Index: liacs/pnbm/project/planar-signaling.cpn
===================================================================
--- liacs/pnbm/project/planar-signaling.cpn	(revision 52)
+++ liacs/pnbm/project/planar-signaling.cpn	(revision 52)
@@ -0,0 +1,3279 @@
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+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <bendpoint id="ID1197574"
+                   serial="2">
+          <posattr x="-240.725968"
+                   y="28.237650"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <bendpoint id="ID1205315"
+                   serial="3">
+          <posattr x="-396.033044"
+                   y="28.237650"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <annot id="ID1177033">
+          <posattr x="-233.000000"
+                   y="-247.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+          <text tool="CPN Tools"
+                version="2.2.0">b</text>
+        </annot>
+      </arc>
+      <arc id="ID1227954"
+           orientation="BOTHDIR"
+           order="1">
+        <posattr x="0.000000"
+                 y="0.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Black"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Black"
+                  bold="false"/>
+        <arrowattr headsize="1.200000"
+                   currentcyckle="2"/>
+        <transend idref="ID1010169"/>
+        <placeend idref="ID876680"/>
+        <bendpoint id="ID1237697"
+                   serial="1">
+          <posattr x="62.828772"
+                   y="-253.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <bendpoint id="ID1241931"
+                   serial="2">
+          <posattr x="62.828772"
+                   y="-392.973965"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <bendpoint id="ID1233633"
+                   serial="3">
+          <posattr x="-416.000000"
+                   y="-392.973965"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <annot id="ID1227955">
+          <posattr x="43.000000"
+                   y="-264.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+          <text tool="CPN Tools"
+                version="2.2.0">b</text>
+        </annot>
+      </arc>
+      <arc id="ID1230022"
+           orientation="BOTHDIR"
+           order="1">
+        <posattr x="0.000000"
+                 y="0.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Black"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Black"
+                  bold="false"/>
+        <arrowattr headsize="1.200000"
+                   currentcyckle="2"/>
+        <transend idref="ID1039195"/>
+        <placeend idref="ID876680"/>
+        <bendpoint id="ID1280733"
+                   serial="1">
+          <posattr x="75.771028"
+                   y="-84.712951"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <bendpoint id="ID1278288"
+                   serial="2">
+          <posattr x="75.771028"
+                   y="-409.445928"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <bendpoint id="ID1249514"
+                   serial="3">
+          <posattr x="-416.000000"
+                   y="-409.445928"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <annot id="ID1230023">
+          <posattr x="50.000000"
+                   y="-96.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+          <text tool="CPN Tools"
+                version="2.2.0">b</text>
+        </annot>
+      </arc>
+      <arc id="ID1232021"
+           orientation="BOTHDIR"
+           order="2">
+        <posattr x="0.000000"
+                 y="0.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Black"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Black"
+                  bold="false"/>
+        <arrowattr headsize="1.200000"
+                   currentcyckle="2"/>
+        <transend idref="ID1037411"/>
+        <placeend idref="ID876680"/>
+        <bendpoint id="ID1305785"
+                   serial="1">
+          <posattr x="96.949266"
+                   y="75.300401"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <bendpoint id="ID1299996"
+                   serial="2">
+          <posattr x="96.949266"
+                   y="-429.447597"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <bendpoint id="ID1295372"
+                   serial="3">
+          <posattr x="-416.000000"
+                   y="-429.447597"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <annot id="ID1232022">
+          <posattr x="60.000000"
+                   y="64.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+          <text tool="CPN Tools"
+                version="2.2.0">b</text>
+        </annot>
+      </arc>
+      <arc id="ID1372781"
+           orientation="PtoT"
+           order="2">
+        <posattr x="0.000000"
+                 y="0.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Black"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Black"
+                  bold="false"/>
+        <arrowattr headsize="1.200000"
+                   currentcyckle="2"/>
+        <transend idref="ID1364928"/>
+        <placeend idref="ID782428"/>
+        <annot id="ID1372782">
+          <posattr x="-75.000000"
+                   y="205.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+          <text tool="CPN Tools"
+                version="2.2.0">(1,0)</text>
+        </annot>
+      </arc>
+      <arc id="ID1380720"
+           orientation="TtoP"
+           order="1">
+        <posattr x="0.000000"
+                 y="0.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Black"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Black"
+                  bold="false"/>
+        <arrowattr headsize="1.200000"
+                   currentcyckle="2"/>
+        <transend idref="ID1364928"/>
+        <placeend idref="ID782428"/>
+        <annot id="ID1380721">
+          <posattr x="-127.000000"
+                   y="209.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+          <text tool="CPN Tools"
+                version="2.2.0">(0,1)</text>
+        </annot>
+      </arc>
+      <arc id="ID1383483"
+           orientation="BOTHDIR"
+           order="1">
+        <posattr x="0.000000"
+                 y="0.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Black"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Black"
+                  bold="false"/>
+        <arrowattr headsize="1.200000"
+                   currentcyckle="2"/>
+        <transend idref="ID1364928"/>
+        <placeend idref="ID876680"/>
+        <bendpoint id="ID1399753"
+                   serial="1">
+          <posattr x="106.361816"
+                   y="254.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <bendpoint id="ID1406222"
+                   serial="2">
+          <posattr x="106.361816"
+                   y="-442.389853"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <bendpoint id="ID1409555"
+                   serial="3">
+          <posattr x="-416.000000"
+                   y="-442.389853"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <annot id="ID1383484">
+          <posattr x="17.000000"
+                   y="265.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+          <text tool="CPN Tools"
+                version="2.2.0">b</text>
+        </annot>
+      </arc>
+      <arc id="ID1385936"
+           orientation="BOTHDIR"
+           order="1">
+        <posattr x="0.000000"
+                 y="0.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Black"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Black"
+                  bold="false"/>
+        <arrowattr headsize="1.200000"
+                   currentcyckle="2"/>
+        <transend idref="ID1367542"/>
+        <placeend idref="ID875717"/>
+        <bendpoint id="ID1415642"
+                   serial="1">
+          <posattr x="-245.432243"
+                   y="-486.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <bendpoint id="ID1528310"
+                   serial="2">
+          <posattr x="-245.432243"
+                   y="67.064419"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+        </bendpoint>
+        <annot id="ID1385937">
+          <posattr x="-190.000000"
+                   y="-475.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+          <text tool="CPN Tools"
+                version="2.2.0">b</text>
+        </annot>
+      </arc>
+      <arc id="ID1388130"
+           orientation="TtoP"
+           order="2">
+        <posattr x="0.000000"
+                 y="0.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Black"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Black"
+                  bold="false"/>
+        <arrowattr headsize="1.200000"
+                   currentcyckle="2"/>
+        <transend idref="ID1367542"/>
+        <placeend idref="ID841537"/>
