MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01CE649F.28501E40" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01CE649F.28501E40 Content-Location: file:///C:/518A1270/NeurApp.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Neurapp - Learning Approximation with Artificial Neural Networks</ti= tle> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"place"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"country-region"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"City"/> <!--[if gte mso 9]><xml> <o:DocumentProperties> <o:Subject>User manual for NeurApp, a software for learning artificial ne= ural network approximation, based on IGLib.</o:Subject> <o:Author>Igor Grešovnik, Tadej Kodelja</o:Author> <o:Keywords>Software, Freeware, Neural Networks, Approximation, Teaching<= /o:Keywords> <o:LastAuthor>Admin</o:LastAuthor> <o:Revision>3</o:Revision> <o:TotalTime>45664</o:TotalTime> <o:LastPrinted>2013-02-28T14:06:00Z</o:LastPrinted> <o:Created>2013-06-08T21:16:00Z</o:Created> <o:LastSaved>2013-06-08T21:23:00Z</o:LastSaved> <o:Pages>1</o:Pages> <o:Words>5730</o:Words> <o:Characters>32666</o:Characters> <o:Category>Software</o:Category> <o:Manager>Igor Grešovnik</o:Manager> <o:Lines>272</o:Lines> <o:Paragraphs>76</o:Paragraphs> <o:CharactersWithSpaces>38320</o:CharactersWithSpaces> <o:Version>11.9999</o:Version> </o:DocumentProperties> </xml><![endif]--><!--[if gte mso 9]><xml> <w:WordDocument> <w:Zoom>120</w:Zoom> <w:ActiveWritingStyle Lang=3D"EN-US" VendorID=3D"8" DLLVersion=3D"513" NL= Check=3D"0">1</w:ActiveWritingStyle> <w:ActiveWritingStyle Lang=3D"EN-GB" VendorID=3D"8" DLLVersion=3D"513" NL= Check=3D"0">1</w:ActiveWritingStyle> <w:ActiveWritingStyle Lang=3D"IT" VendorID=3D"3" DLLVersion=3D"517" NLChe= ck=3D"0">1</w:ActiveWritingStyle> <w:HyphenationZone>21</w:HyphenationZone> <w:DoNotHyphenateCaps/> <w:DrawingGridHorizontalSpacing>5.65 pt</w:DrawingGridHorizontalSpacing> <w:DrawingGridVerticalSpacing>5.65 pt</w:DrawingGridVerticalSpacing> <w:DisplayHorizontalDrawingGridEvery>0</w:DisplayHorizontalDrawingGridEve= ry> <w:DisplayVerticalDrawingGridEvery>0</w:DisplayVerticalDrawingGridEvery> <w:UseMarginsForDrawingGridOrigin/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:DrawingGridHorizontalOrigin>0 pt</w:DrawingGridHorizontalOrigin> <w:DrawingGridVerticalOrigin>0 pt</w:DrawingGridVerticalOrigin> <w:Compatibility> <w:FootnoteLayoutLikeWW8/> <w:ShapeLayoutLikeWW8/> <w:AlignTablesRowByRow/> <w:ForgetLastTabAlignment/> <w:LayoutRawTableWidth/> <w:LayoutTableRowsApart/> <w:UseWord97LineBreakingRules/> <w:SelectEntireFieldWithStartOrEnd/> <w:UseWord2002TableStyleRules/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState=3D"false" LatentStyleCount=3D"156"> </w:LatentStyles> </xml><![endif]--><!--[if !mso]><object classid=3D"clsid:38481807-CA0E-42D2-BF39-B33AF135CC4D" id=3Dieooui></objec= t> <style> st1\:*{behavior:url(#ieooui) } </style> <![endif]--> <style> <!-- /* Font Definitions */ @font-face {font-family:Tahoma; 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mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;} table.MsoTableGrid {mso-style-name:"Table Grid"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; border:solid windowtext 1.0pt; mso-border-alt:solid windowtext .5pt; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-border-insideh:.5pt solid windowtext; mso-border-insidev:.5pt solid windowtext; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; text-align:justify; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;} </style> <![endif]--><!--[if gte mso 9]><xml> <o:shapedefaults v:ext=3D"edit" spidmax=3D"5122"/> </xml><![endif]--><!--[if gte mso 9]><xml> <o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"1"/> </o:shapelayout></xml><![endif]--> </head> <body lang=3DSL link=3Dblue vlink=3Dpurple style=3D'tab-interval:36.0pt'> <div class=3DSection1> <p class=3Dequation style=3D'tab-stops:36.0pt center 212.65pt right 411.1pt= '><span lang=3DEN-US><o:p> </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> </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= ></a><a name=3D"_Hlt56855137"></a><a name=3D"_Hlt107204618"></a><span style=3D'mso-= bookmark: 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'> </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= 'mso-bidi-font-style: 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'>šovnik & Tadej Kodelja</span></span><span style=3D'font-size:1= 4.0pt; mso-ansi-language:SL'> <o:p></o:p></span></p> <p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><!