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a:visited, span.MsoHyperlinkFollowed
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em
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p
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	text-align:center;
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 /* Page Definitions */
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	{mso-page-border-surround-header:no;
	mso-page-border-surround-footer:no;
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@page Section1
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div.Section1
	{page:Section1;
	mso-footnote-numbering-restart:each-page;
	mso-endnote-numbering-style:arabic;
	mso-endnote-numbering-restart:each-section;}
@page Section2
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<div class=3DSection1>

<p class=3Dequation style=3D'tab-stops:36.0pt center 212.65pt right 411.1pt=
'><span
lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p class=3Dequation style=3D'tab-stops:36.0pt center 212.65pt right 411.1pt=
'><span
lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoBodyTextIndent2 style=3D'text-indent:0cm'><a name=3Dmaintitle=
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name=3D"_Hlt56855137"></a><a name=3D"_Hlt107204618"></a><span style=3D'mso-=
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maintitle'><span lang=3DEN-US>NeurApp</span></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoBodyTextIndent2 style=3D'text-indent:0cm'><span lang=3DEN-US
style=3D'font-size:20.0pt;font-style:normal;mso-bidi-font-style:italic'><sp=
an
style=3D'mso-spacerun:yes'>&nbsp;</span>Exploring Approximation <o:p></o:p>=
</span></p>

<p class=3DMsoBodyTextIndent2 style=3D'text-indent:0cm'><span lang=3DEN-US
style=3D'font-size:20.0pt;font-style:normal;mso-bidi-font-style:italic'>by
Artificial Neural Networks<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoBodyTextIndent2 style=3D'text-indent:0cm'><a name=3D"_Hlt5037=
98010"></a><span
lang=3DEN-US style=3D'font-size:20.0pt;font-weight:normal;mso-bidi-font-wei=
ght:
bold;font-style:normal;mso-bidi-font-style:italic'>User Manual<o:p></o:p></=
span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><i style=3D=
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normal'><span lang=3DEN-US style=3D'font-size:16.0pt'>Version <a name=3Drev=
ision>1.</a>1,
<a name=3Dyear>June 201</a>3.</span></i><i style=3D'mso-bidi-font-style:nor=
mal'><span
style=3D'font-size:16.0pt;mso-ansi-language:SL'><o:p></o:p></span></i></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span lang=
=3DEN-US
style=3D'font-size:14.0pt'>by <a name=3Dauthors>Igor Gre</a></span><span
style=3D'mso-bookmark:authors'><span style=3D'font-size:14.0pt;mso-ansi-lan=
guage:
SL'>&#353;ovnik &amp; Tadej Kodelja</span></span><span style=3D'font-size:1=
4.0pt;
mso-ansi-language:SL'> <o:p></o:p></span></p>

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page-break-before:always'>
</span>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><i style=3D'm=
so-bidi-font-style:
normal'><span lang=3DEN-US style=3D'font-size:16.0pt;mso-bidi-font-size:10.=
0pt'>Contents:<o:p></o:p></span></i></b></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoToc1 style=3D'tab-stops:24.0pt right dotted 481.45pt'><!--[if=
 supportFields]><span
lang=3DEN-US><span style=3D'mso-element:field-begin'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>TOC \o &quot;1-3&quot; \h \z \u <sp=
an
style=3D'mso-element:field-separator'></span></span><![endif]--><span lang=
=3DEN-US><span
class=3DMsoHyperlink><span style=3D'mso-no-proof:yes'><a href=3D"#_Toc35849=
4907">1<span
lang=3DSL style=3D'mso-bidi-font-size:12.0pt;color:windowtext;mso-ansi-lang=
uage:
SL;mso-fareast-language:SL;mso-bidi-language:HE;font-weight:normal;font-sty=
le:
normal;text-decoration:none;text-underline:none'><span style=3D'mso-tab-cou=
nt:
1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span>Introduction<span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-tab-count:1 dotted'>. </span></span=
><!--[if supportFields]><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494907 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>1<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900300037000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
></span><span
style=3D'mso-bidi-font-size:12.0pt;mso-ansi-language:SL;mso-fareast-languag=
e:
SL;mso-bidi-language:HE;font-weight:normal;font-style:normal;mso-no-proof:y=
es'><o:p></o:p></span></p>

<p class=3DMsoToc1 style=3D'tab-stops:24.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494908">2<span lang=3DSL style=3D'mso-bidi-font-size:12.0pt;
color:windowtext;mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-lang=
uage:
HE;font-weight:normal;font-style:normal;text-decoration:none;text-underline:
none'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span=
></span>Short
User Manual<span style=3D'color:windowtext;display:none;mso-hide:screen;
text-decoration:none;text-underline:none'><span style=3D'mso-tab-count:1 do=
tted'> </span></span><!--[if supportFields]><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494908 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>1<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900300038000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'mso-bidi-font-size:12.0pt;mso-ansi-language:SL;mso-fareast-languag=
e:
SL;mso-bidi-language:HE;font-weight:normal;font-style:normal;mso-no-proof:y=
es'><o:p></o:p></span></p>

<p class=3DMsoToc2 style=3D'tab-stops:48.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494909">2.1<span lang=3DSL style=3D'font-size:12.0pt;color:=
windowtext;
mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-language:HE;font-weig=
ht:
normal;text-decoration:none;text-underline:none'><span style=3D'mso-tab-cou=
nt:
1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span>Installation and Use<=
span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-tab-count:1 dotted'>. </span></span=
><!--[if supportFields]><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494909 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>1<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900300039000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'font-size:12.0pt;mso-ansi-language:SL;mso-fareast-language:SL;
mso-bidi-language:HE;font-weight:normal;mso-no-proof:yes'><o:p></o:p></span=
></p>

<p class=3DMsoToc2 style=3D'tab-stops:48.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494910">2.2<span lang=3DSL style=3D'font-size:12.0pt;color:=
windowtext;
mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-language:HE;font-weig=
ht:
normal;text-decoration:none;text-underline:none'><span style=3D'mso-tab-cou=
nt:
1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span>One Parametric
Approximations<span style=3D'color:windowtext;display:none;mso-hide:screen;
text-decoration:none;text-underline:none'><span style=3D'mso-tab-count:1 do=
tted'>. </span></span><!--[if supportFields]><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494910 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>2<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900310030000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'font-size:12.0pt;mso-ansi-language:SL;mso-fareast-language:SL;
mso-bidi-language:HE;font-weight:normal;mso-no-proof:yes'><o:p></o:p></span=
></p>

<p class=3DMsoToc3 style=3D'tab-stops:60.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494911">2.2.1<span lang=3DSL style=3D'font-size:12.0pt;colo=
r:windowtext;
mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-language:HE;text-deco=
ration:
none;text-underline:none'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp=
;&nbsp; </span></span>Defining
the Approximated Function and Training Data<span style=3D'color:windowtext;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><sp=
an
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494911 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>3<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900310031000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'font-size:12.0pt;mso-ansi-language:SL;mso-fareast-language:SL;
mso-bidi-language:HE;mso-no-proof:yes'><o:p></o:p></span></p>

<p class=3DMsoToc3 style=3D'tab-stops:60.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494912">2.2.2<span lang=3DSL style=3D'font-size:12.0pt;colo=
r:windowtext;
mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-language:HE;text-deco=
ration:
none;text-underline:none'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp=
;&nbsp; </span></span>Training
the Neural Network<span style=3D'color:windowtext;display:none;mso-hide:scr=
een;
text-decoration:none;text-underline:none'><span style=3D'mso-tab-count:1 do=
tted'>. </span></span><!--[if supportFields]><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494912 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>3<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900310032000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'font-size:12.0pt;mso-ansi-language:SL;mso-fareast-language:SL;
mso-bidi-language:HE;mso-no-proof:yes'><o:p></o:p></span></p>

<p class=3DMsoToc3 style=3D'tab-stops:60.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494913">2.2.3<span lang=3DSL style=3D'font-size:12.0pt;colo=
r:windowtext;
mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-language:HE;text-deco=
ration:
none;text-underline:none'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp=
;&nbsp; </span></span>Safety
Factors<span style=3D'color:windowtext;display:none;mso-hide:screen;text-de=
coration:
none;text-underline:none'><span style=3D'mso-tab-count:1 dotted'>. </span><=
/span><!--[if supportFields]><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494913 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>4<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900310033000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'font-size:12.0pt;mso-ansi-language:SL;mso-fareast-language:SL;
mso-bidi-language:HE;mso-no-proof:yes'><o:p></o:p></span></p>

<p class=3DMsoToc3 style=3D'tab-stops:60.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494914">2.2.4<span lang=3DSL style=3D'font-size:12.0pt;colo=
r:windowtext;
mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-language:HE;text-deco=
ration:
none;text-underline:none'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp=
;&nbsp; </span></span>Checking
Results<span style=3D'color:windowtext;display:none;mso-hide:screen;text-de=
coration:
none;text-underline:none'><span style=3D'mso-tab-count:1 dotted'>. </span><=
/span><!--[if supportFields]><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494914 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>5<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900310034000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'font-size:12.0pt;mso-ansi-language:SL;mso-fareast-language:SL;
mso-bidi-language:HE;mso-no-proof:yes'><o:p></o:p></span></p>

<p class=3DMsoToc2 style=3D'tab-stops:48.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494915">2.3<span lang=3DSL style=3D'font-size:12.0pt;color:=
windowtext;
mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-language:HE;font-weig=
ht:
normal;text-decoration:none;text-underline:none'><span style=3D'mso-tab-cou=
nt:
1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span>Functions of 2 Variab=
les
with 3D Surface Plots<span style=3D'color:windowtext;display:none;mso-hide:=
screen;
text-decoration:none;text-underline:none'><span style=3D'mso-tab-count:1 do=
tted'>. </span></span><!--[if supportFields]><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494915 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>6<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900310035000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'font-size:12.0pt;mso-ansi-language:SL;mso-fareast-language:SL;
mso-bidi-language:HE;font-weight:normal;mso-no-proof:yes'><o:p></o:p></span=
></p>

<p class=3DMsoToc3 style=3D'tab-stops:60.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494916">2.3.1<span lang=3DSL style=3D'font-size:12.0pt;colo=
r:windowtext;
mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-language:HE;text-deco=
ration:
none;text-underline:none'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp=
;&nbsp; </span></span>Defining
the Approximated Function and Training Data<span style=3D'color:windowtext;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><sp=
an
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494916 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>7<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900310036000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'font-size:12.0pt;mso-ansi-language:SL;mso-fareast-language:SL;
mso-bidi-language:HE;mso-no-proof:yes'><o:p></o:p></span></p>

<p class=3DMsoToc3 style=3D'tab-stops:60.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494917">2.3.2<span lang=3DSL style=3D'font-size:12.0pt;colo=
r:windowtext;
mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-language:HE;text-deco=
ration:
none;text-underline:none'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp=
;&nbsp; </span></span>Network
Architecture and Training Parameters<span style=3D'color:windowtext;display=
:none;
mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><sp=
an
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494917 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>7<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900310037000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'font-size:12.0pt;mso-ansi-language:SL;mso-fareast-language:SL;
mso-bidi-language:HE;mso-no-proof:yes'><o:p></o:p></span></p>

<p class=3DMsoToc3 style=3D'tab-stops:60.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494918">2.3.3<span lang=3DSL style=3D'font-size:12.0pt;colo=
r:windowtext;
mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-language:HE;text-deco=
ration:
none;text-underline:none'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp=
;&nbsp; </span></span>Showing
Training Data and Results<span style=3D'color:windowtext;display:none;mso-h=
ide:
screen;text-decoration:none;text-underline:none'><span style=3D'mso-tab-cou=
nt:
1 dotted'>. </span></span><!--[if supportFields]><span style=3D'color:windo=
wtext;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-begin'></span> PAGEREF _Toc358494918 \h </span><=
span
style=3D'color:windowtext;text-decoration:none;text-underline:none'><span
style=3D'display:none;mso-hide:screen'><span style=3D'mso-element:field-sep=
arator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>8<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900310038000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'font-size:12.0pt;mso-ansi-language:SL;mso-fareast-language:SL;
mso-bidi-language:HE;mso-no-proof:yes'><o:p></o:p></span></p>

<p class=3DMsoToc2 style=3D'tab-stops:48.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494919">2.4<span lang=3DSL style=3D'font-size:12.0pt;color:=
windowtext;
mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-language:HE;font-weig=
ht:
normal;text-decoration:none;text-underline:none'><span style=3D'mso-tab-cou=
nt:
1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span>Accessing Help and Web
Pages<span style=3D'color:windowtext;display:none;mso-hide:screen;text-deco=
ration:
none;text-underline:none'><span style=3D'mso-tab-count:1 dotted'>. </span><=
/span><!--[if supportFields]><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494919 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>12<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900310039000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'font-size:12.0pt;mso-ansi-language:SL;mso-fareast-language:SL;
mso-bidi-language:HE;font-weight:normal;mso-no-proof:yes'><o:p></o:p></span=
></p>