+        <annot id="ID1388131">
+          <posattr x="-127.000000"
+                   y="-419.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+          <text tool="CPN Tools"
+                version="2.2.0">(0,1)</text>
+        </annot>
+      </arc>
+      <arc id="ID1390396"
+           orientation="PtoT"
+           order="1">
+        <posattr x="0.000000"
+                 y="0.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Black"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Black"
+                  bold="false"/>
+        <arrowattr headsize="1.200000"
+                   currentcyckle="2"/>
+        <transend idref="ID1367542"/>
+        <placeend idref="ID841537"/>
+        <annot id="ID1390397">
+          <posattr x="-75.000000"
+                   y="-422.000000"/>
+          <fillattr colour="White"
+                    pattern="Solid"
+                    filled="false"/>
+          <lineattr colour="Black"
+                    thick="0"
+                    type="Solid"/>
+          <textattr colour="Black"
+                    bold="false"/>
+          <text tool="CPN Tools"
+                version="2.2.0">(1,0)</text>
+        </annot>
+      </arc>
+      <vguideline id="ID842133"
+                  x="-101.176569">
+        <guideline_elm idref="ID782428"/>
+        <guideline_elm idref="ID782445"/>
+        <guideline_elm idref="ID841537"/>
+        <guideline_elm idref="ID840944"/>
+        <guideline_elm idref="ID1367542"/>
+        <guideline_elm idref="ID1364928"/>
+      </vguideline>
+      <vguideline id="ID888085"
+                  x="-416.000000">
+        <guideline_elm idref="ID880049"/>
+        <guideline_elm idref="ID869744"/>
+        <guideline_elm idref="ID877574"/>
+        <guideline_elm idref="ID876680"/>
+        <guideline_elm idref="ID875717"/>
+        <guideline_elm idref="ID1233633"/>
+        <guideline_elm idref="ID1249514"/>
+        <guideline_elm idref="ID1295372"/>
+        <guideline_elm idref="ID1409555"/>
+        <guideline_elm idref="ID992357"/>
+      </vguideline>
+      <vguideline id="ID918151"
+                  x="-499.000000">
+        <guideline_elm idref="ID904808"/>
+        <guideline_elm idref="ID903262"/>
+      </vguideline>
+      <vguideline id="ID1040841"
+                  x="-6.588785">
+        <guideline_elm idref="ID1010169"/>
+        <guideline_elm idref="ID1037411"/>
+        <guideline_elm idref="ID1039195"/>
+        <guideline_elm idref="ID1597346"/>
+      </vguideline>
+      <vguideline id="ID1042123"
+                  x="-194.839786">
+        <guideline_elm idref="ID782576"/>
+        <guideline_elm idref="ID837477"/>
+        <guideline_elm idref="ID838052"/>
+      </vguideline>
+      <Aux id="ID992357">
+        <posattr x="-416.000000"
+                 y="109.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Navy"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Navy"
+                  bold="false"/>
+        <label/>
+        <text>1. Random direction
+choice</text>
+      </Aux>
+      <Aux id="ID994878">
+        <posattr x="-645.000000"
+                 y="-162.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Fucia"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Fucia"
+                  bold="false"/>
+        <label/>
+        <text>0. Initial value</text>
+      </Aux>
+      <Aux id="ID1593808">
+        <posattr x="-218.000000"
+                 y="221.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Lime"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Lime"
+                  bold="false"/>
+        <label/>
+        <text>Down
+movement</text>
+      </Aux>
+      <Aux id="ID1597346">
+        <posattr x="-6.000000"
+                 y="219.000000"/>
+        <fillattr colour="White"
+                  pattern=""
+                  filled="false"/>
+        <lineattr colour="Maroon"
+                  thick="1"
+                  type="Solid"/>
+        <textattr colour="Maroon"
+                  bold="false"/>
+        <label/>
+        <text>Up 
+movement</text>
+      </Aux>
+    </page>
+    <instances>
+      <instance id="ID2149"
+                page="ID6"/>
+    </instances>
+    <options>
+      <option name="outputdirectory">
+        <value>
+          <text>&lt;same as model&gt;</text>
+        </value>
+      </option>
+      <option name="repavg">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="repciavg">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="repcount">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="repfirstval">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="replastval">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="repmax">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="repmin">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="repssquare">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="repssqdev">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="repstddev">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="repsum">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="repvariance">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="avg">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="ciavg">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="count">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="firstval">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="lastval">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="max">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="min">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="ssquare">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="ssqdev">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="stddev">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="sum">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="variance">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="firstupdate">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="interval">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="lastupdate">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="untimedavg">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="untimedciavg">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="untimedcount">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="untimedfirstval">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="untimedlastval">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="untimedmax">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="untimedmin">
+        <value>
+          <boolean>true</boolean>
+        </value>
+      </option>
+      <option name="untimedssquare">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="untimedssqdev">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
+      <option name="untimedstddev">
+        <value>
+          <boolean>false</boolean>
+        </value>
+      </option>
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Index: liacs/pnbm/project/planer-signaling.cpn
===================================================================
--- liacs/pnbm/project/planer-signaling.cpn	(revision 25)
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-    <monitorblock name="Monitors"/>
-    <IndexNode expanded="true">
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-      <IndexNode expanded="false"/>
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-    </IndexNode>
-  </cpnet>
-</workspaceElements>
Index: liacs/pnbm/project/report.tex
===================================================================
--- liacs/pnbm/project/report.tex	(revision 25)
+++ liacs/pnbm/project/report.tex	(revision 52)
@@ -24,59 +24,87 @@
 \maketitle
 \section{Abstract}
-Planar signaling is the process within the development of the AP axis
-development of the \emph{Xenopus laevis} \cite{Bertens09} in which cells
-accumulate proteins based on the saturation of nearby cells. If one cell
-produces n amount of proteins, it will initiate a transferring cascade to cells
-in the vicinity.  This dissemination of proteins will eventually cease,
-considering that n is a finite variable. There is a gradation in the amount of
-proteins transferred, meaning that neighbouring cells get n/2 the amount of
-proteins of the most saturated cell.
+Planar signaling is a process that is part of the development of the AP axis in
+\emph{Xenopus laevis} \cite{Bertens09}, in which cells accumulate proteins
+based on the saturation of nearby cells. If one cell produces n amount of
+proteins, it will initiate a transferring cascade to cells in the vicinity.
+This dissemination of proteins will eventually cease, considering that n is a
+finite variable. There is a gradation in the amount of proteins transferred,
+meaning that neighboring cells get n/2 the amount of proteins of the most
+saturated cell.
 
