<html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:Wingdings;
panose-1:5 2 1 2 1 8 4 8 7 8;}
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
{mso-style-priority:34;
margin-top:0in;
margin-right:0in;
margin-bottom:0in;
margin-left:.5in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
p.m5981172119576558766msolistparagraph, li.m5981172119576558766msolistparagraph, div.m5981172119576558766msolistparagraph
{mso-style-name:m_5981172119576558766msolistparagraph;
mso-margin-top-alt:auto;
margin-right:0in;
mso-margin-bottom-alt:auto;
margin-left:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
span.EmailStyle21
{mso-style-type:personal-reply;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;
mso-ligatures:none;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
/* List Definitions */
@list l0
{mso-list-id:793476404;
mso-list-template-ids:686195748;}
@list l0:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l0:level2
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:1.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:"Courier New";
mso-bidi-font-family:"Times New Roman";}
@list l0:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l0:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l0:level5
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l0:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l0:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l0:level8
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l0:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l1
{mso-list-id:817456017;
mso-list-template-ids:-171783488;}
@list l1:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l1:level2
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l1:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l1:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l1:level5
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l1:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l1:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l1:level8
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l1:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l2
{mso-list-id:966087148;
mso-list-template-ids:467806290;}
@list l2:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l2:level2
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:1.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:"Courier New";
mso-bidi-font-family:"Times New Roman";}
@list l2:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l2:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l2:level5
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l2:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l2:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l2:level8
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l2:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l3
{mso-list-id:973146131;
mso-list-template-ids:-645113488;}
@list l3:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l3:level2
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:1.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:"Courier New";
mso-bidi-font-family:"Times New Roman";}
@list l3:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l3:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l3:level5
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l3:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l3:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l3:level8
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l3:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l4
{mso-list-id:1117338844;
mso-list-template-ids:628917952;}
@list l4:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l4:level2
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l4:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l4:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l4:level5
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l4:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l4:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l4:level8
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l4:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l5
{mso-list-id:1191332502;
mso-list-template-ids:970641158;}
@list l5:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l5:level2
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:1.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:"Courier New";
mso-bidi-font-family:"Times New Roman";}
@list l5:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l5:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l5:level5
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l5:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l5:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l5:level8
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l5:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l6
{mso-list-id:1192106462;
mso-list-template-ids:244473908;}
@list l6:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l6:level2
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:1.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:"Courier New";
mso-bidi-font-family:"Times New Roman";}
@list l6:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l6:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l6:level5
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l6:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l6:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l6:level8
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l6:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l7
{mso-list-id:1309237846;
mso-list-template-ids:-1323801858;}
@list l7:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l7:level2
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l7:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l7:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l7:level5
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l7:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l7:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l7:level8
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l7:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l8
{mso-list-id:1435056771;
mso-list-template-ids:-322118278;}
@list l8:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l8:level2
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l8:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l8:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l8:level5
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l8:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l8:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l8:level8
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l8:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l9
{mso-list-id:1528522763;
mso-list-template-ids:1857561110;}
@list l9:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l9:level2
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:1.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:"Courier New";
mso-bidi-font-family:"Times New Roman";}
@list l9:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l9:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l9:level5
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l9:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l9:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l9:level8
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l9:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l10
{mso-list-id:1643542353;
mso-list-type:hybrid;
mso-list-template-ids:-495026210 67698689 67698691 67698693 67698689 67698691 67698693 67698689 67698691 67698693;}
@list l10:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;
font-family:Symbol;}
@list l10:level2
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;
font-family:"Courier New";}
@list l10:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;
font-family:Wingdings;}
@list l10:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;
font-family:Symbol;}
@list l10:level5
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;
font-family:"Courier New";}
@list l10:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;
font-family:Wingdings;}
@list l10:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;
font-family:Symbol;}
@list l10:level8
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;
font-family:"Courier New";}
@list l10:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;
font-family:Wingdings;}
@list l11
{mso-list-id:1728145160;
mso-list-template-ids:-528852892;}
@list l11:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l11:level2
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l11:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l11:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l11:level5
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l11:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l11:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l11:level8
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l11:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l12
{mso-list-id:1981377207;
mso-list-template-ids:-1616106532;}
@list l12:level1
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l12:level2
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l12:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:1.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l12:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l12:level5
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:2.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l12:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l12:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:3.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l12:level8
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.0in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
@list l12:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:4.5in;
mso-level-number-position:left;
text-indent:-.25in;
mso-ansi-font-size:10.0pt;
font-family:Symbol;}
ol
{margin-bottom:0in;}
ul
{margin-bottom:0in;}
--></style>
</head>
<body lang="EN-US" link="blue" vlink="purple" style="word-wrap:break-word">
<div class="WordSection1">
<p class="MsoNormal">Hi Paul,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<ul style="margin-top:0in" type="disc">
<li class="MsoListParagraph" style="margin-left:0in;mso-list:l10 level1 lfo13">I find section 4.4.2.5 of v4.0 of the FITS standard, including table 11 to be pretty clear. For most computer languages, I don’t know about Julia, equation 3 would imply scaling
before adding BZERO, but the rest of that section covers the special case for integer pixel types in which case BSCALE = 1.0 (the default) and BZERO is one of 32768 or the three less frequent values of -128 or 2^31 or 2^63. (Footnote 9 suggests alternate handling
for these cases that avoids your issue entirely.) Other than those values, there is nothing special about expressing BZERO as an integer, and one should interpret it as a floating-point number.