<p class=3DMsoToc1 style=3D'tab-stops:24.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494920">3<span lang=3DSL style=3D'mso-bidi-font-size:12.0pt;
color:windowtext;mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-lang=
uage:
HE;font-weight:normal;font-style:normal;text-decoration:none;text-underline:
none'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span=
></span>Screenshots<span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-tab-count:1 dotted'>. </span></span=
><!--[if supportFields]><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494920 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>13<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900320030000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'mso-bidi-font-size:12.0pt;mso-ansi-language:SL;mso-fareast-languag=
e:
SL;mso-bidi-language:HE;font-weight:normal;font-style:normal;mso-no-proof:y=
es'><o:p></o:p></span></p>

<p class=3DMsoToc1 style=3D'tab-stops:24.0pt right dotted 481.45pt'><span
class=3DMsoHyperlink><span lang=3DEN-US style=3D'mso-no-proof:yes'><a
href=3D"#_Toc358494921">4<span lang=3DSL style=3D'mso-bidi-font-size:12.0pt;
color:windowtext;mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-lang=
uage:
HE;font-weight:normal;font-style:normal;text-decoration:none;text-underline:
none'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span=
></span>About
the Software<span style=3D'color:windowtext;display:none;mso-hide:screen;
text-decoration:none;text-underline:none'><span style=3D'mso-tab-count:1 do=
tted'>. </span></span><!--[if supportFields]><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'><span style=3D'mso-element:field-begin'></span> PAGEREF
_Toc358494921 \h </span><span style=3D'color:windowtext;text-decoration:non=
e;
text-underline:none'><span style=3D'display:none;mso-hide:screen'><span
style=3D'mso-element:field-separator'></span></span></span><![endif]--><span
style=3D'color:windowtext;display:none;mso-hide:screen;text-decoration:none;
text-underline:none'>16<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005400=
6F0063003300350038003400390034003900320031000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span style=3D'color:window=
text;
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
style=3D'mso-element:field-end'></span></span><![endif]--></a></span></span=
><span
style=3D'mso-bidi-font-size:12.0pt;mso-ansi-language:SL;mso-fareast-languag=
e:
SL;mso-bidi-language:HE;font-weight:normal;font-style:normal;mso-no-proof:y=
es'><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><!--[if supportFields]><s=
pan
lang=3DEN-US><span style=3D'mso-element:field-end'></span></span><![endif]-=
-><span
lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3Dequation style=3D'tab-stops:36.0pt center 212.65pt right 411.1pt=
'><span
lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

</div>

<span lang=3DEN-US style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;font=
-family:
"Times New Roman";mso-fareast-font-family:"Times New Roman";mso-ansi-langua=
ge:
EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA;layout-grid-mode:l=
ine'><br
clear=3Dall style=3D'page-break-before:auto;mso-break-type:section-break'>
</span>

<div class=3DSection3>

<p class=3Dequation style=3D'tab-stops:36.0pt center 212.65pt right 411.1pt=
'><span
lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<span lang=3DEN-US style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;font=
-family:
"Times New Roman";mso-fareast-font-family:"Times New Roman";mso-ansi-langua=
ge:
EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA;layout-grid-mode:l=
ine'><br
clear=3Dall style=3D'mso-special-character:line-break;page-break-before:alw=
ays'>
</span>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><a name=3D"_Hlt480655247"=
></a><span
lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<h1 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Toc96668183"></a>=
<a
name=3D"_Toc96668344"></a><a name=3D"_Ref111196421"></a><a name=3D"_Ref1620=
60045"></a><a
name=3D"_Ref185235514"></a><a name=3D"_Toc349256589"></a><a name=3D"_Toc358=
494907"><span
style=3D'mso-bookmark:_Toc349256589'><span style=3D'mso-bookmark:_Ref185235=
514'><span
style=3D'mso-bookmark:_Ref162060045'><span style=3D'mso-bookmark:_Ref111196=
421'><span
style=3D'mso-bookmark:_Toc96668344'><span style=3D'mso-bookmark:_Toc9666818=
3'><![if !supportLists]><span
lang=3DEN-US style=3D'text-transform:uppercase'><span style=3D'mso-list:Ign=
ore'>1<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US style=3D'=
text-transform:
uppercase'>Introduction</span></span></span></span></span></span></span></s=
pan></a><span
lang=3DEN-US style=3D'text-transform:uppercase'><o:p></o:p></span></h1>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><a name=3Dsoftwarename><s=
pan
lang=3DEN-US>NeurApp</span></a><span lang=3DEN-US> is an educational softwa=
re
intended used for exploring how neural network approximation works on funct=
ions
of one and two variables. You can input different functions to be approxima=
ted
by an artificial neural networks (ANN), generate training points where the
values of reference function are calculated and used for approximation, set
some parameters of the training procedure, train the neural network on the
generated data, and compare the obtained model (i. e. the approximation
obtained by the trained neural network) to the original function that was u=
sed
for generation of training data.</span></p>

<h1 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Toc358494908"></a=
><a
name=3D"_Toc349256590"></a><a name=3D"_Hlt96752675"></a><![if !supportLists=
]><span
style=3D'mso-bookmark:_Toc358494908'><span style=3D'mso-bookmark:_Toc349256=
590'><span
lang=3DEN-US style=3D'text-transform:uppercase'><span style=3D'mso-list:Ign=
ore'>2<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;
</span></span></span></span></span><![endif]><span dir=3DLTR><span
style=3D'mso-bookmark:_Toc358494908'><span style=3D'mso-bookmark:_Toc349256=
590'><span
lang=3DEN-US style=3D'text-transform:uppercase'>Short User Manual</span></s=
pan></span><span
lang=3DEN-US style=3D'text-transform:uppercase'><o:p></o:p></span></span></=
h1>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<h2 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Toc349256591"></a=
><a
name=3D"_Toc358494909"><span style=3D'mso-bookmark:_Toc349256591'><![if !su=
pportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.1<span style=3D'font:7.0pt "=
Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>Installat=
ion and
Use</span></span></span></a></h2>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Instal=
ling and
using the software is extremely simple. In order to install the software, j=
ust
grab the archive, expand it, and copy the contained file into some director=
y.
Double-click on the executable file in any file browser (such as the Windows
Explorer) in order to execute the software.</span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>In ord=
er to
start using the software, click either on the &#8221;1D Approximation&#8221=
; or
on the &#8220;2D Approximation&#8221; tab, dependent on whether you want to
approximate functions of one or two variables. Then, click on the
&#8220;Generate Data&#8221; button, wait a moment until a graph of the model
function with the generated training points is shown, and then click the
&#8220;Start&#8221; button. This will trigger the training procedure and wh=
en
training is finished, the obtained approximated function will be plotted. <=
/span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Traini=
ng may
take a while, dependent on the value of the number of epochs that are
performed. Everything else is quite intuitive; you can change the number of
generated training points, choose or manually insert the approximated funct=
ion,
and adjust parameters of the training procedure. </span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>When
approximating functions of 2 variables, graphs of the original function and=
 its
approximation will be shown in a separate window rather than in embedded
window. After pressing the &#8220;Generate Data&#8221; button, wait until t=
he
graph window is launched, then you can view it from different angles and zo=
om
it. Before proceeding further, close the graph window. After pressing the
&#8220;Start&#8221; button, wait again until graph is launched, and close t=
he
graph window when viewing is done. You can interact with 3D graphics window=
s by
mouse and keyboard, press the &#8216;R&#8217; key in order to position the
objects in default way, and the &#8216;T&#8217; button in order to change t=
he
interaction mode </span><span style=3D'mso-ansi-language:SL'><o:p></o:p></s=
pan></p>

<h2 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Toc358494910"><![=
if !supportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.2<span style=3D'font:7.0pt "=
Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>One Param=
etric
Approximations</span></span></a></h2>

<p class=3DMsoNormal><span style=3D'mso-ansi-language:SL'><!--[if gte vml 1=
]><v:shape
 id=3D"_x0000_i1027" type=3D"#_x0000_t75" style=3D'width:481.5pt;height:217=
.5pt'
 o:ole=3D"">
 <v:imagedata src=3D"NeurApp_files/image009.emz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D642 height=3D290
src=3D"NeurApp_files/image010.gif" v:shapes=3D"_x0000_i1027"><![endif]><!--=
[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Word.Picture.8" ShapeID=3D"_x0000_i1=
027"
  DrawAspect=3D"Content" ObjectID=3D"_1432239019">
 </o:OLEObject>
</xml><![endif]--></span></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><span lang=3DEN-US>Figure <s=
pan
style=3D'mso-field-code:" SEQ Figure \\* ARABIC "'><span style=3D'mso-no-pr=
oof:
yes'>1</span></span>:</span><span lang=3DEN-US style=3D'font-weight:normal'=
> GUI
for approximation of functions of one variable. <o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>While
approximation of functions of a single variable is the least interesting
problem in ANN-based modeling, playing with such approximations is instruct=
ive
because very clear graphic representations of results can be made. </span><=
/p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Explor=
ing 1D
ANN-based approximations in <span style=3D'mso-field-code:" REF softwarenam=
e \\h "'>NeurApp<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D00000073006F00=
6600740077006100720065006E0061006D0065000000</w:data>
</xml><![endif]--></span> is intuitive and can be learned in a minute. Clic=
king
on the &#8220;<i>1D Approximation</i>&#8221; tab on the top of the
application&#8217;s form activates the user interface for 1D approximations=
. To
see how it works, click first on the &#8220;<i>Generate data</i>&#8221; but=
ton
and then on the &#8220;<i>Start</i>&#8221; button, and that&#8217;s it. </s=
pan></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Clicki=
ng on the
&#8220;<i>Generate data</i>&#8221; button samples the function that you wan=
t to
approximate and is specified next to the &#8220;<i>f(x) =3D</i> &#8221; lab=
el, in
order to generate function values used to train the neural network. After t=
he
training data is generated, it is immediately shown on the graph on the
right-hand side (together with the approximated function on the interval wh=
ere
values are sampled), and the &#8220;<i>Start</i>&#8221; button gets active.
Pressing the start button trains the neural network on the data that has be=
en
generated. </span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>During=
 the
training procedure, the neural network tries to produce an intrinsic functi=
on
that fits well the training data, without knowing anything about the origin=
al
function used to generate that data. After training is done, the graph on t=
he
top right of the form shows the approximation generated by the neural netwo=
rk,
the training data used to generate this approximation, and the original
function used to generated the data. In this way you can visualize how much=
 the
approximated function deviates from the original one. </span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>You ca=
n vary the
number of sampled function values in the training data, change interval on
which training data is generated, modify the approximation function itself,=
 and
change neural network architecture and training parameters and observe how =
any
of these circumstances affect the accuracy of the approximation (i.e., how
closely the approximation fits the original function). In further subsectio=
ns
it is explained how to adjust specific things that influence the approximat=
ion.
</span></p>

<h3 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Ref349776721"></a=
><a
name=3D"_Toc358494911"><span style=3D'mso-bookmark:_Ref349776721'><![if !su=
pportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.2.1<span style=3D'font:7.0pt=
 "Times New Roman"'>&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>Defining =
the
Approximated Function and Training Data</span></span></span></a></h3>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>When s=
tarting
the application, there is already a pre-set default function to be
approximated. You can change the approximated function by using the input f=
ield
next to the &#8220;<i>f(x) =3D</i>&#8221; label, and this can be done in two
ways. If the checkbox &#8220;<i>Function defined by user</i>&#8221; is
unchecked, you can choose one of the pre-defined functions from the drop-do=
wn
list that opens when clicking on the triangular arrow positioned on the
right-hand side of the text field.</span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>In ord=
er to
define at own will an arbitrary function to be approximated, check the &#82=
20;<i>Function
defined by user</i>&#8221; checkbox. When the checkbox is checked, you can
insert expressions defining an arbitrary function in a standard symbolic wa=
y by
using &#8220;<i>x</i>&#8221; for independent variables, standard operators =
such
as +, -, * (multiplication), / (division), a number of standard mathematical
functions, and parentheses for grouping expressions and overriding operator
precedence in order to define order of evaluation. There is no operator for
powers, and you must used the function &#8220;<i>pow</i>&#8221;, e.g. the
expression &#8220;pow(x,3/2)&#8221; means the independent variable x raised=
 to
the power of 3/2 (which is equivalent to calculating square root of x and
raising the obtained value to the third power). </span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Warnin=
g: You can
not insert your own function definition when the &#8220;<i>Function defined=
 by
user</i>&#8221; checkbox is not checked. The text field for inserting funct=
ions
is green when user defined functions are allowed. If you insert an invalid
expression that defines the approximated function (e.g. forget a bracket or=
 use
a mathematical function that is not defined, the text field will turn orange
when you attempt to generate the data.</span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>In the=
 &#8220;<i>Limits</i>&#8221;
box, you can define the interval on which the approximated function is samp=
led
in order to generate the training data. Number of function values to be
generated and used in training is defined next to &#8220;Number of training
samples&#8221;. If the &#8220;<i>Random training data</i>&#8221; is checked
then function will be evaluated in randomly chosen points. Otherwise, it is
sampled in equidistant points on the selected interval.</span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Genera=
tion of
function values used for training (sampling) is triggered by clicking on the
&#8220;Generate Data&#8221; button. Sampled function values are shown as po=
ints
on the graph where the original function is shown, too.</span></p>