-We are going to model this into Petri-Nets beeing a mathematical modeling
-language, which suit well for this purpose as we could nicely model the process
-in graphical interactive representation and could also be used for automated
-model tracking and analyze.
+We are going to model this into Petri-Nets, since it supports a mathematical
+modeling language as well as a graphical interactive representation, which is
+well suited for this purpose, as we could model the process based on algorithms
+and also used it for automated model tracking and analysis, while having a
+visual representation of the process.
 
-\section{Approach}
-First a Petri-Net model will be defined textually and using graphs next the
-modeling will be taking into practice using the modeling tool\emph{CPNTools}
-\footnote{http://wiki.daimi.au.dk/cpntools/cpntools.wiki}.
+\section{Method}
+Our approach to modeling Planar signaling is firstly construct a biological
+model of the process, one that illustrates the phenomenon taking place (shown
+at figure~\ref{fig:ab-model}). Next we decided to create a conceptual model,
+one that abstracts from the biological model and contains some mathematical
+equations that describe the processes occurring in nature.
+
+\begin{figure}[htp]
+\centering
+\caption{Conceptual abstract model}
+\includegraphics[width=\textwidth]{frog-model.eps}
+\label{fig:ab-model}
+\end{figure}
+
+Finally we are going to construct a Petri-Net model using the software
+\emph{CPNTools} \footnote{http://wiki.daimi.au.dk/cpntools/cpntools.wiki}.
 
