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North Carolina State University *

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Oct 30, 2023

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'ownstrKeFGaSm rOisKe ± 89RlopKe ²³²²´±±²´µ±¶·¸ 2FGannOinMg¹s n 89trKeFGaSm %KeJd run º µ·»³» 'KeptNh ºOin¼ ·· $rKeFGa 56 =>X½sKeHIctOion µ ºuppKer¼ 'FGatuSm¾ ¶¶ ´¶»·³¶´´´´´ µ±¶³´»»¶¿·´ NhorOizontFGaRl ºLfroSm RlKeLft LfFGaHIcOinMg JdownstrKeFGaSm¼ vKertOiHIcFGaRl ºJdown¼ NhKeOiMgNht FGaGHbovKe JdKeptNh JdKeptNh GHbKeRlow JdKeRltFGa Jd JdKeRltFGa x <=WOiJdtNh +rFGaHIctOion JdKeRltFGa $ JdKeRltFGa 56 ºOin¼ ºOin¼ ² ±² ·¶ ½± ² ² µ· ² ² ² µ· ±· ·± ½µ ² ½¿ µ· ²³¿¿¿¿¿¿¿¿¿¸ ±»³´´´´´´´´ µ±³²À±À»¶·¿ ´» À´ ´À ¿ ¿ ½µ¸³À µ· µ ´·²³¶À ´·³±·»²¿·´¸ ·¸ ¶µ³À À³À ´¶³À ´¶³À ½´³À µ· µ ·¶·³¶À µ·³´·¿´²´´¸ À´ ¶± · ·² ·² ½· µ· µ ±²¸³À µ·³·±µ»»±²» »À ¶¶ ² ·· ·· ² µ· µ ±´¸ µ· ¶¿ ¶¶ ² ·· ·· ´ µ· µ ±µ» µ·³µÀ´¸±»±± ¸µ ¶À ´ ·µ ·µ ½²³À µ· µ ±²»³´À µ·³²²¸»µµ¿· µ²± ¶À³À µ³À ·µ³À ·µ³À µ»³À µ· µ ·²´³´À ´µ³²²À¸ÀµÀ± µµ¶ À¸ µ¿ µÀ µÀ µ² µÀ µ µÀ² µ¿³²´¶¶À»·¿ µ·´ ±¸ ´¿ À À À ² µ ² À $rKeFGa 56 =>X½sKeHIctOion ´ 'FGatuSm¾ ¿¿ µ¶¿À µ²»³¿Àµ¸²´± NhorOizontFGaRl ºLfroSm RlKe vKertOiHIcFGaRl ºJdown¼ NhKeOiMgNht FGaGHbovKe JdKeptNh JdKeptNh GHbKeRlow JdKeRltFGa Jd JdKeRltFGa x <=WOiJdtNh +rFGaHIctOion JdKeRltFGa $ JdKeRltFGa 56 ºOin¼ ºOin¼ µ² À¸ ´¸ ± ± ½¿ µ² µ ¿² µ´³¿²»´±¿±¶ ´² »¶ ´µ µ´ µ´ ½¿ µ² µ µ»² µ´³¿²»´±¿±¶ ·² ¶À µ· ´² ´² ½¿ µ² µ ´±² µ´³¿²»´±¿±¶ ±² ¿· À ´¿ ´¿ ½À µ² µ ·²À µµ³µ¿²··¸¿¸ À² ¿¿ ² ·· ·· µ µ² µ ·´À µ²³²±¸¿¶À»´ »² ¿¶ µ ·´ ·´ · µ² µ ·²À µ²³±±²·²»Àµ ¶² ¿± ± ´¸ ´¸ µ² µ² µ ´±² µ±³µ±´µ·À»´ ¿² ¶± µ± µ¸ µ¸ µ´ µ² µ µ·² µÀ³»´²±¸¸·À ¸² »´ ´» ² µ ²