<h3 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Ref349777537"></a=
><a
name=3D"_Toc358494912"><span style=3D'mso-bookmark:_Ref349777537'><![if !su=
pportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.2.2<span style=3D'font:7.0pt=
 "Times New Roman"'>&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>Training =
the
Neural Network</span></span></span></a></h3>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>The AN=
N-based
approximation of the original function is calculated by training the neural
network on the sampled values generated before. In this procedure, the inte=
rnal
state of the neural network is continuously updated in such a way that the
discrepancy between the training data and the outputs generated by the netw=
ork
are minimized. Training (generation of the approximation) begins by pressing
the &#8220;<i>Start</i>&#8221; button and finishes either when the prescrib=
ed
accuracy is reached or when the maximal prescribed training time (measured =
in <i>epochs</i>,
i.e. in iterations of the training algorithm) elapses. </span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>The us=
er can
define the required accuracy by setting a tolerance (a small positive numbe=
r)
on the RMS (root mean square) error, which is inserted next to the &#8220;<=
i>RMS</i>&#8221;
label. The training procedure will stop when the error measure drops below =
the
user defined tolerance. In order to prevent infinite looping when the toler=
ance
can not be achieved, the maximal number of epochs can be set next to the
&#8221;<i>Max. Epochs</i>&#8221; label. If the training algorithm performs =
that
number of epochs, it will stop even if the required accuracy is not reached.
The box next to &#8220;<i>Epochs in bundle</i>&#8221; just defines granular=
ity
of convergence checks, which are not performed after every epoch (iteration=
) of
the training procedure, but only after each specified number of iterations
defined by this parameter. This has no significant effect on results in most
cases, but speed ups computation by a small factor.</span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Network
architecture can be defined next to the &#8220;<i>Neurons in hidden layers<=
/i>&#8221;
label. Networks with one or two layers of hidden neurons can be used, and t=
he
number of neurons in each hidden layer can be independently defined in the
corresponding field. The second number can be 0 meaning that a neural netwo=
rk
with a single hidden layer is be used. In general, more neurons in hidden
layers means more connections between neurons, thus more free parameters
(weights) to be adjusted and better fitting capabilities of the network (but
also increased probability for overfitting and longer computation times).
Therefore, approximation of more complex functions (e.g. with wild oscillat=
ions
or sharp transitions) requires more neurons to achieve comparable accuracy =
as
with simple functions, provided of course that the number of training data =
is
also appropriately larger. In a two layer network, each neuron of the first
hidden layer is connected to each neuron in the second layer, meaning that =
the
number of connection increases quadratically with simultaneously increasing
number of neurons in both layers.</span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Two pa=
rameters
of the training procedure, namely the <i>learning rate</i> and the <i>momen=
tum</i>,
can be adjusted in the corresponding text fields. These parameters can be b=
oth
set to positive values lesser than 1. Increasing the learning rate means th=
at
the weights and biases are more quickly adjusted in the opposite direction =
of
the error gradient in order to decrease the error, which means faster decre=
ase
of errors at the beginning, but can cause more numerical instability. Momen=
tum
adds inertia to the training procedure, and simply adds a fraction of the
previous weight update to the current one calculated by error back propagat=
ion.
</span></p>

<h3 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Toc358494913"><![=
if !supportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.2.3<span style=3D'font:7.0pt=
 "Times New Roman"'>&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>Safety Fa=
ctors</span></span></a></h3>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>In neu=
ral
networks used, output signals of neurons are transformed by a sigmoid
activation function that has a range between 0 and 1. In order to approxima=
te
different ranges of values, output of the neural network are scaled by an
affine function that maps the [-1, 1] interval to some other interval, say =
[<i>a,
b</i>]. Only values within that interval are attainable by the neural netwo=
rk
approximation. The question that arises is how to appropriately choose the
interval. An obvious strategy would be to choose a very large interval, lar=
ge
enough to include any value that could be possibly expected to be generated=
 by
the approximated function on the interval of interest. However, making this=
 interval
too large can reduce the approximation capabilities of the neural network d=
ue
to wasting large portions of the output interval that would never contain
realistic values. The interval attainable by the outputs (and thus the mapp=
ing
function) should therefore be set such that there is some space beyond the
values ever expected to be attained by the original (approximated) function,
yet not too big. </span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>It is =
obvious
that the interval should at least contain all the values generated by sampl=
ing,
i.e. all function values contained in the training data. However, since it =
is
likely that some function values on the sampled interval exceed the interval
that contains all sampled values, some extension of the interval should be
provided beyond that, and this is what we call the safety factor. User can =
vary
the output safety factor from 1 upwards by inserting the factor into the te=
xt
field next to the &#8220;<i>Output Safety Factor</i>&#8221; label. </span><=
/p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>As far=
 as inputs
are concerned, any input form minus to plus infinity can be fed to the neur=
al
network to produce the appropriate output. Inputs are transformed by the
sigmoid function before they are sent to the neurons in the next layer.
However, since the slope of the transforming function approaches zero far f=
rom
0, it is numerically desirable that most of the inputs that will be fed to =
the
network fall on the interval [-1, 1].<span style=3D'mso-spacerun:yes'>&nbsp;
</span>Input values are therefore also scaled in a similar way as outputs, =
and
the mapping function is specified in such a way that all inputs from the tr=
aining
data are mapped close to the interval [-1, 1] before they are fed to the ne=
ural
network. The input safety factor defines how much smaller from the reference
[-1, 1] interval is the interval to which all inputs from the training data
fall when scaled before being fed to the network.</span></p>

<h3 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Ref349803946"></a=
><a
name=3D"_Toc358494914"><span style=3D'mso-bookmark:_Ref349803946'><![if !su=
pportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.2.4<span style=3D'font:7.0pt=
 "Times New Roman"'>&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>Checking =
Results</span></span></span></a></h3>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>When t=
he
training procedure is completed (after clicking the &#8220;Generate Data&#8=
221;
and then the &#8220;Start&#8221; buttons), results are shown automatically.=
 The
original function, its neural network approximation calculated by the train=
ing
procedure, and the training data on basis of which the model is calculated =
are
plotted on the graph located on the top-right portion of the form. </span><=
/p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>On the=
 graph
below, inside the &#8220;<i>Approximation error</i>&#8221; box, the course =
of
different error measures during the training procedure can be shown, plotted
against the number of epochs. By clicking on the appropriate radio button y=
ou
can choose which error measure is shown on the graph, while final values for
all error measures are written in the appropriate boxes.</span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'mso-ansi-language:SL'><!--[if gte vml 1]><v:shape id=3D"_x0000_i10=
28"
 type=3D"#_x0000_t75" style=3D'width:381.75pt;height:96.75pt' o:ole=3D"">
 <v:imagedata src=3D"NeurApp_files/image011.emz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D509 height=3D129
src=3D"NeurApp_files/image012.gif" v:shapes=3D"_x0000_i1028"><![endif]><!--=
[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Word.Picture.8" ShapeID=3D"_x0000_i1=
028"
  DrawAspect=3D"Content" ObjectID=3D"_1432239020">
 </o:OLEObject>
</xml><![endif]--></span></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><span lang=3DEN-US>Figure <s=
pan
style=3D'mso-field-code:" SEQ Figure \\* ARABIC "'><span style=3D'mso-no-pr=
oof:
yes'>4</span></span>:</span><span lang=3DEN-US style=3D'font-weight:normal'>
Convergence of different types of errors. <o:p></o:p></span></p>

<p class=3DMsoNormal><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span lang=3D=
EN-US>Max
Training Error<o:p></o:p></span></b></p>

<p class=3DMsoNormal><span lang=3DEN-US>Maximum absolute error calculated on
complete training data set after each set of epochs (Epochs in Bundle) and
shown on graph</span></p>

<p class=3DMsoNormal><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span lang=3D=
EN-US>Rms
Training Error<o:p></o:p></span></b></p>

<p class=3DMsoNormal><span lang=3DEN-US>Root mean square error calculated on
complete training data set after each set of epochs (Epochs in Bundle) and
shown on graph</span></p>

<p class=3DMsoNormal><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span lang=3D=
EN-US>Max
Verification Error<o:p></o:p></span></b></p>

<p class=3DMsoNormal><span lang=3DEN-US>Maximum absolute error calculated on
complete verification data set after each set of epochs (Epochs in Bundle) =
and
shown on graph. Verification data are not used in training procedure, but a=
re
separated from training data and used just for verification the accuracy of=
 ANN
during and after training.</span></p>

<p class=3DMsoNormal><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span lang=3D=
EN-US>Rms
Verification Error<o:p></o:p></span></b></p>

<p class=3DMsoNormal><span lang=3DEN-US>Root mean square error calculated on
complete verification data set after each set of epochs (Epochs in Bundle) =
and
shown on graph. </span></p>

<p class=3DMsoNormal><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<h2 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Toc358494915"><![=
if !supportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.3<span style=3D'font:7.0pt "=
Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>Functions=
 of 2
Variables with 3D Surface Plots</span></span></a></h2>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span style=3D'mso-ansi-l=
anguage:
SL'><!--[if gte vml 1]><v:shape id=3D"_x0000_i1029" type=3D"#_x0000_t75" st=
yle=3D'width:481.5pt;
 height:247.5pt' o:ole=3D"">
 <v:imagedata src=3D"NeurApp_files/image013.emz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D642 height=3D330
src=3D"NeurApp_files/image014.gif" v:shapes=3D"_x0000_i1029"><![endif]><!--=
[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Word.Picture.8" ShapeID=3D"_x0000_i1=
029"
  DrawAspect=3D"Content" ObjectID=3D"_1432239021">
 </o:OLEObject>
</xml><![endif]--></span></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><a name=3D"_Ref349776038"><s=
pan
lang=3DEN-US>Figure <span style=3D'mso-field-code:" SEQ Figure \\* ARABIC "=
'><span
style=3D'mso-no-proof:yes'>2</span></span></span></a><span lang=3DEN-US>:</=
span><span
lang=3DEN-US style=3D'font-weight:normal'> GUI for approximation of functio=
ns of
two variables. <o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Explor=
ing 2D
approximations is just as simple as exploring 2D approximations. You can st=
art
without any special knowledge, just click on the &#8220;<i>2D Approximation=
</i>&#8221;
tab in order to display the appropriate panel (<span style=3D'mso-field-cod=
e:
" REF _Ref349776038 \\h "'>Figure <span style=3D'mso-no-proof:yes'>2</span>=
<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340039003700370036003000330038000000</w:data>
</xml><![endif]--></span>), and then the &#8220;<i>Generate Data</i>&#8221;=
 and
then the &#8220;<i>Start</i>&#8221; button. <u>Before clicking on the &#822=
0;<i>Start</i>&#8221;
button, you should wait until the graphic window showing the approximated
function and sampled data is displayed, and close the window.</u> Graphs are
shown in a separate windows in order to allow better quality and interaction
with 3D graphs. </span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>When t=
he
training procedure completes, the graph showing the result is open immediat=
ely
in a new window. You can interact with the graph (rotate it, zoom in or out,
and translate it) in order to view interesting details from the best
perspective, and you should close the graph before performing other actions=
. </span></p>

<h3 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Toc358494916"><![=
if !supportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.3.1<span style=3D'font:7.0pt=
 "Times New Roman"'>&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>Defining =
the
Approximated Function and Training Data</span></span></a></h3>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>The fu=
nction to
be approximated is defined similarly as for 1D approximation (see Section <=
span
style=3D'mso-field-code:" REF _Ref349776721 \\n \\h "'>&#8206;2.2.1<!--[if =
gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340039003700370036003700320031000000</w:data>
</xml><![endif]--></span>). In the case of user defined function, the
expression defining the function can contain two independent variables deno=
ted
by <i>x</i> and <i>y</i>, respectively. Since there are two variables, four
interval bounds must be defined in the &#8220;<i>Limits</i>&#8221; box.</sp=
an></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Everyt=
hing is
similar rather similar than in 1D approximation, and some differences will =
be
outlined below. Also the number of sampled values is defined by two values
instead of one. If you clear the &#8220;<i>Random Training Data</i>&#8221;
checkbox then values are sampled on a regular grid of points, where the text
field beside &#8220;<i>Samples on X axis</i>&#8221; defines number of point=
s on
the grid in x direction, and &#8220;<i>Samples on Y axis</i>&#8221; defines
number of points on the grid in the perpendicular (y) direction. If the
&#8220;Random Training Data&#8221; checkbox is checked then sampling points=
 are
generated randomly (with uniform distribution) and the two directions are n=
ot
distinguished what concerns the generated points. The total number of the
generated sampling points equals to the product of both numbers, but their
order is interchangeable. </span></p>

