0.5625 0.9375 0.56177 0.93504 MAarrowhead1
% End of user PostScript
.5625 1 m
.56274 .99739 L
s
% Start of user PostScript
0.5625 1. 0.562739 0.997391 MAarrowhead1
% End of user PostScript
.625 .0625 m
.6106 .08927 L
s
% Start of user PostScript
0.625 0.0625 0.610601 0.0892717 MAarrowhead1
% End of user PostScript
.625 .125 m
.61147 .13651 L
s
% Start of user PostScript
0.625 0.125 0.611465 0.136508 MAarrowhead1
% End of user PostScript
.625 .1875 m
.61233 .19392 L
s
% Start of user PostScript
0.625 0.1875 0.61233 0.19392 MAarrowhead1
% End of user PostScript
.625 .25 m
.61319 .25388 L
s
% Start of user PostScript
0.625 0.25 0.613194 0.253876 MAarrowhead1
% End of user PostScript
.625 .3125 m
.61406 .31485 L
s
% Start of user PostScript
0.625 0.3125 0.614059 0.314849 MAarrowhead1
% End of user PostScript
.625 .375 m
.61492 .37633 L
s
% Start of user PostScript
0.625 0.375 0.614923 0.376332 MAarrowhead1
% End of user PostScript
.625 .4375 m
.61579 .4381 L
s
% Start of user PostScript
0.625 0.4375 0.615788 0.438105 MAarrowhead1
% End of user PostScript
.625 .5 m
.61665 .50006 L
s
% Start of user PostScript
0.625 0.5 0.616652 0.50006 MAarrowhead1
% End of user PostScript
.625 .5625 m
.61752 .56214 L
s
% Start of user PostScript
0.625 0.5625 0.617517 0.562136 MAarrowhead1
% End of user PostScript
.625 .625 m
.61838 .6243 L
s
% Start of user PostScript
0.625 0.625 0.618382 0.624296 MAarrowhead1
% End of user PostScript
.625 .6875 m
.61925 .68652 L
s
% Start of user PostScript
0.625 0.6875 0.619246 0.686519 MAarrowhead1
% End of user PostScript
.625 .75 m
.62011 .74879 L
s
% Start of user PostScript
0.625 0.75 0.620111 0.748788 MAarrowhead1
% End of user PostScript
.625 .8125 m
.62098 .81109 L
s
% Start of user PostScript
0.625 0.8125 0.620975 0.811092 MAarrowhead1
% End of user PostScript
.625 .875 m
.62184 .87342 L
s
% Start of user PostScript
0.625 0.875 0.62184 0.873424 MAarrowhead1
% End of user PostScript
.625 .9375 m
.6227 .93578 L
s
% Start of user PostScript
0.625 0.9375 0.622704 0.935779 MAarrowhead1
% End of user PostScript
.625 1 m
.62357 .99815 L
s
% Start of user PostScript
0.625 1. 0.623569 0.998152 MAarrowhead1
% End of user PostScript
.6875 .0625 m
.673 .08513 L
s
% Start of user PostScript
0.6875 0.0625 0.672996 0.0851327 MAarrowhead1
% End of user PostScript
.6875 .125 m
.67376 .13491 L
s
% Start of user PostScript
0.6875 0.125 0.673756 0.134913 MAarrowhead1
% End of user PostScript
.6875 .1875 m
.67452 .19317 L
s
% Start of user PostScript
0.6875 0.1875 0.674517 0.193173 MAarrowhead1
% End of user PostScript
.6875 .25 m
.67528 .25355 L
s
% Start of user PostScript
0.6875 0.25 0.675277 0.253553 MAarrowhead1
% End of user PostScript
.6875 .3125 m
.67604 .31478 L
s
% Start of user PostScript
0.6875 0.3125 0.676037 0.314781 MAarrowhead1
% End of user PostScript
.6875 .375 m
.6768 .37643 L
s
% Start of user PostScript
0.6875 0.375 0.676797 0.376433 MAarrowhead1
% End of user PostScript
.6875 .4375 m
.67756 .43833 L
s
% Start of user PostScript
0.6875 0.4375 0.677557 0.438327 MAarrowhead1
% End of user PostScript
.6875 .5 m
.67832 .50037 L
s
% Start of user PostScript
0.6875 0.5 0.678318 0.500373 MAarrowhead1
% End of user PostScript
.6875 .5625 m
.67908 .56252 L
s
% Start of user PostScript
0.6875 0.5625 0.679078 0.562519 MAarrowhead1
% End of user PostScript
.6875 .625 m
.67984 .62474 L
s
% Start of user PostScript
0.6875 0.625 0.679838 0.624737 MAarrowhead1
% End of user PostScript
.6875 .6875 m
.6806 .68701 L
s
% Start of user PostScript
0.6875 0.6875 0.680598 0.687005 MAarrowhead1
% End of user PostScript
.6875 .75 m
.68136 .74931 L
s
% Start of user PostScript
0.6875 0.75 0.681359 0.749313 MAarrowhead1
% End of user PostScript
.6875 .8125 m
.68212 .81165 L
s
% Start of user PostScript
0.6875 0.8125 0.682119 0.81165 MAarrowhead1
% End of user PostScript
.6875 .875 m
.68288 .87401 L
s
% Start of user PostScript
0.6875 0.875 0.682879 0.87401 MAarrowhead1
% End of user PostScript
.6875 .9375 m
.68364 .93639 L
s
% Start of user PostScript
0.6875 0.9375 0.683639 0.936389 MAarrowhead1
% End of user PostScript
.6875 1 m
.6844 .99878 L
s
% Start of user PostScript
0.6875 1. 0.684399 0.998783 MAarrowhead1
% End of user PostScript
.75 .0625 m
.73539 .08086 L
s
% Start of user PostScript
0.75 0.0625 0.735392 0.0808646 MAarrowhead1
% End of user PostScript
.75 .125 m
.73605 .13319 L
s
% Start of user PostScript
0.75 0.125 0.736048 0.133189 MAarrowhead1
% End of user PostScript
.75 .1875 m
.7367 .1923 L
s
% Start of user PostScript
0.75 0.1875 0.736704 0.192297 MAarrowhead1
% End of user PostScript
.75 .25 m
.73736 .2531 L
s
% Start of user PostScript
0.75 0.25 0.737359 0.253101 MAarrowhead1
% End of user PostScript
.75 .3125 m
.73802 .31458 L
s
% Start of user PostScript
0.75 0.3125 0.738015 0.314583 MAarrowhead1
% End of user PostScript
.75 .375 m
.73867 .3764 L
s
% Start of user PostScript
0.75 0.375 0.738671 0.376405 MAarrowhead1
% End of user PostScript
.75 .4375 m
.73933 .43842 L
s
% Start of user PostScript
0.75 0.4375 0.739327 0.43842 MAarrowhead1
% End of user PostScript
.75 .5 m
.73998 .50056 L
s
% Start of user PostScript
0.75 0.5 0.739983 0.500557 MAarrowhead1
% End of user PostScript
.75 .5625 m
.74064 .56277 L
s
% Start of user PostScript
0.75 0.5625 0.740639 0.562774 MAarrowhead1
% End of user PostScript
.75 .625 m
.74129 .62505 L
s
% Start of user PostScript
0.75 0.625 0.741295 0.625048 MAarrowhead1
% End of user PostScript
.75 .6875 m
.74195 .68736 L
s
% Start of user PostScript
0.75 0.6875 0.741951 0.687363 MAarrowhead1
% End of user PostScript
.75 .75 m
.74261 .74971 L
s
% Start of user PostScript
0.75 0.75 0.742606 0.749708 MAarrowhead1
% End of user PostScript
.75 .8125 m
.74326 .81208 L
s
% Start of user PostScript
0.75 0.8125 0.743262 0.812078 MAarrowhead1
% End of user PostScript
.75 .875 m
.74392 .87447 L
s
% Start of user PostScript
0.75 0.875 0.743918 0.874466 MAarrowhead1
% End of user PostScript
.75 .9375 m
.74457 .93687 L
s
% Start of user PostScript
0.75 0.9375 0.744574 0.936869 MAarrowhead1
% End of user PostScript
.75 1 m
.74523 .99928 L
s
% Start of user PostScript
0.75 1. 0.74523 0.999284 MAarrowhead1
% End of user PostScript
.8125 .0625 m
.79779 .07647 L
s
% Start of user PostScript
0.8125 0.0625 0.797787 0.0764672 MAarrowhead1
% End of user PostScript
.8125 .125 m
.79834 .13134 L
s
% Start of user PostScript
0.8125 0.125 0.798339 0.131335 MAarrowhead1
% End of user PostScript
.8125 .1875 m
.79889 .19129 L
s
% Start of user PostScript
0.8125 0.1875 0.798891 0.191291 MAarrowhead1
% End of user PostScript
.8125 .25 m
.79944 .25252 L
s
% Start of user PostScript
0.8125 0.25 0.799442 0.252519 MAarrowhead1
% End of user PostScript
.8125 .3125 m
.79999 .31426 L
s
% Start of user PostScript
0.8125 0.3125 0.799994 0.314256 MAarrowhead1
% End of user PostScript
.8125 .375 m
.80055 .37625 L
s
% Start of user PostScript
0.8125 0.375 0.800545 0.376247 MAarrowhead1
% End of user PostScript
.8125 .4375 m
.8011 .43838 L
s
% Start of user PostScript
0.8125 0.4375 0.801097 0.438384 MAarrowhead1
% End of user PostScript
.8125 .5 m
.80165 .50061 L
s
% Start of user PostScript
0.8125 0.5 0.801648 0.500611 MAarrowhead1
% End of user PostScript
.8125 .5625 m
.8022 .5629 L
s
% Start of user PostScript
0.8125 0.5625 0.8022 0.562899 MAarrowhead1
% End of user PostScript
.8125 .625 m
.80275 .62523 L
s
% Start of user PostScript
0.8125 0.625 0.802751 0.62523 MAarrowhead1
% End of user PostScript
.8125 .6875 m
.8033 .68759 L
s
% Start of user PostScript
0.8125 0.6875 0.803303 0.687591 MAarrowhead1
% End of user PostScript
.8125 .75 m
.80385 .74998 L
s
% Start of user PostScript
0.8125 0.75 0.803854 0.749975 MAarrowhead1
% End of user PostScript
.8125 .8125 m
.80441 .81238 L
s
% Start of user PostScript
0.8125 0.8125 0.804406 0.812377 MAarrowhead1
% End of user PostScript
.8125 .875 m
.80496 .87479 L
s
% Start of user PostScript
0.8125 0.875 0.804957 0.874793 MAarrowhead1
% End of user PostScript
.8125 .9375 m
.80551 .93722 L
s
% Start of user PostScript
0.8125 0.9375 0.805509 0.937221 MAarrowhead1
% End of user PostScript
.8125 1 m
.80606 .99966 L
s
% Start of user PostScript
0.8125 1. 0.80606 0.999657 MAarrowhead1
% End of user PostScript
.875 .0625 m
.86018 .07194 L
s
% Start of user PostScript
0.875 0.0625 0.860183 0.0719407 MAarrowhead1
% End of user PostScript
.875 .125 m
.86063 .12935 L
s
% Start of user PostScript
0.875 0.125 0.86063 0.129353 MAarrowhead1
% End of user PostScript
.875 .1875 m
.86108 .19016 L
s
% Start of user PostScript
0.875 0.1875 0.861078 0.190157 MAarrowhead1
% End of user PostScript
.875 .25 m
.86152 .25181 L
s
% Start of user PostScript
0.875 0.25 0.861525 0.251809 MAarrowhead1
% End of user PostScript
.875 .3125 m
.86197 .3138 L
s
% Start of user PostScript
0.875 0.3125 0.861972 0.3138 MAarrowhead1
% End of user PostScript
.875 .375 m
.86242 .37596 L
s
% Start of user PostScript
0.875 0.375 0.862419 0.375961 MAarrowhead1
% End of user PostScript
.875 .4375 m
.86287 .43822 L
s
% Start of user PostScript
0.875 0.4375 0.862866 0.438218 MAarrowhead1
% End of user PostScript
.875 .5 m
.86331 .50054 L
s
% Start of user PostScript
0.875 0.5 0.863313 0.500537 MAarrowhead1
% End of user PostScript
.875 .5625 m
.86376 .5629 L
s
% Start of user PostScript
0.875 0.5625 0.863761 0.562895 MAarrowhead1
% End of user PostScript
.875 .625 m
.86421 .62528 L
s
% Start of user PostScript
0.875 0.625 0.864208 0.625282 MAarrowhead1
% End of user PostScript
.875 .6875 m
.86466 .68769 L
s
% Start of user PostScript
0.875 0.6875 0.864655 0.68769 MAarrowhead1
% End of user PostScript
.875 .75 m
.8651 .75011 L
s
% Start of user PostScript
0.875 0.75 0.865102 0.750113 MAarrowhead1
% End of user PostScript
.875 .8125 m
.86555 .81255 L
s
% Start of user PostScript
0.875 0.8125 0.865549 0.812547 MAarrowhead1
% End of user PostScript
.875 .875 m
.866 .87499 L
s
% Start of user PostScript
0.875 0.875 0.865997 0.874991 MAarrowhead1
% End of user PostScript
.875 .9375 m
.86644 .93744 L
s
% Start of user PostScript
0.875 0.9375 0.866444 0.937443 MAarrowhead1
% End of user PostScript
.875 1 m
.86689 .9999 L
s
% Start of user PostScript
0.875 1. 0.866891 0.999901 MAarrowhead1
% End of user PostScript
.9375 .0625 m
.92258 .06728 L
s
% Start of user PostScript
0.9375 0.0625 0.922579 0.0672849 MAarrowhead1
% End of user PostScript
.9375 .125 m
.92292 .12724 L
s
% Start of user PostScript
0.9375 0.125 0.922922 0.127241 MAarrowhead1
% End of user PostScript
.9375 .1875 m
.92326 .18889 L
s
% Start of user PostScript
0.9375 0.1875 0.923264 0.188893 MAarrowhead1
% End of user PostScript
.9375 .25 m
.92361 .25097 L
s
% Start of user PostScript
0.9375 0.25 0.923607 0.250969 MAarrowhead1
% End of user PostScript
.9375 .3125 m
.92395 .31321 L
s
% Start of user PostScript
0.9375 0.3125 0.92395 0.313215 MAarrowhead1
% End of user PostScript
.9375 .375 m
.92429 .37554 L
s
% Start of user PostScript
0.9375 0.375 0.924293 0.375545 MAarrowhead1
% End of user PostScript
.9375 .4375 m
.92464 .43792 L
s
% Start of user PostScript
0.9375 0.4375 0.924636 0.437924 MAarrowhead1
% End of user PostScript
.9375 .5 m
.92498 .50033 L
s
% Start of user PostScript
0.9375 0.5 0.924979 0.500333 MAarrowhead1
% End of user PostScript
.9375 .5625 m
.92532 .56276 L
s
% Start of user PostScript
0.9375 0.5625 0.925322 0.562762 MAarrowhead1
% End of user PostScript
.9375 .625 m
.92566 .62521 L
s
% Start of user PostScript
0.9375 0.625 0.925664 0.625206 MAarrowhead1
% End of user PostScript
.9375 .6875 m
.92601 .68766 L
s
% Start of user PostScript
0.9375 0.6875 0.926007 0.687659 MAarrowhead1
% End of user PostScript
.9375 .75 m
.92635 .75012 L
s
% Start of user PostScript
0.9375 0.75 0.92635 0.750121 MAarrowhead1
% End of user PostScript
.9375 .8125 m
.92669 .81259 L
s
% Start of user PostScript
0.9375 0.8125 0.926693 0.812588 MAarrowhead1
% End of user PostScript
.9375 .875 m
.92704 .87506 L
s
% Start of user PostScript
0.9375 0.875 0.927036 0.87506 MAarrowhead1
% End of user PostScript
.9375 .9375 m
.92738 .93754 L
s
% Start of user PostScript
0.9375 0.9375 0.927379 0.937536 MAarrowhead1
% End of user PostScript
.9375 1 m
0 0 rlineto s
.9375 1 m
.9375 1 L
s
% Start of user PostScript
0.9375 1. 0.927721 1.00001 MAarrowhead1
% End of user PostScript
1 .0625 m
.98497 .0625 L
s
% Start of user PostScript
1. 0.0625 0.984974 0.0625 MAarrowhead1
% End of user PostScript
1 .125 m
.98521 .125 L
s
% Start of user PostScript
1. 0.125 0.985213 0.125 MAarrowhead1
% End of user PostScript
1 .1875 m
.98545 .1875 L
s
% Start of user PostScript
1. 0.1875 0.985451 0.1875 MAarrowhead1
% End of user PostScript
1 .25 m
.98569 .25 L
s
% Start of user PostScript
1. 0.25 0.98569 0.25 MAarrowhead1
% End of user PostScript
1 .3125 m
.98593 .3125 L
s
% Start of user PostScript
1. 0.3125 0.985928 0.3125 MAarrowhead1
% End of user PostScript
1 .375 m
.98617 .375 L
s
% Start of user PostScript
1. 0.375 0.986167 0.375 MAarrowhead1
% End of user PostScript
1 .4375 m
.98641 .4375 L
s
% Start of user PostScript
1. 0.4375 0.986405 0.4375 MAarrowhead1
% End of user PostScript
1 .5 m
.98664 .5 L
s
% Start of user PostScript
1. 0.5 0.986644 0.5 MAarrowhead1
% End of user PostScript
1 .5625 m
.98688 .5625 L
s
% Start of user PostScript
1. 0.5625 0.986882 0.5625 MAarrowhead1
% End of user PostScript
1 .625 m
.98712 .625 L
s
% Start of user PostScript
1. 0.625 0.987121 0.625 MAarrowhead1
% End of user PostScript
1 .6875 m
.98736 .6875 L
s
% Start of user PostScript
1. 0.6875 0.987359 0.6875 MAarrowhead1
% End of user PostScript
1 .75 m
.9876 .75 L
s
% Start of user PostScript
1. 0.75 0.987598 0.75 MAarrowhead1
% End of user PostScript
1 .8125 m
.98784 .8125 L
s
% Start of user PostScript
1. 0.8125 0.987836 0.8125 MAarrowhead1
% End of user PostScript
1 .875 m
.98807 .875 L
s
% Start of user PostScript
1. 0.875 0.988075 0.875 MAarrowhead1
% End of user PostScript
1 .9375 m
.98831 .9375 L
s
% Start of user PostScript
1. 0.9375 0.988313 0.9375 MAarrowhead1
% End of user PostScript
1 1 m
.98855 1 L
s
% Start of user PostScript
1. 1. 0.988552 1. MAarrowhead1
% End of user PostScript
0 0 1 r
.5 Mabswid
0 .5 m
0 .5 L
s
0 .5 m
0 .5 L
.04167 .51892 L
.08333 .53933 L
.08791 .54167 L
.125 .5614 L
.16327 .58333 L
.16667 .58537 L
.20833 .61146 L
.22857 .625 L
.25 .64 L
.28571 .66667 L
.29167 .67133 L
.33333 .70588 L
.33613 .70833 L
.375 .74419 L
.38095 .75 L
.41667 .78689 L
.42105 .79167 L
.45714 .83333 L
.45833 .83478 L
.4898 .875 L
.5 .88889 L
.51948 .91667 L
.54167 .9505 L
.54658 .95833 L
.57143 1 L
s
1 0 0 r
0 .25 m
0 .25 L
s
0 .25 m
0 .25 L
.04167 .2587 L
.08333 .26807 L
.125 .27819 L
.16667 .28914 L
.17581 .29167 L
.20833 .3009 L
.25 .31367 L
.29167 .32762 L
.30767 .33333 L
.33333 .34283 L
.375 .35952 L
.41024 .375 L
.41667 .37795 L
.45833 .39831 L
.49228 .41667 L
.5 .42104 L
.54167 .4465 L
.55933 .45833 L
.58333 .47523 L
.6153 .5 L
.625 .50793 L
.66267 .54167 L
.66667 .54545 L
.7032 .58333 L
.70833 .58895 L
.73814 .625 L
.75 .63999 L
.76838 .66667 L
.79167 .70073 L
.79543 .70833 L
.81938 .75 L
.83333 .77419 L
.83775 .79167 L
.85871 .83333 L
.875 .86486 L
.87912 .875 L
.8951 .91667 L
.9097 .95833 L
.91667 .97959 L
.92308 1 L
s
0 .25 m
0 .25 .02 0 365.73 arc
F
gsave
.07 .21 -72 -10.2813 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 20.5625 translate 1 -1 scale
63.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
(ESS) show
81.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  ImageSize->{288, 288},
  ImageMargins->{{0, 0}, {0, 0}},
  ImageRegion->{{0, 1}, {0, 1}},
  ImageCache->GraphicsData["Bitmap", "\<\
CF5dJ6E]HGAYHf4PAg9QL6QYHg<PAVmbKF5d0`40004P000181000`40O003h00Oogoo8Goo003oOolQ
Ool00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol00;9oo`<006]o
o`00]Goo00<007ooOol0J7oo0027Ool30005Ool20003Ool30004Ool30003Ool30003Ool300000goo
00000002Ool20002Ool3001ZOol008Qoo`03001oogoo00=oo`04001oogoo0003Ool00`00Oomoo`04
Ool01@00Oomoogoo00001goo00D007ooOomoo`00009oo`04001oogoo0002Ool00`00Oomoo`1XOol0
08Qoo`<000=oo`04001oogoo0003Ool00`00Oomoo`04Ool01@00Oomoogoo00001goo00D007ooOomo
o`00009oo`04001oogoo0002Ool00`00Oomoo`1XOol008Qoo`04001oogoo0003Ool20004Ool00`00
Oomoo`03Ool20004Ool30003Ool20002Ool40004Ool4001YOol008Qoo`04001oogoo0009Ool00`00
Oomoo`28Ool008Moo`@000Uoo`8000Ioo`03001oogoo00Uoo`03001oogoo07Eoo`00ogoo8Goo003o
OolQOol00?moob5oo`00CGoo0P0017oo0P000goo10008goo0P0017oo0P001Goo0`008Woo0P0017oo
0P000goo0`0097oo0P0017oo0P0017oo0P00:Goo1@000Goo001<Ool01000Oomoo`0027oo00<007oo
Ool08goo00@007ooOol000]oo`03001oogoo021oo`04001oogoo0008Ool01000Oomoo`008Woo00@0
07ooOol000Qoo`04001oogoo000ZOol00`00Oomoo`01Ool004aoo`04001oogoo0009Ool00`00Oomo
o`0ROol01000Oomoo`0027oo1@008Goo00@007ooOol000Qoo`04001oogoo000ROol01000Oomoo`00
27oo00@007ooOol002Yoo`03001oogoo005oo`00C7oo00@007ooOol000Yoo`03001oogoo025oo`04
001oogoo0008Ool01000Oomoo`008Woo00@007ooOol000Qoo`<002=oo`04001oogoo0009Ool2000[
Ool00`00Oomoo`01Ool004aoo`04001oogoo0008Ool01000Oomoo`008Woo00@007ooOol000Uoo`03
001oo`00029oo`04001oogoo0009Ool00`00Oomoo`0ROol01000Oomoo`0027oo00@007ooOol002Yo
o`03001oogoo005oo`00CGoo0P002Woo0P0097oo0P002goo0P008goo0P002Woo0`008goo0P002Woo
0P00:Woo0P000goo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`008goonP00
0goo000SOol00`00Oomoo`09Ool00`00Oomoo`0:Ool00`00Oomoo`09Ool00`00Oomoo`09Ool00`00
Oomoo`0:Ool00`00Oomoo`09Ool00`00Oomoo`0:Ool00`00Oomoo`09Ool00`00Oomoo`0:Ool00`00
Oomoo`09Ool00`00Oomoo`0:Ool00`00Oomoo`09Ool00`00Oomoo`09Ool00`00Oomoo`0:Ool00`00
Oomoo`09Ool00`00Oomoo`0:Ool00`00Oomoo`09Ool00`00Oomoo`0:Ool00`00Oomoo`09Ool00`00
Oomoo`0:Ool00`00Oomoo`01Ool002=oo`03001oogoo0?Ioo`03001oogoo005oo`008goo00<007oo
Ool0mWoo00<007ooOol00Goo000SOol00`00Oomoo`3fOol00`00Oomoo`01Ool002=oo`03001oogoo
0?Ioo`03001oogoo005oo`008goo00<007ooOol0mWoo00<007ooOol00Goo000SOol00`00Oomoo`3f
Ool00`00Oomoo`01Ool002=oo`03001oogoo0?Ioo`03001oogoo005oo`008goo00<007ooOol0mWoo
00<007ooOol00Goo000SOol00`00Oomoo`3fOol00`00Oomoo`01Ool002=oo`03001oogoo0?Ioo`03
001oogoo005oo`008goo0P00mWoo0P000goo000SOol00`00Oomoo`3fOol00`00Oomoo`01Ool002=o
o`03001oogoo0<Ioo`03001oogoo00eoo`03001oogoo00eoo`8000eoo`<0009oo`008goo00<007oo
Ool037oo00<007ooOol03Goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol037oo00<007oo
Ool03Goo00<007ooOol03Goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol037oo00<007oo
Ool03Goo00<007ooOol02goo0P003Goo0`003Goo0`0037oo10002Woo1P000Woo000SOol00`00Oomo
o`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomo
o`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomo
o`0;Ool2000>Ool2000=Ool4000;Ool50009Ool6000=Ool30002Ool002=oo`03001oogoo00aoo`03
001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00aoo`03001oogoo00eoo`03
001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00]oo`8000ioo`<000aoo`@0
00]oo`@000aoo`<001moo`03001oogoo005oo`008goo00<007ooOol02goo00<007ooOol03Goo00<0
07ooOol037oo00<007ooOol03Goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol03Goo00<0
07ooOol037oo00<007ooOol02goo0P003Woo0`0037oo0`003Goo0`0037oo0P003Goo0P008Goo00<0
07ooOol00Goo000SOol00`00Oomoo`0;Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=
Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0;Ool3000=Ool3000=
Ool2000=Ool2000=Ool3000<Ool00`00Oomoo`0`Ool00`00Oomoo`01Ool002=oo`03001oogoo00]o
o`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00eo
o`03001oogoo00]oo`8000eoo`@000aoo`8000eoo`8000eoo`8000ioo`03001oogoo03moo`03001o
ogoo005oo`008goo00<007ooOol02goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol037oo
00<007ooOol037oo00<007ooOol037oo0`003Goo0`0037oo0`0037oo0P003Woo0P003Goo00<007oo
Ool0Cgoo00<007ooOol00Goo000SOol00`00Oomoo`0;Ool00`00Oomoo`0<Ool00`00Oomoo`0<Ool0
0`00Oomoo`0<Ool2000=Ool4000<Ool3000=Ool2000=Ool2000=Ool2000>Ool00`00Oomoo`1NOol0
0`00Oomoo`01Ool002=oo`03001oogoo00Yoo`03001oogoo00eoo`03001oogoo00]oo`8000ioo`<0
00aoo`<000eoo`8000eoo`8000ioo`8000eoo`03001oogoo06ioo`03001oogoo005oo`008goo00<0
07ooOol02Woo00<007ooOol02goo100037oo0`003Goo0P003Goo0`003Goo0P003Goo0P003Woo00<0
07ooOol0OGoo00<007ooOol00Goo000OOol20002Ool2000:Ool3000<Ool3000=Ool2000=Ool2000>
Ool2000>Ool00`00Oomoo`0<Ool00`00Oomoo`2<Ool20003Ool001moo`D000]oo`<000aoo`<000eo
o`8000eoo`8000ioo`8000ioo`03001oogoo09aoo`03001oogoo005oo`007goo0`0000=oo`00Ool0
2Woo0P003Goo0P003Woo00<007ooOol037oo00<007ooOol03Goo00<007ooOol0[7oo00<007ooOol0
0Goo000OOol20002Ool00`00Oomoo`09Ool2000=Ool2000>Ool00`00Oomoo`3;Ool00`00Oomoo`01
Ool001moo`80009oo`03001oogoo00Uoo`03001oogoo00aoo`03001oogoo08eoo`03001oogoo00ao
o`03001oogoo00eoo`03001oogoo00eoo`03001oogoo00aoo`8000ioo`03001oogoo005oo`007goo
00D007ooOomoo`0000]oo`03001oogoo03eoo`03001oogoo00eoo`03001oogoo00eoo`03001oogoo
00aoo`03001oogoo00eoo`03001oogoo00eoo`03001oogoo00aoo`8000eoo`<000eoo`8000ioo`80
00aoo`@000eoo`<0009oo`008Goo00<007oo00003Goo0P003Goo00<007oo00003Goo0P003Woo0P00
3Goo0P003Woo0P003Goo0`0037oo0`003Goo100037oo0`0037oo10002goo1@002Woo1@002goo1@00
2Goo1P002Woo1P000Woo000QOol3000=Ool3000<Ool3000=Ool3000<Ool4000;Ool4000<Ool4000<
Ool3000<Ool4000;Ool4000<Ool3000<Ool3000=Ool3000;Ool3000=Ool6000<Ool3000=Ool30002
Ool0025oo`<000aoo`<000eoo`8000eoo`<000eoo`<000aoo`<000eoo`<000aoo`<000aoo`@000ao
o`8000ioo`8000aoo`8000ioo`80041oo`03001oogoo005oo`0087oo0P0000=oo`00Ool02goo0P00
3Goo0P003Woo0P003Goo0`0037oo0`003Goo0`003Goo0P003Goo0P003Goo00<007ooOol03Goo00<0
07ooOol0GWoo00<007ooOol00Goo000POol200000goo001oo`0:Ool2000>Ool2000=Ool2000>Ool0
0`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`2=Ool00`00Oomoo`01Ool0
021oo`04001oogoo000;Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`3;Ool00`00Oomo
o`01Ool002=oo`800?Ioo`8000=oo`008goo00<007ooOol0mWoo00<007ooOol00Goo000SOol00`00
Oomoo`3fOol00`00Oomoo`01Ool002=oo`03001oogoo0?Ioo`03001oogoo005oo`008goo00<007oo
Ool0mWoo00<007ooOol00Goo000SOol00`00Oomoo`3fOol00`00Oomoo`01Ool002=oo`03001oogoo
0?Ioo`03001oogoo005oo`008goo0P003Woo00<007ooOol037oo00<007ooOol03Goo00<007ooOol0
37oo00<007ooOol03Goo00<007ooOol0Z7oo00<007ooOol00Goo000SOol2000=Ool3000<Ool3000=