<o:p></o:p></li></ul>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal" style="margin-left:.5in">Others are encouraged to correct or extend my remarks.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<ul style="margin-top:0in" type="disc">
<li class="MsoListParagraph" style="margin-left:0in;mso-list:l10 level1 lfo13">FITS is certainly not mandated by NASA’s Planetary Data System. We have submitted many tile-compressed FITS files but could have archived other image formats. Some of our tables
are FITS binary tables, but more are other formats. That said, pressure from a funding agency is not exactly peer pressure. And I am unaware of any funding agencies mandating 2880-byte ASCII header records.<o:p></o:p></li></ul>
<p class="MsoNormal"><o:p> </o:p></p>
<ul style="margin-top:0in" type="disc">
<li class="MsoListParagraph" style="margin-left:0in;mso-list:l10 level1 lfo13">As I think you imply, Julia’s competitor is Python, not C/C++ or FORTRAN. If Julia or Numba/NumPy can directly handle Rice compressed tiles as a native numerical format, I may switch
myself, especially if it can be deployed as functions called from PostgreSQL or MariaDB queries.<o:p></o:p></li></ul>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Rob<o:p></o:p></p>
<div style="mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;padding:0in 0in 1.0pt 0in">
<p class="MsoNormal" style="border:none;padding:0in"><o:p> </o:p></p>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<div id="mail-editor-reference-message-container">
<div>
<div>
<p class="MsoNormal" style="margin-left:.5in">On 3/12/24, 7:58 AM, "Barrett, Paul" wrote:<o:p></o:p></p>
</div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
<div>
<div>
<p class="MsoNormal" style="margin-left:.5in">I'll ask this question one more time and then I'll let it go.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">I understand that the default behaviour for BZERO and BSCALE creates a floating point array because of the typical upconversion rules. However, I'm not clear about the data type for the special case where BZERO
is an integer. In this case, it appears that BZERO is added first to the integer array before converting it to a floating point array, because BSCALE = 1.0 implies upconversion. Is this correct?<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">As for your comments:<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">* I disagree with your first comment. FITS is used because of peer pressure. It is mandated by NASA. That means a large sector of the community HAS to use it.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">* Yes, dynamic languages are dynamic enough. In the case of Julia, it can do everything that C/C++, FORTRAN, and Python can do.