<h3 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Toc358494917"><![=
if !supportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.3.2<span style=3D'font:7.0pt=
 "Times New Roman"'>&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>Network
Architecture and Training Parameters</span></span></a></h3>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Things=
 related
to the network architecture and parameters of the training algorithm are
defined in the same way as in the case of 1D approximation (see Section <sp=
an
style=3D'mso-field-code:" REF _Ref349777537 \\n \\h "'>&#8206;2.2.2<!--[if =
gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340039003700370037003500330037000000</w:data>
</xml><![endif]--></span>). </span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Just t=
ake into
account that in general, in the case of two independent variables, more deg=
rees
of freedom are needed for the same quality of approximation as in 1D. This
means that the number of neurons in each hidden layer should usually be hig=
her
than in the 1D case, but consequently also the number of sampling points sh=
ould
be higher. To be precise, this is a bit simplified and overly generalized
statement since the optimal number of neurons varies from case to case and
depends primarily on the complexity of the function to be approximated.
However, on average over a large range of functions, the statement is valid=
. </span></p>

<h3 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Toc358494918"><![=
if !supportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.3.3<span style=3D'font:7.0pt=
 "Times New Roman"'>&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>Showing T=
raining
Data and Results</span></span></a></h3>

<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:36.0=
pt'><i><span
lang=3DEN-US style=3D'mso-bidi-font-size:12.0pt'><!--[if gte vml 1]><v:shap=
e id=3D"_x0000_i1030"
 type=3D"#_x0000_t75" style=3D'width:255pt;height:241.5pt'>
 <v:imagedata src=3D"NeurApp_files/image004.jpg" o:title=3D"neurapp_title_s=
mall"/>
</v:shape><![endif]--><![if !vml]><img width=3D340 height=3D322
src=3D"NeurApp_files/image015.jpg" v:shapes=3D"_x0000_i1030"><![endif]></sp=
an></i><span
lang=3DEN-US style=3D'mso-bidi-font-size:12.0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp; </span><!--[if gte vml 1]><v:=
shape
 id=3D"_x0000_i1031" type=3D"#_x0000_t75" style=3D'width:141.75pt;height:17=
7pt'>
 <v:imagedata src=3D"NeurApp_files/image016.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D189 height=3D236
src=3D"NeurApp_files/image017.jpg" v:shapes=3D"_x0000_i1031"><![endif]></sp=
an></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><a name=3D"_Ref349805353"><s=
pan
lang=3DEN-US>Figure <span style=3D'mso-field-code:" SEQ Figure \\* ARABIC "=
'><span
style=3D'mso-no-proof:yes'>3</span></span></span></a><span lang=3DEN-US>:</=
span><span
lang=3DEN-US style=3D'font-weight:normal'> Results of a 2 parametric approx=
imation
are shown as 3D graph. Right-hand side: window that shows the original func=
tion
sand training data. 3D graphics is rendered by the VTK graphical engine. <o=
:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Traini=
ng data
and the approximated function are shown, after clicking on the &#8220;Gener=
ate
data&#8221;, in a separate interactive 3D window. In a similar way, the
resulting approximation is shown, together with the approximated function a=
nd
training data, after clicking the &#8220;Start&#8221; button (<span
style=3D'mso-field-code:" REF _Ref349805353 \\h "'>Figure <span style=3D'ms=
o-no-proof:
yes'>3</span><!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340039003800300035003300350033000000</w:data>
</xml><![endif]--></span>). You user can interact with 3D graphs by mouse a=
nd
keyboard in order to adjust the viewing angles, position and zoom as desire=
d.
Close the window after viewing is done, since failing to do so may result in
undesirable effects, depending on the operating system. </span></p>

<h4 style=3D'margin-left:0cm;text-indent:0cm'><![if !supportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.3.3.1<span style=3D'font:7.0=
pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>Interacti=
on with
the 3D Graphic Windows</span></span></h4>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>You ca=
n interact
with the graphs by using mouse and keyboards. Click on the window in order =
to
make it active and interact with it. The relevant commands are listed below=
:</span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>r</spa=
n></b><span
lang=3DEN-US> &#8211; <u>r</u>esets the viewpoint along the viewing directi=
on
such that all graphic objects are within the viewing areal. This centers and
zooms the view appropriately. If the graphics window opens and nothing is
visible, press the <i>r</i> key because objects may just be out of scope.</=
span></span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>j</spa=
n></b><span
lang=3DEN-US> / <b>t</b> &#8211; toggles between <u>j</u>oystick or <u>t</u=
>rackball
mode. In joystick mode, motion occurs continuously as long as mouse button =
is
pressed. In trackball mode, motion occurs only during dragging (when the mo=
use
button is pressed and the mouse cursor moves). The trackball mode is more
suitable for finely adjusting the view.</span></span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>left m=
ouse
button</span></b><span lang=3DEN-US> &#8211; rotates the camera (in the cam=
era
mode, switched on by pressing the <i>c</i> key) or graphic objects (in the
actor mode, switched on by pressing <i>a</i>). The camera is rotated around=
 the
focal point (which can be repositioned by pressing the <i>f</i> key over a
graphic primitive). In trackball mode, you must press the button and move t=
he
mouse cursor, while in joystick mode pressing the button is enough (switch
between the two modes by pressing the <i>t</i> or the <i>j</i> key).</span>=
</span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>Ctrl +=
 left
mouse button</span></b><span lang=3DEN-US> &#8211; rotates the camera (in c=
amera
mode, switched on by presing the <i>c</i> key) or graphic objects (or actor=
s,
switched on by pressing the <i>a</i> keys) around the axis perpendicular to=
 the
projection plane.</span></span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>Shift =
+ left
mouse button</span></b><span lang=3DEN-US> &#8211; pans the camera (moves it
parallel to the projection plane) in camera mode or translates the graphic
objects (actors) in actor mode. Does the same as the middle mouse button.</=
span></span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>middle=
 mouse
button</span></b><span lang=3DEN-US> &#8211; pans the camera (moves it para=
llel
to the projection plane) in camera mode (switched on by pressing the <i>c</=
i>
key) or translates the graphic objects (actors) in actor mode (the <i>a</i>
key). In joystick mode, translation is from the center of viewport toward t=
he
mouse cursor position (toggled by pressing <i>j</i> for joystick and <i>t</=
i>
for trackball mode). Camera mode is switched on by pressing the <i>c</i> key
and actor mode by pressing the <i>a</i> key.</span></span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>right =
mouse
button</span></b><span lang=3DEN-US> &#8211; zooms the camera (in camera mo=
de,
switched on by pressing the <i>c</i> key) or the graphic objects (actors). =
In
joystick mode (switched on by pressing the <i>j</i> key) the direction of z=
oom
depends on whether the mouse cursor is located in the top half of the windo=
w or
viewport (zooms in) or in the lower half (zooms out) while the zoom speed
depends on the distance from the horizontal centerline.</span></span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>mouse =
wheel</span></b><span
lang=3DEN-US> &#8211; zooms in or out, dependent on the direction of rotati=
on.</span></span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol;mso-bidi-=
font-weight:
bold'><span style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Ti=
mes New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>f</spa=
n></b><span
lang=3DEN-US> &#8211; <u>f</u>lies to the point under the mouse cursor, and=
 sets
the focal point on it (rotations then occur around that point). This command
works only when the mouse cursor is located closely enough over a graphic
primitive (auxiliary objects such as axes do not count). It centers the gra=
ph
around the point under the mouse cursor. If later on the graph is translate=
d,
the point of rotation still remains on the same point until the next &#8221;
fly to&#8221; operation is performed.<b><o:p></o:p></b></span></span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>c</spa=
n></b><span
lang=3DEN-US> / <b>a</b> &#8211; toggles between <u>c</u>amera and <u>a</u>=
ctor
modes. In camera mode, user interaction affects the camera position and foc=
al
point, while in actor mode it affects the object (&#8220;actor&#8221; in VTK
terminology) under the mouse pointer. Therefore in actor mode one can rotate
and translate different objects independently. This enables e.g. separation=
 of
different graphic objects. You can press <i>a</i>, then click on the graph =
of
the original function with the middle mouse button and drag it away from ot=
her
objects, then press <i>c</i> and center the view around the graphs of the
approximation and sampled points in order to view them together, without the
original function.</span></span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>p</spa=
n></b><span
lang=3DEN-US> &#8211; pick operation. This shows a wire frame around the ob=
ject
under the mouse cursor. This may turn useful in rare occasions in order to =
see
to which object the graphic primitive under the cursor belongs, e.g. when
separating objects in actor mode.</span></span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>s</spa=
n></b><span
lang=3DEN-US> / <b>w</b> &#8211; all objects become represented as surfaces=
 / in
wire frame. You will seldom need this command.</span></span></p>

<p class=3Dsbullet3><![if !supportLists]><span lang=3DEN-US style=3D'font-f=
amily:
Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>e</spa=
n></b><span
lang=3DEN-US> / <b>q</b> &#8211; exits / quits the graphic window. </span><=
/span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>User i=
nteraction
capabilities can be used to precisely position the view in order to make
interesting details appear more obvious, but also for achieving some special
effect. <span style=3D'mso-field-code:" REF _Ref349820886 \\h "'>Figure <sp=
an
style=3D'mso-no-proof:yes'>4</span><!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340039003800320030003800380036000000</w:data>
</xml><![endif]--></span> demonstrates, for example, how actor mode (switch=
ed
on by pressing the <i>a</i> key and switched off by pressing the <i>c</i> k=
ey
to go back to camera mode) can be used to move the graph of the approximati=
on
apart from the graphs of the approximated function and sampled values used =
for
training. This has been done in the following way. First the trackball mode=
 was
switched on by pressing <i>t</i>. Then the graph was rotated (<i>left mouse
button</i>, with holding the <i>Ctrl</i> key for rotation in the projection
plane), translated (<i>Shift + left mouse button</i>) and zoomed (<i>right
mouse button</i> or <i>mouse wheel</i>) in order to achieve the appropriate
view. Then, the actor mode was switched on by pressing the <i>a</i> key, and
the approximation (the colored surface) was moved away from the original
location to the right by pressing and holding the <i>Shift</i> key and pres=
sing
the <i>left mouse button</i> and moving the mouse to the right. Finally, th=
e <i>c</i>
key was pressed in order to get back to the camera mode and finely tune the
whole graph by translation of the camera. Since objects were not zoomed whi=
le
in the actor mode and since rotations were not performed since entering the
actor mode, one can see the realistic ratios between the original function
(blue wireframe) and its approximation (colored surface) and it is obvious =
that
the approximation has lesser total span than the original.</span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>In the=
 camera
mode (switched on by pressing the <i>c</i> key), all graphic objects stand
still and the camera rotates and translates around. In the actor mode (swit=
ched
on by pressing the <i>a</i> key), camera remains still and the selected gra=
phic
object (which may consist of many graphic primitives, such as the whole sur=
face
in the above described case) moves and rotates (thus it can also change
position with respect to other objects).</span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><!--[i=
f gte vml 1]><v:shape
 id=3D"_x0000_i1032" type=3D"#_x0000_t75" style=3D'width:339.75pt;height:26=
1.75pt'>
 <v:imagedata src=3D"NeurApp_files/image018.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D453 height=3D349
src=3D"NeurApp_files/image019.jpg" v:shapes=3D"_x0000_i1032"><![endif]></sp=
an></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><a name=3D"_Ref349820886"><s=
pan
lang=3DEN-US>Figure <span style=3D'mso-field-code:" SEQ Figure \\* ARABIC "=
'><span
style=3D'mso-no-proof:yes'>4</span></span></span></a><span lang=3DEN-US>:</=
span><span
lang=3DEN-US style=3D'font-weight:normal'> Separation of the graph of the o=
riginal
function and sampling points (left-hand side) and approximation (right-hand
side) by using the actor mode. Case is the same as shown in <span
style=3D'mso-field-code:" REF _Ref349805353 \\h &#1; \\* MERGEFORMAT "'>Fig=
ure <span
style=3D'mso-no-proof:yes'>3</span><!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340039003800300035003300350033000000</w:data>
</xml><![endif]--></span>. <o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt;tab-stops:292.4pt'><span
lang=3DEN-US><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></p>

<h4 style=3D'margin-left:0cm;text-indent:0cm'><![if !supportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.3.3.2<span style=3D'font:7.0=
pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>Showing
Convergence Path</span></span></h4>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>This is
equivalent as in 1D case (Section <span style=3D'mso-field-code:" REF _Ref3=
49803946 \\n \\h "'>&#8206;2.2.4<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340039003800300033003900340036000000</w:data>
</xml><![endif]--></span>). Final values of different error measures are sh=
own
in the &#8220;<i>Approximation error</i>&#8221; box and course of the selec=
ted
error measure is shown on the graph on the right of error values. Radio but=
tons
are used to select the error measure to be shown on the graph ().</span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'mso-ansi-language:SL'><!--[if gte vml 1]><v:shape id=3D"_x0000_i10=
33"
 type=3D"#_x0000_t75" style=3D'width:381.75pt;height:96.75pt' o:ole=3D"">
 <v:imagedata src=3D"NeurApp_files/image011.emz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D509 height=3D129
src=3D"NeurApp_files/image012.gif" v:shapes=3D"_x0000_i1033"><![endif]><!--=
[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Word.Picture.8" ShapeID=3D"_x0000_i1=
033"
  DrawAspect=3D"Content" ObjectID=3D"_1432239022">
 </o:OLEObject>
</xml><![endif]--></span></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><span lang=3DEN-US>Figure <s=
pan
style=3D'mso-field-code:" SEQ Figure \\* ARABIC "'><span style=3D'mso-no-pr=
oof:
yes'>4</span></span>:</span><span lang=3DEN-US style=3D'font-weight:normal'>
Convergence of different types of errors. <o:p></o:p></span></p>