Ool2000=Ool3000=Ool2000?Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00
Oomoo`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0<Ool2000>Ool2000=Ool2000=
Ool30002Ool0029oo`@000]oo`D000Yoo`D000]oo`@000]oo`D000]oo`@000eoo`8000eoo`8000io
o`8000eoo`<000eoo`8000ioo`8000eoo`8000aoo`@000aoo`@000]oo`@000Yoo`H0009oo`0047oo
0P0017oo0P000goo10000Woo0`003Goo0`0037oo0`003Goo0`0037oo0`003Goo0`0037oo1@002goo
10002goo1@002goo1@002Woo1@002goo1@002Woo1@002Goo1`002Goo1P002Goo1P0037oo10000Woo
000?Ool01000Oomoo`0027oo00<007ooOol00Woo0P0000=oo`00Ool02goo0P003Goo0P003Woo0P00
3Goo0P003Woo0P003Goo0`003Goo0`0037oo0`003Goo0`0037oo0`003Goo0`0037oo0`00?goo0P00
0Woo000?Ool01000Oomoo`002Goo00<007ooOol017oo0P00mGoo0`000goo000?Ool01000Oomoo`00
2Woo00<007ooOol00goo00<007ooOol01Goo1G`00Woo0g`00goo0g`0hGoo00<007ooOol00Goo000?
Ool01000Oomoo`0027oo00@007ooOol000Aoo`03001oogoo00Ioo`04O01oogooO002Ool017`0Oomo
og`00Woo00Al07ooOoml0>1oo`03001oogoo005oo`0047oo0P002Woo0P001Goo00<007ooOol01Woo
00=l07ooOol01Woo00=l07ooOol00goo00=l07ooOol0gWoo00<007ooOol00Goo000SOol00`00Oomo
o`06Ool2O005Ool2O004Ool2O03QOol00`00Oomoo`01Ool002=oo`03001oogoo00Ioo`04O01oogoo
O002Ool017`0Oomoog`00Woo00Al07ooOoml0>1oo`03001oogoo005oo`008goo00<007ooOol01Goo
1G`00Woo17`00Woo17`0h7oo00<007ooOol00Goo000SOol00`00Oomoo`3fOol00`00Oomoo`01Ool0
02=oo`03001oogoo0?Ioo`03001oogoo005oo`007goo1g`0mWoo00<007ooOol00Goo000OOol8O03e
Ool00`00Oomoo`01Ool001ioo`Ul00eoo`8000ioo`03001oogoo00eoo`03001oogoo00aoo`03001o
ogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001o
ogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00aoo`8001eo
o`03001oogoo005oo`007Woo2W`02Woo100037oo0`003Goo0`003Goo0P003Goo0P003Goo0`003Goo
0P003Goo0`003Goo0P003Goo0`003Goo0P003Goo0`003Goo0P0037oo100037oo0`003Goo0`000Woo
000NOol:O008Ool6000:Ool6000:Ool5000;Ool5000:Ool5000:Ool6000:Ool5000:Ool5000;Ool5
000:Ool5000;Ool5000:Ool5000;Ool50009Ool60009Ool6000:Ool60002Ool001ioo`el00Qoo`<0
00eoo`<000Uoo`<000eoo`<000aoo`<000aoo`@000aoo`<000aoo`<000eoo`<000aoo`H000Yoo`H0
00Uoo`H000Yoo`H000aoo`<000aoo`<000eoo`<0009oo`007Woo2G`017oo1G`0k7oo00<007ooOol0
0Goo000OOol7O00:Ool5O03WOol00`00Oomoo`01Ool0025oo`El00moo`Al0>=oo`03001oogoo005o
o`008goo0W`057oo17`0ggoo00<007ooOol00Goo000SOol00`00Oomoo`0GOol4O03KOol00`00Oomo
o`01Ool002=oo`03001oogoo01]oo`=l0=Qoo`03001oogoo005oo`008goo00<007ooOol07Woo0g`0
eGoo00<007ooOol00Goo000SOol00`00Oomoo`0QOol4O03AOol00`00Oomoo`01Ool002=oo`03001o
ogoo02Eoo`El0<aoo`03001oogoo005oo`008goo00<007ooOol0:Woo0g`0bGoo00<007ooOol00Goo
000SOol2000^Ool3O035Ool20003Ool002=oo`03001oogoo031oo`=l0<=oo`03001oogoo005oo`00
8Goo0`00=Goo0g`01Woo0`003Goo0P003Woo0P003Goo0P003Woo00<007ooOol037oo0P003Goo0P00
3Woo0P003Goo0P003Woo00<007ooOol037oo0P003Woo00<007ooOol02goo0`000Woo000ROol3000<
Ool3000<Ool6000:Ool60006Ool4O005000;Ool4000<Ool4000;Ool4000<Ool3000<Ool4000;Ool4
000<Ool4000;Ool4000<Ool3000<Ool4000<Ool3000:Ool60002Ool002=oo`@000]oo`D000Yoo`D0
00]oo`@000]oo`=l008000Uoo`H000Yoo`H000Uoo`H000Yoo`H000Uoo`H000Uoo`L000Uoo`H000Uo
o`H000Yoo`H000Uoo`H000Yoo`H000]oo`@0009oo`008goo0`003Goo0`003Goo0`003Goo0P003Woo
0g`0UWoo0`003Goo0`003Goo0P000Woo000SOol00`00Ool0000?Ool00`00Oomoo`0=Ool00`00Oomo
o`0NOol4O02bOol00`00Oomoo`01Ool002=oo`03001oogoo04Aoo`9l0;1oo`03001oogoo005oo`00
8goo00<007ooOol0AWoo0W`0[Woo00<007ooOol00Goo0002Ool00`00Oomoo`02Ool00`00Oomoo`0I
Ool00`00Oomoo`18Ool3O02[Ool00`00Oomoo`01Ool0009oo`H001]oo`03001oogoo04]oo`Al0:Mo
o`03001oogoo005oo`000Woo00<007oo00000Woo00<007ooOol06Goo00<007ooOol0Cgoo0g`0Y7oo
00<007ooOol00Goo0002Ool00`00Ool00002Ool00`00Oomoo`0IOol00`00Oomoo`1BOol2O02ROol0
0`00Oomoo`01Ool000=oo`04001oo`00000LOol2001EOol3O02NOol20003Ool002=oo`03001oogoo
05Moo`9l09eoo`03001oogoo005oo`008goo00<007ooOol0FGoo0g`0VWoo00<007ooOol00Goo0004
Ool01000Oomoo`006goo00<007ooOol0G7oo0W`0V7oo00<007ooOol00Goo0004Ool4000JOol2001P
Ool2O00ZOol2000>Ool00`00Oomoo`0<Ool2000=Ool2000lOol00`00Oomoo`01Ool000Aoo`04001o
ogoo000JOol2000=Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool2000=Ool3000@Ool3000<Ool30002
Ool2O009Ool2000=Ool3000;Ool4000<Ool3000<Ool4000;Ool4000=Ool3000<Ool3000=Ool3000<
Ool30002Ool000Aoo`04001oogoo000JOol2000=Ool2000?Ool2000=Ool3000<Ool5000:Ool60009
Ool60004Ool2O004Ool5000:Ool60009Ool6000:Ool60009Ool60009Ool70009Ool60009Ool6000:
Ool60009Ool60002Ool002=oo`8000eoo`<000eoo`@000aoo`@000aoo`<000]oo`@000eoo`<000Io
o`9l00Eoo`<000aoo`<000aoo`<000eoo`<000aoo`<000aoo`@000aoo`<000aoo`<000eoo`<000ao
o`<0009oo`008goo0`0037oo10003Goo0P003Woo0P003goo00<007ooOol02goo0P0067oo0W`0SWoo
00<007ooOol00Goo0005Ool2000LOol2000>Ool2000?Ool00`00Oomoo`0=Ool00`00Oomoo`0gOol2
O02<Ool00`00Oomoo`01Ool000Aoo`800003Ool007oo00Moo`8000Aoo`8000Eoo`<000=oo`03001o
ogoo06Yoo`9l08Yoo`03001oogoo005oo`0017oo0P0000=oo`00Ool01Woo00@007ooOol000]oo`03
001oogoo009oo`03001oogoo06aoo`9l08Qoo`03001oogoo005oo`001Goo00<007oo00001goo00@0
07ooOol000Qoo`D000=oo`8006moo`9l08Aoo`<000=oo`003goo00@007ooOol000Qoo`04001oogoo
0004Ool00`00Oomoo`1`Ool2O024Ool00`00Oomoo`01Ool000moo`04001oogoo0009Ool00`00Ool0
0004Ool00`00Oomoo`1bOol2O022Ool00`00Oomoo`01Ool000Eoo`8000Uoo`8000]oo`8000Aoo`03
001oogoo07Aoo`9l081oo`03001oogoo005oo`0017oo0P0000=oo`00Ool06Woo00<007ooOol0MWoo
0W`0OWoo00<007ooOol00Goo0004Ool200000goo001oo`0JOol00`00Oomoo`1hOol2O01lOol00`00
Oomoo`01Ool000Eoo`03001oo`0001]oo`03001oogoo07Yoo`9l07Yoo`03001oogoo005oo`008Woo
0P00OWoo00=l07ooOol0Mgoo00<007ooOol00Goo000ROol2000>Ool00`00Oomoo`0<Ool00`00Oomo
o`0<Ool00`00Oomoo`1=Ool300000g`0Oomoo`0;Ool00`00Oomoo`0<Ool2000=Ool2000>Ool00`00
Oomoo`0<Ool2000=Ool2000>Ool2000=Ool20002Ool000Eoo`8001]oo`8000ioo`03001oogoo00ao
o`8000eoo`<000eoo`03001oogoo00aoo`<000aoo`L000Uoo`H000Uoo`H00003Ooml07`000Uoo`<0
00aoo`@000]oo`@000aoo`<000aoo`@000]oo`@000aoo`@000]oo`@0009oo`0017oo00@007ooOol0
01Yoo`8000ioo`8000eoo`<000eoo`@000aoo`8000eoo`D000Yoo`H000Yoo`D000Yoo`D000=oo`03
O01oogoo00Aoo`H000Uoo`H000Uoo`H000Yoo`H000Uoo`H000Uoo`H000Yoo`H000Uoo`H0009oo`00
0Woo00<007oo00000Woo00<007ooOol067oo0`003Goo0P003Woo0`003Goo10002goo100037oo0`00
3Goo0`003Woo0P003Goo0P0017oo0W`01goo0`0037oo0`0037oo0`003Goo0`0037oo0`0037oo0`00
3Goo0`0037oo0`000Woo0002Ool6000JOol3000=Ool3000=Ool4000<Ool3000=Ool2000?Ool00`00
Oomoo`0=Ool00`00Oomoo`0SOol00g`0Oomoo`1`Ool00`00Oomoo`01Ool000Moo`03001oogoo01Uo
o`8000eoo`8000ioo`8000moo`03001oogoo00eoo`03001oogoo04Aoo`9l06moo`8000=oo`008goo
00<007ooOol0QWoo0W`0KWoo00<007ooOol00Goo000SOol00`00Oomoo`28Ool00g`0Oomoo`1[Ool0
0`00Oomoo`01Ool000Aoo`04001oogoo000KOol00`00Oomoo`29Ool2O01[Ool00`00Oomoo`01Ool0
009oo`03001oo`0000<001]oo`03001oogoo08]oo`03O01oogoo06Qoo`03001oogoo005oo`001goo
00<007ooOol06Goo00<007ooOol0S7oo0W`0J7oo00<007ooOol00Goo000SOol00`00Oomoo`2>Ool0
0g`0Oomoo`1UOol00`00Oomoo`01Ool000Aoo`04001oogoo000KOol00`00Oomoo`2?Ool00g`0Oomo
o`1TOol00`00Oomoo`01Ool000Aoo`@001]oo`03001oogoo091oo`9l06Aoo`03001oogoo005oo`00
17oo00<007ooOol077oo00<007ooOol0TWoo00=l07ooOol0HGoo00<007ooOol00Goo0004Ool00`00
Oomoo`0LOol00`00Oomoo`0<Ool00`00Oomoo`0<Ool00`00Oomoo`1eOol00g`0Oomoo`1POol00`00
Oomoo`01Ool000Eoo`<001]oo`03001oogoo00aoo`03001oogoo00aoo`8000ioo`03001oogoo00ao
o`03001oogoo00aoo`8000ioo`80021oo`<000aoo`<000Moo`9l00=oo`<000aoo`<000eoo`<000ao
o`<000aoo`<000eoo`<000aoo`<0009oo`001goo00<007ooOol067oo00<0000O00003Goo0P003Goo
0P003Woo0P003Goo0P003Woo0`003Goo0`002goo1P002Goo1`002Goo1P002Goo00=l000000000`00
2Goo1P002Woo1P002Goo1P002Goo1P002Woo1P002Goo1P000Woo000ROol2000201l;Ool3000=Ool3
000=Ool2000>Ool3000<Ool5000<Ool4000:Ool4000<Ool4000<Ool4000:Ool00g`0Ool00002000<
Ool3000=Ool3000<Ool3000<Ool3000=Ool3000<Ool30002Ool000Eoo`80009oo`03001oogoo01Eo
o`@00003Ool07`0O00Uoo`@000aoo`<000eoo`<000eoo`@000aoo`<000ioo`8000eoo`8000ioo`80
00ioo`8000]oo`03O01oogoo05]oo`03001oogoo005oo`0017oo00H007ooOol007oo000GOol40003
Ool201l7Ool4000<Ool4000<Ool4000=Ool2000>Ool00`00Oomoo`0>Ool00`00Oomoo`0iOol00g`0
Oomoo`1JOol00`00Oomoo`01Ool000Aoo`06001oogoo001oo`006Goo00<007ooOol017oo0P0O5Goo
0P003Woo0P003goo00<007ooOol0Fgoo0W`0FWoo00<007ooOol00Goo0004Ool5000JOol00`00Oomo
o`06Ool201nDOol00g`0Oomoo`1GOol00`00Oomoo`01Ool000Aoo`03001oogoo01aoo`03001oogoo
00Qoo`807i=oo`03O01oogoo05Ioo`03001oogoo005oo`008goo00<007ooOol02Woo0P0OTWoo00=l
07ooOol0EGoo00<007ooOol00Goo000SOol00`00Oomoo`0<Ool201nAOol2O01EOol00`00Oomoo`01
Ool002=oo`03001oogoo00ioo`807i5oo`03O01oogoo059oo`03001oogoo005oo`008goo00<007oo
Ool047oo100OSWoo00=l07ooOol0DGoo00<007ooOol00Goo000SOol00`00Oomoo`0DOol201n=Ool0
0g`0Oomoo`1@Ool00`00Oomoo`01Ool002=oo`03001oogoo01Ioo`807haoo`03O01oogoo04moo`03
001oogoo005oo`0017oo00<007ooOol00Woo00<007ooOol05goo0P003Woo00<007ooOol027oo0P0O
Rgoo00=l07ooOol0CGoo0P000goo0004Ool6000IOol00`00Oomoo`0=Ool00`00Oomoo`0:Ool201l0
0`00Oomoo`0<Ool00`00Oomoo`0<Ool00`00Oomoo`1YOol017`0Oomoogoo0P003Goo0P003Goo0P00
3Woo0P003Goo0P003Goo0P000Woo0004Ool01P00Oomoo`00Ool001Qoo`8000ioo`8000ioo`0301mo
ogoo00aoo`03001oogoo00aoo`8000ioo`03001oogoo00aoo`8000eoo`<000eoo`H000Uoo`H000ao
o`<000]oo`03O0000000008000]oo`@000]oo`@000aoo`@000]oo`@000]oo`@0009oo`0017oo00@0
07ooOol001Yoo`<000eoo`8000ioo`0300007`0O00aoo`8000eoo`8000ioo`8000ioo`<000aoo`D0
00]oo`D000Yoo`D000Uoo`H000Yoo`03001l000000<000Uoo`H000Uoo`H000Yoo`H000Uoo`H000Uo
o`H0009oo`001Goo0P006Woo100037oo0`003Goo0`0000=oo`0OOol02Goo0`003Woo0P003Goo0`00
3Goo1@002goo0`003Goo0`003Woo0P0037oo0`0037oo00Al0000000000aoo`<000aoo`<000eoo`<0
00aoo`<000aoo`<0009oo`008Goo100037oo0`003Goo0`000Woo0P0O27oo10003Goo0P003Woo0`00
3Goo0`003Woo00<007ooOol03Goo00<007ooOol0:Woo00=l07ooOol0BWoo00<007ooOol00Goo000S
Ool00`00Oomoo`0KOol30004Ool00`0OOomoo`05Ool4000=Ool3000=Ool2000?Ool00`00Oomoo`1;
Ool00g`0Oomoo`19Ool00`00Oomoo`01Ool000Aoo`04001oogoo000KOol00`00Oomoo`0SOol201n6
Ool00g`0Oomoo`18Ool00`00Oomoo`01Ool000Aoo`@001]oo`03001oogoo02Eoo`807hEoo`03O01o
ogoo04Moo`03001oogoo005oo`0017oo00@007ooOol001]oo`03001oogoo02Moo`807hAoo`03O01o
ogoo04Ioo`03001oogoo005oo`0017oo00@007ooOol000Qoo`8000Aoo`8000=oo`<000Eoo`03001o
ogoo02Uoo`0301moogoo089oo`03O01oogoo04Eoo`03001oogoo005oo`003goo00@007ooOol000Qo
o`04001oogoo0004Ool00`00Oomoo`0ZOol201n3Ool00g`0Oomoo`14Ool00`00Oomoo`01Ool000mo
o`04001oogoo0008Ool01000Oomoo`0017oo0P00;Goo0P0OPGoo00=l07ooOol0@Woo0`000goo0005
Ool20008Ool01000Oomoo`0027oo0`001Goo00<007ooOol0;Woo00<07gooOol0Ogoo00=l07ooOol0
@goo00<007ooOol00Goo0004Ool01000Oomoo`001goo00@007ooOol000Uoo`03001oogoo00Aoo`03
001oogoo02moo`807h1oo`03O01oogoo049oo`03001oogoo005oo`0017oo00@007ooOol000Qoo`80
00Yoo`<000Aoo`80039oo`0301moogoo07ioo`03O01oogoo045oo`03001oogoo005oo`001Goo0P00
77oo0P003Woo00<007ooOol037oo00<007ooOol03Goo00<007ooOol00goo0P0OOWoo00=l07ooOol0
@Goo00<007ooOol00Goo000SOol2000=Ool2000>Ool00`00Oomoo`0<Ool20007Ool201l5Ool00`00
Oomoo`0<Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0^Ool3000<Ool30007Ool00g`0
Oomoo`02Ool3000<Ool3000=Ool3000<Ool3000<Ool30002Ool0009oo`03001oogoo009oo`03001o
ogoo01Qoo`8000eoo`<000eoo`8000ioo`8000Uoo`0301moogoo009oo`03001oogoo00aoo`8000eo
o`8000moo`03001oogoo00]oo`H000Uoo`H000Yoo`H000Uoo`H000Qoo`03O000000000@000Uoo`H0
00Yoo`H000Uoo`H000Uoo`H0009oo`000Woo1P006Woo0P003Goo0`003Goo0P003Woo0P002Woo00D0
7gooOomoo`0000ioo`8000ioo`8000ioo`<000aoo`D000]oo`@000]oo`@000aoo`@000Uoo`03O01o
ogoo00<000aoo`<000eoo`<000aoo`<000aoo`<0009oo`0017oo00@007ooOol001Uoo`<000aoo`@0
00aoo`<000eoo`<000]oo`807`<000eoo`<000eoo`<000ioo`<000aoo`<000ioo`8000eoo`8000io
o`8000Uoo`03O01oogoo03ioo`03001oogoo005oo`0017oo00@007ooOol001]oo`03001oogoo00ao
o`8000aoo`<000eoo`<000eoo`0301l0000000eoo`@000eoo`<000eoo`8000moo`03001oogoo03Mo
o`03O01oogoo03eoo`03001oogoo005oo`001Goo0P0077oo00<007ooOol0>Woo00<0000O00003Goo
0P003goo0P003goo00<007ooOol0B7oo00=l07ooOol0?7oo00<007ooOol00Goo000SOol00`00Oomo
o`0lOol00`0OOomoo`1iOol00g`0Oomoo`0kOol00`00Oomoo`01Ool002=oo`8003ioo`807gUoo`03
O01oogoo03Yoo`8000=oo`008goo00<007ooOol0?goo00<07gooOol0Mgoo00=l07ooOol0>Woo00<0
07ooOol00Goo0007Ool00`00Oomoo`0IOol00`00Oomoo`10Ool00`0OOomoo`1gOol00g`0Oomoo`0i
Ool00`00Oomoo`01Ool000Moo`03001oogoo01Uoo`03001oogoo045oo`807gQoo`03O01oogoo03Qo
o`03001oogoo005oo`008goo00<007ooOol0@goo00<07gooOol0MGoo00=l07ooOol0>7oo00<007oo
Ool00Goo000SOol00`00Oomoo`14Ool00`0OOomoo`1eOol00g`0Oomoo`0gOol00`00Oomoo`01Ool0
02=oo`03001oogoo04Eoo`0301moogoo07Eoo`03O01oogoo03Ioo`03001oogoo005oo`008goo0P00
3Woo00<007ooOol03Goo00<007ooOol09Woo0P0OMGoo00=l07ooOol0=Woo00<007ooOol00Goo000S
Ool2000=Ool2000>Ool2000>Ool00`00Oomoo`0<Ool00`00Oomoo`0:Ool00`0OOol0001cOol00g`0
Oomoo`08Ool2000=Ool2000=Ool2000=Ool00`00Oomoo`01Ool0029oo`<000aoo`<000ioo`8000eo
o`8000ioo`03001oogoo00]oo`0301l007oo00ioo`03001oogoo00aoo`03001oogoo00aoo`8000io
o`<000aoo`H000aoo`<000aoo`<000Aoo`03O01oogoo00Eoo`@000]oo`@000]oo`@000aoo`<0009o
o`008Woo0P003Goo0`003Goo0P003Goo0`003Goo0P003Woo0P0O3Woo00<007ooOol037oo0P003Woo
0`003Goo1@002Woo1@002Goo1P002Goo1P001Goo00=l07ooOol00Woo1P002Goo1P002Goo1P002Goo
1P000Woo000QOol3000<Ool4000=Ool2000=Ool3000=Ool2000=Ool300000`0OOomoo`0;Ool2000>
Ool3000=Ool4000<Ool3000<Ool3000=Ool3000<Ool30005Ool00g`0Oomoo`05Ool3000<Ool3000<
Ool3000<Ool30002Ool0029oo`8000ioo`8000aoo`<000aoo`@000aoo`<000eoo`@0000301moogoo
00Yoo`8000ioo`@000eoo`8000moo`03001oogoo00aoo`03001oogoo02=oo`03O01oogoo039oo`03
001oogoo005oo`008goo0P00;7oo0P0037oo0`003Goo100000=oo`0O01l02Woo0`003Woo0P003goo
00<007ooOol0@goo00=l07ooOol0<7oo0P000goo000SOol00`00Oomoo`1@Ool00`0OOomoo`07Ool2
000?Ool00`00Oomoo`1DOol00g`0Oomoo`0aOol00`00Oomoo`01Ool002=oo`03001oogoo051oo`03
01moogoo071oo`03O01oogoo031oo`03001oogoo005oo`008goo00<007ooOol0DGoo00<07gooOol0
L7oo00=l07ooOol0;goo00<007ooOol00Goo000SOol00`00Oomoo`1BOol00`0OOomoo`1_Ool00g`0
Oomoo`0_Ool00`00Oomoo`01Ool002=oo`03001oogoo05=oo`0301moogoo06moo`03O01oogoo02io
o`03001oogoo005oo`008goo00<007ooOol0E7oo00<07gooOol0KWoo00=l07ooOol0;Woo00<007oo
Ool00Goo000SOol00`00Oomoo`1EOol201m_Ool00g`0Oomoo`0]Ool00`00Oomoo`01Ool002=oo`03
001oogoo05Moo`0301moogoo06eoo`03O01oogoo02aoo`03001oogoo005oo`008goo00<007oo0000
3Woo00<007ooOol0Agoo00<07gooOol0K7oo00=l07ooOol0;7oo00<007ooOol00Goo000SOol3000=
Ool2000>Ool00`00Oomoo`0<Ool00`00Oomoo`0ZOol00`0OOomoo`1/Ool00g`0Oomoo`0[Ool00`00
Oomoo`01Ool002=oo`8000eoo`<000eoo`8000eoo`8000moo`03001oogoo00aoo`03001oogoo00ao
o`0301moogoo00aoo`03001oogoo03eoo`<000aoo`<000eoo`03O000000000aoo`<000aoo`<000ao
o`<0009oo`008Woo0`0037oo0`003Goo0`0037oo0`003Woo0P003Goo0P003Woo00<0000OOol037oo
0P003Woo00<007ooOol037oo0`0037oo1P002Goo1P002Goo1P002Woo100000=l0000Ool027oo1P00
2Goo1P002Goo1P000Woo000QOol3000<Ool4000=Ool2000=Ool2000>Ool3000<Ool3000>Ool00`00
Ool07`0<Ool2000>Ool2000>Ool5000:Ool4000<Ool4000;Ool4000<Ool200000g`0001oo`0:Ool4
000;Ool4000;Ool40002Ool0029oo`8000ioo`8000aoo`<000aoo`<000ioo`8000eoo`<000eoo`<0
0003Ool07goo00Yoo`<000ioo`<000eoo`<000eoo`8000ioo`8000eoo`8000ioo`03001l07oo00ao
o`8000eoo`8000eoo`80009oo`008goo00<007ooOol06goo0P003Goo0P003Goo0`0037oo10003Goo
0`000Woo00<07gooOol02Goo0P003Woo10003Goo00<007ooOol0?7oo00=l07ooOol0:Goo00<007oo
Ool00Goo000SOol00`00Oomoo`0jOol2000>Ool2000=Ool30003Ool00`0OOomoo`08Ool3000>Ool2
001>Ool00g`0Oomoo`0XOol00`00Oomoo`01Ool002=oo`03001oogoo061oo`0301moogoo00Moo`80
05moo`03O01oogoo02Qoo`03001oogoo005oo`008goo00<007ooOol0HGoo00<07gooOol0J7oo00=l
07ooOol09goo00<007ooOol00Goo000SOol00`00Oomoo`1ROol00`0OOomoo`1WOol00g`0Oomoo`0W
Ool00`00Oomoo`01Ool002=oo`03001oogoo06=oo`0301moogoo06Ioo`03O01oogoo02Moo`03001o
ogoo005oo`008goo00<007ooOol0I7oo00<07gooOol0IWoo00=l07ooOol09Woo00<007ooOol00Goo
000SOol00`00Oomoo`1TOol00`0OOomoo`1VOol00g`0Oomoo`0VOol00`00Oomoo`01Ool0011oo`80
00Aoo`8000Aoo`8000Eoo`03001oogoo06Eoo`0301moogoo06Eoo`03O01oogoo02Ioo`03001oogoo
005oo`003goo00@007ooOol000Qoo`04001oogoo0004Ool00`00Ool0001VOol00`0OOomoo`1TOol0
0g`0Oomoo`0VOol00`00Oomoo`01Ool000moo`04001oogoo0008Ool01000Oomoo`0017oo0`003Woo
00<007ooOol03Goo00<007ooOol0AWoo00<07gooOol0I7oo00=l07ooOol08goo0`000goo000?Ool0
1000Oomoo`002Goo0P001Goo0P003Woo0P003Woo0P003Woo00<007ooOol037oo00<007ooOol037oo
00<007ooOol06Woo00<07gooOol0Hgoo00=l07ooOol09Goo00<007ooOol00Goo000?Ool01000Oomo
o`0027oo00@007ooOol000=oo`<000eoo`<000eoo`8000ioo`8000eoo`8000eoo`8000ioo`03001o
ogoo00aoo`0301l007oo00eoo`03001oogoo00aoo`8000eoo`<000moo`<000eoo`<000aoo`<000Ao
o`03O01oogoo00Eoo`<000aoo`<000aoo`<0009oo`0047oo0P002Woo0P000goo0`003Goo0`003Goo
0`0037oo0`003Goo0`0037oo0`003Goo0P003Woo00<07`00Ool03Goo0P003Woo0`0037oo1@002Goo
1P002Woo1@002Woo1P0017oo00=l07ooOol00Woo1P002Goo1P002Goo1P000Woo000ROol2000>Ool2
000<Ool3000<Ool4000<Ool3000=Ool2000>Ool2000>Ool00`0001moo`0=Ool2000>Ool5000;Ool3
000<Ool4000<Ool3000=Ool30005Ool00g`0Oomoo`04Ool3000<Ool3000<Ool30002Ool002=oo`03
001oogoo00eoo`03001oogoo00]oo`8000eoo`8000aoo`@000aoo`<000eoo`<000ioo`80000301mo
ogoo00aoo`8000ioo`<000ioo`03001oogoo00aoo`8002Aoo`03O01oogoo02=oo`03001oogoo005o
o`008goo00<007ooOol0:goo00<007ooOol037oo0P003Goo0P003Goo0`003Goo100000<07gooOol0
2goo0`003Woo00<007ooOol0@goo00=l07ooOol08Woo00<007ooOol00Goo000SOol00`00Oomoo`1I
Ool2000=Ool400000goo01moo`0;Ool2001EOol00g`0Oomoo`0ROol00`00Oomoo`01Ool002=oo`03
001oogoo06ioo`807f9oo`03O01oogoo025oo`03001oogoo005oo`008goo00<007ooOol0L7oo00<0
7gooOol0Ggoo00=l07ooOol08Goo00<007ooOol00Goo000SOol00`00Oomoo`1aOol00`0OOomoo`1O
Ool00g`0Oomoo`0POol00`00Oomoo`01Ool002=oo`03001oogoo075oo`0301moogoo05moo`03O01o
ogoo021oo`03001oogoo005oo`008goo0P00Lgoo00<07gooOol0Ggoo00=l07ooOol07Woo0P000goo
000SOol00`00Oomoo`1cOol00`0OOomoo`1NOol00g`0Oomoo`0OOol00`00Oomoo`01Ool002=oo`03
001oogoo07Aoo`0301moogoo05ioo`03O01oogoo01ioo`03001oogoo005oo`008goo00@007ooOol0
00ioo`03001oogoo06=oo`0301moogoo05eoo`03O01oogoo01ioo`03001oogoo005oo`008goo0`00
3Woo0P003Woo00<007ooOol037oo00<007ooOol037oo00<007ooOol0=Woo00<07gooOol0GWoo00=l
07ooOol07Goo00<007ooOol00Goo000ROol3000=Ool3000>Ool00`00Oomoo`0<Ool2000=Ool2000?
Ool00`00Oomoo`0<Ool00`00Oomoo`0<Ool00`00Oomoo`09Ool00`0OOomoo`10Ool3000<Ool3000;
Ool017`00000000037oo0`003Goo0P000Woo000QOol4000<Ool4000<Ool3000<Ool3000=Ool2000>
Ool3000=Ool2000=Ool2000<Ool00`0OOol0000>Ool2000=Ool3000=Ool60009Ool60009Ool60009
Ool300000g`000000009Ool6000:Ool50002Ool0029oo`8000ioo`8000aoo`<000aoo`@000aoo`<0
00eoo`<000eoo`<000eoo`8000aoo`0301moo`0000ioo`8000ioo`D000]oo`@000aoo`@000]oo`@0
00]oo`04001l0000000;Ool4000;Ool40002Ool002=oo`03001oogoo00eoo`03001oogoo00]oo`80
00eoo`8000aoo`<000eoo`@000aoo`<000eoo`<000eoo`0301l0000000ioo`<000eoo`<000ioo`80
00ioo`8000eoo`8000eoo`03O00007oo00aoo`8000eoo`80009oo`008goo00<007ooOol0:goo00<0
07ooOol02goo0P003Woo0P0037oo10003Goo0`003Goo00<07`0000003Woo10003Woo00<007ooOol0
>Woo00=l07ooOol06goo00<007ooOol00Goo000SOol00`00Oomoo`1:Ool00`00Oomoo`0<Ool2000<
Ool4000=Ool0100001l000003Woo0P00C7oo00=l07ooOol06goo00<007ooOol00Goo000SOol00`00
Oomoo`1YOol2000=Ool200000`0OOomoo`0=Ool00`00Oomoo`1<Ool00g`0Oomoo`0JOol00`00Oomo
o`01Ool002=oo`03001oogoo07Yoo`0301moogoo05aoo`03O01oogoo01Yoo`03001oogoo005oo`00
8goo0P00O7oo00<07gooOol0G7oo00=l07ooOol067oo0P000goo000SOol00`00Oomoo`1lOol00`0O
Oomoo`1KOol00g`0Oomoo`0IOol00`00Oomoo`01Ool002=oo`03001oogoo07eoo`0301moogoo05Yo
o`03O01oogoo01Uoo`03001oogoo005oo`008goo00<007ooOol0OGoo00<07gooOol0Fgoo00=l07oo
Ool067oo00<007ooOol00Goo000SOol00`00Oomoo`1nOol00`0OOomoo`1JOol00g`0Oomoo`0HOol0
0`00Oomoo`01Ool002=oo`04001oogoo001nOol00`0OOomoo`1IOol00g`0Oomoo`0HOol00`00Oomo
o`01Ool002=oo`04001oo`00000>Ool00`00Oomoo`0<Ool00`00Oomoo`1NOol00`0OOomoo`1JOol0
0g`0Oomoo`0GOol00`00Oomoo`01Ool002=oo`<000ioo`03001oogoo00aoo`8000ioo`8000ioo`03
001oogoo00aoo`03001oogoo035oo`0301moogoo05Uoo`03O01oogoo01Moo`03001oogoo005oo`00
8Woo100037oo0`0037oo0`003Goo0`003Goo0P003Woo0P003Woo00<007ooOol037oo00<007ooOol0
37oo00<007ooOol017oo00<07gooOol01Goo00<007ooOol03Goo00<007ooOol07Woo0`0037oo0`00
37oo0`000goo00=l07ooOol01Woo0`003Goo0`000Goo000SOol2000<Ool3000<Ool4000;Ool4000<
Ool3000=Ool3000>Ool00`00Oomoo`0<Ool2000>Ool00`00Oomoo`05Ool00`0OOomoo`04Ool2000>
Ool2000=Ool60009Ool60009Ool60009Ool60003Ool00g`0Oomoo`03Ool6000:Ool60001Ool002=o
o`8000eoo`8000eoo`8000eoo`<000]oo`@000aoo`@000aoo`<000eoo`<000eoo`8000Qoo`0301mo
ogoo00=oo`8000moo`<000aoo`@000aoo`@000aoo`<000aoo`<000=oo`03O01oogoo00Ioo`<000eo
o`<0005oo`008goo00<007ooOol077oo00<007ooOol037oo00<007ooOol02goo0P003Woo0P0037oo
0`003Woo0P003Woo0P0027oo00<07gooOol017oo0P003goo0`003Goo0P003Woo0P008Woo00=l07oo
Ool05Goo00<007ooOol00Goo000SOol2001;Ool00`00Oomoo`0;Ool2000=Ool3000=Ool30009Ool0
0`0OOomoo`03Ool2000?Ool20012Ool00g`0Oomoo`0DOol20003Ool002=oo`03001oogoo06Qoo`80
00eoo`<000Yoo`0301moogoo009oo`<000moo`03001oogoo045oo`03O01oogoo01Aoo`03001oogoo
005oo`008goo00<007ooOol0QGoo00<07gooOol0Egoo00=l07ooOol057oo00<007ooOol00Goo000S
Ool00`00Oomoo`26Ool00`0OOomoo`1FOol00g`0Oomoo`0DOol00`00Oomoo`01Ool002=oo`03001o
ogoo08Ioo`0301moogoo05Moo`03O01oogoo01=oo`03001oogoo005oo`008goo00<007ooOol0Qgoo
00<07gooOol0EWoo00=l07ooOol04goo00<007ooOol00Goo000SOol00`00Oomoo`27Ool00`0OOomo
o`1GOol00g`0Oomoo`0BOol00`00Oomoo`01Ool002=oo`03001oogoo08Qoo`0301moogoo05Ioo`03
O01oogoo019oo`03001oogoo005oo`008goo00<007ooOol0RGoo00<07gooOol0EGoo00=l07ooOol0
4Woo00<007ooOol00Goo000SOol00`00Oomoo`02000>Ool00`00Oomoo`1fOol00`0OOomoo`1EOol0
0g`0Oomoo`0BOol00`00Oomoo`01Ool001]oo`D000=oo`@000eoo`8000ioo`8000ioo`03001oogoo
00aoo`03001oogoo04Yoo`0301moogoo05Eoo`03O01oogoo015oo`03001oogoo005oo`007Goo00<0
07ooOol00Woo100037oo100037oo0`003Goo0`003Goo00<007ooOol03Goo00<007ooOol037oo00<0
07ooOol00Woo00<007ooOol01goo00<007ooOol07Goo00<07gooOol01Goo00<007ooOol0;goo00@0
07ooOomoo`<000aoo`<000Qoo`03O01oogoo009oo`8000eoo`<0005oo`007Goo00<007ooOol00goo
SP0000<07`000000E00000=l0000000050000Goo000MOol00`00Oomoo`04Ool00`00Oomoo`0;Ool3
000<Ool3000;Ool4000<Ool3000<Ool4000<Ool3000=Ool2000?Ool2000>Ool00`00Oomoo`0<Ool2
000>Ool5000;Ool4000;Ool4000;Ool4000;Ool4000<Ool40001Ool001eoo`03001oogoo01=oo`03
001oogoo00aoo`03001oogoo00]oo`8000eoo`<000eoo`8000aoo`@000aoo`<000eoo`<000ioo`80
00moo`<000eoo`<000ioo`8000eoo`8000eoo`8000eoo`8000ioo`80005oo`0077oo0P00@Woo00<0
07ooOol03Goo00<007ooOol02goo0P0037oo0`003Goo10003Woo0P003goo10003Woo00<007ooOol0
C7oo001oOol00`00Oomoo`0;Ool2000>Ool2000>Ool3000@Ool2001NOol009ioo`03001oogoo00ao
o`<0011oo`03001oogoo05eoo`00ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo0000\
\>"],
  ImageRangeCache->{{{0, 287}, {287, 0}} -> {-0.141609, -0.11738, 0.00401977, \
0.00401977}}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
Case 2 : c < 1-r 
(r=0.5, c=0.2)\
\>", "Subsubsection",
  FontSize->17],