<i>Think of Julia as Python with Numba built-in.</i><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"> -- Paul<o:p></o:p></p>
</div>
</div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
<div>
<div>
<p class="MsoNormal" style="margin-left:.5in">On Tue, Mar 12, 2024 at 9:39 AM Seaman, Robert Lewis - (rseaman) via fitsbits <<a href="mailto:fitsbits@listmgr.nrao.edu">fitsbits@listmgr.nrao.edu</a>> wrote:<o:p></o:p></p>
</div>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in">
<div>
<div>
<div>
<div id="m_5981172119576558766mail-editor-reference-message-container">
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in">
Howdy,<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in">
<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in">
It is always good to see a spirited FITS discussion! A few more peppy points:<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in">
<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.0in;text-indent:-.25in;mso-list:l4 level1 lfo1">
<![if !supportLists]><span style="font-size:10.0pt;font-family:Symbol"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>There is always an assertion that it would be preferable to use a “modern” format<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.5in;text-indent:-.25in;mso-list:l2 level2 lfo2">
<![if !supportLists]><span style="font-size:10.0pt;font-family:"Courier New""><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>Yet projects often end up using FITS<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.5in;text-indent:-.25in;mso-list:l2 level2 lfo2">
<![if !supportLists]><span style="font-size:10.0pt;font-family:"Courier New""><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>This choice does not result from peer pressure<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in">
<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.0in;text-indent:-.25in;mso-list:l11 level1 lfo3">
<![if !supportLists]><span style="font-size:10.0pt;font-family:Symbol"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>There is nothing magic about IEEE floating point or twos-complement integers<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.5in;text-indent:-.25in;mso-list:l3 level2 lfo4">
<![if !supportLists]><span style="font-size:10.0pt;font-family:"Courier New""><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>Efficient (compressed) data representations may not even be binary (Rice is unary)<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.5in;text-indent:-.25in;mso-list:l3 level2 lfo4">
<![if !supportLists]><span style="font-size:10.0pt;font-family:"Courier New""><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>Are dynamically typed languages dynamic enough?<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in">
<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.0in;text-indent:-.25in;mso-list:l7 level1 lfo5">
<![if !supportLists]><span style="font-size:10.0pt;font-family:Symbol"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>A tile-compressed image is a simple binary table<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.5in;text-indent:-.25in;mso-list:l6 level2 lfo6">
<![if !supportLists]><span style="font-size:10.0pt;font-family:"Courier New""><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>My first encounter with FITS data (c. 1983) was writing a FITS image reader from scratch by consulting the original journal article(s) (possibly also my first encounter with C)<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.5in;text-indent:-.25in;mso-list:l6 level2 lfo6">
<![if !supportLists]><span style="font-size:10.0pt;font-family:"Courier New""><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>I am confident young Rob could have written a reader for tile-compressed binary data with little more effort (or code) just from reading the current FITS standard<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in">
<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.0in;text-indent:-.25in;mso-list:l1 level1 lfo7">
<![if !supportLists]><span style="font-size:10.0pt;font-family:Symbol"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>FITS documentation is pretty good<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.5in;text-indent:-.25in;mso-list:l9 level2 lfo8">
<![if !supportLists]><span style="font-size:10.0pt;font-family:"Courier New""><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>(Comments about other projects’ documentation omitted)<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in">
<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.0in;text-indent:-.25in;mso-list:l12 level1 lfo9">
<![if !supportLists]><span style="font-size:10.0pt;font-family:Symbol"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>Most FITS discussions/disagreements are about metadata<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.5in;text-indent:-.25in;mso-list:l5 level2 lfo10">
<![if !supportLists]><span style="font-size:10.0pt;font-family:"Courier New""><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>Only a small minority of FITS metadata is strictly required to enforce the structure of each extension<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.5in;text-indent:-.25in;mso-list:l5 level2 lfo10">
<![if !supportLists]><span style="font-size:10.0pt;font-family:"Courier New""><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>Science metadata (astronomical and computer science) would be legal (and trivial) to represent, using any schema you like, in a binary table structure, described in a convention or appendix or chapter of the standard<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.5in;text-indent:-.25in;mso-list:l5 level2 lfo10">
<![if !supportLists]><span style="font-size:10.0pt;font-family:"Courier New""><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>Schemata could also include language-specific pragma, for data-typing purposes or otherwise<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in">
<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.0in;text-indent:-.25in;mso-list:l8 level1 lfo11">
<![if !supportLists]><span style="font-size:10.0pt;font-family:Symbol"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>It is perhaps peer pressure that pushes projects to use 80-char ASCII header keywords in 2880-byte records<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.5in;text-indent:-.25in;mso-list:l0 level2 lfo12">
<![if !supportLists]><span style="font-size:10.0pt;font-family:"Courier New""><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>Consider, rather, what is the optimal tiled representation for your project, and separately<o:p></o:p></p>
<p class="m5981172119576558766msolistparagraph" style="margin-left:1.5in;text-indent:-.25in;mso-list:l0 level2 lfo12">
<![if !supportLists]><span style="font-size:10.0pt;font-family:"Courier New""><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]>How can your project’s (and community) metadata best be represented in a schema realized as a binary table?<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in">
<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in">
Rob<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in">
<o:p></o:p></p>
</div>
</div>
</div>
</div>
</div>
<p class="MsoNormal" style="margin-left:.5in">_______________________________________________<br>
fitsbits mailing list<br>
<a href="mailto:fitsbits@listmgr.nrao.edu" target="_blank">fitsbits@listmgr.nrao.edu</a><br>
<a href="https://listmgr.nrao.edu/mailman/listinfo/fitsbits" target="_blank">https://listmgr.nrao.edu/mailman/listinfo/fitsbits</a><o:p></o:p></p>
</div>
</blockquote>
</div>
</div>
</div>
</div>
</body>
</html>