<p class=3DMsoNormal><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span lang=3D=
EN-US>Max
Training Error<o:p></o:p></span></b></p>

<p class=3DMsoNormal><span lang=3DEN-US>Maximum absolute error calculated on
complete training data set after each set of epochs (Epochs in Bundle) and
shown on graph</span></p>

<p class=3DMsoNormal><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span lang=3D=
EN-US>Rms
Training Error<o:p></o:p></span></b></p>

<p class=3DMsoNormal><span lang=3DEN-US>Root mean square error calculated on
complete training data set after each set of epochs (Epochs in Bundle) and
shown on graph</span></p>

<p class=3DMsoNormal><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span lang=3D=
EN-US>Max
Verification Error<o:p></o:p></span></b></p>

<p class=3DMsoNormal><span lang=3DEN-US>Maximum absolute error calculated on
complete verification data set after each set of epochs (Epochs in Bundle) =
and
shown on graph. Verification data are not used in training procedure, but a=
re
separated from training data and used just for verification the accuracy of=
 ANN
during and after training.</span></p>

<p class=3DMsoNormal><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span lang=3D=
EN-US>Rms
Verification Error<o:p></o:p></span></b></p>

<p class=3DMsoNormal><span lang=3DEN-US>Root mean square error calculated on
complete verification data set after each set of epochs (Epochs in Bundle) =
and
shown on graph. </span></p>

<p class=3DMsoNormal><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<h2 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Toc349256594"></a=
><a
name=3D"_Toc358494919"><span style=3D'mso-bookmark:_Toc349256594'><![if !su=
pportLists]><span
lang=3DEN-US><span style=3D'mso-list:Ignore'>2.4<span style=3D'font:7.0pt "=
Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US>Accessing=
 Help
and Web Pages</span></span></span></a></h2>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span style=3D'mso-ansi-l=
anguage:
SL'><!--[if gte vml 1]><v:shape id=3D"_x0000_i1034" type=3D"#_x0000_t75" st=
yle=3D'width:481.5pt;
 height:264pt' o:ole=3D"">
 <v:imagedata src=3D"NeurApp_files/image020.emz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D642 height=3D352
src=3D"NeurApp_files/image021.gif" v:shapes=3D"_x0000_i1034"><![endif]><!--=
[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Word.Picture.8" ShapeID=3D"_x0000_i1=
034"
  DrawAspect=3D"Content" ObjectID=3D"_1432239023">
 </o:OLEObject>
</xml><![endif]--></span></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><span lang=3DEN-US>Figure <s=
pan
style=3D'mso-field-code:" SEQ Figure \\* ARABIC "'><span style=3D'mso-no-pr=
oof:
yes'>5</span></span>:</span><span lang=3DEN-US style=3D'font-weight:normal'>
Accessing help and other information. <o:p></o:p></span></p>

<h1 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Toc349256595"></a=
><a
name=3D"_Toc358494920"><span style=3D'mso-bookmark:_Toc349256595'><![if !su=
pportLists]><span
lang=3DEN-US style=3D'text-transform:uppercase'><span style=3D'mso-list:Ign=
ore'>3<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US style=3D'=
text-transform:
uppercase'>Screenshots</span></span></span></a><span lang=3DEN-US
style=3D'text-transform:uppercase'><o:p></o:p></span></h1>

<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:36.0=
pt'><span
style=3D'mso-ansi-language:SL'><!--[if gte vml 1]><v:shape id=3D"_x0000_i10=
35"
 type=3D"#_x0000_t75" style=3D'width:414pt;height:264pt' o:ole=3D"">
 <v:imagedata src=3D"NeurApp_files/image022.emz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D552 height=3D352
src=3D"NeurApp_files/image023.gif" v:shapes=3D"_x0000_i1035"><![endif]><!--=
[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Word.Picture.8" ShapeID=3D"_x0000_i1=
035"
  DrawAspect=3D"Content" ObjectID=3D"_1432239024">
 </o:OLEObject>
</xml><![endif]--></span></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><span lang=3DEN-US>Figure <s=
pan
style=3D'mso-field-code:" SEQ Figure \\* ARABIC "'><span style=3D'mso-no-pr=
oof:
yes'>6</span></span>:</span><span lang=3DEN-US style=3D'font-weight:normal'=
> <span
style=3D'mso-field-code:" REF softwarename \\h &#1; \\* MERGEFORMAT "'>Neur=
App<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D00000073006F00=
6600740077006100720065006E0061006D0065000000</w:data>
</xml><![endif]--></span> has a very intuitive user interface. All you have=
 to
remember is to press the &#8220;Generate Data&#8221; and then the
&#8220;Start&#8221; button. Other things are for changing parameters of the
training procedure, bounds for the training data, and the function to be
approximated.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span style=3D'mso-ansi-l=
anguage:
SL'><!--[if gte vml 1]><v:shape id=3D"_x0000_i1036" type=3D"#_x0000_t75" st=
yle=3D'width:202.5pt;
 height:140.25pt' o:ole=3D"">
 <v:imagedata src=3D"NeurApp_files/image024.emz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D270 height=3D187
src=3D"NeurApp_files/image025.gif" v:shapes=3D"_x0000_i1036"><![endif]><!--=
[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Word.Picture.8" ShapeID=3D"_x0000_i1=
036"
  DrawAspect=3D"Content" ObjectID=3D"_1432239025">
 </o:OLEObject>
</xml><![endif]--></span></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><span lang=3DEN-US>Figure <s=
pan
style=3D'mso-field-code:" SEQ Figure \\* ARABIC "'><span style=3D'mso-no-pr=
oof:
yes'>7</span></span>:</span><span lang=3DEN-US style=3D'font-weight:normal;
mso-bidi-font-weight:bold'> After generation of data, you can immediately s=
ee the
graph of the original function and data that will be used for training.</sp=
an><span
lang=3DEN-US style=3D'font-weight:normal'><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:36.0=
pt'><span
style=3D'mso-ansi-language:SL'><!--[if gte vml 1]><v:shape id=3D"_x0000_i10=
37"
 type=3D"#_x0000_t75" style=3D'width:414pt;height:264pt' o:ole=3D"">
 <v:imagedata src=3D"NeurApp_files/image026.emz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D552 height=3D352
src=3D"NeurApp_files/image027.gif" v:shapes=3D"_x0000_i1037"><![endif]><!--=
[if gte mso 9]><xml>
 <o:OLEObject Type=3D"Embed" ProgID=3D"Word.Picture.8" ShapeID=3D"_x0000_i1=
037"
  DrawAspect=3D"Content" ObjectID=3D"_1432239026">
 </o:OLEObject>
</xml><![endif]--></span></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><span lang=3DEN-US>Figure <s=
pan
style=3D'mso-field-code:" SEQ Figure \\* ARABIC "'><span style=3D'mso-no-pr=
oof:
yes'>8</span></span>:</span><span lang=3DEN-US style=3D'font-weight:normal;
mso-bidi-font-weight:bold'> After pressing the &#8220;Start&#8221; button,
training of the neural network begins, and the result is shown immediately
after training is complete. It is easy to compare the generated ANN model w=
ith
the original function. Smaller graph shows how error was reduced during the
training procedure, making possible to correct some parameters such as
tolerances and maximal number of epochs if results are not as expected.</sp=
an><span
lang=3DEN-US style=3D'font-weight:normal'><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:36.0=
pt'><span
lang=3DEN-US><!--[if gte vml 1]><v:shape id=3D"_x0000_i1038" type=3D"#_x000=
0_t75"
 style=3D'width:340.5pt;height:273pt'>
 <v:imagedata src=3D"NeurApp_files/image028.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D454 height=3D364
src=3D"NeurApp_files/image029.jpg" v:shapes=3D"_x0000_i1038"><![endif]></sp=
an></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><span lang=3DEN-US>Figure <s=
pan
style=3D'mso-field-code:" SEQ Figure \\* ARABIC "'><span style=3D'mso-no-pr=
oof:
yes'>9</span></span>:</span><span lang=3DEN-US style=3D'font-weight:normal;
mso-bidi-font-weight:bold'> Example 3D plot of the original function of 2
variables and the generated training data on the surface of the function gr=
aph.</span><span
lang=3DEN-US style=3D'font-weight:normal'><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:36.0=
pt'><span
lang=3DEN-US><!--[if gte vml 1]><v:shape id=3D"_x0000_i1039" type=3D"#_x000=
0_t75"
 style=3D'width:340.5pt;height:348pt'>
 <v:imagedata src=3D"NeurApp_files/image030.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D454 height=3D464
src=3D"NeurApp_files/image031.jpg" v:shapes=3D"_x0000_i1039"><![endif]></sp=
an></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><span lang=3DEN-US>Figure <s=
pan
style=3D'mso-field-code:" SEQ Figure \\* ARABIC "'><span style=3D'mso-no-pr=
oof:
yes'>10</span></span>:</span><span lang=3DEN-US style=3D'font-weight:normal;
mso-bidi-font-weight:bold'> After training of the neural network is complet=
e, a
surface plot of the approximated function is shown together with the origin=
al
function and with the generated training data. Error magnitude is shown in
color scale.</span><span lang=3DEN-US style=3D'font-weight:normal'><o:p></o=
:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:36.0=
pt'><span
lang=3DEN-US><!--[if gte vml 1]><v:shape id=3D"_x0000_i1040" type=3D"#_x000=
0_t75"
 style=3D'width:339.75pt;height:306.75pt'>
 <v:imagedata src=3D"NeurApp_files/image032.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D453 height=3D409
src=3D"NeurApp_files/image033.jpg" v:shapes=3D"_x0000_i1040"><![endif]></sp=
an></p>

<p class=3DMsoCaption style=3D'margin-top:0cm'><span lang=3DEN-US>Figure <s=
pan
style=3D'mso-field-code:" SEQ Figure \\* ARABIC "'><span style=3D'mso-no-pr=
oof:
yes'>11</span></span>:</span><span lang=3DEN-US style=3D'font-weight:normal;
mso-bidi-font-weight:bold'> One can interactively adjust the viewing angle =
and
zoom in order to inspect properties of the approximation in detail.</span><=
span
lang=3DEN-US style=3D'font-weight:normal'><o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt;tab-stops:224.85pt'><span
lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<h1 style=3D'margin-left:0cm;text-indent:0cm'><a name=3D"_Toc349256596"></a=
><a
name=3D"_Toc358494921"><span style=3D'mso-bookmark:_Toc349256596'><![if !su=
pportLists]><span
lang=3DEN-US style=3D'text-transform:uppercase'><span style=3D'mso-list:Ign=
ore'>4<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;
</span></span></span><![endif]><span dir=3DLTR><span lang=3DEN-US style=3D'=
text-transform:
uppercase'>About the Software</span></span></span></a><span lang=3DEN-US
style=3D'text-transform:uppercase'><o:p></o:p></span></h1>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Softwa=
re was
developed by Igor Gre&#353;ovnik and Tadej Kodelja as an easy to use and
intuitive tool for exploring features of approximation by the artificial ne=
ural
networks (ANN). Authors have developed the software while working on ANN-ba=
sed
model of process parameters in material production in the Centre of Excelle=
nce
for Biosensors, Instrumentation and Process Control (<a
href=3D"http://www.cobik.si/index?lang=3Deng">COBIK</a>). In the scope of h=
is work
at COBIK, Tadej Kodelja was also working on his Ph.D. thesis under supervis=
ion
of Prof. Bo&#382;idar &#352;arler and Igor Gre&#353;ovnik.</span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>The so=
ftware is
based on the <i>Investigative Generic Library</i> (<i>IGLib</i>), a framewo=
rk
library for development of technical applications. The library itself is ba=
sed
on the .NET framework and relies on a number of third party libraries. It h=
as
been used by several commercial software projects as well as in research
projects. Among the others, it serves as code base for the software for
industrial ANN-based modeling, which is developed by the authors of <span
style=3D'mso-field-code:" REF softwarename \\h "'>NeurApp<!--[if gte mso 9]=
><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D00000073006F00=
6600740077006100720065006E0061006D0065000000</w:data>
</xml><![endif]--></span>. This is a complex software used as support to ta=
ckle
most challenging ANN modeling problems in industry. It requires some expert=
ise
and skills to use that software, but with the benefit of a powerful and
flexible problem solving tool. The software is used internally for performi=
ng
research and providing services to industry, but authors are open for all k=
inds
of collaboration where the software can be utilized.</span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Motiva=
tion for
development of the software came partially from authors&#8217; personal nee=
ds,
since authors wanted to gain better insight in features and function of the
ANN-based approximations, gained from practical experience and on fast and
intuitive way. Therefore they devised a software where one can conceive
arbitrary functions of one and two variables, input these functions through=
 a
graphical user interface and set them as the reference functions for ANN-ba=
sed
models, sample function values on a regular grid or in randomly distributed
values, train the neural network to obtain an approximate model, and inspect
properties of the obtained model by observing various statistics and by vis=
ual comparison
of the model and the original reference function. In this way, it is easy to
develop an intuitive feeling for the capabilities and limitations of the
ANN-based modeling. </span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Additi=
onal
motivation was in creating a tool that could be easily utilized to demonstr=
ate
some features of the artificial neural networks to our colleagues. Often pe=
ople
have wrong expectations about the ANN-based modeling. Many times they heavi=
ly
overestimate the capabilities of the neural network modeling, considering t=
his
tool as a kind of Panacea, an almighty remedy for all problems. It is somet=
imes
difficult to explain that ANNs are just an ordinary (though very strong in =
some
aspects) utility for black box modeling. As such, it crucially depends on t=
he
availability and quality of data, thus being susceptible to many kinds of d=
ata
deficiency and absolutely adherent to the &#8220;garbage in, garbage out&#8=
221;
principle. By a tool such as <span style=3D'mso-field-code:" REF softwarena=
me \\h "'>NeurApp<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D00000073006F00=
6600740077006100720065006E0061006D0065000000</w:data>
</xml><![endif]--></span>, it is easier to plastically demonstrate how
ANN-based modeling works.</span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