$rKeFGa 56 =>X½sKeHIctOion · 'FGatuSm¾ ¶µ À»¸³······· »¶³¶²··À»·À NhorOizontFGaRl ºLfroSm RlKe vKertOiHIcFGaRl ºJdown¼ NhKeOiMgNht FGaGHbovKe JdKeptNh JdKeptNh GHbKeRlow JdKeRltFGa Jd JdKeRltFGa x <=WOiJdtNh +rFGaHIctOion JdKeRltFGa $ JdKeRltFGa 56 ºOin¼ ºOin¼ ² ·² À¿ ½´À ² ² µ´ ² ² ² µ´ ·± À± ½´µ ² ² µ´ ² ² ² ´± ±µ ±¶ ½µ± ² ² µ´ ² ² ² ·» ±± ±± ½µµ ² ² µ´ ² ² ² ±¿ À´ ·» ½· ² ½· µ´ ²³À ¸ »³¶²¿´²·¸·´ »² À¿ ·² · · ½µµ µ´ µ µ²´ µ»³´¶¿¿´²» ¶´ »¸ µ¸ µ± µ± ½´ µ´ µ µ¿² µ´³µ»ÀÀ´À²» ¿± ¶µ µ¶ µ» µ» ± µ´ µ µ»¿ µ´³»±¸µµ²»± ¸» »¶ ´µ µ´ µ´ µ´ µ µ²´ µ·³¿¸´±±·¸¸ µ²¿ »² ´¿ À À À µ´ ²³´¶¶¶¶¶¶¶¶¿ ¿³········· »³²²¸´À´µ´» µ´² ±´ ±» ½µ· ² ² µ´ ² ² ² µ·´ ·» À´ ½µ¸ ² ² ² ² ² ² $rKeFGa 56 =>X½sKeHIctOion ± 'FGatuSm¾ »¸³À ±·»³¶¶´±¶±µ À¶³¸¶¿¿¶¸¶» NhorOizontFGaRl ºLfroSm RlKe vKertOiHIcFGaRl ºJdown¼ NhKeOiMgNht FGaGHbovKe JdKeptNh JdKeptNh GHbKeRlow JdKeRltFGa Jd JdKeRltFGa x <=WOiJdtNh +rFGaHIctOion JdKeRltFGa $ JdKeRltFGa 56 ºOin¼ ºOin¼ ² ´· »À ½·´ ² ² µÀ ² ² ² µÀ ·À³À À´³À ½µ¸³À ² ² µÀ ² ² ² ·² ·¿³¶À ±¸³´À ½µ»³´À ² ½¸ µÀ ²³·À»±·À»±·» ´±³²À¸±²À¸± µ²³±»¿·²»µµ ±À »± ´± ¸ ¸ ½À³À µÀ µ µ¶»³´À µÀ³¸¶»À±À·µ »² »¸³À µ¿³À µ±³À µ±³À À³´À µÀ µ µ¶¿³µ´À µÀ³¿¸´´µÀ²¿ ¶À »±³´À ´·³¶À ¸³´À ¸³´À ¸³´À µÀ ²³¿±²¸²¸²¸²¸ À¿³··¿²»¿µ¿ µÀ³»±µ¿µ·´¶ ¸² À·³´À ·±³¶À ½µ³¶À ² ² µÀ ² ² ² µ²À ·¸³´À ±¿³¶À ½µÀ³¶À ² ² µÀ ² ² ² µ´² ·² À¿ ½´À ² ² ² ² ² ² $rKeFGa 56 =>X½sKeHIctOion À 'FGatuSm¾ »±³À ´À¶³´µ¶·¸µ· ±¸³µÀ²´¿²»» NhorOizontFGaRl ºLfroSm RlKe vKertOiHIcFGaRl ºJdown¼ NhKeOiMgNht FGaGHbovKe JdKeptNh JdKeptNh GHbKeRlow JdKeRltFGa Jd JdKeRltFGa x <=WOiJdtNh +rFGaHIctOion JdKeRltFGa $ JdKeRltFGa 56
ºOin¼ ºOin¼ ² µ¿³À »¸³À ½·»³À ² ² µ¶ ² ² ² µ¶ ´À »· ½·² ² ² µ¶ ² ² ² ·± ·» À´ ½µ¸ ² ² µ¶ ² ² ² Àµ ÀÀ ·· ² ² ½¸³À µ¶ µ ¿²³¶À µ¸³±¶±·±´²¸ »¿ »±³À ´·³À ¸³À ¸³À ´³À µ¶ µ µ±²³´À µ¶³µ¿´¿±²´¿ ¿À »´ ´» µ¶ ²³»²¿»¸À»À´´ ·»³´µ¶·¸µ· µ´³±¸·²¸¿´¿ µ²´ À²³À ·¶³À ½±³À ² ² µ¶ ² ² ² µµ¸ ·» À´ ½µ¸ ² ² µ¶ ² ² ² µ·» ´À »· ½·² ² ² ² ² ² ²