 \section{Modeling}
-To model this process we will take a modular approach using coloured Petri-Nets
-(see Fig~\ref{fig:model}), since the goal of this assignment is to have a
-solution that can be applied to any configuration of cells. We start with a
-building block that is an abstraction of a cell (figure: circle), which can then
-be coupled to other cells (figure: arrows). The abstraction contains two
-different types. First the proteins are modelled (figure: red), secondly the
-proteins (figure: blue) are leading in a second process of the creation of
-posterisation which also needs modeling. We assume a 1:1 mapping between the amount
-of proteins and the posterisation -this taken into consideration- ones an
-\texttt{INITIAL} protein is 'used' (e.g. has on posterisation counterpart) in
-this process it
-get called \texttt{ACTIVATED}. We assume that the proteins to posterisation
-process is taking place at the same time as the proteins distribution. And in a
-special format (figure: object B). It tries to matches the posterisation to the
-same level as the proteins present. But the moment the protein level lowers,
-the posterisation will remain the same. In pseudo-code:
+\begin{figure}[htp]
+\centering
+\caption{Planar signaling model}
+\includegraphics[width=100mm]{planar-signaling-model.eps}
+\label{fig:model}
+\end{figure}
+
+For the conceptual model (Fig.~\ref{fig:model}) we start with a building block
+that is an abstraction of a cell (figure: circle), which can then be coupled to
+other cells (figure: arrows). The abstraction contains two different token
+types. For one the proteins are modeled through red tokens, and secondly the
+proteins generate a second process, the level of posterisation (blue tokens)
+which is also required in the model. We assume a 1:1 mapping between the amount
+of proteins and the posterisation, taking into consideration that when an
+\texttt{INITIAL} protein is âusedâ (e.g. has a posterisation counterpart) in
+this process is called \texttt{ACTIVATED}. We assume that the âproteins to
+posterisationâ process is taking place at the same time as the proteins
+distribution. This is represented in a special format, represented by the
+square B in the figure. It tries to match the posterisation to the same level
+as the proteins present. The moment the protein level lowers, the posterisation
+will remain the same. In pseudo-code:
 \begin{verbatim}
 if numPos < numProteins then
-    numPos = numPos + 1
+  numPos = numPos + 1
 endif
 \end{verbatim}
+
 \texttt{numProteins} is the proteins available and \texttt{numPos} is the
 posterisation present.
 