</div>

<span lang=3DEN-US style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;font=
-family:
"Times New Roman";mso-fareast-font-family:"Times New Roman";mso-ansi-langua=
ge:
EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA;layout-grid-mode:l=
ine'><br
clear=3Dall style=3D'page-break-before:auto;mso-break-type:section-break'>
</span>

<div class=3DSection4>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<span lang=3DEN-US style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;font=
-family:
"Times New Roman";mso-fareast-font-family:"Times New Roman";mso-ansi-langua=
ge:
EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA;layout-grid-mode:l=
ine'><br
clear=3Dall style=3D'mso-special-character:line-break;page-break-before:alw=
ays'>
</span>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><a name=3Dreferences></a>=
<a
name=3D"_Hlt96670121"></a><span style=3D'mso-bookmark:references'><b
style=3D'mso-bidi-font-weight:normal'><i style=3D'mso-bidi-font-style:norma=
l'><span
lang=3DEN-US style=3D'font-size:14.0pt;mso-bidi-font-size:10.0pt'>Some Refe=
rences</span></i></b></span><b
style=3D'mso-bidi-font-weight:normal'><i style=3D'mso-bidi-font-style:norma=
l'><span
lang=3DEN-US style=3D'font-size:14.0pt;mso-bidi-font-size:10.0pt'><o:p></o:=
p></span></i></b></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Below =
there is a
collection of selected references and links that are in some way related to=
 the
<span style=3D'mso-field-code:" REF softwarename \\h "'>NeurApp<!--[if gte =
mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D00000073006F00=
6600740077006100720065006E0061006D0065000000</w:data>
</xml><![endif]--></span> software. They are mainly related to the
authors&#8217; past work that brought to the situation where <span
style=3D'mso-field-code:" REF softwarename \\h "'>NeurApp<!--[if gte mso 9]=
><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D00000073006F00=
6600740077006100720065006E0061006D0065000000</w:data>
</xml><![endif]--></span> was created. References <span style=3D'mso-field-=
code:
" REF _Ref342050823 \\h "'>[<span style=3D'mso-no-proof:yes'>1</span><!--[i=
f gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340032003000350030003800320033000000</w:data>
</xml><![endif]--></span>] - <span style=3D'mso-field-code:" REF _Ref342050=
851 \\h "'>[<span
style=3D'mso-no-proof:yes'>3</span><!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340032003000350030003800350031000000</w:data>
</xml><![endif]--></span>] are some papers published within the scope of our
work at the . <span style=3D'mso-field-code:" REF _Ref343474114 \\h "'>[<sp=
an
style=3D'mso-no-proof:yes'>4</span><!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340033003400370034003100310034000000</w:data>
</xml><![endif]--></span>] - <span style=3D'mso-field-code:" REF _Ref349458=
151 \\h "'>[<span
style=3D'mso-no-proof:yes'>9</span><!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340039003400350038003100350031000000</w:data>
</xml><![endif]--></span>] are references related to optimization shell <i>=
Inverse</i>,
which is a complex industrial &amp; research optimization software written =
in C
that preceded the <i>IGLib</i> library, and where many concepts and ideas u=
sed
in the <i>IGLib</i> library (a framework library for development of technic=
al
applications reference developed by Igor Gre</span><span style=3D'mso-ansi-=
language:
SL'>&#353;ovnik, reference</span> <span lang=3DEN-US><span style=3D'mso-fie=
ld-code:
" REF _Ref342050944 \\h "'>[<span style=3D'mso-no-proof:yes'>10</span><!--[=
if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340032003000350030003900340034000000</w:data>
</xml><![endif]--></span>]) come from. Aforge.Net (reference <span
style=3D'mso-field-code:" REF _Ref340767727 \\h "'>[<span style=3D'mso-no-p=
roof:
yes'>11</span><!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340030003700360037003700320037000000</w:data>
</xml><![endif]--></span>]) is a library that is used as neural networks
computation engine in <span style=3D'mso-field-code:" REF softwarename \\h =
"'>NeurApp<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D00000073006F00=
6600740077006100720065006E0061006D0065000000</w:data>
</xml><![endif]--></span>. </span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>Refere=
nces <span
style=3D'mso-field-code:" REF _Ref349458686 \\h "'>[<span style=3D'mso-no-p=
roof:
yes'>12</span><!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340039003400350038003600380036000000</w:data>
</xml><![endif]--></span>] and <span style=3D'mso-field-code:" REF _Ref3494=
58689 \\h "'>[<span
style=3D'mso-no-proof:yes'>13</span><!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340039003400350038003600380039000000</w:data>
</xml><![endif]--></span>] are links to the institution </span><span
lang=3DEN-US style=3D'mso-bidi-font-size:14.0pt'>Centre of Excellence for
biosensors, instrumentation and process control </span><span lang=3DEN-US>(=
COBIK)
and the laboratory where the authors currently work. Within COBIK, authors =
are
developing methodologies for application of artificial neural networks to
modeling of industrial processes. The problem solving software developed in=
 the
scope of this work is based on the IGLib (<span style=3D'mso-field-code:" R=
EF _Ref342050944 \\h "'>[<span
style=3D'mso-no-proof:yes'>10</span><!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200=
650066003300340032003000350030003900340034000000</w:data>
</xml><![endif]--></span>]). This is also the case with <span style=3D'mso-=
field-code:
" REF softwarename \\h "'>NeurApp<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D00000073006F00=
6600740077006100720065006E0061006D0065000000</w:data>
</xml><![endif]--></span>, which is just a side product of the above work
initially developed as a simple tool for authors&#8217; training in basic f=
eatures
of ANN-based approximation. </span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US>The mo=
re
professional software used for actual research &amp; industrial work is qui=
te
complex and requires a high level of expertise from the user, and it is
interpreter - centered rather than a GUI - based. It is used internally for
performing research tasks and to offer services to industry, with interface=
s to
a number of partner software and with some specialized interfaces for users=
 in
partner institutions. This software is designed to be highly flexible and
quickly adaptable to new problems and customer requirements. It does not
targeted any specific range of tasks, but is a good base for a wide range of
specialized modules or applications for specific and well defined tasks. The
software is not available for purchase, but authors will welcome any sugges=
tion
for collaboration on research, development or industrial projects or request
for development of software needed, where they can provide reliable and
professional service. </span></p>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
nbsp;</o:p></span></p>

<p class=3Dlit><a name=3D"_Ref78865871"></a><a name=3D"_Ref472079565"></a><a
name=3D"_Ref343779729"></a><a name=3D"_Ref342050823"></a><a name=3D"_Hlt817=
54371"></a><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref343779729'><span style=3D'mso-bookmark:_Ref342050=
823'><span
lang=3DEN-US>[<span style=3D'mso-field-code:" SEQ \[ \\* ARABIC "'><span
style=3D'mso-no-proof:yes'>1</span></span></span></span><span lang=3DEN-US>=
]<span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></sp=
an></span></span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref343779729'><span lang=3DEN-US style=3D'mso-bidi-f=
ont-size:
12.0pt'>Gre&#353;ovnik, <st1:place w:st=3D"on">I.</st1:place>; Kodelja, T.;
Vertnik, R.; &#352;arler, B. (2012): A software Framework for Optimization
Parameters in Material Production. Applied Mechanics and Materialds, vol.
101-102, pp. 838-841. Trans Tech Publications, <st1:place w:st=3D"on"><st1:=
country-region
 w:st=3D"on">Switzerland</st1:country-region></st1:place>.</span></span></s=
pan></span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
lang=3DEN-US style=3D'mso-bidi-font-size:12.0pt'><o:p></o:p></span></span><=
/span></p>

<p class=3Dlit><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso=
-bookmark:
_Ref472079565'><a name=3D"_Ref341342485"><span lang=3DEN-US>[<span
style=3D'mso-field-code:" SEQ \[ \\* ARABIC "'><span style=3D'mso-no-proof:=
yes'>2</span></span></span></a><span
lang=3DEN-US>]<span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
; </span></span></span></span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
lang=3DEN-US style=3D'mso-bidi-font-size:12.0pt'>Gre&#353;ovnik, <st1:place=
 w:st=3D"on">I.</st1:place>;
Kodelja, T.; Vertnik, R.; &#352;arler, B. (2012): </span><span lang=3DEN-US=
>Application
of artificial neural networks to improve steel production process. Bruzzone=
, A.
G.; Hamza, M. H. Proceedings of the 15th International Conference on Artifi=
cial
Intelligence and Soft Computing, <st1:place w:st=3D"on"><st1:City w:st=3D"o=
n">Napoli</st1:City>,
 <st1:country-region w:st=3D"on">Italy</st1:country-region></st1:place>, pp.
249-255.</span></span></span></p>

<p class=3Dlit><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso=
-bookmark:
_Ref472079565'><a name=3D"_Ref340647856"></a><a name=3D"_Ref342050851"><span
style=3D'mso-bookmark:_Ref340647856'><span lang=3DEN-US>[<span style=3D'mso=
-field-code:
" SEQ \[ \\* ARABIC "'><span style=3D'mso-no-proof:yes'>3</span></span></sp=
an></span></a><span
style=3D'mso-bookmark:_Ref340647856'><span lang=3DEN-US>]<span style=3D'mso=
-tab-count:
1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Gre&#353;ovnik, <st1:place w:st=3D=
"on">I.</st1:place>;
Kodelja, T.; Vertnik, R.; Sen&#269;i&#269;. B.; Kova&#269;i&#269;, M.;
&#352;arler, B. (2012): Application of artificial neural networks in design=
 of
steel production path. Computers, Materials and Continua, vol. 30, pp. 19-3=
8.</span></span></span></span></p>

<p class=3Dlit><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso=
-bookmark:
_Ref472079565'><span style=3D'mso-bookmark:_Ref340647856'><a name=3D"_Ref34=
3474114"><span
lang=3DEN-US>[<span style=3D'mso-field-code:" SEQ \[ \\* ARABIC "'><span
style=3D'mso-no-proof:yes'>4</span></span></span></a><span lang=3DEN-US>]<s=
pan
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Gresovnik, =
I.
(2000): A General Purpose Computational Shell for Solving Inverse and
Optimisation Problems - Applications to Metal Forming Processes, Ph. D. the=
sis,
University of Wales Swansea, U.K.</span></span></span></span></p>

<p class=3Dlit><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso=
-bookmark:
_Ref472079565'><span style=3D'mso-bookmark:_Ref340647856'><span lang=3DEN-U=
S>[<span
style=3D'mso-field-code:" SEQ \[ \\* ARABIC "'><span style=3D'mso-no-proof:=
yes'>5</span></span>]<span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></sp=
an></span></span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span lang=3DEN-US style=3D'mso-fareas=
t-font-family:
KaiTi_GB2312'>Gre&#353;ovnik, <st1:place w:st=3D"on">I.</st1:place> (2012):
Optimization shell Inverse, </span></span></span></span><a
href=3D"http://www2.arnes.si/~ljc3m2/inverse/"><span style=3D'mso-bookmark:=
_Ref78865871'><span
style=3D'mso-bookmark:_Ref472079565'><span style=3D'mso-bookmark:_Ref340647=
856'><span
lang=3DEN-US style=3D'mso-fareast-font-family:KaiTi_GB2312'>http://www2.arn=
es.si/~ljc3m2/inverse/</span></span></span></span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'></span></span></span></a><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span lang=3DEN-US style=3D'mso-fareas=
t-font-family:
KaiTi_GB2312'>.</span></span></span></span></p>