Cell[BoxData[
    \(rex = 0.5; cex = 0.2;\)], "Input"],

Cell[BoxData[
    \(\(fieldplot = 
        PlotVectorField[{dWd\[Pi][rex, cex, z, p], \ 
            dWdb[rex, cex, z, p]}, \n\ \ \ \ \ \ \ \ \ \ \ \ \ {p, \ 0, \ 
            1}, \ {z, \ 0, \ 1}, PlotPoints -> 17];\)\)], "Input"],

Cell[BoxData[
    \(\(equillines = 
        ImplicitPlot[{dWd\[Pi][rex, cex, z, p] \[Equal] 0, \ 
            dWdb[rex, cex, z, p] \[Equal] 0}, {p, 0, 1}, {z, 0, 1}, 
          PlotStyle \[Rule] {RGBColor[0, 0, 1], RGBColor[1, 0, 0]}, 
          DisplayFunction \[Rule] Identity];\)\)], "Input"],

Cell[BoxData[
    \(\(\(ESS = 
        Graphics[{\[IndentingNewLine]{RGBColor[0, 0, 1], 
              Disk[{1, 1}, 0.02]}, \[IndentingNewLine]{RGBColor[0, 0, 1], 
              Text["\<ESS\>", {0.95, 
                  0.96}]}, \[IndentingNewLine]}];\)\(\ \ \ \ \ \)\)\)], \
"Input"],