--[if gte vml= 1]><v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" o:preferrelative= =3D"t" path=3D"m@4@5l@4@11@9@11@9@5xe" filled=3D"f" stroked=3D"f"> <v:stroke joinstyle=3D"miter"/> <v:formulas> <v:f eqn=3D"if lineDrawn pixelLineWidth 0"/> <v:f eqn=3D"sum @0 1 0"/> <v:f eqn=3D"sum 0 0 @1"/> <v:f eqn=3D"prod @2 1 2"/> <v:f eqn=3D"prod @3 21600 pixelWidth"/> <v:f eqn=3D"prod @3 21600 pixelHeight"/> <v:f eqn=3D"sum @0 0 1"/> <v:f eqn=3D"prod @6 1 2"/> <v:f eqn=3D"prod @7 21600 pixelWidth"/> <v:f eqn=3D"sum @8 21600 0"/> <v:f eqn=3D"prod @7 21600 pixelHeight"/> <v:f eqn=3D"sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok=3D"f" gradientshapeok=3D"t" o:connecttype=3D"rect"/> <o:lock v:ext=3D"edit" aspectratio=3D"t"/> </v:shapetype><v:shape id=3D"_x0000_s1032" type=3D"#_x0000_t75" alt=3D"Drag= onfly Server Logo." style=3D'position:absolute;margin-left:351.4pt;margin-top:172.1pt;width:95= .8pt; height:73.25pt;z-index:2'> <v:imagedata src=3D"NeurApp_files/image002.jpg" o:title=3D"dragonfly_serve= r_small"/> </v:shape><![endif]--><![if !vml]><span style=3D'mso-ignore:vglayout;positi= on: absolute;z-index:2;margin-left:468px;margin-top:229px;width:128px;height:98= px'><img width=3D128 height=3D98 src=3D"NeurApp_files/image003.jpg" alt=3D"Dragonfly Server Logo." v:shapes=3D"_x0000_s1= 032"></span><![endif]><span lang=3DEN-US style=3D'mso-bidi-font-size:12.0pt'><!--[if gte vml 1]><v:shap= e id=3D"_x0000_i1026" type=3D"#_x0000_t75" style=3D'width:235.5pt;height:223.5pt'> <v:imagedata src=3D"NeurApp_files/image004.jpg" o:title=3D"neurapp_title_s= mall"/> </v:shape><![endif]--><![if !vml]><img width=3D314 height=3D298 src=3D"NeurApp_files/image005.jpg" v:shapes=3D"_x0000_i1026"><![endif]><o:p= ></o:p></span></p> <p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><!--[if mso & != supportInlineShapes & supportFields]><i><span lang=3DEN-US style=3D'mso-bidi-font-size:12.0pt'><span style=3D'mso-element= :field-begin; mso-field-lock:yes'></span><span style=3D'mso-spacerun:yes'> </span>SH= APE <span style=3D'mso-spacerun:yes'> </span>\* MERGEFORMAT <span style=3D'mso-e= lement: field-separator'></span></span></i><![endif]--><i><span lang=3DEN-US style=3D'mso-bidi-font-size:12.0pt'><!--[if gte vml 1]><v:shapetype id=3D"_= x0000_t202" coordsize=3D"21600,21600" o:spt=3D"202" path=3D"m,l,21600r21600,l21600,xe"> <v:stroke joinstyle=3D"miter"/> <v:path gradientshapeok=3D"t" o:connecttype=3D"rect"/> </v:shapetype><v:shape id=3D"_x0000_s1049" type=3D"#_x0000_t202" style=3D'w= idth:486pt; height:106.15pt;mso-position-horizontal-relative:char; mso-position-vertical-relative:line' filled=3D"f" stroked=3D"f"> <v:textbox> <![if !mso]> <table cellpadding=3D0 cellspacing=3D0 width=3D"100%"> <tr> <td><![endif]> <div> <p class=3DMsoNormal align=3Dright style=3D'text-align:right'><span lan= g=3DEN-US><o:p> </o:p></span></p> <p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span lang= =3DEN-US style=3D'font-size:10.0pt'>This software is based on the Investigative Generic Library (IGLib). <o:p></o:p></span></p> <p class=3DMsoNormal><span lang=3DEN-US style=3D'font-size:10.0pt'>It w= as originally created as auxiliary tool for authors’ work at COBIK. <o:p></o:p>= </span></p> <p class=3DMsoNormal style=3D'tab-stops:right 467.8pt'><span style=3D'f= ont-size: 10.0pt;mso-ansi-language:SL;mso-fareast-language:SL;mso-bidi-language:H= E'><v:shape id=3D"_x0000_i1041" type=3D"#_x0000_t75" alt=3D"CO BIK" style=3D'width= :111pt; height:42pt'> <v:imagedata src=3D"NeurApp_files/image006.gif" o:href=3D"http://www.c= obik.si/assets/templates/cobik/images/logo-eng.gif"/> </v:shape></span><span lang=3DEN-US><span style=3D'mso-tab-count:1'>&nb= sp;            =             &nb= sp;            =             &nb= sp;            =             </span><= /span><span style=3D'font-size:10.0pt;mso-ansi-language:SL;mso-fareast-language:SL; mso-bidi-language:HE'><v:shape id=3D"_x0000_i1042" type=3D"#_x0000_t75" style=3D'width:133.5pt;height:42pt'> <v:imagedata src=3D"NeurApp_files/image007.gif" o:href=3D"http://www.c= obik.si/assets/templates/cobik/images/eu_skladeng.gif"/> </v:shape></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> <w:wrap type=3D"none"/> <w:anchorlock/> </v:shape><![endif]--><![if !vml]><img width=3D652 height=3D146 src=3D"NeurApp_files/image008.gif" alt=3D"Text Box: This software is based on the Investigative Generic Librar= y (IGLib). It was originally created as auxiliary tool for author= s’ work at COBIK. " v:shapes=3D"_x0000_s1049"><![endif]></span></i><!