-The connectors between the cells (the membranes) has a special properly. One
-can see them as pressure valves others as siphons (see Fig~\ref{fig:pressure}).
-The moment the 'volume' at complies with the following properly $A / 2 < B$
-then the pressure closes, else it passes volume from A to B at an certain rate
-(\texttt{flowSpeed}). This rate could depend on the difference, actual value present
-or something else. Please do mind that negative values could ever appear hence
-the checking whether the source is bigger or equal then the flowSpeed.
+The connectors between the cells (the membranes) have a special property. One
+can see them as pressure valves (like figure~\ref{fig:pressure}) that close
+when the âvolumeâ in the containers (cells) complies with the following
+property $A/2 < B$, or siphons when the property before is not achieved,
+passing volume from $A$ to $B$ at a certain rate (\texttt{flowSpeed}). This
+rate could depend on the difference, actual value present or something else.
+Please keep in mind that negative values could sometimes appear, hence there is
+a need to check whether the source is bigger or equal than the
+\texttt{flowSpeed}. 
 
-For the case there exists no standard Petri-Net 'component', hence  this require
-the creation of a new property (figure: $2:1$), with the following properties:
+\begin{figure}[htp]
+\centering
+\caption{Pressure valve example}
+\includegraphics[height=60mm]{pressure-valve.eps}
+\label{fig:pressure}
+\end{figure}
 
+For this case there exists no standard Petri-Net âcomponentâ, hence this
+requires the creation of a new property, which is described in pseudo-code
+below:
 \begin{verbatim}
 flowSpeed = n
@@ -90,48 +118,29 @@
 \end{verbatim}
 
-Planar signaling could theoretically start in every cell, by
-inserting some amount of proteins. In our model represented as a bunch of
-\texttt{INITIAL} tokens being put in a random cell.
+Planar signaling could theoretically start in every cell, by inserting some
+amount of proteins. In our model this is represented as $n$ \texttt{INITIAL}
+tokens being put in a cell chosen at random.
 
-\begin{figure}[htp]
-\centering
-\caption{Planar signaling model}
-\includegraphics[width=100mm]{planar-signaling-model.eps}
-\label{fig:model}
-\end{figure}
 
-\begin{figure}[htp]
-\centering
-\caption{Pressure valve example}
-\includegraphics[height=60mm]{pressure-valve.eps}
-\label{fig:pressure}
-\end{figure}
+\section{CPNTools implementation}
+CPNTools has some shortcomings when it comes to modeling higher level
+developmental biology. One is the shortcoming of âbalancingâ. It does not allow
+the reading of how many tokens are present in a certain state and base action
+upon them.
 