<p class=3Dlit><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso=
-bookmark:
_Ref472079565'><span style=3D'mso-bookmark:_Ref340647856'><a name=3D"_Ref34=
2050943"><span
lang=3DEN-US>[<span style=3D'mso-field-code:" SEQ \[ \\* ARABIC "'><span
style=3D'mso-no-proof:yes'>6</span></span></span></a><span lang=3DEN-US>]<s=
pan
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></sp=
an></span></span><a
name=3D"_Ref295434474"><span style=3D'mso-bookmark:_Ref340647856'><span
style=3D'mso-bookmark:_Ref472079565'><span style=3D'mso-bookmark:_Ref788658=
71'><span
lang=3DEN-US style=3D'mso-fareast-font-family:KaiTi_GB2312'>Gre&#353;ovnik,=
 </span></span></span></span></a><st1:place
w:st=3D"on"><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bo=
okmark:
 _Ref472079565'><span style=3D'mso-bookmark:_Ref340647856'><span
 style=3D'mso-bookmark:_Ref295434474'><span lang=3DEN-US style=3D'mso-farea=
st-font-family:
 KaiTi_GB2312'>I.</span></span></span></span></span></st1:place><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span style=3D'mso-bookmark:_Ref295434=
474'><span
lang=3DEN-US style=3D'mso-fareast-font-family:KaiTi_GB2312'> (2012): IoptLi=
b User
Manual. </span><span lang=3DEN-US>Available at:</span></span></span></span>=
</span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span style=3D'mso-bookmark:_Ref295434=
474'><span
lang=3DEN-US style=3D'mso-fareast-font-family:KaiTi_GB2312'> </span></span>=
</span></span></span><a
href=3D"http://www2.arnes.si/~ljc3m2/igor/ioptlib/doc/optlib.pdf"><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span style=3D'mso-bookmark:_Ref295434=
474'><span
lang=3DEN-US style=3D'mso-fareast-font-family:KaiTi_GB2312'>http://www2.arn=
es.si/~ljc3m2/igor/ioptlib/doc/optlib.pdf</span></span></span></span></span=
><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span style=3D'mso-bookmark:_Ref295434=
474'></span></span></span></span></a><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span style=3D'mso-bookmark:_Ref295434=
474'><span
lang=3DEN-US style=3D'mso-fareast-font-family:KaiTi_GB2312'>.</span></span>=
</span></span></span></p>

<p class=3Dlit><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso=
-bookmark:
_Ref472079565'><span style=3D'mso-bookmark:_Ref340647856'><span lang=3DEN-U=
S>[<span
style=3D'mso-field-code:" SEQ \[ \\* ARABIC "'><span style=3D'mso-no-proof:=
yes'>7</span></span>]<span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></sp=
an></span></span><a
name=3D"_Ref295434476"><span style=3D'mso-bookmark:_Ref340647856'><span
style=3D'mso-bookmark:_Ref472079565'><span style=3D'mso-bookmark:_Ref788658=
71'><span
lang=3DEN-US style=3D'mso-fareast-font-family:KaiTi_GB2312'>Gre&#353;ovnik,=
 </span></span></span></span></a><st1:place
w:st=3D"on"><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bo=
okmark:
 _Ref472079565'><span style=3D'mso-bookmark:_Ref340647856'><span
 style=3D'mso-bookmark:_Ref295434476'><span lang=3DEN-US style=3D'mso-farea=
st-font-family:
 KaiTi_GB2312'>I.</span></span></span></span></span></st1:place><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span style=3D'mso-bookmark:_Ref295434=
476'><span
lang=3DEN-US style=3D'mso-fareast-font-family:KaiTi_GB2312'> (2007): The us=
e of
moving least squares for a smooth approximation of sampled data. Journal of
Mechanical Engineering, vol. 9, pp. 582-598.</span></span></span></span></s=
pan></p>

<p class=3Dlit><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso=
-bookmark:
_Ref472079565'><span style=3D'mso-bookmark:_Ref340647856'><span lang=3DEN-U=
S>[<span
style=3D'mso-field-code:" SEQ \[ \\* ARABIC "'><span style=3D'mso-no-proof:=
yes'>8</span></span>]<span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></sp=
an></span></span><a
name=3D"_Ref295434555"><span style=3D'mso-bookmark:_Ref340647856'><span
style=3D'mso-bookmark:_Ref472079565'><span style=3D'mso-bookmark:_Ref788658=
71'><span
lang=3DEN-US style=3D'mso-fareast-font-family:KaiTi_GB2312'>Gre&#353;ovnik,=
 </span></span></span></span></a><st1:place
w:st=3D"on"><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bo=
okmark:
 _Ref472079565'><span style=3D'mso-bookmark:_Ref340647856'><span
 style=3D'mso-bookmark:_Ref295434555'><span lang=3DEN-US style=3D'mso-farea=
st-font-family:
 KaiTi_GB2312'>I.</span></span></span></span></span></st1:place><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span style=3D'mso-bookmark:_Ref295434=
555'><span
lang=3DEN-US style=3D'mso-fareast-font-family:KaiTi_GB2312'> (2009): Simplex
Algorithms for Nonlinear Constrained Optimization Problems, technical repor=
t.
Available at: </span></span></span></span></span><a
href=3D"http://www2.arnes.si/~ljc3m2/igor/doc/rep/optalgsimplex.pdf"><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span style=3D'mso-bookmark:_Ref295434=
555'><span
lang=3DEN-US style=3D'mso-fareast-font-family:KaiTi_GB2312'>http://www2.arn=
es.si/~ljc3m2/igor/doc/rep/optalgsimplex.pdf</span></span></span></span></s=
pan><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span style=3D'mso-bookmark:_Ref295434=
555'></span></span></span></span></a><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span style=3D'mso-bookmark:_Ref295434=
555'><span
lang=3DEN-US style=3D'mso-fareast-font-family:KaiTi_GB2312'>.</span></span>=
</span></span></span></p>

<p class=3Dlit><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso=
-bookmark:
_Ref472079565'><span style=3D'mso-bookmark:_Ref340647856'><a name=3D"_Ref34=
9458151"><span
lang=3DEN-US>[<span style=3D'mso-field-code:" SEQ \[ \\* ARABIC "'><span
style=3D'mso-no-proof:yes'>9</span></span></span></a><span lang=3DEN-US>]<s=
pan
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></sp=
an></span></span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span lang=3DEN-US style=3D'mso-fareas=
t-font-family:
KaiTi_GB2312'>Gre&#353;ovnik, <st1:place w:st=3D"on">I.</st1:place> (2012):=
 </span><span
lang=3DEN-US>IOptLib &#8211; library for solving inverse and optimization
problems. Available at: </span></span></span></span><a
href=3D"http://www2.arnes.si/~ljc3m2/igor/ioptlib/"><span style=3D'mso-book=
mark:
_Ref78865871'><span style=3D'mso-bookmark:_Ref472079565'><span style=3D'mso=
-bookmark:
_Ref340647856'><span lang=3DEN-US>http://www2.arnes.si/~ljc3m2/igor/ioptlib=
/</span></span></span></span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'></span></span></span></a><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
style=3D'mso-bookmark:_Ref340647856'><span lang=3DEN-US> </span></span></sp=
an></span></p>

<p class=3Dlit><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso=
-bookmark:
_Ref472079565'><span style=3D'mso-bookmark:_Ref340647856'><a name=3D"_Ref34=
2050944"><span
lang=3DEN-US>[<span style=3D'mso-field-code:" SEQ \[ \\* ARABIC "'><span
style=3D'mso-no-proof:yes'>10</span></span></span></a></span><span lang=3DE=
N-US>]<span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp; </span>Gre&#353;ovnik, <st1:pl=
ace
w:st=3D"on">I.</st1:place> (2012): IGLib.net - investigative generic librar=
y.
Available at: </span></span></span><a
href=3D"http://www2.arnes.si/~ljc3m2/igor/iglib/"><span style=3D'mso-bookma=
rk:_Ref78865871'><span
style=3D'mso-bookmark:_Ref472079565'><span lang=3DEN-US>http://www2.arnes.s=
i/~ljc3m2/igor/iglib/</span></span></span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'></span></span></a><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
lang=3DEN-US>. </span></span></span></p>

<p class=3Dlit><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso=
-bookmark:
_Ref472079565'><a name=3D"_Ref340767727"><span lang=3DEN-US>[<span
style=3D'mso-field-code:" SEQ \[ \\* ARABIC "'><span style=3D'mso-no-proof:=
yes'>11</span></span></span></a><span
lang=3DEN-US>]<span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp; </span></s=
pan></span></span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
lang=3DEN-US style=3D'mso-bidi-font-size:14.0pt'>Aforge.Net. (2012): Artifi=
cial
intelligence library. Available at: </span></span></span><a
href=3D"http://www.aforgenet.com/"><span style=3D'mso-bookmark:_Ref78865871=
'><span
style=3D'mso-bookmark:_Ref472079565'><span lang=3DEN-US style=3D'mso-bidi-f=
ont-size:
14.0pt'>http://www.aforgenet.com/</span></span></span><span style=3D'mso-bo=
okmark:
_Ref78865871'><span style=3D'mso-bookmark:_Ref472079565'></span></span></a>=
<span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
lang=3DEN-US style=3D'mso-bidi-font-size:14.0pt'>.<o:p></o:p></span></span>=
</span></p>

<p class=3Dlit><span style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso=
-bookmark:
_Ref472079565'><a name=3D"_Ref349458686"><span lang=3DEN-US>[<span
style=3D'mso-field-code:" SEQ \[ \\* ARABIC "'><span style=3D'mso-no-proof:=
yes'>12</span></span></span></a><span
lang=3DEN-US>]<span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp; </span></s=
pan></span></span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
lang=3DEN-US style=3D'mso-bidi-font-size:14.0pt'>Centre of Excellence for b=
iosensors,
instrumentation and process control (COBIK) </span></span></span><a
href=3D"http://www.cobik.si/index?lang=3Deng"><span style=3D'mso-bookmark:_=
Ref78865871'><span
style=3D'mso-bookmark:_Ref472079565'><span lang=3DEN-US style=3D'mso-bidi-f=
ont-size:
14.0pt'>http://www.cobik.si/index?lang=3Deng</span></span></span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'></span></span></a><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
lang=3DEN-US style=3D'mso-bidi-font-size:14.0pt'>.<o:p></o:p></span></span>=
</span></p>

<p class=3Dlit style=3D'tab-stops:49.6pt 217.35pt'><span style=3D'mso-bookm=
ark:_Ref78865871'><span
style=3D'mso-bookmark:_Ref472079565'><a name=3D"_Ref349458689"><span lang=
=3DEN-US>[<span
style=3D'mso-field-code:" SEQ \[ \\* ARABIC "'><span style=3D'mso-no-proof:=
yes'>13</span></span></span></a><span
lang=3DEN-US>]<span style=3D'mso-tab-count:2'>&nbsp;&nbsp;&nbsp;&nbsp; </sp=
an>Laboratory
for Advanced Materials Systems, COBIK: </span></span></span><a
href=3D"http://www.cobik.si/laboratoriji/laboratorij-za-sisteme-z-naprednim=
i-materiali?lang=3Deng"><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'><span
lang=3DEN-US>http://www.cobik.si/laboratoriji/laboratorij-za-sisteme-z-napr=
ednimi-materiali?lang=3Deng</span></span></span><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'></span></span></a><span
style=3D'mso-bookmark:_Ref78865871'><span style=3D'mso-bookmark:_Ref4720795=
65'></span></span></p>

<span style=3D'mso-bookmark:_Ref472079565'></span><span style=3D'mso-bookma=
rk:_Ref78865871'></span>

<p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&=
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  .05pt;mso-height-rule:exactly'><span lang=3DEN-US style=3D'font-size:6.0p=
t;
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  </td>
 </tr>
</table>

</div>

<p class=3DMsoHeader><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

</div>

<div style=3D'mso-element:header' id=3Dh1>

<p class=3DMsoHeader style=3D'tab-stops:right 404.0pt 432.0pt'><span lang=
=3DEN-US
style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span=
></p>

<p class=3DMsoHeader style=3D'tab-stops:right 404.0pt 432.0pt'><span lang=
=3DEN-US
style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span=
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<p class=3DMsoHeader align=3Dleft style=3D'margin-right:-.05pt;text-align:l=
eft;
tab-stops:right 474.9pt'><span lang=3DEN-US style=3D'mso-bidi-font-size:12.=
0pt'><span
style=3D'mso-field-code:" REF authors \\h &#1; \\* MERGEFORMAT "'>Igor
Gre&#353;ovnik<span lang=3DSL style=3D'mso-ansi-language:SL'> &amp; Tadej</=
span><span
lang=3DSL style=3D'font-size:14.0pt;mso-ansi-language:SL'> Kodelja</span><!=
--[if gte mso 9]><xml>
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740068006F00720073000000</w:data>
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h &#1; \\* MERGEFORMAT "'>NeurApp<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000A0000006D006100=
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<div style=3D'mso-element:para-border-div;border:none;border-bottom:solid w=
indowtext 2.25pt;
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<p class=3DMsoHeader style=3D'tab-stops:36.0pt center 216.0pt right 432.0pt;
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mso-padding-alt:0cm 0cm 1.0pt 0cm'><span lang=3DEN-US style=3D'font-size:3.=
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<p class=3DMsoHeader style=3D'tab-stops:36.0pt center 216.0pt right 432.0pt=
'><span
lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