--[if mso & !supportInline= Shapes & supportFields]><i><span lang=3DEN-US style=3D'mso-bidi-font-size:12.0pt'><v:shape id=3D"_x0000_i102= 5" type=3D"#_x0000_t75" style=3D'width:486pt;height:106.15pt'> <v:imagedata croptop=3D"-65520f" cropbottom=3D"65520f"/> </v:shape><span style=3D'mso-element:field-end'></span></span></i><![endif]= --><i><span lang=3DEN-US style=3D'mso-bidi-font-size:12.0pt'><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 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=3DSection2><span style=3D'font-size:12.0pt;font-family:"Times Ne= w Roman"; mso-fareast-font-family:"Times New Roman";mso-ansi-language:SL;mso-fareast-= language: SL;mso-bidi-language:HE'><br clear=3Dall style=3D'mso-special-character:lin= e-break; 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'> </span>TOC \o "1-3" \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'>      </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'>      </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'>       </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'>       </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'>   = ;  </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'>   = ;  </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'>   = ;  </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'>   = ;  </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'>       </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'>   = ;  </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'>   = ;  </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'>   = ;  </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'>       </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'>      </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'>      </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> </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> </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> </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> </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"'>      =    </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"'>      =    </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"'>      </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 ”1D Approximation”= ; or on the “2D Approximation” tab, dependent on whether you want to approximate functions of one or two variables. Then, click on the “Generate Data” button, wait a moment until a graph of the model function with the generated training points is shown, and then click the “Start” 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 “Generate Data” 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 “Start” 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 ‘R’ key in order to position the objects in default way, and the ‘T’ 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"'>      </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 “<i>1D Approximation</i>” tab on the top of the application’s form activates the user interface for 1D approximations= . To see how it works, click first on the “<i>Generate data</i>” but= ton and then on the “<i>Start</i>” button, and that’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 “<i>Generate data</i>” button samples the function that you wan= t to approximate and is specified next to the “<i>f(x) =3D</i> ” 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 “<i>Start</i>” 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"'>    </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 “<i>f(x) =3D</i>” label, and this can be done in two ways. If the checkbox “<i>Function defined by user</i>” 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 R= 20;<i>Function defined by user</i>” checkbox. When the checkbox is checked, you can insert expressions defining an arbitrary function in a standard symbolic wa= y by using “<i>x</i>” 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 “<i>pow</i>”, e.g. the expression “pow(x,3/2)” 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 “<i>Function defined= by user</i>” 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= “<i>Limits</i>” 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 “Number of training samples”. If the “<i>Random training data</i>” 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 “Generate Data” 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"'>    </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 “<i>Start</i>” 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 “<= i>RMS</i>” 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 ”<i>Max. Epochs</i>” 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 “<i>Epochs in bundle</i>” 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 “<i>Neurons in hidden layers<= /i>” 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"'>    </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 “<i>Output Safety Factor</i>” 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'>  </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"'>    </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 “Generate Data= 221; and then the “Start” 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 “<i>Approximation error</i>” 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> </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> </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> </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> </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> </o:p></span></p> <p