-\section{CPNTools 'implementation'}
-CPNTools has quite some shortcomings when it comes to modeling (higher level
-developmental) biology.
+As workaround for this (see Fig~\ref{fig:CPNplanar}) we used a âdumpâ gradation
+function.  In our case it simply takes 3 tokens and pushes 1 forward while
+converting 2 directly to \texttt{ACTIVATED}. This does not take into
+consideration if some external source changes the amount further up. 
 
-One it the shortcoming of the 'balancing'. It does not allow reading of how
-many tokens are present in a certain state and base action upon them. As
-workaround for this (see Fig~\ref{fig:CPNplanar}) we used a 'dump' gradation
-function. In our case it simply take 3 tokens and pushes 1 forward and
-converting 2 directly to \texttt{ACTIVATED}. This does not take in
-consideration if the amount get changed in 'further-up', by some external
-source.
-
-Secondly it is missing a possibility to for easy random initialisation for
-modeling purposes. As a dirty quirk we 'hacked' it to choose between starting
-at the head or the tail.
-
-In this implementation the proteins to gradients  process is taking place at
-cell $A$ at the same time that the proteins get transferred from cell $A$ to
-$B$. 
-
-Also it should be noted that it missing a notion of timed firing sequences;
-meaning firing sequences which will occur at an certain time. This could for
-example used to 'trigger' a timed activation of the \texttt{INITIAL} to
-\texttt{ACTIVATED} process as modeled in fig~\ref{fig:model}. An initial idea
-is shown at fig~\ref{fig:time-idea} in appendix~\ref{sec:timer-idea}.
-
+Secondly it misses the possibility to easily randomize the initialization. As a
+quick fix we âhackedâ it to choose between starting at the head or the tail. In
+this implementation the protein to gradient process is taking place at cell $A$
+at the same time that the proteins get transferred from cell $A$ to $B$. It
+should be noted that the model avoids the notion of timed firing sequences;
+meaning that the firing sequences will not occur at pre-determined times. This
+could be changed in the future to âtriggerâ a timed activation of the
+\texttt{INITIAL} to \texttt{ACTIVATED} process as modeled in
+figure~\ref{fig:model}.
 
 \begin{figure}[htp]
@@ -140,13 +149,17 @@
 \advance\leftskip-2cm
 \advance\rightskip+2cm
-\includegraphics[width=1.3\textwidth]{planer-signaling.eps}
+\includegraphics[width=1.3\textwidth]{planar-signaling.eps}
 \label{fig:CPNplanar}
 \end{figure}
 
 \section{Conclusion}
-Using Petri-Nets for modeling biology processes is a powerful framework, which
-could be well expandable. The Proof Of Concept implementations and
-visualisations how-ever are lacking. \emph{CPNTools} for example does not
-provide a powerful enough tool-set for the modeling purposes.
+Using Petri-Nets for modeling biology processes is a powerful framework, one
+which could be well expandable. The proof of concept implementation and
+visualization however is lacking. \emph{CPNTools} does not currently provide a
+powerful enough tool-set for the modeling purposes. This could be improved with
+the support of a programming language that can produce algorithms that can
+replace the mathematical functions of arcs.
+
+
 
 \bibliographystyle{amsalpha}
@@ -156,13 +169,3 @@
 laevis Extended Abstract, 2009
 \end{thebibliography}
-\appendix
-\section{Timer Idea}
-\label{sec:timer-idea}
-
-\begin{figure}[htp]
-\centering
-\caption{Timed transition idea}
-\includegraphics[width=0.5\textwidth]{timer-proposal.eps}
-\label{fig:time-idea}
-\end{figure}
 \end{document}