</div>

<div style=3D'mso-element:footer' id=3Def1>

<div style=3D'mso-element:frame;mso-element-wrap:around;mso-element-anchor-=
vertical:
paragraph;mso-element-anchor-horizontal:margin;mso-element-left:center;
mso-element-top:.05pt;mso-height-rule:exactly'>

<table cellspacing=3D0 cellpadding=3D0 hspace=3D0 vspace=3D0 align=3Dcenter>
 <tr>
  <td valign=3Dtop align=3Dleft style=3D'padding-top:0cm;padding-right:0cm;
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  <p class=3DMsoFooter style=3D'mso-element:frame;mso-element-wrap:around;
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n;
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pan
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AGE  "'><span
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 </tr>
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<p class=3DMsoFooter style=3D'margin-right:18.0pt'><span lang=3DEN-US><o:p>=
&nbsp;</o:p></span></p>

</div>

<div style=3D'mso-element:footer' id=3Df1>

<p class=3DMsoFooter><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-f=
ont-size:
10.0pt'><o:p>&nbsp;</o:p></span></p>

<div style=3D'mso-element:para-border-div;border:none;border-top:solid wind=
owtext 1.5pt;
padding:1.0pt 0cm 0cm 0cm'>

<p class=3DMsoFooter style=3D'border:none;mso-border-top-alt:solid windowte=
xt 1.5pt;
padding:0cm;mso-padding-alt:1.0pt 0cm 0cm 0cm'><span lang=3DEN-US
style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span=
></p>

</div>

<p class=3DMsoFooter align=3Dcenter style=3D'text-align:center'><span
class=3DMsoPageNumber><span lang=3DEN-US><span style=3D'mso-field-code:" PA=
GE "'><span
style=3D'mso-no-proof:yes'>i</span></span></span></span></p>

<p class=3DMsoFooter><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-f=
ont-size:
10.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoFooter><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-f=
ont-size:
10.0pt'><o:p>&nbsp;</o:p></span></p>

</div>

<div style=3D'mso-element:header' id=3Dfh1>

<p class=3DMsoHeader style=3D'tab-stops:right 404.0pt 432.0pt'><span lang=
=3DEN-US
style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span=
></p>

<p class=3DMsoHeader style=3D'tab-stops:right 404.0pt 432.0pt'><span lang=
=3DEN-US
style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span=
></p>

<p class=3DMsoHeader align=3Dleft style=3D'margin-right:-.05pt;text-align:l=
eft;
tab-stops:right 411.1pt 432.0pt'><span lang=3DEN-US><span style=3D'mso-fiel=
d-code:
" REF maintitle \\h "'>NeurApp<!--[if gte mso 9]><xml>
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<div style=3D'mso-element:para-border-div;border:none;border-bottom:solid w=
indowtext 2.25pt;
padding:0cm 0cm 1.0pt 0cm'>

<p class=3DMsoHeader style=3D'tab-stops:36.0pt center 216.0pt right 432.0pt;
border:none;mso-border-bottom-alt:solid windowtext 2.25pt;padding:0cm;
mso-padding-alt:0cm 0cm 1.0pt 0cm'><span lang=3DEN-US style=3D'font-size:3.=
0pt;
mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span></p>

</div>

<p class=3DMsoHeader style=3D'tab-stops:36.0pt center 216.0pt right 432.0pt=
'><span
lang=3DEN-US style=3D'font-size:6.0pt;mso-bidi-font-size:10.0pt'><o:p>&nbsp=
;</o:p></span></p>

<p class=3DMsoHeader style=3D'tab-stops:36.0pt center 216.0pt right 432.0pt=
'><span
lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

</div>

<div style=3D'mso-element:footer' id=3Dff1>

<p class=3DMsoFooter><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-f=
ont-size:
10.0pt'><o:p>&nbsp;</o:p></span></p>

<div style=3D'mso-element:para-border-div;border:none;border-top:solid wind=
owtext 1.5pt;
padding:1.0pt 0cm 0cm 0cm'>

<p class=3DMsoFooter style=3D'border:none;mso-border-top-alt:solid windowte=
xt 1.5pt;
padding:0cm;mso-padding-alt:1.0pt 0cm 0cm 0cm'><span lang=3DEN-US
style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span=
></p>

</div>

<p class=3DMsoFooter align=3Dcenter style=3D'text-align:center'><span lang=
=3DEN-US><span
style=3D'mso-field-code:" PAGE  \\* MERGEFORMAT "'><span style=3D'mso-no-pr=
oof:
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<p class=3DMsoFooter><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-f=
ont-size:
10.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoFooter><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-f=
ont-size:
10.0pt'><o:p>&nbsp;</o:p></span></p>

</div>

<div style=3D'mso-element:footer' id=3Df2>

<p class=3DMsoFooter><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-f=
ont-size:
10.0pt'><o:p>&nbsp;</o:p></span></p>

<div style=3D'mso-element:para-border-div;border:none;border-top:solid wind=
owtext 1.5pt;
padding:1.0pt 0cm 0cm 0cm'>

<p class=3DMsoFooter style=3D'border:none;mso-border-top-alt:solid windowte=
xt 1.5pt;
padding:0cm;mso-padding-alt:1.0pt 0cm 0cm 0cm'><span lang=3DEN-US
style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span=
></p>

</div>

<p class=3DMsoFooter align=3Dcenter style=3D'text-align:center'><span
class=3DMsoPageNumber><span lang=3DEN-US><span style=3D'mso-field-code:" PA=
GE "'><span
style=3D'mso-no-proof:yes'>ii</span></span></span></span></p>

<p class=3DMsoFooter><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-f=
ont-size:
10.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoFooter><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-f=
ont-size:
10.0pt'><o:p>&nbsp;</o:p></span></p>

</div>

<div style=3D'mso-element:header' id=3Dh3>

<p class=3DMsoHeader style=3D'tab-stops:right 404.0pt 432.0pt'><span lang=
=3DEN-US
style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span=
></p>

<p class=3DMsoHeader align=3Dleft style=3D'margin-right:-.05pt;text-align:l=
eft;
tab-stops:right 474.9pt'><span lang=3DEN-US style=3D'mso-bidi-font-size:12.=
0pt'><span
style=3D'mso-field-code:" STYLEREF \0022Heading 1\0022\\n  \\* MERGEFORMAT =
"'><b><span
lang=3DSL style=3D'mso-ansi-language:SL;mso-no-proof:yes'>&#8206;4</span></=
b></span>.
<span style=3D'mso-field-code:" STYLEREF \0022Heading 1\0022 \\* MERGEFORMA=
T "'><b><span
lang=3DSL style=3D'mso-ansi-language:SL;mso-no-proof:yes'>About</span></b><=
span
lang=3DSL style=3D'mso-ansi-language:SL;mso-no-proof:yes'> </span><span
style=3D'mso-no-proof:yes'>the Software</span></span><span
style=3D'mso-spacerun:yes'>&nbsp; </span><span style=3D'mso-tab-count:1'>&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp; </span><span
style=3D'mso-field-code:" REF maintitle \\h &#1; \\* MERGEFORMAT "'>NeurApp=
<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000A0000006D006100=
69006E007400690074006C0065000000</w:data>
</xml><![endif]--></span><o:p></o:p></span></p>

<div style=3D'mso-element:para-border-div;border:none;border-bottom:solid w=
indowtext 2.25pt;
padding:0cm 0cm 1.0pt 0cm'>

<p class=3DMsoHeader style=3D'tab-stops:35.4pt center 216.0pt right 432.0pt;
border:none;mso-border-bottom-alt:solid windowtext 2.25pt;padding:0cm;
mso-padding-alt:0cm 0cm 1.0pt 0cm'><span lang=3DEN-US style=3D'font-size:3.=
0pt;
mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span></p>

</div>

<p class=3DMsoHeader style=3D'tab-stops:35.4pt center 216.0pt right 432.0pt=
'><span
lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

</div>

<div style=3D'mso-element:footer' id=3Df3>

<p class=3DMsoFooter><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-f=
ont-size:
10.0pt'><o:p>&nbsp;</o:p></span></p>

<div style=3D'mso-element:para-border-div;border:none;border-top:solid wind=
owtext 1.5pt;
padding:1.0pt 0cm 0cm 0cm'>

<p class=3DMsoFooter style=3D'border:none;mso-border-top-alt:solid windowte=
xt 1.5pt;
padding:0cm;mso-padding-alt:1.0pt 0cm 0cm 0cm'><span lang=3DEN-US
style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span=
></p>

</div>

<p class=3DMsoFooter align=3Dcenter style=3D'text-align:center'><span
class=3DMsoPageNumber><span lang=3DEN-US><span style=3D'mso-field-code:" PA=
GE "'><span
style=3D'mso-no-proof:yes'>22</span></span></span></span></p>

<p class=3DMsoFooter><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-f=
ont-size:
10.0pt'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoFooter><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-f=
ont-size:
10.0pt'><o:p>&nbsp;</o:p></span></p>

</div>

<div style=3D'mso-element:header' id=3Dh4>

<p class=3DMsoHeader style=3D'tab-stops:right 404.0pt 432.0pt'><span lang=
=3DEN-US
style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span=
></p>

<p class=3DMsoHeader align=3Dleft style=3D'margin-right:-.05pt;text-align:l=
eft;
tab-stops:right 474.9pt'><span lang=3DEN-US>References<span
style=3D'mso-spacerun:yes'>&nbsp; </span><span style=3D'mso-tab-count:1'>&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span=
><!--[if supportFields]><span
lang=3DEN-US><span style=3D'mso-element:field-begin'></span></span><span
lang=3DEN-US style=3D'font-size:10.0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;</span>REF maintitle \h </span><span lang=
=3DEN-US><span
style=3D'mso-element:field-separator'></span></span><![endif]--><span lang=
=3DEN-US>NeurApp<!--[if gte mso 9]><xml>
 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000A0000006D006100=
69006E007400690074006C0065000000</w:data>
</xml><![endif]--></span><!--[if supportFields]><span lang=3DEN-US><span
style=3D'mso-element:field-end'></span></span><![endif]--><span lang=3DEN-US
style=3D'font-size:10.0pt'><o:p></o:p></span></p>

<div style=3D'mso-element:para-border-div;border:none;border-bottom:solid w=
indowtext 2.25pt;
padding:0cm 0cm 1.0pt 0cm'>

<p class=3DMsoHeader style=3D'tab-stops:35.4pt center 216.0pt right 432.0pt;
border:none;mso-border-bottom-alt:solid windowtext 2.25pt;padding:0cm;
mso-padding-alt:0cm 0cm 1.0pt 0cm'><span lang=3DEN-US style=3D'font-size:3.=
0pt;
mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span></p>

</div>

<p class=3DMsoHeader style=3D'tab-stops:35.4pt center 216.0pt right 432.0pt=
'><span
lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

</div>

<div style=3D'mso-element:header' id=3Dh5>

<p class=3DMsoHeader style=3D'tab-stops:right 404.0pt 432.0pt'><span lang=
=3DEN-US
style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span=
></p>

<p class=3DMsoHeader style=3D'tab-stops:right 404.0pt 432.0pt'><span lang=
=3DEN-US
style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt;color:red'><o:p>&nbsp;</=
o:p></span></p>

<p class=3DMsoHeader align=3Dleft style=3D'margin-right:-.05pt;text-align:l=
eft;
tab-stops:right 474.9pt'><b style=3D'mso-bidi-font-weight:normal'><i
style=3D'mso-bidi-font-style:normal'><span lang=3DEN-US style=3D'font-size:=
14.0pt;
color:red'><span style=3D'mso-spacerun:yes'>&nbsp; </span>Sandbox<span
style=3D'mso-spacerun:yes'>&nbsp; </span></span></i></b><b style=3D'mso-bid=
i-font-weight:
normal'><i style=3D'mso-bidi-font-style:normal'><span lang=3DEN-US
style=3D'font-size:14.0pt;color:maroon'><span style=3D'mso-tab-count:1'>&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></i></b><i
style=3D'mso-bidi-font-style:normal'><span lang=3DEN-US style=3D'font-size:=
14.0pt;
color:maroon'><span style=3D'mso-spacerun:yes'>&nbsp;</span><o:p></o:p></sp=
an></i></p>

<div style=3D'mso-element:para-border-div;border:none;border-bottom:solid w=
indowtext 2.25pt;
padding:0cm 0cm 1.0pt 0cm'>

<p class=3DMsoHeader style=3D'tab-stops:36.0pt center 216.0pt right 432.0pt;
border:none;mso-border-bottom-alt:solid windowtext 2.25pt;padding:0cm;
mso-padding-alt:0cm 0cm 1.0pt 0cm'><span lang=3DEN-US style=3D'font-size:3.=
0pt;
mso-bidi-font-size:10.0pt'><o:p>&nbsp;</o:p></span></p>

</div>

<p class=3DMsoHeader style=3D'tab-stops:36.0pt center 216.0pt right 432.0pt=
'><span
lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

</div>

</body>

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////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
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</xml>
------=_NextPart_01CE649F.28501E40--