class=3DMsoNormal><span lang=3DEN-US><o:p> </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"'>      </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 “<i>2D Approximation= </i>” 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 “<i>Generate Data</i>”= and then the “<i>Start</i>” button. <u>Before clicking on the ̶= 0;<i>Start</i>” 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"'>    </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 "'>‎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 “<i>Limits</i>” 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 “<i>Random Training Data</i>” checkbox then values are sampled on a regular grid of points, where the text field beside “<i>Samples on X axis</i>” defines number of point= s on the grid in x direction, and “<i>Samples on Y axis</i>” defines number of points on the grid in the perpendicular (y) direction. If the “Random Training Data” 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"'>    </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 "'>‎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"'>    </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'>    </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 “Gener= ate data”, 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 “Start” 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"'>       </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'>·<span style=3D'font:7.0pt "Times New Roma= n"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>r</spa= n></b><span lang=3DEN-US> – <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'>·<span style=3D'font:7.0pt "Times New Roma= n"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>j</spa= n></b><span lang=3DEN-US> / <b>t</b> – 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'>·<span style=3D'font:7.0pt "Times New Roma= n"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>left m= ouse button</span></b><span lang=3DEN-US> – 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'>·<span style=3D'font:7.0pt "Times New Roma= n"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>Ctrl += left mouse button</span></b><span lang=3DEN-US> – 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'>·<span style=3D'font:7.0pt "Times New Roma= n"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>Shift = + left mouse button</span></b><span lang=3DEN-US> – 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'>·<span style=3D'font:7.0pt "Times New Roma= n"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>middle= mouse button</span></b><span lang=3DEN-US> – 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'>·<span style=3D'font:7.0pt "Times New Roma= n"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>right = mouse button</span></b><span lang=3DEN-US> – 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'>·<span style=3D'font:7.0pt "Times New Roma= n"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>mouse = wheel</span></b><span lang=3DEN-US> – 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'>·<span style=3D'font:7.0pt "Ti= mes New Roman"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>f</spa= n></b><span lang=3DEN-US> – <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 ” fly to” 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'>·<span style=3D'font:7.0pt "Times New Roma= n"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>c</spa= n></b><span lang=3DEN-US> / <b>a</b> – 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 (“actor” 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'>·<span style=3D'font:7.0pt "Times New Roma= n"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>p</spa= n></b><span lang=3DEN-US> – 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'>·<span style=3D'font:7.0pt "Times New Roma= n"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>s</spa= n></b><span lang=3DEN-US> / <b>w</b> – 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'>·<span style=3D'font:7.0pt "Times New Roma= n"'>         </span></span></span><![endif]><span dir=3DLTR><b><span lang=3DEN-US>e</spa= n></b><span lang=3DEN-US> / <b>q</b> – 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  \\* 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'>     =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =       </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"'>       </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 "'>‎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 “<i>Approximation error</i>” 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> </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> </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> </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> </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> </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"'>      </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"'>      =    </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  \\* 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 “Generate Data” and then the “Start” 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 “Start” 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> </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"'>      =    </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 Grešovnik 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. Božidar Šarler and Igor Grešovnik.