Cell["With c < 1-r, the system tends to the all-policing optimum :", "Text",
  FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
    \(Show[{fieldplot, equillines, ESS}, AspectRatio -> 1, Frame -> True, 
      PlotRange -> {{0, 1}, {0, 1}}, 
      FrameLabel -> {"\<Policing\>", "\<Breeding prob.\>"}]\)], "Input"],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: 1 
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10  scalefont  setfont
% Scaling calculations
0 1 0 1 [
[.2 -0.0125 -9 -9 ]
[.2 -0.0125 9 0 ]
[.4 -0.0125 -9 -9 ]
[.4 -0.0125 9 0 ]
[.6 -0.0125 -9 -9 ]
[.6 -0.0125 9 0 ]
[.8 -0.0125 -9 -9 ]
[.8 -0.0125 9 0 ]
[1 -0.0125 -3 -9 ]
[1 -0.0125 3 0 ]
[ 0 0 -0.125 0 ]
[.5 -0.0125 -26 -21.5625 ]
[.5 -0.0125 26 -9 ]
[-0.0125 .2 -18 -4.5 ]
[-0.0125 .2 0 4.5 ]
[-0.0125 .4 -18 -4.5 ]
[-0.0125 .4 0 4.5 ]
[-0.0125 .6 -18 -4.5 ]
[-0.0125 .6 0 4.5 ]
[-0.0125 .8 -18 -4.5 ]
[-0.0125 .8 0 4.5 ]
[-0.0125 1 -6 -4.5 ]
[-0.0125 1 0 4.5 ]
[ 0 0 -0.125 0 ]
[-0.01875 .5 -30.5625 -44 ]
[-0.01875 .5 -18 44 ]
[ 0 1 .125 0 ]
[ 1 0 .125 0 ]
[ 0 0 0 0 ]
[ 1 1 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.2 0 m
.2 .00625 L
s
[(0.2)] .2 -0.0125 0 1 Mshowa
.4 0 m
.4 .00625 L
s
[(0.4)] .4 -0.0125 0 1 Mshowa
.6 0 m
.6 .00625 L
s
[(0.6)] .6 -0.0125 0 1 Mshowa
.8 0 m
.8 .00625 L
s
[(0.8)] .8 -0.0125 0 1 Mshowa
1 0 m
1 .00625 L
s
[(1)] 1 -0.0125 0 1 Mshowa
.125 Mabswid
.05 0 m
.05 .00375 L
s
.1 0 m
.1 .00375 L
s
.15 0 m
.15 .00375 L
s
.25 0 m
.25 .00375 L
s
.3 0 m
.3 .00375 L
s
.35 0 m
.35 .00375 L
s
.45 0 m
.45 .00375 L
s
.5 0 m
.5 .00375 L
s
.55 0 m
.55 .00375 L
s
.65 0 m
.65 .00375 L
s
.7 0 m
.7 .00375 L
s
.75 0 m
.75 .00375 L
s
.85 0 m
.85 .00375 L
s
.9 0 m
.9 .00375 L
s
.95 0 m
.95 .00375 L
s
.25 Mabswid
0 0 m
1 0 L
s
gsave
.5 -0.0125 -87 -25.5625 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 20.5625 translate 1 -1 scale
63.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(Policing) show
111.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 .2 m
.00625 .2 L
s
[(0.2)] -0.0125 .2 1 0 Mshowa
0 .4 m
.00625 .4 L
s
[(0.4)] -0.0125 .4 1 0 Mshowa
0 .6 m
.00625 .6 L
s
[(0.6)] -0.0125 .6 1 0 Mshowa
0 .8 m
.00625 .8 L
s
[(0.8)] -0.0125 .8 1 0 Mshowa
0 1 m
.00625 1 L
s
[(1)] -0.0125 1 1 0 Mshowa
.125 Mabswid
0 .05 m
.00375 .05 L
s
0 .1 m
.00375 .1 L
s
0 .15 m
.00375 .15 L
s
0 .25 m
.00375 .25 L
s
0 .3 m
.00375 .3 L
s
0 .35 m
.00375 .35 L
s
0 .45 m
.00375 .45 L
s
0 .5 m
.00375 .5 L
s
0 .55 m
.00375 .55 L
s
0 .65 m
.00375 .65 L
s
0 .7 m
.00375 .7 L
s
0 .75 m
.00375 .75 L
s
0 .85 m
.00375 .85 L
s
0 .9 m
.00375 .9 L
s
0 .95 m
.00375 .95 L
s
.25 Mabswid
0 0 m
0 1 L
s
gsave
-0.01875 .5 -129.281 -10.2813 Mabsadd m
1 1 Mabs scale
currentpoint translate
105 10.2813 translate
90 rotate
-105 -10.2813 translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 20.5625 translate 1 -1 scale
63.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(Breeding) show
117.000 12.813 moveto
(prob) show
141.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(.) show
147.000 12.813 moveto
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 .99375 m
0 1 L
s
.2 .99375 m
.2 1 L
s
.4 .99375 m
.4 1 L
s
.6 .99375 m
.6 1 L
s
.8 .99375 m
.8 1 L
s
.125 Mabswid
.05 .99625 m
.05 1 L
s
.1 .99625 m
.1 1 L
s
.15 .99625 m
.15 1 L
s
.25 .99625 m
.25 1 L
s
.3 .99625 m
.3 1 L
s
.35 .99625 m
.35 1 L
s
.45 .99625 m
.45 1 L
s
.5 .99625 m
.5 1 L
s
.55 .99625 m
.55 1 L
s
.65 .99625 m
.65 1 L
s
.7 .99625 m
.7 1 L
s
.75 .99625 m
.75 1 L
s
.85 .99625 m
.85 1 L
s
.9 .99625 m
.9 1 L
s
.95 .99625 m
.95 1 L
s
.25 Mabswid
0 1 m
1 1 L
s
.99375 0 m
1 0 L
s
.99375 .2 m
1 .2 L
s
.99375 .4 m
1 .4 L
s
.99375 .6 m
1 .6 L
s
.99375 .8 m
1 .8 L
s
.125 Mabswid
.99625 .05 m
1 .05 L
s
.99625 .1 m
1 .1 L
s
.99625 .15 m
1 .15 L
s
.99625 .25 m
1 .25 L
s
.99625 .3 m
1 .3 L
s
.99625 .35 m
1 .35 L
s
.99625 .45 m
1 .45 L
s
.99625 .5 m
1 .5 L
s
.99625 .55 m
1 .55 L
s
.99625 .65 m
1 .65 L
s
.99625 .7 m
1 .7 L
s
.99625 .75 m
1 .75 L
s
.99625 .85 m
1 .85 L
s
.99625 .9 m
1 .9 L
s
.99625 .95 m
1 .95 L
s
.25 Mabswid
1 0 m
1 1 L
s
0 0 m
1 0 L
1 1 L
0 1 L
closepath
clip
newpath
% Start of user PostScript
/mathtops {
gsave
MBeginOrig
moveto
MEndOrig
currentpoint
grestore
} bind def
/MAtocoords {
mathtops 4 2 roll mathtops
4 copy pop pop
3 -1 roll sub
/arry exch def
exch sub
/arrx exch def
arrx dup mul
arry dup mul
add sqrt
/arrl exch def
translate
} bind def
/MAarrowhead1 {
gsave
MAtocoords
arrl 0. eq
{ 0 0 Mdot }
{
[ arrx arrl div
arry arrl div
-1 arry mul arrl div
arrx arrl div
0 0 ]
concat
-0.02 0.005 moveto 0 0 lineto
-0.02 -0.005 lineto fill
-0.02 0.005 moveto 0 0 lineto
-0.02 -0.005 lineto
-0.02 0.005 lineto stroke
} ifelse
grestore
} def
/MAarrowzero1 {
gsave
mathtops translate
0 0 Mdot
grestore
} def
% End of user PostScript
.0001 w
0 .0625 m
0 0 rlineto s
% Start of user PostScript
0 0.0625 -0.00139474 0.124984 MAarrowhead1
% End of user PostScript
0 .125 m
0 0 rlineto s
% Start of user PostScript
0 0.125 -0.00100421 0.151779 MAarrowhead1
% End of user PostScript
0 .1875 m
0 0 rlineto s
% Start of user PostScript
0 0.1875 -0.000613686 0.202377 MAarrowhead1
% End of user PostScript
0 .25 m
0 0 rlineto s
% Start of user PostScript
0 0.25 -0.000223159 0.258926 MAarrowhead1
% End of user PostScript
0 .3125 m
.00017 .31786 L
s
% Start of user PostScript
0 0.3125 0.000167369 0.317856 MAarrowhead1
% End of user PostScript
0 .375 m
.00056 .37798 L
s
% Start of user PostScript
0 0.375 0.000557897 0.377975 MAarrowhead1
% End of user PostScript
0 .4375 m
.00095 .43878 L
s
% Start of user PostScript
0 0.4375 0.000948424 0.438775 MAarrowhead1
% End of user PostScript
0 .5 m
.00134 .5 L
s
% Start of user PostScript
0 0.5 0.00133895 0.5 MAarrowhead1
% End of user PostScript
0 .5625 m
.00173 .56151 L
s
% Start of user PostScript
0 0.5625 0.00172948 0.561508 MAarrowhead1
% End of user PostScript
0 .625 m
.00212 .62321 L
s
% Start of user PostScript
0 0.625 0.00212001 0.623215 MAarrowhead1
% End of user PostScript
0 .6875 m
.00251 .68507 L
s
% Start of user PostScript
0 0.6875 0.00251054 0.685066 MAarrowhead1
% End of user PostScript
0 .75 m
.0029 .74702 L
s
% Start of user PostScript
0 0.75 0.00290106 0.747025 MAarrowhead1
% End of user PostScript
0 .8125 m
.00329 .80907 L
s
% Start of user PostScript
0 0.8125 0.00329159 0.809067 MAarrowhead1
% End of user PostScript
0 .875 m
.00368 .87117 L
s
% Start of user PostScript
0 0.875 0.00368212 0.871174 MAarrowhead1
% End of user PostScript
0 .9375 m
.00407 .93333 L
s
% Start of user PostScript
0 0.9375 0.00407265 0.933334 MAarrowhead1
% End of user PostScript
0 1 m
.00446 .99554 L
s
% Start of user PostScript
0 1. 0.00446317 0.995537 MAarrowhead1
% End of user PostScript
.0625 .0625 m
.06109 .12139 L
s
% Start of user PostScript
0.0625 0.0625 0.0610948 0.121393 MAarrowhead1
% End of user PostScript
.0625 .125 m
.06147 .15042 L
s
% Start of user PostScript
0.0625 0.125 0.0614749 0.150419 MAarrowhead1
% End of user PostScript
.0625 .1875 m
.06185 .20176 L
s
% Start of user PostScript
0.0625 0.1875 0.0618549 0.201761 MAarrowhead1
% End of user PostScript
.0625 .25 m
.06223 .25868 L
s
% Start of user PostScript
0.0625 0.25 0.062235 0.258682 MAarrowhead1
% End of user PostScript
.0625 .3125 m
.06262 .31783 L
s
% Start of user PostScript
0.0625 0.3125 0.0626151 0.317835 MAarrowhead1
% End of user PostScript
.0625 .375 m
.063 .3781 L
s
% Start of user PostScript
0.0625 0.375 0.0629951 0.378103 MAarrowhead1
% End of user PostScript
.0625 .4375 m
.06338 .43901 L
s
% Start of user PostScript
0.0625 0.4375 0.0633752 0.439009 MAarrowhead1
% End of user PostScript
.0625 .5 m
.06376 .50031 L
s
% Start of user PostScript
0.0625 0.5 0.0637553 0.500314 MAarrowhead1
% End of user PostScript
.0625 .5625 m
.06414 .56188 L
s
% Start of user PostScript
0.0625 0.5625 0.0641353 0.561884 MAarrowhead1
% End of user PostScript
.0625 .625 m
.06452 .62364 L
s
% Start of user PostScript
0.0625 0.625 0.0645154 0.62364 MAarrowhead1
% End of user PostScript
.0625 .6875 m
.0649 .68553 L
s
% Start of user PostScript
0.0625 0.6875 0.0648955 0.685532 MAarrowhead1
% End of user PostScript
.0625 .75 m
.06528 .74752 L
s
% Start of user PostScript
0.0625 0.75 0.0652755 0.747524 MAarrowhead1
% End of user PostScript
.0625 .8125 m
.06566 .8096 L
s
% Start of user PostScript
0.0625 0.8125 0.0656556 0.809595 MAarrowhead1
% End of user PostScript
.0625 .875 m
.06604 .87173 L
s
% Start of user PostScript
0.0625 0.875 0.0660357 0.871727 MAarrowhead1
% End of user PostScript
.0625 .9375 m
.06642 .93391 L
s
% Start of user PostScript
0.0625 0.9375 0.0664157 0.933909 MAarrowhead1
% End of user PostScript
.0625 1 m
.0668 .99613 L
s
% Start of user PostScript
0.0625 1. 0.0667958 0.99613 MAarrowhead1
% End of user PostScript
.125 .0625 m
.12358 .11776 L
s
% Start of user PostScript
0.125 0.0625 0.123584 0.11776 MAarrowhead1
% End of user PostScript
.125 .125 m
.12395 .14902 L
s
% Start of user PostScript
0.125 0.125 0.123954 0.149017 MAarrowhead1
% End of user PostScript
.125 .1875 m
.12432 .2011 L
s
% Start of user PostScript
0.125 0.1875 0.124324 0.201103 MAarrowhead1
% End of user PostScript
.125 .25 m
.12469 .2584 L
s
% Start of user PostScript
0.125 0.25 0.124693 0.258396 MAarrowhead1
% End of user PostScript
.125 .3125 m
.12506 .31777 L
s
% Start of user PostScript
0.125 0.3125 0.125063 0.317772 MAarrowhead1
% End of user PostScript
.125 .375 m
.12543 .37819 L
s
% Start of user PostScript
0.125 0.375 0.125432 0.378189 MAarrowhead1
% End of user PostScript
.125 .4375 m
.1258 .4392 L
s
% Start of user PostScript
0.125 0.4375 0.125802 0.439202 MAarrowhead1
% End of user PostScript
.125 .5 m
.12617 .50059 L
s
% Start of user PostScript
0.125 0.5 0.126172 0.500586 MAarrowhead1
% End of user PostScript
.125 .5625 m
.12654 .56222 L
s
% Start of user PostScript
0.125 0.5625 0.126541 0.562218 MAarrowhead1
% End of user PostScript
.125 .625 m
.12691 .62402 L
s
% Start of user PostScript
0.125 0.625 0.126911 0.624024 MAarrowhead1
% End of user PostScript
.125 .6875 m
.12728 .68596 L
s
% Start of user PostScript
0.125 0.6875 0.12728 0.685956 MAarrowhead1
% End of user PostScript
.125 .75 m
.12765 .74798 L
s
% Start of user PostScript
0.125 0.75 0.12765 0.747982 MAarrowhead1
% End of user PostScript
.125 .8125 m
.12802 .81008 L
s
% Start of user PostScript
0.125 0.8125 0.12802 0.810082 MAarrowhead1
% End of user PostScript
.125 .875 m
.12839 .87224 L
s
% Start of user PostScript
0.125 0.875 0.128389 0.872238 MAarrowhead1
% End of user PostScript
.125 .9375 m
.12876 .93444 L
s
% Start of user PostScript
0.125 0.9375 0.128759 0.934441 MAarrowhead1
% End of user PostScript
.125 1 m
.12913 .99668 L
s
% Start of user PostScript
0.125 1. 0.129128 0.996681 MAarrowhead1
% End of user PostScript
.1875 .0625 m
.18607 .11408 L
s
% Start of user PostScript
0.1875 0.0625 0.186074 0.114085 MAarrowhead1
% End of user PostScript
.1875 .125 m
.18643 .14757 L
s
% Start of user PostScript
0.1875 0.125 0.186433 0.147574 MAarrowhead1
% End of user PostScript
.1875 .1875 m
.18679 .2004 L
s
% Start of user PostScript
0.1875 0.1875 0.186792 0.200404 MAarrowhead1
% End of user PostScript
.1875 .25 m
.18715 .25807 L
s
% Start of user PostScript
0.1875 0.25 0.187151 0.258069 MAarrowhead1
% End of user PostScript
.1875 .3125 m
.18751 .31767 L
s
% Start of user PostScript
0.1875 0.3125 0.18751 0.317668 MAarrowhead1
% End of user PostScript
.1875 .375 m
.18787 .37823 L
s
% Start of user PostScript
0.1875 0.375 0.18787 0.378233 MAarrowhead1
% End of user PostScript
.1875 .4375 m
.18823 .43935 L
s
% Start of user PostScript
0.1875 0.4375 0.188229 0.439352 MAarrowhead1
% End of user PostScript
.1875 .5 m
.18859 .50082 L
s
% Start of user PostScript
0.1875 0.5 0.188588 0.500816 MAarrowhead1
% End of user PostScript
.1875 .5625 m
.18895 .56251 L
s
% Start of user PostScript
0.1875 0.5625 0.188947 0.56251 MAarrowhead1
% End of user PostScript
.1875 .625 m
.18931 .62437 L
s
% Start of user PostScript
0.1875 0.625 0.189306 0.624365 MAarrowhead1
% End of user PostScript
.1875 .6875 m
.18967 .68634 L
s
% Start of user PostScript
0.1875 0.6875 0.189665 0.686338 MAarrowhead1
% End of user PostScript
.1875 .75 m
.19002 .7484 L
s
% Start of user PostScript
0.1875 0.75 0.190024 0.748398 MAarrowhead1
% End of user PostScript
.1875 .8125 m
.19038 .81053 L
s
% Start of user PostScript
0.1875 0.8125 0.190384 0.810526 MAarrowhead1
% End of user PostScript
.1875 .875 m
.19074 .87271 L
s
% Start of user PostScript
0.1875 0.875 0.190743 0.872708 MAarrowhead1
% End of user PostScript
.1875 .9375 m
.1911 .93493 L
s
% Start of user PostScript
0.1875 0.9375 0.191102 0.934931 MAarrowhead1
% End of user PostScript
.1875 1 m
.19146 .99719 L
s
% Start of user PostScript
0.1875 1. 0.191461 0.99719 MAarrowhead1
% End of user PostScript
.25 .0625 m
.24856 .11037 L
s
% Start of user PostScript
0.25 0.0625 0.248563 0.110368 MAarrowhead1
% End of user PostScript
.25 .125 m
.24891 .14609 L
s
% Start of user PostScript
0.25 0.125 0.248912 0.146088 MAarrowhead1
% End of user PostScript
.25 .1875 m
.24926 .19966 L
s
% Start of user PostScript
0.25 0.1875 0.249261 0.199662 MAarrowhead1
% End of user PostScript
.25 .25 m
.24961 .2577 L
s
% Start of user PostScript
0.25 0.25 0.249609 0.257699 MAarrowhead1
% End of user PostScript
.25 .3125 m
.24996 .31752 L
s
% Start of user PostScript
0.25 0.3125 0.249958 0.317521 MAarrowhead1
% End of user PostScript
.25 .375 m
.25031 .37824 L
s
% Start of user PostScript
0.25 0.375 0.250307 0.378236 MAarrowhead1
% End of user PostScript
.25 .4375 m
.25066 .43946 L
s
% Start of user PostScript
0.25 0.4375 0.250656 0.439461 MAarrowhead1
% End of user PostScript
.25 .5 m
.251 .501 L
s
% Start of user PostScript
0.25 0.5 0.251004 0.501004 MAarrowhead1
% End of user PostScript
.25 .5625 m
.25135 .56276 L
s
% Start of user PostScript
0.25 0.5625 0.251353 0.56276 MAarrowhead1
% End of user PostScript
.25 .625 m
.2517 .62467 L
s
% Start of user PostScript
0.25 0.625 0.251702 0.624665 MAarrowhead1
% End of user PostScript
.25 .6875 m
.25205 .68668 L
s
% Start of user PostScript
0.25 0.6875 0.25205 0.686678 MAarrowhead1
% End of user PostScript
.25 .75 m
.2524 .74877 L
s
% Start of user PostScript
0.25 0.75 0.252399 0.748773 MAarrowhead1
% End of user PostScript
.25 .8125 m
.25275 .81093 L
s
% Start of user PostScript
0.25 0.8125 0.252748 0.810929 MAarrowhead1
% End of user PostScript
.25 .875 m
.2531 .87314 L
s
% Start of user PostScript
0.25 0.875 0.253096 0.873135 MAarrowhead1
% End of user PostScript
.25 .9375 m
.25345 .93538 L
s
% Start of user PostScript
0.25 0.9375 0.253445 0.93538 MAarrowhead1
% End of user PostScript
.25 1 m
.25379 .99766 L
s
% Start of user PostScript
0.25 1. 0.253794 0.997657 MAarrowhead1
% End of user PostScript
.3125 .0625 m
.31105 .10661 L
s
% Start of user PostScript
0.3125 0.0625 0.311053 0.106609 MAarrowhead1
% End of user PostScript
.3125 .125 m
.31139 .14456 L
s
% Start of user PostScript
0.3125 0.125 0.311391 0.144561 MAarrowhead1
% End of user PostScript
.3125 .1875 m
.31173 .19888 L
s
% Start of user PostScript
0.3125 0.1875 0.311729 0.198879 MAarrowhead1
% End of user PostScript
.3125 .25 m
.31207 .25729 L
s
% Start of user PostScript
0.3125 0.25 0.312068 0.257288 MAarrowhead1
% End of user PostScript
.3125 .3125 m
.31241 .31733 L
s
% Start of user PostScript
0.3125 0.3125 0.312406 0.317333 MAarrowhead1
% End of user PostScript
.3125 .375 m
.31274 .3782 L
s
% Start of user PostScript
0.3125 0.375 0.312744 0.378196 MAarrowhead1
% End of user PostScript
.3125 .4375 m
.31308 .43953 L
s
% Start of user PostScript
0.3125 0.4375 0.313082 0.439527 MAarrowhead1
% End of user PostScript
.3125 .5 m
.31342 .50115 L
s
% Start of user PostScript
0.3125 0.5 0.313421 0.501151 MAarrowhead1
% End of user PostScript
.3125 .5625 m
.31376 .56297 L
s
% Start of user PostScript
0.3125 0.5625 0.313759 0.562969 MAarrowhead1
% End of user PostScript
.3125 .625 m
.3141 .62492 L
s
% Start of user PostScript
0.3125 0.625 0.314097 0.624923 MAarrowhead1
% End of user PostScript
.3125 .6875 m
.31444 .68698 L
s
% Start of user PostScript
0.3125 0.6875 0.314435 0.686977 MAarrowhead1
% End of user PostScript
.3125 .75 m
.31477 .74911 L
s
% Start of user PostScript
0.3125 0.75 0.314773 0.749105 MAarrowhead1
% End of user PostScript
.3125 .8125 m
.31511 .81129 L
s
% Start of user PostScript
0.3125 0.8125 0.315112 0.81129 MAarrowhead1
% End of user PostScript
.3125 .875 m
.31545 .87352 L
s
% Start of user PostScript
0.3125 0.875 0.31545 0.873521 MAarrowhead1
% End of user PostScript
.3125 .9375 m
.31579 .93579 L
s
% Start of user PostScript
0.3125 0.9375 0.315788 0.935787 MAarrowhead1
% End of user PostScript
.3125 1 m
.31613 .99808 L
s
% Start of user PostScript
0.3125 1. 0.316126 0.998082 MAarrowhead1
% End of user PostScript
.375 .0625 m
.37354 .10281 L
s
% Start of user PostScript
0.375 0.0625 0.373542 0.102808 MAarrowhead1
% End of user PostScript
.375 .125 m
.37387 .14299 L
s
% Start of user PostScript
0.375 0.125 0.37387 0.142992 MAarrowhead1
% End of user PostScript
.375 .1875 m
.3742 .19805 L
s
% Start of user PostScript
0.375 0.1875 0.374198 0.198054 MAarrowhead1
% End of user PostScript
.375 .25 m
.37453 .25683 L
s
% Start of user PostScript
0.375 0.25 0.374526 0.256834 MAarrowhead1
% End of user PostScript
.375 .3125 m
.37485 .3171 L
s
% Start of user PostScript
0.375 0.3125 0.374854 0.317103 MAarrowhead1
% End of user PostScript
.375 .375 m
.37518 .37811 L
s
% Start of user PostScript
0.375 0.375 0.375181 0.378115 MAarrowhead1
% End of user PostScript
.375 .4375 m
.37551 .43955 L
s
% Start of user PostScript
0.375 0.4375 0.375509 0.439552 MAarrowhead1
% End of user PostScript
.375 .5 m
.37584 .50126 L
s
% Start of user PostScript
0.375 0.5 0.375837 0.501255 MAarrowhead1
% End of user PostScript
.375 .5625 m
.37616 .56314 L
s
% Start of user PostScript
0.375 0.5625 0.376165 0.563135 MAarrowhead1
% End of user PostScript
.375 .625 m
.37649 .62514 L
s
% Start of user PostScript
0.375 0.625 0.376492 0.625139 MAarrowhead1
% End of user PostScript
.375 .6875 m
.37682 .68723 L
s
% Start of user PostScript
0.375 0.6875 0.37682 0.687234 MAarrowhead1
% End of user PostScript
.375 .75 m
.37715 .7494 L
s
% Start of user PostScript
0.375 0.75 0.377148 0.749396 MAarrowhead1
% End of user PostScript
.375 .8125 m
.37748 .81161 L
s
% Start of user PostScript
0.375 0.8125 0.377476 0.81161 MAarrowhead1
% End of user PostScript
.375 .875 m
.3778 .87386 L
s
% Start of user PostScript
0.375 0.875 0.377803 0.873864 MAarrowhead1
% End of user PostScript
.375 .9375 m
.37813 .93615 L
s
% Start of user PostScript
0.375 0.9375 0.378131 0.936152 MAarrowhead1
% End of user PostScript
.375 1 m
.37846 .99847 L
s
% Start of user PostScript
0.375 1. 0.378459 0.998466 MAarrowhead1
% End of user PostScript
.4375 .0625 m
.43603 .09897 L
s
% Start of user PostScript
0.4375 0.0625 0.436032 0.0989655 MAarrowhead1
% End of user PostScript
.4375 .125 m
.43635 .14138 L
s
% Start of user PostScript
0.4375 0.125 0.436349 0.141381 MAarrowhead1
% End of user PostScript
.4375 .1875 m
.43667 .19719 L
s
% Start of user PostScript
0.4375 0.1875 0.436667 0.197186 MAarrowhead1
% End of user PostScript
.4375 .25 m
.43698 .25634 L
s
% Start of user PostScript
0.4375 0.25 0.436984 0.256339 MAarrowhead1
% End of user PostScript
.4375 .3125 m
.4373 .31683 L
s
% Start of user PostScript
0.4375 0.3125 0.437301 0.316831 MAarrowhead1
% End of user PostScript
.4375 .375 m
.43762 .37799 L
s
% Start of user PostScript
0.4375 0.375 0.437619 0.377992 MAarrowhead1
% End of user PostScript
.4375 .4375 m
.43794 .43954 L
s
% Start of user PostScript
0.4375 0.4375 0.437936 0.439535 MAarrowhead1
% End of user PostScript
.4375 .5 m
.43825 .50132 L
s
% Start of user PostScript
0.4375 0.5 0.438253 0.501318 MAarrowhead1
% End of user PostScript
.4375 .5625 m
.43857 .56326 L
s
% Start of user PostScript
0.4375 0.5625 0.43857 0.56326 MAarrowhead1
% End of user PostScript
.4375 .625 m
.43889 .62531 L
s
% Start of user PostScript
0.4375 0.625 0.438888 0.625314 MAarrowhead1
% End of user PostScript
.4375 .6875 m
.43921 .68745 L
s