</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’ 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 “garbage in, garbage out= 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’ 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 & 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'>šovnik, 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’ 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 & 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'>      </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'>Grešovnik, <st1:place w:st=3D"on">I.</st1:place>; Kodelja, T.; Vertnik, R.; Šarler, 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'>     = ; </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'>Grešovnik, <st1:place= w:st=3D"on">I.</st1:place>; Kodelja, T.; Vertnik, R.; Šarler, 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'>      </span>Grešovnik, <st1:place w:st=3D= "on">I.</st1:place>; Kodelja, T.; Vertnik, R.; Senčič. B.; Kovačič, M.; Šarler, 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'>      </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'>      </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'>Grešovnik, <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'>      </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'>Grešovnik,= </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'>      </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'>Grešovnik,= </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'>      </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'>Grešovnik,= </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'>      </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'>Grešovnik, <st1:place w:st=3D"on">I.</st1:place> (2012):= </span><span lang=3DEN-US>IOptLib – 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'>    </span>Grešovnik, <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'>    </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'>    </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'>     </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>&= 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> </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=3DSection5> <p class=3DMsoNormal style=3D'text-indent:36.0pt'><span lang=3DEN-US><o:p>&= nbsp;</o:p></span></p> </div> </body> </html> ------=_NextPart_01CE649F.28501E40 Content-Location: file:///C:/518A1270/NeurApp_files/image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGgAdAPQKAAAAAIAAAACAAICAAAAAgIAAgACAgICAgAQEBAQE/Ly8vKRULNzc3P8A/wD/ /////zQ0DJxk/JyczJycNMzMzGQENGScNDQENMDAwP8AAAD/AP//AAAA//8A/wD//////yH/C01T T0ZGSUNFOS4wGAAAAAxtc09QTVNPRkZJQ0U5LjAgJPn1cgAh/wtNU09GRklDRTkuMBgAAAAMY21Q 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margin;mso-element-left:center;mso-element-top:.05pt;mso-height-rule:exac= tly'><span lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nb= sp;</o:p></span></p> <p class=3DMsoHeader align=3Dleft style=3D'margin-right:-.05pt;text-align= :left; tab-stops:right 17.0cm;mso-element:frame;mso-element-wrap:around;mso-elem= ent-anchor-vertical: paragraph;mso-element-anchor-horizontal:margin;mso-element-left:center; mso-element-top:.05pt;mso-height-rule:exactly'><span lang=3DEN-US><span style=3D'mso-field-code:" STYLEREF \0022Heading 1\0022\\n \\* MERGEFORMA= T "'><span style=3D'mso-no-proof:yes'>‎1</span></span>. <span style=3D'mso-fie= ld-code: " STYLEREF \0022Heading 1\0022 \\* MERGEFORMAT "'><span style=3D'mso-no-p= roof: yes'>Introduction</span></span><span style=3D'mso-tab-count:1'> &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;       </span><span style=3D'mso-field-code:" STYLEREF \0022Heading 2\0022\\n \\* MERGEFORMA= T "'><span style=3D'mso-no-proof:yes'>‎2.1</span></span>. <span style=3D'mso-f= ield-code: " STYLEREF \0022Heading 2\0022 \\* MERGEFORMAT "'><span style=3D'mso-no-p= roof: yes'>Installation and Use</span></span></span></p> <div style=3D'mso-element:para-border-div;border:none;border-bottom:solid= windowtext 2.25pt; padding:0cm 0cm 1.0pt 0cm'> <p class=3DMsoHeader style=3D'tab-stops:36.0pt center 216.0pt right 432.0= pt; border:none;mso-border-bottom-alt:solid windowtext 2.25pt;padding:0cm; mso-padding-alt:0cm 0cm 1.0pt 0cm;mso-element:frame;mso-element-wrap:arou= nd; mso-element-anchor-vertical:paragraph;mso-element-anchor-horizontal:margi= n; mso-element-left:center;mso-element-top:.05pt;mso-height-rule:exactly'><s= pan lang=3DEN-US style=3D'font-size:3.0pt;mso-bidi-font-size:10.0pt'><o:p>&nb= sp;</o:p></span></p> </div> <p class=3DMsoHeader style=3D'tab-stops:36.0pt center 216.0pt right 432.0= pt; mso-element:frame;mso-element-wrap:around;mso-element-anchor-vertical:par= agraph; mso-element-anchor-horizontal:margin;mso-element-left:center;mso-element-= top: .05pt;mso-height-rule:exactly'><span lang=3DEN-US style=3D'font-size:6.0p= t; mso-bidi-font-size:10.0pt'><o:p> </o:p></span></p> </td> </tr> </table> </div> <p class=3DMsoHeader><span lang=3DEN-US><o:p> </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> </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> </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:" REF authors \\h  \\* MERGEFORMAT "'>Igor Grešovnik<span lang=3DSL style=3D'mso-ansi-language:SL'> & Tadej</= span><span lang=3DSL style=3D'font-size:14.0pt;mso-ansi-language:SL'> Kodelja</span><!= --[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000800000061007500= 740068006F00720073000000</w:data> </xml><![endif]--></span>: <span style=3D'mso-field-code:" REF maintitle \\= h  \\* 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: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> </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> </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; padding-bottom:0cm;padding-left:0cm'> <p class=3DMsoFooter style=3D'mso-element:frame;mso-element-wrap:around; mso-element-anchor-vertical:paragraph;mso-element-anchor-horizontal:margi= n; mso-element-left:center;mso-element-top:.05pt;mso-height-rule:exactly'><s= pan class=3DMsoPageNumber><span lang=3DEN-US><span style=3D'mso-field-code:"P= AGE "'><span style=3D'mso-no-proof:yes'>2</span></span><o:p></o:p></span></span></p> </td> </tr> </table> </div> <p class=3DMsoFooter style=3D'margin-right:18.0pt'><span lang=3DEN-US><o:p>=  </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> </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> </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> </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> </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> </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> </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> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000A0000006D006100= 69006E007400690074006C0065000000</w:data> </xml><![endif]--></span></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: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> </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> = ;</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> </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> </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> </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: yes'>1</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> </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> </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> </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> </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> </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> </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> </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'>‎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'>  </span><span style=3D'mso-tab-count:1'>&n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;    </span><span style=3D'mso-field-code:" REF maintitle \\h  \\* 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> </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> </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> </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> </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> </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> </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> </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'>  </span><span style=3D'mso-tab-count:1'>&n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;           </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'> </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> </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> </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> </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> </= 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'>  </span>Sandbox<span style=3D'mso-spacerun:yes'>  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