% Start of user PostScript
0.4375 0.6875 0.439205 0.687449 MAarrowhead1
% End of user PostScript
.4375 .75 m
.43952 .74964 L
s
% Start of user PostScript
0.4375 0.75 0.439522 0.749644 MAarrowhead1
% End of user PostScript
.4375 .8125 m
.43984 .81189 L
s
% Start of user PostScript
0.4375 0.8125 0.43984 0.811887 MAarrowhead1
% End of user PostScript
.4375 .875 m
.44016 .87417 L
s
% Start of user PostScript
0.4375 0.875 0.440157 0.874166 MAarrowhead1
% End of user PostScript
.4375 .9375 m
.44047 .93647 L
s
% Start of user PostScript
0.4375 0.9375 0.440474 0.936475 MAarrowhead1
% End of user PostScript
.4375 1 m
.44079 .99881 L
s
% Start of user PostScript
0.4375 1. 0.440792 0.998807 MAarrowhead1
% End of user PostScript
.5 .0625 m
.49852 .09508 L
s
% Start of user PostScript
0.5 0.0625 0.498522 0.0950812 MAarrowhead1
% End of user PostScript
.5 .125 m
.49883 .13973 L
s
% Start of user PostScript
0.5 0.125 0.498828 0.139728 MAarrowhead1
% End of user PostScript
.5 .1875 m
.49914 .19628 L
s
% Start of user PostScript
0.5 0.1875 0.499135 0.196278 MAarrowhead1
% End of user PostScript
.5 .25 m
.49944 .2558 L
s
% Start of user PostScript
0.5 0.25 0.499442 0.255802 MAarrowhead1
% End of user PostScript
.5 .3125 m
.49975 .31652 L
s
% Start of user PostScript
0.5 0.3125 0.499749 0.316517 MAarrowhead1
% End of user PostScript
.5 .375 m
.50006 .37783 L
s
% Start of user PostScript
0.5 0.375 0.500056 0.377827 MAarrowhead1
% End of user PostScript
.5 .4375 m
.50036 .43948 L
s
% Start of user PostScript
0.5 0.4375 0.500363 0.439477 MAarrowhead1
% End of user PostScript
.5 .5 m
.50067 .50134 L
s
% Start of user PostScript
0.5 0.5 0.500669 0.501339 MAarrowhead1
% End of user PostScript
.5 .5625 m
.50098 .56334 L
s
% Start of user PostScript
0.5 0.5625 0.500976 0.563343 MAarrowhead1
% End of user PostScript
.5 .625 m
.50128 .62545 L
s
% Start of user PostScript
0.5 0.625 0.501283 0.625446 MAarrowhead1
% End of user PostScript
.5 .6875 m
.50159 .68762 L
s
% Start of user PostScript
0.5 0.6875 0.50159 0.687622 MAarrowhead1
% End of user PostScript
.5 .75 m
.5019 .74985 L
s
% Start of user PostScript
0.5 0.75 0.501897 0.749851 MAarrowhead1
% End of user PostScript
.5 .8125 m
.5022 .81212 L
s
% Start of user PostScript
0.5 0.8125 0.502204 0.812122 MAarrowhead1
% End of user PostScript
.5 .875 m
.50251 .87443 L
s
% Start of user PostScript
0.5 0.875 0.502511 0.874426 MAarrowhead1
% End of user PostScript
.5 .9375 m
.50282 .93676 L
s
% Start of user PostScript
0.5 0.9375 0.502817 0.936756 MAarrowhead1
% End of user PostScript
.5 1 m
.50312 .99911 L
s
% Start of user PostScript
0.5 1. 0.503124 0.999107 MAarrowhead1
% End of user PostScript
.5625 .0625 m
.56101 .09115 L
s
% Start of user PostScript
0.5625 0.0625 0.561011 0.091155 MAarrowhead1
% End of user PostScript
.5625 .125 m
.56131 .13803 L
s
% Start of user PostScript
0.5625 0.125 0.561307 0.138034 MAarrowhead1
% End of user PostScript
.5625 .1875 m
.5616 .19533 L
s
% Start of user PostScript
0.5625 0.1875 0.561604 0.195327 MAarrowhead1
% End of user PostScript
.5625 .25 m
.5619 .25522 L
s
% Start of user PostScript
0.5625 0.25 0.5619 0.255223 MAarrowhead1
% End of user PostScript
.5625 .3125 m
.5622 .31616 L
s
% Start of user PostScript
0.5625 0.3125 0.562197 0.316161 MAarrowhead1
% End of user PostScript
.5625 .375 m
.56249 .37762 L
s
% Start of user PostScript
0.5625 0.375 0.562493 0.37762 MAarrowhead1
% End of user PostScript
.5625 .4375 m
.56279 .43938 L
s
% Start of user PostScript
0.5625 0.4375 0.562789 0.439376 MAarrowhead1
% End of user PostScript
.5625 .5 m
.56309 .50132 L
s
% Start of user PostScript
0.5625 0.5 0.563086 0.501318 MAarrowhead1
% End of user PostScript
.5625 .5625 m
.56338 .56338 L
s
% Start of user PostScript
0.5625 0.5625 0.563382 0.563384 MAarrowhead1
% End of user PostScript
.5625 .625 m
.56368 .62554 L
s
% Start of user PostScript
0.5625 0.625 0.563679 0.625537 MAarrowhead1
% End of user PostScript
.5625 .6875 m
.56397 .68775 L
s
% Start of user PostScript
0.5625 0.6875 0.563975 0.687753 MAarrowhead1
% End of user PostScript
.5625 .75 m
.56427 .75002 L
s
% Start of user PostScript
0.5625 0.75 0.564271 0.750016 MAarrowhead1
% End of user PostScript
.5625 .8125 m
.56457 .81232 L
s
% Start of user PostScript
0.5625 0.8125 0.564568 0.812316 MAarrowhead1
% End of user PostScript
.5625 .875 m
.56486 .87464 L
s
% Start of user PostScript
0.5625 0.875 0.564864 0.874644 MAarrowhead1
% End of user PostScript
.5625 .9375 m
.56516 .937 L
s
% Start of user PostScript
0.5625 0.9375 0.56516 0.936996 MAarrowhead1
% End of user PostScript
.5625 1 m
.56546 .99937 L
s
% Start of user PostScript
0.5625 1. 0.565457 0.999365 MAarrowhead1
% End of user PostScript
.625 .0625 m
.6235 .08719 L
s
% Start of user PostScript
0.625 0.0625 0.623501 0.0871869 MAarrowhead1
% End of user PostScript
.625 .125 m
.62379 .1363 L
s
% Start of user PostScript
0.625 0.125 0.623787 0.136297 MAarrowhead1
% End of user PostScript
.625 .1875 m
.62407 .19433 L
s
% Start of user PostScript
0.625 0.1875 0.624072 0.194334 MAarrowhead1
% End of user PostScript
.625 .25 m
.62436 .2546 L
s
% Start of user PostScript
0.625 0.25 0.624358 0.254603 MAarrowhead1
% End of user PostScript
.625 .3125 m
.62464 .31576 L
s
% Start of user PostScript
0.625 0.3125 0.624644 0.315764 MAarrowhead1
% End of user PostScript
.625 .375 m
.62493 .37737 L
s
% Start of user PostScript
0.625 0.375 0.62493 0.377371 MAarrowhead1
% End of user PostScript
.625 .4375 m
.62522 .43923 L
s
% Start of user PostScript
0.625 0.4375 0.625216 0.439233 MAarrowhead1
% End of user PostScript
.625 .5 m
.6255 .50126 L
s
% Start of user PostScript
0.625 0.5 0.625502 0.501255 MAarrowhead1
% End of user PostScript
.625 .5625 m
.62579 .56338 L
s
% Start of user PostScript
0.625 0.5625 0.625788 0.563383 MAarrowhead1
% End of user PostScript
.625 .625 m
.62607 .62559 L
s
% Start of user PostScript
0.625 0.625 0.626074 0.625586 MAarrowhead1
% End of user PostScript
.625 .6875 m
.62636 .68784 L
s
% Start of user PostScript
0.625 0.6875 0.62636 0.687842 MAarrowhead1
% End of user PostScript
.625 .75 m
.62665 .75014 L
s
% Start of user PostScript
0.625 0.75 0.626646 0.750139 MAarrowhead1
% End of user PostScript
.625 .8125 m
.62693 .81247 L
s
% Start of user PostScript
0.625 0.8125 0.626932 0.812468 MAarrowhead1
% End of user PostScript
.625 .875 m
.62722 .87482 L
s
% Start of user PostScript
0.625 0.875 0.627218 0.874821 MAarrowhead1
% End of user PostScript
.625 .9375 m
.6275 .93719 L
s
% Start of user PostScript
0.625 0.9375 0.627504 0.937193 MAarrowhead1
% End of user PostScript
.625 1 m
.62779 .99958 L
s
% Start of user PostScript
0.625 1. 0.627789 0.999582 MAarrowhead1
% End of user PostScript
.6875 .0625 m
.68599 .08318 L
s
% Start of user PostScript
0.6875 0.0625 0.68599 0.083177 MAarrowhead1
% End of user PostScript
.6875 .125 m
.68627 .13452 L
s
% Start of user PostScript
0.6875 0.125 0.686266 0.134519 MAarrowhead1
% End of user PostScript
.6875 .1875 m
.68654 .1933 L
s
% Start of user PostScript
0.6875 0.1875 0.686541 0.1933 MAarrowhead1
% End of user PostScript
.6875 .25 m
.68682 .25394 L
s
% Start of user PostScript
0.6875 0.25 0.686817 0.25394 MAarrowhead1
% End of user PostScript
.6875 .3125 m
.68709 .31532 L
s
% Start of user PostScript
0.6875 0.3125 0.687092 0.315324 MAarrowhead1
% End of user PostScript
.6875 .375 m
.68737 .37708 L
s
% Start of user PostScript
0.6875 0.375 0.687367 0.37708 MAarrowhead1
% End of user PostScript
.6875 .4375 m
.68764 .43905 L
s
% Start of user PostScript
0.6875 0.4375 0.687643 0.439049 MAarrowhead1
% End of user PostScript
.6875 .5 m
.68792 .50115 L
s
% Start of user PostScript
0.6875 0.5 0.687918 0.501151 MAarrowhead1
% End of user PostScript
.6875 .5625 m
.68819 .56334 L
s
% Start of user PostScript
0.6875 0.5625 0.688194 0.563341 MAarrowhead1
% End of user PostScript
.6875 .625 m
.68847 .62559 L
s
% Start of user PostScript
0.6875 0.625 0.688469 0.625593 MAarrowhead1
% End of user PostScript
.6875 .6875 m
.68874 .68789 L
s
% Start of user PostScript
0.6875 0.6875 0.688745 0.68789 MAarrowhead1
% End of user PostScript
.6875 .75 m
.68902 .75022 L
s
% Start of user PostScript
0.6875 0.75 0.68902 0.750221 MAarrowhead1
% End of user PostScript
.6875 .8125 m
.6893 .81258 L
s
% Start of user PostScript
0.6875 0.8125 0.689296 0.812578 MAarrowhead1
% End of user PostScript
.6875 .875 m
.68957 .87496 L
s
% Start of user PostScript
0.6875 0.875 0.689571 0.874955 MAarrowhead1
% End of user PostScript
.6875 .9375 m
.68985 .93735 L
s
% Start of user PostScript
0.6875 0.9375 0.689847 0.937349 MAarrowhead1
% End of user PostScript
.6875 1 m
.69012 .99976 L
s
% Start of user PostScript
0.6875 1. 0.690122 0.999756 MAarrowhead1
% End of user PostScript
.75 .0625 m
.74848 .07913 L
s
% Start of user PostScript
0.75 0.0625 0.74848 0.0791253 MAarrowhead1
% End of user PostScript
.75 .125 m
.74874 .1327 L
s
% Start of user PostScript
0.75 0.125 0.748745 0.132699 MAarrowhead1
% End of user PostScript
.75 .1875 m
.74901 .19222 L
s
% Start of user PostScript
0.75 0.1875 0.74901 0.192224 MAarrowhead1
% End of user PostScript
.75 .25 m
.74927 .25324 L
s
% Start of user PostScript
0.75 0.25 0.749275 0.253236 MAarrowhead1
% End of user PostScript
.75 .3125 m
.74954 .31484 L
s
% Start of user PostScript
0.75 0.3125 0.74954 0.314843 MAarrowhead1
% End of user PostScript
.75 .375 m
.7498 .37675 L
s
% Start of user PostScript
0.75 0.375 0.749805 0.376748 MAarrowhead1
% End of user PostScript
.75 .4375 m
.75007 .43882 L
s
% Start of user PostScript
0.75 0.4375 0.75007 0.438823 MAarrowhead1
% End of user PostScript
.75 .5 m
.75033 .501 L
s
% Start of user PostScript
0.75 0.5 0.750335 0.501004 MAarrowhead1
% End of user PostScript
.75 .5625 m
.7506 .56326 L
s
% Start of user PostScript
0.75 0.5625 0.7506 0.563256 MAarrowhead1
% End of user PostScript
.75 .625 m
.75086 .62556 L
s
% Start of user PostScript
0.75 0.625 0.750865 0.625558 MAarrowhead1
% End of user PostScript
.75 .6875 m
.75113 .6879 L
s
% Start of user PostScript
0.75 0.6875 0.75113 0.687896 MAarrowhead1
% End of user PostScript
.75 .75 m
.75139 .75026 L
s
% Start of user PostScript
0.75 0.75 0.751395 0.75026 MAarrowhead1
% End of user PostScript
.75 .8125 m
.75166 .81265 L
s
% Start of user PostScript
0.75 0.8125 0.75166 0.812646 MAarrowhead1
% End of user PostScript
.75 .875 m
.75192 .87505 L
s
% Start of user PostScript
0.75 0.875 0.751925 0.875048 MAarrowhead1
% End of user PostScript
.75 .9375 m
.75219 .93746 L
s
% Start of user PostScript
0.75 0.9375 0.75219 0.937463 MAarrowhead1
% End of user PostScript
.75 1 m
.75245 .99989 L
s
% Start of user PostScript
0.75 1. 0.752455 0.999888 MAarrowhead1
% End of user PostScript
.8125 .0625 m
.81097 .07503 L
s
% Start of user PostScript
0.8125 0.0625 0.810969 0.0750318 MAarrowhead1
% End of user PostScript
.8125 .125 m
.81122 .13084 L
s
% Start of user PostScript
0.8125 0.125 0.811224 0.130837 MAarrowhead1
% End of user PostScript
.8125 .1875 m
.81148 .19111 L
s
% Start of user PostScript
0.8125 0.1875 0.811478 0.191105 MAarrowhead1
% End of user PostScript
.8125 .25 m
.81173 .25249 L
s
% Start of user PostScript
0.8125 0.25 0.811733 0.25249 MAarrowhead1
% End of user PostScript
.8125 .3125 m
.81199 .31432 L
s
% Start of user PostScript
0.8125 0.3125 0.811987 0.31432 MAarrowhead1
% End of user PostScript
.8125 .375 m
.81224 .37637 L
s
% Start of user PostScript
0.8125 0.375 0.812242 0.376374 MAarrowhead1
% End of user PostScript
.8125 .4375 m
.8125 .43856 L
s
% Start of user PostScript
0.8125 0.4375 0.812497 0.438555 MAarrowhead1
% End of user PostScript
.8125 .5 m
.81275 .50082 L
s
% Start of user PostScript
0.8125 0.5 0.812751 0.500816 MAarrowhead1
% End of user PostScript
.8125 .5625 m
.81301 .56313 L
s
% Start of user PostScript
0.8125 0.5625 0.813006 0.56313 MAarrowhead1
% End of user PostScript
.8125 .625 m
.81326 .62548 L
s
% Start of user PostScript
0.8125 0.625 0.81326 0.625481 MAarrowhead1
% End of user PostScript
.8125 .6875 m
.81351 .68786 L
s
% Start of user PostScript
0.8125 0.6875 0.813515 0.687859 MAarrowhead1
% End of user PostScript
.8125 .75 m
.81377 .75026 L
s
% Start of user PostScript
0.8125 0.75 0.813769 0.750258 MAarrowhead1
% End of user PostScript
.8125 .8125 m
.81402 .81267 L
s
% Start of user PostScript
0.8125 0.8125 0.814024 0.812672 MAarrowhead1
% End of user PostScript
.8125 .875 m
.81428 .8751 L
s
% Start of user PostScript
0.8125 0.875 0.814278 0.875099 MAarrowhead1
% End of user PostScript
.8125 .9375 m
.81453 .93753 L
s
% Start of user PostScript
0.8125 0.9375 0.814533 0.937535 MAarrowhead1
% End of user PostScript
.8125 1 m
.81479 .99998 L
s
% Start of user PostScript
0.8125 1. 0.814787 0.999979 MAarrowhead1
% End of user PostScript
.875 .0625 m
.87346 .0709 L
s
% Start of user PostScript
0.875 0.0625 0.873459 0.0708963 MAarrowhead1
% End of user PostScript
.875 .125 m
.8737 .12893 L
s
% Start of user PostScript
0.875 0.125 0.873703 0.128933 MAarrowhead1
% End of user PostScript
.875 .1875 m
.87395 .18995 L
s
% Start of user PostScript
0.875 0.1875 0.873947 0.189945 MAarrowhead1
% End of user PostScript
.875 .25 m
.87419 .2517 L
s
% Start of user PostScript
0.875 0.25 0.874191 0.251702 MAarrowhead1
% End of user PostScript
.875 .3125 m
.87444 .31376 L
s
% Start of user PostScript
0.875 0.3125 0.874435 0.313755 MAarrowhead1
% End of user PostScript
.875 .375 m
.87468 .37596 L
s
% Start of user PostScript
0.875 0.375 0.874679 0.375958 MAarrowhead1
% End of user PostScript
.875 .4375 m
.87492 .43825 L
s
% Start of user PostScript
0.875 0.4375 0.874923 0.438245 MAarrowhead1
% End of user PostScript
.875 .5 m
.87517 .50059 L
s
% Start of user PostScript
0.875 0.5 0.875167 0.500586 MAarrowhead1
% End of user PostScript
.875 .5625 m
.87541 .56296 L
s
% Start of user PostScript
0.875 0.5625 0.875411 0.562962 MAarrowhead1
% End of user PostScript
.875 .625 m
.87566 .62536 L
s
% Start of user PostScript
0.875 0.625 0.875656 0.625363 MAarrowhead1
% End of user PostScript
.875 .6875 m
.8759 .68778 L
s
% Start of user PostScript
0.875 0.6875 0.8759 0.687781 MAarrowhead1
% End of user PostScript
.875 .75 m
.87614 .75021 L
s
% Start of user PostScript
0.875 0.75 0.876144 0.750214 MAarrowhead1
% End of user PostScript
.875 .8125 m
.87639 .81266 L
s
% Start of user PostScript
0.875 0.8125 0.876388 0.812657 MAarrowhead1
% End of user PostScript
.875 .875 m
.87663 .87511 L
s
% Start of user PostScript
0.875 0.875 0.876632 0.875108 MAarrowhead1
% End of user PostScript
.875 .9375 m
.87688 .93757 L
s
% Start of user PostScript
0.875 0.9375 0.876876 0.937565 MAarrowhead1
% End of user PostScript
.875 1 m
0 0 rlineto s
.875 1 m
.875 1 L
s
% Start of user PostScript
0.875 1. 0.87712 1.00003 MAarrowhead1
% End of user PostScript
.9375 .0625 m
.93595 .06672 L
s
% Start of user PostScript
0.9375 0.0625 0.935948 0.0667191 MAarrowhead1
% End of user PostScript
.9375 .125 m
.93618 .12699 L
s
% Start of user PostScript
0.9375 0.125 0.936182 0.126988 MAarrowhead1
% End of user PostScript
.9375 .1875 m
.93642 .18874 L
s
% Start of user PostScript
0.9375 0.1875 0.936416 0.188744 MAarrowhead1
% End of user PostScript
.9375 .25 m
.93665 .25087 L
s
% Start of user PostScript
0.9375 0.25 0.936649 0.250872 MAarrowhead1
% End of user PostScript
.9375 .3125 m
.93688 .31315 L
s
% Start of user PostScript
0.9375 0.3125 0.936883 0.313149 MAarrowhead1
% End of user PostScript
.9375 .375 m
.93712 .3755 L
s
% Start of user PostScript
0.9375 0.375 0.937116 0.3755 MAarrowhead1
% End of user PostScript
.9375 .4375 m
.93735 .43789 L
s
% Start of user PostScript
0.9375 0.4375 0.93735 0.437894 MAarrowhead1
% End of user PostScript
.9375 .5 m
.93758 .50031 L
s
% Start of user PostScript
0.9375 0.5 0.937584 0.500314 MAarrowhead1
% End of user PostScript
.9375 .5625 m
.93782 .56275 L
s
% Start of user PostScript
0.9375 0.5625 0.937817 0.562752 MAarrowhead1
% End of user PostScript
.9375 .625 m
.93805 .6252 L
s
% Start of user PostScript
0.9375 0.625 0.938051 0.625202 MAarrowhead1
% End of user PostScript
.9375 .6875 m
.93828 .68766 L
s
% Start of user PostScript
0.9375 0.6875 0.938285 0.687662 MAarrowhead1
% End of user PostScript
.9375 .75 m
.93852 .75013 L
s
% Start of user PostScript
0.9375 0.75 0.938518 0.750128 MAarrowhead1
% End of user PostScript
.9375 .8125 m
.93875 .8126 L
s
% Start of user PostScript
0.9375 0.8125 0.938752 0.812599 MAarrowhead1
% End of user PostScript
.9375 .875 m
.93899 .87507 L
s
% Start of user PostScript
0.9375 0.875 0.938985 0.875075 MAarrowhead1
% End of user PostScript
.9375 .9375 m
.93922 .93755 L
s
% Start of user PostScript
0.9375 0.9375 0.939219 0.937553 MAarrowhead1
% End of user PostScript
.9375 1 m
0 0 rlineto s
.9375 1 m
.9375 1 L
s
% Start of user PostScript
0.9375 1. 0.939453 1.00003 MAarrowhead1
% End of user PostScript
1 .0625 m
.99844 .0625 L
s
% Start of user PostScript
1. 0.0625 0.998438 0.0625 MAarrowhead1
% End of user PostScript
1 .125 m
.99866 .125 L
s
% Start of user PostScript
1. 0.125 0.998661 0.125 MAarrowhead1
% End of user PostScript
1 .1875 m
.99888 .1875 L
s
% Start of user PostScript
1. 0.1875 0.998884 0.1875 MAarrowhead1
% End of user PostScript
1 .25 m
.99911 .25 L
s
% Start of user PostScript
1. 0.25 0.999107 0.25 MAarrowhead1
% End of user PostScript
1 .3125 m
.99933 .3125 L
s
% Start of user PostScript
1. 0.3125 0.999331 0.3125 MAarrowhead1
% End of user PostScript
1 .375 m
.99955 .375 L
s
% Start of user PostScript
1. 0.375 0.999554 0.375 MAarrowhead1
% End of user PostScript
1 .4375 m
.99978 .4375 L
s
% Start of user PostScript
1. 0.4375 0.999777 0.4375 MAarrowhead1
% End of user PostScript
1 .5 m
1 .5 L
s
% Start of user PostScript
1. 0.5 MAarrowzero1
% End of user PostScript
1 .5625 m
0 0 rlineto s
1 .5625 m
1 .5625 L
s
% Start of user PostScript
1. 0.5625 1.00022 0.5625 MAarrowhead1
% End of user PostScript
1 .625 m
0 0 rlineto s
1 .625 m
1 .625 L
s
% Start of user PostScript
1. 0.625 1.00045 0.625 MAarrowhead1
% End of user PostScript
1 .6875 m
0 0 rlineto s
1 .6875 m
1 .6875 L
s
% Start of user PostScript
1. 0.6875 1.00067 0.6875 MAarrowhead1
% End of user PostScript
1 .75 m
0 0 rlineto s
1 .75 m
1 .75 L
s
% Start of user PostScript
1. 0.75 1.00089 0.75 MAarrowhead1
% End of user PostScript
1 .8125 m
0 0 rlineto s
1 .8125 m
1 .8125 L
s
% Start of user PostScript
1. 0.8125 1.00112 0.8125 MAarrowhead1
% End of user PostScript
1 .875 m
0 0 rlineto s
1 .875 m
1 .875 L
s
% Start of user PostScript
1. 0.875 1.00134 0.875 MAarrowhead1
% End of user PostScript
1 .9375 m
0 0 rlineto s
1 .9375 m
1 .9375 L
s
% Start of user PostScript
1. 0.9375 1.00156 0.9375 MAarrowhead1
% End of user PostScript
1 1 m
0 0 rlineto s
1 1 m
1 1 L
s
% Start of user PostScript
1. 1. 1.00179 1. MAarrowhead1
% End of user PostScript
0 0 1 r
.5 Mabswid
.33333 .33333 m
.33333 .33333 L
.33333 .33333 L
s
0 .28571 m
.04167 .29091 L
.04762 .29167 L
.08333 .2963 L
.125 .30189 L
.16667 .30769 L
.20833 .31373 L
.25 .32 L
.29167 .32653 L
.33333 .33333 L
.33333 .33333 L
.375 .34043 L
.41667 .34783 L
.45833 .35556 L
.5 .36364 L
.54167 .37209 L
.55556 .375 L
.58333 .38095 L
.625 .39024 L
.66667 .4 L
.70833 .41026 L
.73333 .41667 L
.75 .42105 L
.79167 .43243 L
.83333 .44444 L
.875 .45714 L
.87879 .45833 L
.91667 .47059 L
.95833 .48485 L
1 .5 L
s
1 0 0 r
.66667 .83333 m
.66667 .83333 L
s
.33333 .625 m
.33333 .625 L
s
0 .5 m
0 .5 L
0 .5 L
s
.83333 1 m
.83333 1 L
.83333 1 L
s
0 .5 m
.04167 .51281 L
.08333 .52631 L
.125 .54054 L
.1282 .54167 L
.16667 .55555 L
.20833 .57142 L
.23808 .58333 L
.25 .58823 L
.29167 .60605 L
.33333 .625 L
.33333 .625 L
.375 .64515 L
.41667 .66667 L
.41667 .66667 L
.45833 .68965 L
.49016 .70833 L
.5 .71428 L
.54167 .74074 L
.55546 .75 L
.58333 .76923 L
.61394 .79167 L
.625 .8 L
.66667 .83333 L
.66667 .83333 L
.70833 .86956 L
.714 .875 L
.75 .90909 L
.75696 .91667 L
.79167 .95238 L
.79604 .95833 L
.83333 1 L
s
0 0 1 r
1 1 m
1 1 .02 0 365.73 arc
F
gsave
.95 .96 -72 -10.2813 Mabsadd m
1 1 Mabs scale
currentpoint translate
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding ISOLatin1Encoding def
        currentdict
    end

    newfontname exch definefont pop
} def

0 20.5625 translate 1 -1 scale
63.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
0.000 0.000 rmoveto
63.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
(ESS) show
81.000 12.813 moveto
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  ImageSize->{288, 288},
  ImageMargins->{{0, 0}, {0, 0}},
  ImageRegion->{{0, 1}, {0, 1}},
  ImageCache->GraphicsData["Bitmap", "\<\
CF5dJ6E]HGAYHf4PAg9QL6QYHg<PAVmbKF5d0`40004P000181000`40O003h00Oogoo8Goo003oOolQ
Ool00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol00;9oo`<006]o
o`00]Goo00<007ooOol0J7oo0027Ool30005Ool20003Ool30004Ool30003Ool30003Ool300000goo
00000002Ool20002Ool3001ZOol008Qoo`03001oogoo00=oo`04001oogoo0003Ool00`00Oomoo`04
Ool01@00Oomoogoo00001goo00D007ooOomoo`00009oo`04001oogoo0002Ool00`00Oomoo`1XOol0
08Qoo`<000=oo`04001oogoo0003Ool00`00Oomoo`04Ool01@00Oomoogoo00001goo00D007ooOomo
o`00009oo`04001oogoo0002Ool00`00Oomoo`1XOol008Qoo`04001oogoo0003Ool20004Ool00`00
Oomoo`03Ool20004Ool30003Ool20002Ool40004Ool4001YOol008Qoo`04001oogoo0009Ool00`00
Oomoo`28Ool008Moo`@000Uoo`8000Ioo`03001oogoo00Uoo`03001oogoo07Eoo`00ogoo8Goo003o
OolQOol00?moob5oo`00CGoo0P0017oo0P000goo10008goo0P0017oo0P001Goo0`008Woo0P0017oo
0P000goo0`0097oo0P0017oo0P0017oo0P00:Goo1@000Goo001<Ool01000Oomoo`0027oo00<007oo
Ool08goo00@007ooOol000]oo`03001oogoo021oo`04001oogoo0008Ool01000Oomoo`008Woo00@0
07ooOol000Qoo`04001oogoo000ZOol00`00Oomoo`01Ool004aoo`04001oogoo0009Ool00`00Oomo
o`0ROol01000Oomoo`0027oo1@008Goo00@007ooOol000Qoo`04001oogoo000ROol01000Oomoo`00
27oo00@007ooOol002Yoo`03001oogoo005oo`00C7oo00@007ooOol000Yoo`03001oogoo025oo`04
001oogoo0008Ool01000Oomoo`008Woo00@007ooOol000Qoo`<002=oo`04001oogoo0009Ool2000[
Ool00`00Oomoo`01Ool004aoo`04001oogoo0008Ool01000Oomoo`008Woo00@007ooOol000Uoo`03
001oo`00029oo`04001oogoo0009Ool00`00Oomoo`0ROol01000Oomoo`0027oo00@007ooOol002Yo
o`03001oogoo005oo`00CGoo0P002Woo0P0097oo0P002goo0P008goo0P002Woo0`008goo0P002Woo
0P00:Woo0P000goo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`008goonP00
0goo000SOol00`00Oomoo`09Ool00`00Oomoo`0:Ool00`00Oomoo`09Ool00`00Oomoo`09Ool00`00
Oomoo`0:Ool00`00Oomoo`09Ool00`00Oomoo`0:Ool00`00Oomoo`09Ool00`00Oomoo`0:Ool00`00
Oomoo`09Ool00`00Oomoo`0:Ool00`00Oomoo`09Ool00`00Oomoo`09Ool00`00Oomoo`0:Ool00`00
Oomoo`09Ool00`00Oomoo`0:Ool00`00Oomoo`09Ool00`00Oomoo`0:Ool00`00Oomoo`09Ool00`00
Oomoo`0:Ool00`00Oomoo`01Ool002=oo`03001oogoo0?Ioo`03001oogoo005oo`008goo00<007oo
Ool0mWoo00<007ooOol00Goo000SOol00`00Oomoo`3fOol00`00Oomoo`01Ool002=oo`03001oogoo
0?Ioo`03001oogoo005oo`008goo00<007ooOol0mWoo00<007ooOol00Goo000SOol00`00Oomoo`3f
Ool00`00Oomoo`01Ool002=oo`03001oogoo0?Ioo`03001oogoo005oo`008goo00<007ooOol0mWoo
00<007ooOol00Goo000SOol00`00Oomoo`3fOol00`00Oomoo`01Ool002=oo`03001oogoo0>Ioo`03
001oogoo00eoo`03001oogoo005oo`008goo0P00egoo00<007ooOol03Goo0`0037oo0P000goo000S
Ool00`00Oomoo`36Ool00`00Oomoo`0=Ool3000=Ool2000>Ool00`00Oomoo`01Ool002=oo`03001o
ogoo0;Ioo`8000ioo`<000eoo`8000ioo`8000ioo`03001oo`00004000008goo00<007ooOol037oo
00<007ooOol03Goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol037oo00<007ooOol03Goo
00<007ooOol03Goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol037oo00<007ooOol02goo
0`003Goo100037oo0P003Woo0P003Woo00<007ooOol037oo1@00000SOol00`00Oomoo`0<Ool00`00
Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00
Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0;Ool2000=Ool4000<Ool3000=
Ool2000>Ool00`00Oomoo`0=Ool00`00Oomoo`0=Ool00`00Ool00001000002=oo`03001oogoo00ao
o`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eo
o`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00]oo`<000eoo`<000aoo`<000ioo`8000eo
o`03001oogoo00eoo`03001oogoo01eoo`03001oogoo005oo`008goo00<007ooOol037oo00<007oo
Ool03Goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol037oo00<007ooOol03Goo00<007oo
Ool03Goo00<007ooOol02goo0`0037oo100037oo0`003Goo0P003Woo00<007ooOol037oo00<007oo
Ool0;Goo00<007ooOol00Goo000SOol00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool0
0`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0;Ool4000<Ool3000<Ool3
000>Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0lOol00`00Oomoo`01Ool002=oo`03
001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03
001oogoo00aoo`<000aoo`@000aoo`<000eoo`8000ioo`03001oogoo00aoo`03001oogoo04aoo`03
001oogoo005oo`008goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol037oo00<007ooOol0
3Goo00<007ooOol02goo0`003Goo0`0037oo0`003Woo00<007ooOol037oo00<007ooOol03Goo00<0
07ooOol0Fgoo00<007ooOol00Goo000SOol00`00Oomoo`0<Ool00`00Oomoo`0<Ool00`00Oomoo`0=
Ool00`00Oomoo`0;Ool4000<Ool3000=Ool3000=Ool2000>Ool00`00Oomoo`0<Ool00`00Oomoo`1[
Ool00`00Oomoo`01Ool002=oo`03001oogoo00aoo`03001oogoo00aoo`03001oogoo00aoo`<000ao
o`@000aoo`<000ioo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo07Yoo`03001oogoo005o
o`008goo00<007ooOol037oo00<007ooOol02goo100037oo0`003Goo0`003Goo00<007ooOol03Goo
00<007ooOol037oo00<007ooOol0RWoo00<007ooOol00Goo000SOol2000<Ool3000<Ool4000<Ool3
000=Ool2000>Ool00`00Oomoo`0=Ool00`00Oomoo`2HOol20003Ool0025oo`@000aoo`<000aoo`<0
00ioo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo0:Uoo`03001oogoo005oo`008Goo1000
37oo0`003Goo0P003Woo00<007ooOol03Goo00<007ooOol0R7oo0P003Woo10003Woo00<007ooOol0
2goo00<007ooOol00Goo000QOol3000>Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`1i
Ool3000=Ool3000<Ool4000<Ool3000>Ool4000;Ool00`00Oomoo`01Ool0029oo`8000ioo`03001o
ogoo00aoo`03001oogoo05Yoo`03001oogoo00eoo`<000aoo`@000aoo`<000eoo`<000aoo`<000eo
o`<000ioo`<000aoo`03001oogoo005oo`008Woo0P003Woo00<007ooOol0BWoo0`0037oo100037oo
0`003Goo0`0037oo100037oo0P003Woo0P003Woo0P003Goo0P003Woo0`003Goo00<007oo00000@00
000ROol2000>Ool00`00Oomoo`0=Ool00`00Oomoo`0;Ool2000>Ool3000<Ool4000<Ool3000<Ool4
000<Ool3000=Ool2000=Ool3000=Ool2000>Ool2000>Ool00`00Oomoo`0<Ool2000>Ool00`00Oomo
o`0<Ool50000025oo`<000eoo`<000eoo`<000aoo`@000aoo`<000aoo`@000aoo`<000aoo`<000io
o`03001oogoo00aoo`8000ioo`8000eoo`03001oogoo00eoo`03001oogoo00eoo`03001oogoo00ao
o`03001oogoo01eoo`03001oo`00004000008Goo100037oo0`003Goo0`0037oo0`003Goo0`0037oo
0`003Woo00<007ooOol037oo0P003Woo00<007ooOol037oo00<007ooOol03Goo00<007ooOol037oo
00<007ooOol03Goo00<007ooOol0?7oo00<007ooOol00Goo000QOol3000=Ool3000=Ool3000=Ool2
000>Ool00`00Oomoo`0<Ool2000>Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool0
0`00Oomoo`0=Ool00`00Oomoo`1KOol00`00Oomoo`01Ool0029oo`8000ioo`03001oogoo00eoo`03
001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03
001oogoo08Yoo`03001oogoo005oo`008Woo0P003Woo00<007ooOol03Goo00<007ooOol037oo00<0
07ooOol03Goo00<007ooOol037oo00<007ooOol0ZGoo00<007ooOol00Goo000ROol3000=Ool00`00
Oomoo`0=Ool00`00Oomoo`3FOol20003Ool002=oo`03001oogoo0?Ioo`03001oogoo005oo`008goo
00<007ooOol0mWoo00<007ooOol00Goo000SOol00`00Oomoo`3fOol00`00Oomoo`01Ool002=oo`03
001oogoo0?Ioo`03001oogoo005oo`008goo00<007ooOol0]goo00<007ooOol03Goo00<007ooOol0
3Goo00<007ooOol03Woo00<007ooOol02goo00<007ooOol00Goo000SOol00`00Oomoo`1hOol2000>
Ool3000<Ool4000<Ool4000<Ool3000=Ool3000=Ool3000>Ool2000<Ool00`00Oomoo`01Ool002=o
o`03001oogoo03Yoo`<000aoo`@000aoo`<000eoo`<000aoo`@000aoo`<000aoo`@000aoo`@000ao
o`<000eoo`8000ioo`8000ioo`@000]oo`03001oogoo005oo`008Goo100037oo100037oo0`0037oo
100037oo0`0037oo100037oo0`003Goo0`0037oo100037oo0P003Goo0`003Goo0`003Goo0P003Woo
0P003Goo0P003goo0`0037oo00<007oo00000@00000QOol4000<Ool4000<Ool3000<Ool4000<Ool3
000<Ool3000=Ool3000=Ool2000=Ool3000=Ool2000>Ool2000>Ool2000=Ool2000>Ool00`00Oomo
o`0<Ool2000>Ool3000<Ool50000011oo`8000Aoo`8000=oo`@000=oo`<000aoo`<000eoo`<000ao
o`<000ioo`03001oogoo00aoo`8000ioo`03001oogoo00aoo`8000ioo`8000eoo`03001oogoo00eo
o`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eo
o`03001oogoo00eoo`@000003goo00@007ooOol000Qoo`03001oogoo00Aoo`8000ioo`8000ioo`03
001oogoo00aoo`8000ioo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo
00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo
03aoo`03001oogoo004000003goo00@007ooOol000Uoo`03001oogoo00Aoo`8000eoo`03001oogoo
00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo
00aoo`03001oogoo00eoo`03001oogoo07Qoo`<000=oo`003goo00@007ooOol000Yoo`03001oogoo
00=oo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo0<Qoo`03001oogoo
005oo`003goo00@007ooOol000Qoo`04001oogoo0004Ool00`00Oomoo`3fOol00`00Oomoo`01Ool0
011oo`8000Yoo`8000Eoo`03001oogoo0?Ioo`03001oogoo005oo`008goo00<007ooOol0mWoo00<0
07ooOol00Goo000SOol00`00Oomoo`3fOol00`00Oomoo`01Ool002=oo`03001oogoo0?Ioo`03001o
ogoo005oo`008goo00<007ooOol0mWoo00<007ooOol00Goo000SOol00`00Oomoo`37Ool00`00Oomo
o`0=Ool00`00Oomoo`0LOol00`00Oomoo`01Ool002=oo`03001oogoo06Uoo`03001oogoo00aoo`80
00ioo`<000eoo`<000aoo`@000aoo`<000eoo`<000eoo`<000moo`03001oogoo00Yoo`03001oogoo
005oo`008Woo0`0037oo100037oo0`0037oo100037oo0`0037oo100037oo0`003Goo0`0037oo1000
37oo0`003Goo0`0037oo100037oo0`003Goo0`003Goo0P003goo0P0037oo00<007ooOol00Goo000R
Ool3000<Ool4000<Ool3000<Ool4000<Ool3000<Ool4000<Ool3000=Ool2000=Ool3000=Ool3000=
Ool2000=Ool3000=Ool2000>Ool2000=Ool2000?Ool4000;Ool00`00Oomoo`01Ool0029oo`<000ao
o`<000eoo`<000aoo`<000eoo`<000aoo`<000eoo`<000eoo`8000ioo`8000ioo`03001oogoo00ao
o`8000ioo`8000eoo`8000ioo`8000eoo`8000moo`<000aoo`03001oo`00004000008goo0P003Goo
0P003Woo00<007ooOol037oo0P003Woo00<007ooOol037oo0P003Woo00<007ooOol037oo0P003Woo
00<007ooOol03Goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol037oo00<007ooOol03Goo
00<007ooOol037oo00<007ooOol03Goo0P003Goo1@00000SOol00`00Oomoo`0<Ool00`00Oomoo`0=
Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<
Ool00`00Oomoo`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<
Ool00`00Oomoo`0=Ool00`00Oomoo`0/Ool00`00Ool00001000002=oo`03001oogoo00aoo`03001o
ogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001o
ogoo09Uoo`03001oogoo005oo`008goo00<007ooOol0mWoo00<007ooOol00Goo000SOol00`00Oomo
o`3fOol00`00Oomoo`01Ool002=oo`03001oogoo0?Ioo`03001oogoo005oo`008goo00<007ooOol0
mWoo00<007ooOol00Goo000SOol00`00Oomoo`3fOol00`00Oomoo`01Ool002=oo`03001oogoo0?Io
o`03001oogoo005oo`008goo1@0Om7oo00<007ooOol00Goo000SOol00`00Oomoo`02Ool;01oYOol0
0`00Oomoo`01Ool002=oo`03001oogoo00eoo`L07fAoo`8000ioo`<000eoo`03001oogoo00aoo`80
00ioo`<000eoo`<000eoo`03001oogoo01aoo`03001oogoo005oo`008Goo100037oo0`001Woo1P0O
00Aoo`00000000aoo`<000eoo`<000aoo`@000aoo`<000eoo`<000aoo`@000aoo`<000eoo`<000ao
o`@000aoo`<000eoo`<000eoo`<000moo`03001oogoo00Uoo`8000=oo`008Goo100037oo0`0037oo
1`0O2Goo0`003Goo0`0037oo100037oo0`003Goo0`0037oo0`003Goo0`003Goo0P003Goo0`003Goo
0P003Woo0P003Woo0P003goo0`002goo00<007ooOol00Goo000ROol3000<Ool3000=Ool30003Ool8
01l017oo000000003Goo0`0037oo0`003Goo0`003Goo0`003Goo0P003Woo00<007ooOol037oo0P00
3Woo0P003Goo0P003Woo0P003Goo0P003goo1@002Woo00<007oo00000@00000ROol2000>Ool00`00
Oomoo`0=Ool00`00Oomoo`0:Ool601l<Ool00`00Oomoo`0<Ool2000>Ool00`00Oomoo`0=Ool00`00
Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00
Oomoo`0=Ool00`00Oomoo`0<Ool2000>Ool4000;Ool5000002=oo`03001oogoo00aoo`03001oogoo
00eoo`03001oogoo00aoo`04001oogooOol701l5Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00
Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00
Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool2000>Ool4000002=oo`03
001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00Qoo`P07`aoo`03001oogoo
00eoo`03001oogoo00eoo`03001oogoo08Uoo`03001oogoo004000008goo00<007ooOol0?Woo1@0O
/goo00<007ooOol00Goo000SOol00`00Oomoo`13Ool501n^Ool00`00Oomoo`01Ool002=oo`03001o
ogoo04Qoo`H07`9oo`0301moogoo0:=oo`03001oogoo005oo`000Woo00<007ooOol00Woo00<007oo
Ool06Goo00<007ooOol0CWoo1`0OXGoo00<007ooOol00Goo0002Ool6000KOol00`00Oomoo`1EOol8
01nIOol00`00Oomoo`01Ool0009oo`03001oo`00009oo`03001oogoo01Uoo`03001oogoo05eoo`D0
7iAoo`03001oogoo005oo`000Woo00<007oo00000Woo00<007ooOol06Goo00<007ooOol0HWoo1@0O
Sgoo00<007ooOol00Goo0003Ool01000Ool0000077oo0P00J7oo1P0OR7oo0P000goo000SOol00`00
Oomoo`1]Ool501leOol00`00Oomoo`0<Ool3000=Ool2000>Ool2000NOol00`00Oomoo`01Ool0025o
o`<000aoo`@000aoo`@000]oo`@000aoo`@000aoo`<000aoo`@000aoo`@000Ioo`D07`@000aoo`@0
00aoo`<000eoo`<000aoo`<000eoo`@000aoo`@000ioo`03001oogoo00]oo`03001oogoo005oo`00
17oo00@007ooOol001Uoo`<000aoo`@000aoo`@000]oo`@000aoo`@000aoo`<000aoo`@000aoo`@0
00]oo`D07`]oo`@000aoo`<000eoo`<000aoo`<000eoo`<000eoo`<000ioo`@000]oo`03001oogoo
005oo`0017oo10006Woo0P003Goo0`003Goo0`0037oo0`003Goo0`003Goo0P003Goo0`003Goo0`00
37oo0`0000=oo`0O01l00`0O1goo0`0037oo0`003Goo0`003Goo00<007ooOol03Goo0P003Goo0P00
3goo0`0037oo00<007ooOol00Goo0004Ool01000Oomoo`006Woo0P003Goo0P003Woo0P003Goo0P00
3Woo0P003Woo0P003Goo0P003Woo0P003Goo0P001goo100O0goo0P003Woo00<007ooOol03Goo00<0
07ooOol037oo00<007ooOol03Goo00<007ooOol037oo0P003Woo0`003Goo00<007oo00000@000004
Ool01000Oomoo`006goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol037oo00<007ooOol0
3Goo00<007ooOol037oo0P003Woo00<007ooOol03Goo00<007ooOol037oo00<007ooOol02Goo1P0O
3Goo00<007ooOol03Goo00<007ooOol037oo00<007ooOol03Goo00<007ooOol037oo00<007ooOol0
3Goo00<007ooOol037oo1@00000SOol00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool0
0`00Oomoo`0=Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool0
0`00Oomoo`0=Ool00`00Ool07`0401l8Ool00`00Oomoo`0=Ool00`00Oomoo`1;Ool00`00Ool00001
000002=oo`03001oogoo091oo`<07f=oo`03001oogoo005oo`001Goo0P0077oo00<007ooOol0Tgoo
100OGgoo00<007ooOol00Goo0004Ool200000goo001oo`07Ool20004Ool20005Ool30003Ool00`00
Oomoo`2GOol401mKOol00`00Oomoo`01Ool000Aoo`800003Ool007oo00Ioo`04001oogoo000;Ool0
0`00Oomoo`02Ool00`00Oomoo`2KOol601mEOol00`00Oomoo`01Ool000Eoo`03001oo`0000Moo`04
001oogoo0008Ool50003Ool2002ROol401m?Ool30003Ool000moo`04001oogoo0008Ool01000Oomo
o`0017oo00<007ooOol0YGoo0`0OCWoo00<007ooOol00Goo000?Ool01000Oomoo`002Goo00<007oo
000017oo00<007ooOol0Z7oo100OBWoo00<007ooOol00Goo0005Ool20009Ool2000;Ool20004Ool0
0`00Oomoo`2/Ool401m6Ool00`00Oomoo`01Ool000Aoo`800003Ool007oo01Yoo`03001oogoo0;1o
o`D07d5oo`03001oogoo005oo`0017oo0P0000=oo`00Ool067oo00<007oo00003Goo00<007ooOol0
3Goo00<007ooOol037oo0P003Woo00<007ooOol03Goo0P003Woo00<007ooOol02goo0`003Woo00<0
07ooOol02goo0`0037oo10003Goo0`002goo100O3Goo0`0037oo10003Woo00<007ooOol037oo00<0
07ooOol00Goo0005Ool00`00Ool0000HOol200000goo001oo`0:Ool3000=Ool3000<Ool4000<Ool3
000=Ool4000<Ool3000=Ool3000<Ool3000=Ool3000<Ool4000=Ool3000;Ool4000401l9Ool3000<
Ool4000>Ool3000<Ool00`00Oomoo`01Ool001moo`D000aoo`8000ioo`8000eoo`<000eoo`8000io
o`<000aoo`<000ioo`8000aoo`<000ioo`8000eoo`<000eoo`<000aoo`<000Aoo`@07`Eoo`<000ao
o`<000moo`8000eoo`03001oogoo005oo`0087oo100037oo0`003Goo0`003Goo0`0037oo0`003Goo
0`003Goo0P003Woo0P003Goo0P003Woo0P003Goo0P003goo00<007ooOol02goo0P002Goo0`0O0goo
00<007ooOol037oo0P003Woo0P003Woo00<007ooOol00@000005Ool2000JOol3000=Ool2000>Ool2
000>Ool2000=Ool2000>Ool2000=Ool2000?Ool00`00Oomoo`0;Ool2000?Ool00`00Oomoo`0<Ool0
0`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0:Ool301l00`00Oomoo`0<Ool00`00Oomoo`0=
Ool2000>Ool4000000Aoo`04001oogoo000KOol00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomo
o`0<Ool2000>Ool00`00Oomoo`0<Ool2000>Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomo
o`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool401l;Ool0
0`00Oomoo`0=Ool00`00Oomoo`0<Ool50000009oo`03001oo`00009oo`03001oogoo01Uoo`03001o
ogoo0<]oo`<07bQoo`03001oo`00004000000Woo1P006goo00<007ooOol0cWoo0`0O9Goo00<007oo
Ool00Goo0007Ool00`00Oomoo`0IOol2003BOol401lPOol20003Ool002=oo`03001oogoo0=Eoo`80
7amoo`03001oogoo005oo`008goo00<007ooOol0egoo0P0O7Goo00<007ooOol00Goo0004Ool01000
Oomoo`006goo00<007ooOol0fGoo0`0O6Woo00<007ooOol00Goo0002Ool00`00Ool00003000KOol0
0`00Oomoo`3LOol401lFOol00`00Oomoo`01Ool000Moo`03001oogoo01Uoo`03001oogoo0>1oo`<0
7a=oo`03001oogoo005oo`008goo00<007ooOol0hgoo0`0O47oo00<007ooOol00Goo0004Ool01000
Oomoo`006goo00<007ooOol0R7oo00<007ooOol037oo0P003Woo0P003Goo00<007ooOol03Goo00<0
07ooOol037oo00<007ooOol03Goo00<0000O01l00P0O37oo00<007ooOol00Goo0004Ool4000KOol0
0`00Oomoo`0hOol00`00Oomoo`0=Ool00`00Oomoo`0>Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool0
0`00Oomoo`0;Ool3000<Ool4000<Ool4000;Ool3000=Ool3000<Ool3000?Ool30002Ool301l9Ool0
0`00Oomoo`01Ool000Aoo`03001oogoo01aoo`03001oogoo01Qoo`03001oogoo00eoo`03001oogoo
00aoo`<000eoo`<000eoo`<000aoo`<000eoo`<000ioo`8000eoo`<000eoo`<000aoo`8000ioo`80
00eoo`8000moo`<000Eoo`<07`Ioo`03001oogoo005oo`0017oo00<007ooOol077oo00<007ooOol0
27oo0P003Goo0`003Goo0`003Goo0`0037oo10003Woo0P003Goo0`003Goo0P003Woo0`0037oo0`00
3Goo0`0037oo0`003Goo0`0037oo0`003goo00<007ooOol01goo0P0O17oo00<007ooOol00Goo0005
Ool3000FOol30002Ool00`00Oomoo`07Ool5000;Ool5000;Ool5000<Ool3000=Ool3000>Ool2000=
Ool2000>Ool2000>Ool2000=Ool2000>Ool2000=Ool2000>Ool2000=Ool2000?Ool00`00Oomoo`09
Ool301l00goo001oo`02Ool000Moo`03001oogoo01Aoo`D0009l00Qoo`L000aoo`<000eoo`<000eo
o`8000ioo`8000ioo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00ao
o`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eo
o`03001oogoo00aoo`807`=oo`007Woo0`000Woo00<007ooO0000W`0m7oo00<007ooOol00Goo0005
Ool20002Ool00`00Oomoo`0GOol00`00Oomoo`02Ool4O03`Ool00`00Oomoo`01Ool000Aoo`06001o
ogoo001oo`006Goo00<007ooOol01Woo0g`0kGoo00<007ooOol00Goo0004Ool01P00Oomoo`00Ool0
01Uoo`03001oogoo00Uoo`9l0>]oo`03001oogoo005oo`0017oo1@006Woo00<007ooOol02goo0g`0
j7oo00<007ooOol00Goo0004Ool00`00Oomoo`0LOol00`00Oomoo`0>Ool2O03VOol00`00Oomoo`01
Ool002=oo`03001oogoo011oo`=l0>=oo`03001oogoo005oo`008goo00<007ooOol04goo17`0ggoo
00<007ooOol00Goo000SOol00`00Oomoo`0GOol4O03KOol00`00Oomoo`01Ool002=oo`03001oogoo
01]oo`Al0=Moo`03001oogoo005oo`008goo00<007ooOol07goo0W`0MGoo00<007ooOol03Goo00<0
07ooOol037oo00<007ooOol037oo00<007ooOol077oo00<007ooOol047oo00<007ooOol00Goo000S
Ool00`00Oomoo`0QOol2O00cOol00`00Oomoo`0>Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00
Oomoo`0<Ool2000=Ool3000=Ool2000=Ool3000=Ool00`00Oomoo`0<Ool3000AOol00`00Oomoo`01
Ool000Aoo`03001oogoo009oo`03001oogoo01Moo`8002Aoo`9l035oo`8000ioo`<000aoo`<000eo
o`<000aoo`@000eoo`<000]oo`@000aoo`<000aoo`<000eoo`<0011oo`8000=oo`0017oo1P006Goo
00<007ooOol09Goo0g`000<007ooOol037oo00<007ooOol037oo0P003Goo100037oo100037oo0`00
37oo10003Goo0`003Woo0P0037oo0`003Goo0`002goo10003Goo0`0047oo00<007ooOol00Goo0004
Ool01P00Oomoo`00Ool001Qoo`8000ioo`8001Uoo`04001l07`0O00;Ool4000<Ool4000;Ool5000=
Ool3000<Ool3000=Ool3000=Ool3000>Ool2000<Ool3000=Ool2000:Ool6000=Ool2000@Ool00`00
Oomoo`01Ool000Aoo`04001oogoo000HOol4000<Ool3000:Ool6000:Ool40002O009Ool6000:Ool6
000<Ool3000>Ool2000=Ool2000>Ool2000>Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomo
o`0=Ool00`00Oomoo`0:Ool4000>Ool00`00Oomoo`0=Ool00`00Oomoo`01Ool000Eoo`8001Moo`@0
0003Ool007oo00Uoo`@000]oo`D000]oo`<000=oo`=l0<Ioo`03001oogoo005oo`007Woo0`000Woo
00<007ooOol027oo0`003Goo0P005Woo0g`0`goo00<007ooOol00Goo000OOol01@00Oomoogoo0000
2goo00<007ooOol09goo0W`0`Goo00<007ooOol00Goo0004Ool01000Oomoo`006goo00<007ooOol0
=Goo0W`0_goo00<007ooOol00Goo0004Ool4000KOol00`00Oomoo`0gOol3O02lOol00`00Oomoo`01
Ool000Aoo`04001oogoo000KOol00`00Oomoo`0jOol3O02iOol00`00Oomoo`01Ool000Aoo`04001o
ogoo0008Ool20004Ool20003Ool30005Ool00`00Oomoo`0mOol2O02gOol00`00Oomoo`01Ool000mo
o`04001oogoo0008Ool01000Oomoo`0017oo00<007ooOol0?goo0g`0]7oo00<007ooOol00Goo000?
Ool01000Oomoo`0027oo00@007ooOol000Aoo`8004=oo`9l0;1oo`<000=oo`001Goo0P0027oo00@0
07ooOol000Qoo`<000Eoo`03001oogoo04Aoo`=l0:moo`03001oogoo005oo`0017oo00@007ooOol0
00Moo`04001oogoo0009Ool00`00Oomoo`04Ool00`00Oomoo`17Ool2O01<Ool00`00Oomoo`0=Ool0
0`00Oomoo`0<Ool00`00Oomoo`0oOol00`00Oomoo`01Ool000Aoo`04001oogoo0008Ool2000:Ool3
0004Ool00`00Oomoo`19Ool2O00KOol00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool3
000=Ool3000<Ool3000>Ool00`00Oomoo`0<Ool00`00Oomoo`0<Ool00`00Oomoo`0AOol00`00Oomo
o`01Ool000Eoo`8001aoo`03001oogoo04]oo`9l00Uoo`03001oogoo00eoo`8000eoo`8000eoo`<0
00eoo`<000aoo`@000aoo`@000aoo`<000aoo`<000aoo`<0019oo`03001oogoo005oo`008goo00<0
07ooOol0AWoo0`0017oo0W`01goo0`0037oo1@002Woo1@002goo1@0037oo0`003Goo0`003Goo0`00
2Woo1@002goo1@002Woo1@002goo0`000Woo00<007ooOol00Goo0002Ool00`00Oomoo`02Ool00`00
Oomoo`0IOol00`00Oomoo`0;Ool3000<Ool3000:Ool60009Ool6000:Ool60003Ool2O004Ool6000:
Ool60009Ool6000=Ool3000=Ool2000>Ool2000>Ool2000<Ool3000=Ool3000<Ool3000:Ool60003
Ool0009oo`H001Uoo`<000Yoo`D000Yoo`D000]oo`@000]oo`D000]oo`<000Qoo`9l009oo`<009Uo
o`<0009oo`03001oogoo005oo`0017oo00@007ooOol001Moo`<00003Ool007oo00Uoo`@000]oo`@0
00aoo`8000ioo`8001Yoo`9l0:5oo`03001oogoo005oo`0017oo00@007ooOol001Moo`<00003Ool0
07oo00Yoo`8000eoo`03001oogoo03Yoo`9l09moo`03001oogoo005oo`001Goo0P006Goo00@007oo
Ool000]oo`03001oogoo04]oo`9l09eoo`03001oogoo005oo`008goo00<007ooOol0FGoo0W`0Vgoo
00<007ooOol00Goo000SOol2001LOol2O02HOol20003Ool002=oo`03001oogoo05eoo`9l09Moo`03
001oogoo005oo`001goo00<007ooOol06Goo00<007ooOol0Ggoo00=l07ooOol0U7oo00<007ooOol0
0Goo0007Ool00`00Oomoo`0IOol00`00Oomoo`1POol2O02DOol00`00Oomoo`01Ool002=oo`03001o
ogoo069oo`9l0003Ooml07oo08moo`03001oogoo005oo`008goo00<007ooOol0I7oo0W`0T7oo00<0
07ooOol00Goo000SOol00`00Oomoo`1VOol2O02>Ool00`00Oomoo`01Ool002=oo`03001oogoo06Qo
o`9l02Yoo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03001o
ogoo00eoo`03001oogoo015oo`03001oogoo005oo`008goo00<007ooOol0JWoo0W`02Goo0P003Goo
0P003Goo100037oo0`0037oo100037oo0`003Goo0`0037oo0`004Woo00<007ooOol00Goo000SOol0
0`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`0;Ool3000XOol3000=Ool30004Ool2O006Ool5
000;Ool4000;Ool6000:Ool5000:Ool6000:Ool5000:Ool6000:Ool5000;Ool30002Ool00`00Oomo
o`01Ool0029oo`8000eoo`8000eoo`<000Yoo`D000Yoo`H000Yoo`H000Uoo`H000Yoo`H000=oo`9l
00Aoo`L000Uoo`H000aoo`@000aoo`<000aoo`@000aoo`<000Uoo`L000aoo`<000Yoo`H000=oo`00
87oo10002goo0`0037oo0`0037oo10002goo1@002goo100037oo10002goo0`0027oo0W`0Ogoo0`00
0Woo00<007ooOol00Goo000OOol5000:Ool4000<Ool3000=Ool2000=Ool2000=Ool2000>Ool2000J
Ool00g`0Oomoo`21Ool00`00Oomoo`01Ool0021oo`800003Ool0000000Yoo`8000ioo`03001oogoo
00aoo`03001oogoo04Qoo`9l081oo`8000=oo`008Goo00<007oo0000Mgoo0W`0Ogoo00<007ooOol0
0Goo000SOol00`00Oomoo`1gOol00g`0Oomoo`1lOol00`00Oomoo`01Ool002=oo`03001oogoo07Qo
o`9l07aoo`03001oogoo005oo`008goo00<007ooOol0NWoo0W`0NWoo00<007ooOol00Goo000SOol0
0`00Oomoo`1lOol00g`0Oomoo`1gOol00`00Oomoo`01Ool002=oo`03001oogoo07eoo`03O01oogoo
07Ioo`03001oogoo005oo`008goo00<007ooOol0OWoo0W`0MWoo00<007ooOol00Goo000SOol00`00
Oomoo`20Ool00g`0Oomoo`1cOol00`00Oomoo`01Ool002=oo`03001oogoo085oo`9l07=oo`03001o
ogoo005oo`008goo00<007ooOol0Pgoo00=l07ooOol07Goo0P003Woo0P003Goo0P003Woo0P008Woo
00<007ooOol00Goo000SOol00`00Oomoo`24Ool2O0000`00Oomoo`0;Ool3000<Ool4000<Ool4000;
Ool4000<Ool4000;Ool3000=Ool30002Ool00`00Oomoo`01Ool002=oo`8000eoo`8000ioo`03001o
ogoo00]oo`<000eoo`<000aoo`<000Uoo`L000Uoo`H000Uoo`L000Uoo`80009l008000Yoo`H000Uo
o`H000Yoo`H000Uoo`H000Yoo`H000Uoo`H000Yoo`H000=oo`008Goo0`0037oo0`003Goo0P002goo
1@002Woo1P002Woo1@002Woo1P002Woo10002goo1@002goo10000W`02Woo10002goo0`003Goo0`00
37oo0`003Goo0`0037oo100037oo100000=oo`00Ool00Woo000OOol5000:Ool4000<Ool3000<Ool4
000<Ool4000;Ool4000<Ool3000<Ool2000>Ool2000=Ool20004Ool00g`0Oomoo`07Ool2001;Ool2
000>Ool20003Ool00`00Oomoo`01Ool0021oo`800003Ool007oo00Yoo`<000aoo`<000eoo`03001o
ogoo00eoo`03001oogoo00aoo`03001oogoo00aoo`03001oogoo039oo`03O01oogoo06Qoo`03001o
ogoo005oo`008Goo00<007oo000037oo00<007ooOol037oo00<007ooOol0L7oo0W`0J7oo00<007oo
Ool00Goo000SOol00`00Oomoo`2>Ool00g`0Oomoo`1UOol00`00Oomoo`01Ool002=oo`03001oogoo
08moo`03O01oogoo06Aoo`03001oogoo005oo`008goo00<007ooOol0T7oo00=l07ooOol0Hgoo00<0
07ooOol00Goo000SOol00`00Oomoo`2AOol2O01SOol00`00Oomoo`01Ool002=oo`03001oogoo09=o
o`03O01oogoo061oo`03001oogoo005oo`008goo00<007ooOol0U7oo00=l07ooOol0Ggoo00<007oo
Ool00Goo000@Ool20004Ool20004Ool20005Ool00`00Oomoo`2EOol00g`0Oomoo`1NOol00`00Oomo
o`01Ool000moo`04001oogoo0008Ool01000Oomoo`0017oo00<007ooOol0UWoo0W`0GWoo00<007oo
Ool00Goo000?Ool01000Oomoo`0027oo00@007ooOol000Aoo`8009Uoo`03O01oogoo05Uoo`<000=o
o`003goo00@007ooOol000Uoo`8000Eoo`03001oogoo09Uoo`9l05]oo`03001oogoo005oo`003goo
00@007ooOol000Qoo`04001oogoo0004Ool2000>Ool00`00Oomoo`0<Ool2000=Ool2000>Ool20017
Ool3000=Ool30004Ool00g`0Oomoo`05Ool3000=Ool3000<Ool3000=Ool3000<Ool3000=Ool30002
Ool00`00Oomoo`01Ool0011oo`8000Yoo`8000Aoo`8000ioo`03001oogoo00]oo`<000aoo`<000eo
o`<000eoo`<000Yoo`H000Uoo`H000Yoo`H000Uoo`H000Yoo`H0009oo`03O01oogoo00Aoo`H000Yo
o`H000Uoo`H000Yoo`H000Uoo`H000Yoo`H000=oo`0087oo100037oo0P0037oo10002goo100037oo
10002goo1@002goo1@002Woo1@002goo10002goo100037oo0`001Woo0W`017oo0`003Goo0`0037oo
0`003Goo0`0037oo0`003Goo0`000Woo00<007ooOol00Goo000OOol5000;Ool3000=Ool3000<Ool3
000<Ool3000<Ool4000<Ool3000=Ool2000=Ool2000=Ool2000IOol00g`0Oomoo`1DOol00`00Oomo
o`01Ool0021oo`800003Ool007oo00]oo`03001oogoo00eoo`03001oogoo00aoo`03001oogoo00ao
o`03001oogoo00aoo`03001oogoo00aoo`03001oogoo04Moo`03O01oogoo05=oo`03001oogoo005o
o`008goo00<007ooOol0XGoo0W`0Dgoo00<007ooOol00Goo000SOol00`00Oomoo`2SOol00g`0Oomo
o`1@Ool00`00Oomoo`01Ool002=oo`03001oogoo0:Aoo`03O01oogoo04moo`03001oogoo005oo`00
8goo00<007ooOol0YGoo00=l07ooOol0CWoo00<007ooOol00Goo000SOol00`00Oomoo`2VOol00g`0
Oomoo`1=Ool00`00Oomoo`01Ool002=oo`800:Qoo`03O01oogoo04]oo`8000=oo`008goo00<007oo
Ool0Z7oo0W`0C7oo00<007ooOol00Goo000SOol00`00Oomoo`2ZOol00g`0Oomoo`19Ool00`00Oomo
o`01Ool002=oo`03001oogoo0:]oo`03O01oogoo04Qoo`03001oogoo005oo`008goo00<007ooOol0
[7oo00=l07ooOol08goo0P003Woo00<007ooOol04Goo00<007ooOol00Goo000SOol2002EOol3000<
Ool30007Ool00g`0Oomoo`03Ool3000=Ool2000=Ool4000<Ool3000<Ool30002Ool00`00Oomoo`01
Ool0029oo`8000ioo`8000ioo`8000eoo`8000eoo`<000aoo`<000eoo`<000Uoo`H000Yoo`H000Uo
o`H000Yoo`H000Uoo`H000Eoo`03O01oogoo009oo`H000Uoo`H000Yoo`H000Uoo`H000Yoo`H000=o
o`0087oo10003Goo0P003Goo0`0037oo0`002goo1@002Woo1@002goo1@002Woo1@002goo10002goo
100037oo10002goo100027oo00Al07ooOomoo`<000aoo`<000eoo`<000aoo`<000eoo`@00003Ool0
07oo009oo`007goo1@002goo0`0037oo10002goo100037oo10002goo100037oo0`003Goo0`0037oo
0P003Goo0P003Woo0P003Goo0P002goo00=l07ooOol0?Woo0P000goo00<007ooOol00Goo000POol4
000;Ool3000=Ool3000<Ool3000=Ool00`00Oomoo`0<Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool0
0`00Oomoo`18Ool00g`0Oomoo`12Ool00`00Oomoo`01Ool0025oo`03001oo`0000aoo`03001oogoo
00eoo`03001oogoo00aoo`03001oogoo08Ioo`03O01oogoo045oo`03001oogoo005oo`008goo00<0
07ooOol0/goo00=l07ooOol0@7oo00<007ooOol00Goo000SOol00`00Oomoo`2dOol00g`0Oomoo`0o
Ool00`00Oomoo`01Ool002=oo`800;Ioo`03O01oogoo03eoo`8000=oo`008goo00<007ooOol0]Woo
00=l07ooOol0?Goo00<007ooOol00Goo000SOol00`00Oomoo`2gOol00g`0Oomoo`0lOol00`00Oomo
o`01Ool002=oo`03001oogoo0;Qoo`03O01oogoo03]oo`03001oogoo005oo`008goo00<007ooOol0
^Goo00=l07ooOol0>Woo00<007ooOol00Goo000SOol00`00Oomoo`2jOol00g`0Oomoo`0iOol00`00
Oomoo`01Ool002=oo`03001oogoo0;]oo`03O01oogoo03Qoo`03001oogoo005oo`008goo00<007oo
Ool0_7oo00=l07ooOol0=goo00<007ooOol00Goo000SOol2000>Ool00`00Oomoo`0<Ool2000=Ool2
000>Ool2000=Ool2000hOol3000=Ool3000<Ool3000=Ool30007Ool00g`0Oomoo`02Ool3000=Ool3
000<Ool3000=Ool30002Ool00`00Oomoo`01Ool0029oo`8000eoo`8000eoo`<000aoo`<000eoo`<0
00aoo`<000]oo`H000Uoo`H000Yoo`H000Uoo`H000Yoo`H000Uoo`H000Yoo`H000Eoo`04O01oogoo
Ool6000:Ool60009Ool6000:Ool60003Ool0021oo`@000]oo`<000aoo`@000]oo`@000aoo`@000]o
o`@000aoo`D000Yoo`D000]oo`@000aoo`@000]oo`@000]oo`<000eoo`<000Uoo`03O01oogoo00<0
00eoo`<000aoo`<000eoo`<0009oo`03001oogoo005oo`007goo1@002goo0`003Goo0`0037oo0`00
37oo0`0037oo0`003Woo0`0037oo0`0037oo0P003Woo0P003Goo0P00:Woo00=l07ooOol0<goo00<0
07ooOol00Goo000POol200000goo0000000;Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomo
o`0<Ool00`00Oomoo`0<Ool00`00Oomoo`0=Ool00`00Oomoo`0<Ool00`00Oomoo`1HOol00g`0Oomo
o`0aOol20003Ool002=oo`03001oogoo0<9oo`03O01oogoo01]oo`D07`9oo`<07`=oo`<07`Ioo`03
001oogoo005oo`008goo00<007ooOol0`goo00=l07ooOol06goo00@07gooOol07`9oo`0401moogoo
01l2Ool0100OOomoo`0O1Goo00<007ooOol00Goo000SOol00`00Oomoo`34Ool00g`0Oomoo`0JOol0
0`0OOomoo`06Ool00`0OOomoo`03Ool00`0OOomoo`03Ool00`00Oomoo`01Ool002=oo`03001oogoo
0<Eoo`03O01oogoo01Uoo`807`Eoo`807`Aoo`807`Ioo`03001oogoo005oo`008goo00<007ooOol0
aWoo00=l07ooOol067oo00@07gooOol07`9oo`0401moogoo01l2Ool0100OOomoo`0O1Goo00<007oo
Ool00Goo000SOol00`00Oomoo`37Ool00g`0Oomoo`0FOol501l2Ool401l2Ool401l5Ool00`00Oomo
o`01Ool002=oo`03001oogoo0<Moo`03O01oogoo02aoo`03001oogoo005oo`008goo00<007ooOol0
b7oo00=l07ooOol0:goo00<007ooOol00Goo000SOol00`00Oomoo`39Ool00g`0Oomoo`0VOol701l1
Ool001]oo`D000=oo`03001oogoo0<Yoo`03O01oogoo02Aoo`T07`007Goo00<007ooOol00goo0P00
;goo00<007ooOol0;goo00<007ooOol0;goo00<007ooOol07Woo0`0037oo0`001Woo00=l07ooOol0
17oo0`0037oo0`003Goo2@0O000MOol00`00Oomoo`02Ooo@00000g`00000000R000901l001eoo`03
001oogoo00@000eoo`8000eoo`<000eoo`8000]oo`D000Yoo`D000]oo`D000Yoo`D000]oo`D000Yo
o`D000]oo`@000]oo`D000]oo`@000]oo`@000aoo`@000]oo`@000aoo`T07`007Goo00<007oo0000
0`0037oo0`0037oo100037oo0`0037oo100037oo0`0037oo10002goo100037oo0`003Goo0`0037oo
0P003Woo0P003Goo0P003Goo0P003Woo0P003Goo0P003Woo2@0O000LOol20002Ool3000<Ool3000=
Ool3000<Ool3000=Ool2000=Ool3000=Ool00`00Oomoo`0<Ool00`00Oomoo`0<Ool00`00Oomoo`0=
Ool00`00Oomoo`1ZOol801l0025oo`03001oogoo00aoo`03001oogoo00eoo`03001oogoo00aoo`03
001oogoo00aoo`03001oogoo00eoo`03001oogoo0:Moo`L07`5oo`00ogoo6Woo100O0goo003oOolQ
Ool00?moob5oo`00ogoo8Goo003oOolQOol00001\
\>"],
  ImageRangeCache->{{{0, 287}, {287, 0}} -> {-0.141609, -0.11738, 0.00401977, \
0.00401977}}]
}, Open  ]]
}, Closed]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["2.3 Questions & Answers", "Section",
  FontSize->25],

Cell[CellGroupData[{

Cell["\<\
1. Whenever policing is favoured, will this necessarily lead to a more \
efficient running of a society than if it is not?\
\>", "Subsection",
  FontFamily->"Times New Roman",
  FontSize->16,
  FontWeight->"Plain",
  FontVariations->{"CompatibilityType"->0}],

Cell[TextData[StyleBox["Yes, it should, although animals would also waste a \
lot of energy on mutual inhibition of each other's selfishness (e.g. on \
aggression, see the c parameter in the model).",
  FontSlant->"Italic"]], "Text"]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
2. When a social insect colony loses its queen it seems likely that not all \
workers are totipotent and can switch to a reproductive role (this should be \
true especially for foragers with regressed ovaries). Also, the workers that \
do become reproductive may be able to both lay eggs and do some foraging. How \
could this be accomodated in the model?\
\>", "Subsection",
  FontFamily->"Times New Roman",
  FontSize->16,
  FontWeight->"Plain",
  FontVariations->{"CompatibilityType"->0}],

Cell[TextData[StyleBox["If t is the fraction of totipotent workers then a \
fraction (1-t) might keep foraging. This tends to reduce the costs to colony \
function, making a higher level of breeding favourable from the perspective \
of the totipotent workers. To take this into account in Model 1, let colony \
success be (1-z(1-t)) instead of just (1-z). By the same methods as above, \
this yields an ESS probability of becoming  a reproductive worker of \
(1-r)/(1-t) :",
  FontSlant->"Italic"]], "Text",
  FontSize->16],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(w = \((y/z)\)*\((1 - z*\((1 - t)\))\);\)\), "\[IndentingNewLine]", 
    \(\(dwdg = 
        Dt[w, g] /. {Dt[y, g] \[Rule] 1, Dt[z, g] \[Rule] r, 
            Dt[t, g] \[Rule] 0, y \[Rule] z};\)\), "\[IndentingNewLine]", 
    \(mESS[r_, 
        t_] = \(\(\(Solve[dwdg \[Equal] 0, 
              z]\)[\([1]\)]\)[\([1]\)]\)[\([2]\)]\)}], "Input"],

Cell[BoxData[
    \(\(\(-1\) + r\)\/\(\(-1\) + t\)\)], "Output"]
}, Open  ]],

Cell[TextData[StyleBox["For example, if half of the workers are totipotent at \
the time the queen is lost (t=0.5), then 50% of them should become \
reproductives instead of just 25% if all are totipotent (this assumes single \
mating). \nIf reproductive workers can spend a fraction f of their time \
foraging, then, again costs to colony function would not be as severe. \
Formally, colony success would become (1-z.(1-f)) rather than just (1-z). So \
this affects the ESS in the same way as above.  ",
  FontSlant->"Italic"]], "Text",
  FontSize->16]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
3. Above we assumed that workers become reproductives with some ESS \
probability in the event the queen is lost. In other words, the ESS is what \
is often called a mixed ESS. Alternatively, it could be that the ESS reflects \
how each worker will divide its time between reproduction and foraging over \
its entire lifetime. In that case, the ESS reflects a continuous ESS. Does \
the model apply to both situations? And how does this relate to the level of \
skew predicted by Model 1? How does policing interact with the predicted \
level of reproductive skew? What are the more general implications for skew \
theory?  \
\>", "Subsection",
  FontFamily->"Times New Roman",
  FontSize->16,
  FontWeight->"Plain",
  FontVariations->{"CompatibilityType"->0}],

Cell[TextData[StyleBox["The continuous and mixed ESS situation are very \
similar, and it seems reasonable to assume that the fitness function for each \
case is identical. Therefore, the model adequately predicts the right ESS for \
each situation. In terms of reproductive skew, the probabilistic (mixed ESS) \
model predicts high skew in high relatedness groups (just a few workers \
should lay eggs), but low skew in low relatedness groups (many workers should \
lay eggs). But the continuous ESS model would cause each worker to contribute \
equally to male production irrespective of relatedness, i.e. it  predicts low \
skew under all circumstances. So even though these two situations are \
theoretically almost identical they lead to very different skew predictions. \
\nPolicing will tend to increase skew since it should cause fewer individuals \
in the group to reproduce than is dictated by their own inclusive fitness \
preferences. But since policing is favoured especially at low relatedness, it \
makes the opposite prediction as above: it should favour high skew at low \
relatedness (due to policing) and low skew at high relatedness (due to the \
absence of policing and limited self restraint). \nAll this means that any \
attempt to simply relate skew to relatedness patterns is probably in vain - \
any pattern is possible depending on the specific biology. We already know \
this from the long series of theoretical papers on skew theory, but it is \
also easy to see from the simple models above. Message: don't worry about \
skew theory but construct a specific model for the problem at hand. And if \
necessary, provide intuitive explanations in terms of Hamilton's rule - the \
only truly fundamental principle in social evolution theory. ",
  FontSlant->"Italic"]], "Text",
  FontSize->16]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
4. Suppose that group success is not a decreasing linear but a decreasing \
concave or a convex function of the proportion of selfish individuals within \
the group. How would this affect the predictions of the model?\
\>", "Subsection",
  FontFamily->"Times New Roman",
  FontSize->16,
  FontWeight->"Plain",
  FontVariations->{"CompatibilityType"->0}],

Cell[TextData[{
  StyleBox["With a concave colony productivity function unrestrained breeding \
would reduce group output more than with a linear cost function. The \
consequence would be that in Model 1, the ESS probability of breeding would \
be lower than with a linear cost function. The inverse is true for a convex \
productivity function. To formalise this, let group success be G=",
    FontSlant->"Italic"],
  Cell[BoxData[
      \(TraditionalForm\`\((1 - z)\)\^k\)],
    FontSlant->"Italic"],
  StyleBox["  instead of just (1-z) in Model 1 (k=1, >1 and <1 then \
correspond to a linear, a concave and a convex cost function).  By the same \
methods as above, this yields an ESS probability of becoming a reproductive \
worker of z*=(1-r)/(1+r.(k-1)) :",
    FontSlant->"Italic"]
}], "Text",
  FontSize->16],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(w = \((y/z)\)*\((1 - z)\)\^k;\)\), "\[IndentingNewLine]", 
    \(\(dwdg = 
        FullSimplify[
          Dt[w, g] /. {Dt[y, g] \[Rule] 1, Dt[z, g] \[Rule] r, 
              Dt[k, g] \[Rule] 0, y \[Rule] z}];\)\), "\[IndentingNewLine]", 
    \(mESS[r_, 
        k_] = \(\(\(Solve[dwdg \[Equal] 0, 
              z]\)[\([2]\)]\)[\([1]\)]\)[\([2]\)]\)}], "Input"],

Cell[BoxData[
    \(\(-\(\(\(-1\) + r\)\/\(1 - r + k\ r\)\)\)\)], "Output"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
5. Frank discusses his model in rather broad terms, arguing that it might be \
relevant to explain cooperation among slime mould cells, among homologous \
chromosomes within diploid cells (Mendelism), etc... But do you think the \
assumptions of the model really warrant such a broad discussion? E.g. think \
about the slime mould case. What fraction of slug cells should develop into \
spore rather than stalk cells according to Model 1? But how realistic is it \
that an average cells' success is a linear decreasing function of the \
proportion of spore forming cells? And what about meiotic drive?\
\>", "Subsection",
  FontFamily->"Times New Roman",
  FontSize->16,
  FontWeight->"Plain",
  FontVariations->{"CompatibilityType"->0}],

Cell[TextData[{
  StyleBox["Slime moulds: Frank assumes that the group optimum is near zero \
allocation to reproduction. This is probably an OK assumption for the worker \
reproduction problem and for the level of queen production in swarming social \
insects (see section 3). But for slime moulds it seems likely that some \
intermediate allocation to spores is the group optimum. A case in point is \
that even when slime moulds are composed of single clones (so that cell-cell \
relatedness is 1), 20% of all cells become stalk cells and 80% become spores. \
",
    FontSlant->"Italic"],
  "\n",
  StyleBox["Mendelism/Meiotic drive: driving and cooperative genes typically \
reach a pure strategy equilibrium; Frank models a mixed/continuous ESS. \
Wenseleers & Ratnieks (submitted) analyses meiotic drive as a social \
interaction using a generalised version of Hamilton's rule; alternatively, \
the 2-player  pure strategy analysis of Section 1.2 could be used. ",
    FontSlant->"Italic"]
}], "Text",
  FontSize->16]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
6. Hammerstein (1995) commented on Frank's study, saying that the policing \
model wasn't quite convincing at explaining cooperation in low relatedness \
groups, because at least in genetically unrelated groups no individual should \
care about the reproduction of others in the group (since there could be no \
inclusive fitness gains). What did Hammerstein overlook?\
\>", "Subsection",
  FontFamily->"Times New Roman",
  FontSize->16,
  FontWeight->"Plain",
  FontVariations->{"CompatibilityType"->0}],

Cell[TextData[StyleBox["Policing increases overall group productivity, and \
since the policing individual makes up a fraction 1/N of the total group (if \
N is group size), policing will have a 1/N selfish benefit (cf. r = (1/N) + \
r'.(N-1)/N with r'=pairwise genetic relatedness). Even in genetically \
unrelated groups, therefore, policing is selected for, even though the motive \
is then ultimately selfish. For the same reason, a slight degree of restraint \
is favoured in unrelated groups. In D.S. Wilson's terminology (Wilson 1990), \
the 1/N selfish component of restrained breeding causes weak altruism within \
social groups (Pepper 2000 discusses the matter more fully). Although the 1/N \
component can probably be neglected for the worker reproduction problem \
(colony sizes are typically large), it may be important in other contexts. \
For example, no parent-offspring conflict over the exploitation rate of \
parental resources is expected if parents have only one offspring (N=1, it \
will then only compete with itself). ",
  FontSlant->"Italic"]], "Text",
  FontSize->16]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
7. In what sense does the type of policing assumed in Frank's model differ \
from Ratnieks' (1988) concept of \"worker policing\" (mutual inhibition of \
worker laying under queenright condition)? What are the commonalities?\
\>", "Subsection",
  FontFamily->"Times New Roman",
  FontSize->16,
  FontWeight->"Plain",
  FontVariations->{"CompatibilityType"->0}],

Cell[TextData[StyleBox["In Frank's model, policing is favoured because it \
increases group output. This has inclusive fitness benefits in case group \
members are related (e.g. increased production of nephews) or a 1/N selfish \
benefit in case group members are unrelated (if N is group size). Worker \
policing as envisaged by Ratnieks (1988) is selected for when workers are \
related more to the males they kill (nephews) than to the males they spare \
(brothers). Here policing can have no direct selfish benefits. Common to all \
policing models is that they address the question of when individuals are \
selected to inhibit each other's selfish tendencies (i.e. when is what I do \
not OK for others to do).  ",
  FontSlant->"Italic"]], "Text",
  FontSize->16]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
8. How could the model be extended so that it also applies to the evolution \
of worker laying under queenright condition (hint: first take a look at \
Section 3 on caste conflict)? Should the predicted proportion of reproductive \
workers be higher or lower? And if worker policing is allowed for, could it \
be that it is favoured at any queen mating frequency, rather than just at \
queen mating frequencies higher than two, as predicted by Ratnieks (1988)?\
\>", "Subsection",
  FontFamily->"Times New Roman",
  FontSize->16,
  FontWeight->"Plain",
  FontVariations->{"CompatibilityType"->0}],

Cell[TextData[StyleBox["Haven't done this yet, but the predicted level of \
worker laying should be lower than under queenless condition, because worker \
reproduction would also reduce the number of queens reared, i.e. it would \
have additional inclusive fitness costs. The idea that worker reproduction \
would reduce colony productivity would still apply, and therefore it seems \
likely that if policing can be performed at low cost, it would be favoured at \
any queen mating frequency (although for a different reason than envisaged by \
Ratnieks (1988), see Question 7).  ",
  FontSlant->"Italic"]], "Text",
  FontSize->16]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
9. Tragedies of the commons have been extensively discussed in economics \
(e.g. livestock owners that overexploit common grazing land to increase \
revenues relative to others using the same piece of land, see e.g. Hardin \
1968). What are the formal differences between calculating the best rational \
strategy in economics and calculating an ESS in biology? Have concepts such \
as relatedness any meaning in economics? \
\>", "Subsection",
  FontFamily->"Times New Roman",
  FontSize->16,
  FontWeight->"Plain",
  FontVariations->{"CompatibilityType"->0}],

Cell[TextData[StyleBox["George Price was perhaps among the first evolutionary \
biologists to see the strong similarities between tragedies of the commons in \
economics and some problems of group selection in biology (Frank 1995b p. \
386). The differences mainly pertain to what is assumed to be maximised: \
utility in economics, fitness in biology. Economic models are also purely \
phenotypic models, i.e. instead of gene frequency change they investigate \
phenotypic strategy change. Much more could probably be learned by explicit \
carry over of concepts between both fields. For example, phenotypic versions \
of relatedness (e.g. Queller 1984) have sometimes been described as measuring \
\"better than average information about a social interactant's \
behaviour/strategy\" (Frank 1997). Such a relatedness coefficient does have a \
meaning in economics: if anyone has better than average information about the \
likely behaviour of others (i.e. r>0), then that would tend to favour \
strategies that benefit the global economy (a Pareto optimal outcome) (for \
more on this, see Aumann 198; Skyrms 1994, 1996).Currently, economists often \
use evolutionary rather than classical game theory on the premise that even \
though strategies may not necessarily be heritable, the succesful ones are \
copied (imitated) more often by others.",
  FontSlant->"Italic"]], "Text",
  FontSize->16]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["2.4 References", "Section",
  FontSize->25],

Cell[TextData[{
  "Aumann, R. J. 1987. Correlated equilibrium as an expression of Bayesian \
rationality. ",
  StyleBox["Econometrica",
    FontSlant->"Italic"],
  " 55: 1-18.\nFrank, S.A. 1995a. Mutual policing and repression of \
competition in the evolution of cooperative groups. ",
  StyleBox["Nature ",
    FontSlant->"Italic"],
  "377: 520-522.\nFrank, S.A. 1995b. George Price's contributions to \
evolutionary genetics. ",
  StyleBox["Journal of Theoretical Biology ",
    FontSlant->"Italic"],
  "175: 373-\n388.\nFrank, S.A. 1996. Policing and group cohesion when \
resources vary. ",
  StyleBox["Animal Behaviour ",
    FontSlant->"Italic"],
  "52: 1163-1169.\nFrank, S.A. 1998. ",
  StyleBox["Foundations of Social Evolution. ",
    FontSlant->"Italic"],
  "Princeton University Press, Princeton, New Jersey.\nHammerstein, P. 1995. \
A twofold tragedy unfolds. ",
  StyleBox["Nature ",
    FontSlant->"Italic"],
  "377: 478.\nHardin, G. 1968. The tragedy of the commons. ",
  StyleBox["Science ",
    FontSlant->"Italic"],
  "162: 1243-1244.\nPepper, J. W. 2000. Relatedness in trait group models of \
social evolution. ",
  StyleBox["Journal of Theoretical Biology",
    FontSlant->"Italic"],
  " 206: 355-68.\nQueller, D.C. 1984. Kin selection and frequency-dependence \
- a game theoretic approach. ",
  StyleBox["Biological Journal of the Linnean Society ",
    FontSlant->"Italic"],
  "23: 133-143\nRatnieks, F.L.W. 1988. Reproductive harmony via mutual \
policing by workers in eusocial Hymenoptera. ",
  StyleBox["American Naturalist ",
    FontSlant->"Italic"],
  "132: 217-236.\nSkyrms, B. 1994. Darwin meets the logic of decision - \
Correlation in evolutionary game theory. ",
  StyleBox["Philosophy of Science",
    FontSlant->"Italic"],
  " 61: 503-528.\nSkyrms, B. 1996. ",
  StyleBox["Evolution of the Social Contract.",
    FontSlant->"Italic"],
  " Cambridge University Press, Cambridge.\nWenseleers, T. & Ratnieks, F.L.W. \
Towards a general theory of conflict: the sociobiology of mendelian \
segregation. Submitted.\nWilson, D. S. 1990. Weak altruism, strong group \
selection. ",
  StyleBox["Oikos",
    FontSlant->"Italic"],
  " 59: 135-140."
}], "Text",
  FontSize->16]
}, Closed]]
},
FrontEndVersion->"4.0 for Microsoft Windows",
ScreenRectangle->{{0, 800}, {0, 555}},
WindowSize->{792, 433},
WindowMargins->{{-8, Automatic}, {Automatic, 1}},
PrintingCopies->1,
PrintingPageRange->{Automatic, Automatic},
StyleDefinitions -> "Classroom.nb"
]


(***********************************************************************
Cached data follows.  If you edit this Notebook file directly, not using
Mathematica, you must remove the line containing CacheID at the top of 
the file.  The cache data will then be recreated when you save this file 
from within Mathematica.
***********************************************************************)

(*CellTagsOutline
CellTagsIndex->{}
*)

(*CellTagsIndex
CellTagsIndex->{}
*)

(*NotebookFileOutline
Notebook[{
Cell[1717, 49, 268, 10, 154, "Title"],
Cell[1988, 61, 244, 7, 91, "Text"],

Cell[CellGroupData[{
Cell[2257, 72, 44, 1, 67, "Section"],
Cell[2304, 75, 2254, 39, 425, "Text"]
}, Open  ]],

Cell[CellGroupData[{
Cell[4595, 119, 48, 1, 67, "Section"],
Cell[4646, 122, 464, 8, 102, "Text"]
}, Open  ]],

Cell[CellGroupData[{
Cell[5147, 135, 59, 1, 67, "Section"],
Cell[5209, 138, 240, 7, 142, "Text"],
Cell[5452, 147, 223, 5, 74, "Definition"],
Cell[5678, 154, 63, 1, 30, "Text"],
Cell[5744, 157, 63, 1, 50, "Input"],
Cell[5810, 160, 551, 9, 90, "Text"],
Cell[6364, 171, 116, 3, 53, "Definition"],
Cell[6483, 176, 111, 3, 30, "Text"],

Cell[CellGroupData[{
Cell[6619, 183, 174, 3, 50, "Input"],
Cell[6796, 188, 64, 1, 62, "Output"]
}, Open  ]],
Cell[6875, 192, 53, 1, 30, "Text"],
Cell[6931, 195, 1467, 22, 306, "Text"],
Cell[8401, 219, 68, 1, 53, "Definition"],
Cell[8472, 222, 130, 4, 30, "Text"],

Cell[CellGroupData[{
Cell[8627, 230, 72, 1, 50, "Input"],
Cell[8702, 233, 53, 1, 49, "Output"]
}, Open  ]],
Cell[8770, 237, 1488, 23, 646, "Text"]
}, Closed]],

Cell[CellGroupData[{
Cell[10295, 265, 60, 1, 47, "Section"],

Cell[CellGroupData[{
Cell[10380, 270, 63, 1, 52, "Subsection"],
Cell[10446, 273, 488, 11, 286, "Text"],
Cell[10937, 286, 229, 5, 74, "Definition"],
Cell[11169, 293, 264, 5, 50, "Text"],
Cell[11436, 300, 289, 5, 190, "Input"],
Cell[11728, 307, 117, 3, 53, "Definition"],
Cell[11848, 312, 336, 6, 70, "Text"],
Cell[12187, 320, 108, 3, 30, "Text"],

Cell[CellGroupData[{
Cell[12320, 327, 131, 3, 50, "Input"],
Cell[12454, 332, 197, 4, 62, "Output"]
}, Open  ]],
Cell[12666, 339, 149, 4, 30, "Text"],
Cell[12818, 345, 154, 4, 30, "Text"],
Cell[12975, 351, 135, 4, 30, "Text"],

Cell[CellGroupData[{
Cell[13135, 359, 135, 3, 50, "Input"],
Cell[13273, 364, 84, 1, 49, "Output"]
}, Open  ]],
Cell[13372, 368, 162, 4, 30, "Text"],
Cell[13537, 374, 89, 1, 53, "Definition"],
Cell[13629, 377, 511, 9, 122, "Text"],

Cell[CellGroupData[{
Cell[14165, 390, 61, 1, 50, "Input"],
Cell[14229, 393, 64, 1, 49, "Output"]
}, Open  ]],
Cell[14308, 397, 51, 1, 30, "Text"],
Cell[14362, 400, 1385, 24, 290, "Text"]
}, Closed]],

Cell[CellGroupData[{
Cell[15784, 429, 62, 1, 36, "Subsection"],
Cell[15849, 432, 115, 3, 30, "Text"],
Cell[15967, 437, 328, 6, 110, "Input"],

Cell[CellGroupData[{
Cell[16320, 447, 90, 1, 62, "Subsubsection"],
Cell[16413, 450, 168, 3, 50, "Input"],
Cell[16584, 455, 230, 4, 70, "Input"],
Cell[16817, 461, 295, 5, 70, "Input"],
Cell[17115, 468, 323, 7, 110, "Input"],
Cell[17441, 477, 282, 6, 82, "Text"],

Cell[CellGroupData[{
Cell[17748, 487, 199, 3, 70, "Input"],
Cell[17950, 492, 70137, 2579, 296, 41965, 2227, "GraphicsData", "PostScript", \
"Graphics"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{
Cell[88136, 3077, 81, 4, 54, "Subsubsection"],
Cell[88220, 3083, 54, 1, 50, "Input"],
Cell[88277, 3086, 230, 4, 70, "Input"],
Cell[88510, 3092, 295, 5, 70, "Input"],
Cell[88808, 3099, 284, 6, 110, "Input"],
Cell[89095, 3107, 92, 1, 30, "Text"],

Cell[CellGroupData[{
Cell[89212, 3112, 199, 3, 70, "Input"],
Cell[89414, 3117, 70605, 2615, 296, 42222, 2260, "GraphicsData", \
"PostScript", "Graphics"]
}, Open  ]]
}, Closed]]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{
Cell[160092, 5740, 58, 1, 47, "Section"],

Cell[CellGroupData[{
Cell[160175, 5745, 268, 7, 49, "Subsection"],
Cell[160446, 5754, 233, 3, 56, "Text"]
}, Closed]],

Cell[CellGroupData[{
Cell[160716, 5762, 501, 10, 75, "Subsection"],
Cell[161220, 5774, 523, 8, 102, "Text"],

Cell[CellGroupData[{
Cell[161768, 5786, 367, 7, 90, "Input"],
Cell[162138, 5795, 64, 1, 62, "Output"]
}, Open  ]],
Cell[162217, 5799, 553, 8, 137, "Text"]
}, Closed]],

Cell[CellGroupData[{
Cell[162807, 5812, 770, 14, 138, "Subsection"],
Cell[163580, 5828, 1818, 24, 402, "Text"]
}, Closed]],

Cell[CellGroupData[{
Cell[165435, 5857, 363, 8, 54, "Subsection"],
Cell[165801, 5867, 816, 16, 148, "Text"],

Cell[CellGroupData[{
Cell[166642, 5887, 385, 8, 90, "Input"],
Cell[167030, 5897, 75, 1, 62, "Output"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{
Cell[167154, 5904, 747, 13, 117, "Subsection"],
Cell[167904, 5919, 1023, 18, 229, "Text"]
}, Closed]],

Cell[CellGroupData[{
Cell[168964, 5942, 514, 10, 75, "Subsection"],
Cell[169481, 5954, 1094, 15, 217, "Text"]
}, Closed]],

Cell[CellGroupData[{
Cell[170612, 5974, 370, 8, 54, "Subsection"],
Cell[170985, 5984, 769, 11, 148, "Text"]
}, Closed]],

Cell[CellGroupData[{
Cell[171791, 6000, 606, 11, 96, "Subsection"],
Cell[172400, 6013, 631, 9, 125, "Text"]
}, Closed]],

Cell[CellGroupData[{
Cell[173068, 6027, 569, 11, 96, "Subsection"],
Cell[173640, 6040, 1398, 19, 286, "Text"]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{
Cell[175087, 6065, 49, 1, 47, "Section"],
Cell[175139, 6068, 2205, 54, 638, "Text"]
}, Closed]]
}
]
*)




(***********************************************************************
End of Mathematica Notebook file.
***********************************************************************)