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=>X½sKeHIctOion µ =>X½sKeHIctOion ´ JdKeptNh ºOin¼ $rKeFGa ºOin^´¼ <=WKet 56KerOiSm ºOin¼ -yJdr rFGaJd ºOin¼ OinOitOiFGaRls JdKeptNh ºOin¼ $rKeFGa ºOin^´¼ <=WKet 56KerOiSm ºOin¼ -yJdr rFGaJd ºOin¼ OinOitOiFGaRls µ³À² ·µ³»¿¶À ´¸³À·ÀÀ±µ¿» µ³²¶ µ³À² µ´³»»»»»»»¶ µÀ³µ±±²´¿»¶ ²³¿± ·³²² µ²µ³»·»·»·» À±³±µ·¿À±´¸ µ³¿¶ ·³²² ±²³»»»»»»»¶ ´·³¶µ¿´¿·¿¸ µ³¶µ ±³À² µ¿¿³µ±À±À±À »±³´»»±²¶»· ´³¸· ±³À² ¿²³·¶À ·µ³´À¸À¸±¿µ ´³À¶ »³²² ´¿¶³À»²»²»µ ¶´³²¶´´±À¶µ ·³¸¸ »³²² µ´¶³»´À ·»³²¸¸¶·²´ ·³À± ¶³À² ·¸´³ÀµÀµÀµÀ ¶À³¶¿±»À··µ À³µ¿ ¶³À² µ¿²³²·µ´À ±²³»´´´´´µ· ±³±· ¸³²² À²²³¶±´±´±´ ¶¸³±¸¶²»²¸µ »³·² ¸³²² ´·¶³À ±À³µ±±¶µ±²¶ À³´» ¸³´À Àµ¸³²¸¿±¿±¿ ¿²³µµÀ¶¸ÀÀµ »³±¿ ¸³´À ´±¶³À¶²·µ´À ±À³¿¸¿±»´¶´ À³·¸ =>X½sKeHIctOion · =>X½sKeHIctOion ± JdKeptNh ºOin¼ $rKeFGa ºOin^´¼ <=WKet 56KerOiSm ºOin¼ -yJdr rFGaJd ºOin¼ JdKeptNh ºOin¼ JdKeptNh ºOin¼ $rKeFGa ºOin^´¼ <=WKet 56KerOiSm ºOin¼ -yJdr rFGaJd ºOin¼ OinOitOiFGaRls µ¿³²² ±³À ¸³´À ²³±¸ µ¸³À² ´³¶¸ À³¸· ²³±¶ µ¸³À² ´¶³Àµµ·»·»± ´²³¿µ µ³·´ ´µ³²² µ¶³±À µ±³¿· µ³µ¿ ´µ³²² »´³µ¿µ¿µ¿µ¿ ´¶³¶¶ ´³´± ´´³À² ±±³»¿ ´·³¶· µ³¿¿ ´´³À² µ²±³»µ²·¿¸» ·´³¸¶ ·³µ¶ ´±³²² ¿±³±´ ·´³´¸ ´³»µ ´±³²² µÀ·³·À²»±¸± ·¿³µ¶ ±³²´ ´À³À² µ·´³µ· ·»³À¶ ·³»µ ´À³À² ´²¿³±²´À¸¶± ±·³·» ±³¿µ ´¶³²² µ¿±³´À ±²³¿À ±³Àµ ´¶³²² ´»¸³¶»»´··¿ ±¿³À» À³À» ´¿³À² ´±²³¶¶ ±À³µ± À³·· =>X½sKeHIctOion À ºRlowKer¼ JdKeptNh ºOin¼ $rKeFGa ºOin^´¼ <=WKet 56KerOiSm ºOin¼ -yJdr rFGaJd ºOin¼ OinOitOiFGaRls ´±³²² µ³²¶·»¿±´µµ ±³±» ²³´± ´À³À² µ¶³µ¶¿¸±¶·¶ µ¶³¿À ²³¸» ´¶³²² ±¸³¸±¸»À»¶À ´»³µ± µ³¸µ ´¿³À² ¸²³¶·¶¸¿»´¶ ·µ³¿¸ ´³¿± ·²³²² µ·¿³¿¶¿¶µ¿À ·¶³»À ·³»¸ ·µ³À µ¸±³·¶µ¿À·À ±·³±² ±³±¿
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'ownstrKeFGaSm rOisKeºOin¼ ± 89RlopKe ²³²²´±±²´µ±¶· 2FGannOinMg¹s n 89trKeFGaSm %KeJd run ºLft¼ µ·»³» =>X½sKeHIctOion µ ºuppKer¼ =>X½sKeHIctOion ´ =>X½sKeHIctOion · =>X½sKeHIctOion ± =>X½sKeHIctOion À ºRlowKer¼ NhorOizontFGaRl ºLfroSm RlKeLft LfFGaHIcOinMg JdownstrKeFGaSm¼ vKertOiHIcFGaRl ºJdown¼ NhorOizontFGaRl ºLfroSm RlKeLft LfFGaHIcOinMg JdownstrKeFGaSm¼ vKertOiHIcFGaRl ºJdown¼ NhorOizontFGaRl ºLfroSm RlKeLft LfFGaHIcOinMg JdownstrKeFGaSm¼ vKertOiHIcFGaRl ºJdown¼ NhorOizontFGaRl ºLfroSm RlKeLft LfFGaHIcOinMg JdownstrKeFGaSm¼ vKertOiHIcFGaRl ºJdown¼ NhorOizontFGaRl ºLfroSm RlKeLft LfFGaHIcOinMg JdownstrKeFGaSm¼ vKertOiHIcFGaRl ºJdown¼ ºOin¼ ºOin¼ ºOin¼ ºOin¼ ºOin¼ ºOin¼ ºOin¼ ºOin¼ ºOin¼ ºOin¼ ² ±² µ² À¸ ² ·² ² ´· ² µ¿³À µ· ±· ´² »¶ µ´ ·± µÀ ·À³À µ¶ ´À ´» À´ ·² ¶À ´± ±µ ·² ·¿³¶À ·± ·» ·¸ ¶µ³À ±² ¿· ·» ±± ±À »± Àµ ÀÀ À´ ¶± À² ¿¿ ±¿ À´ »² »¸³À »¿ »±³À »À ¶¶ »² ¿¶ »² À¿ ¶À »±³´À ¿À »´ ¶¿ ¶¶ ¶² ¿± ¶´ »¸ ¸² À·³´À µ²´ À²³À ¸µ ¶À ¿² ¶± ¿± ¶µ µ²À ·¸³´À µµ¸ ·» µ²± ¶À³À ¸² »´ ¸» »¶ µ´² ·² µ·» ´À µµ¶ À¸ µ²¿ »² µ·´ ±¸ µ´² ±´ ±¸ µ·´ ·» ±¸ ±¸ ±¸ ±¸ ±¸ ±¸ 2$=>X vKert vFGaRluKes ¶¶ ¿¿ ¶µ »¸³À »±³À =>X½89KeHIctOion µ =>X½89KeHIctOion ´ =>X½89KeHIctOion · =>X½89KeHIctOion ± =>X½89KeHIctOion À NhorOizontFGaRl -KeOiMgNht FGaGHbov NhorOizontFGaRl -KeOiMgNht FGaGHbovKe Rlo NhorOizontFGaRl -KeOiMgNht FGaGHb NhorOizontFGaRl -KeOiMgNht FGa NhorOizontFGaRl -KeOiMgNht FGaGHbovKe RlowKest poOint ² ·¶ µ² ´¸ ² ±µ ² ±»³À ² ±» µ· ·± ´² ´µ µ´ ·¶ µÀ ·± µ¶ ·¸³À ´» ´À ·² µ· ´± ·² ·² ·²³¶À ·± ´¿³À ·¸ À³À ±² À ·» ´¶ ±À À³À Àµ ¸³À À´ · À² ² ±¿ µ¸ »² ² »¿ ² »À ² »² µ »² µ· ¶À À³´À ¿À ´³À ¶¿ ² ¶² ± ¶´ ´ ¸² µ»³´À µ²´ µ±
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¸µ ´ ¿² µ± ¿± ² µ²À ·²³´À µµ¸ ´¿³À µ²± µ³À ¸² ´» ¸» ± µ´² ·¸³À µ·» ·¸³À µµ¶ µ¿ ¿¿ µ²¿ µµ »¸³À »±³À µ·´ ´¿ ¿¿ µ´² ´¸ »¸³À »±³À ´¿ ¿¿ µ·´ ·À »¸³À »±³À ´¿ ¿¿ ¶µ »¸³À »±³À ´¿ ¿¿ ¶µ »¸³À »±³À ´¿ ¿¿ ¶µ »¸³À »±³À ´¿ ¿¿ ¶µ »¸³À »±³À ´¿ ¿¿ ¶µ »¸³À »±³À ´¿ ¿¿ ¶µ »¸³À »±³À 2FGax :;sFGaGHbRlKe -KeOiMgNht 2FGax :;sFGaGHbRlKe -KeOiMgNht 2FGax :;sFGaGHbRlKe -KeOiMgNht 2FGax :;sFGaGHbRlKe -KeOiMgNht 2FGax :;sFGaGHbRlKe -KeOiMgNht
'KeptNh µ¿Á ² ½·¿³À ½±¸ µ± ´µ »· ´¿ µ²¿³À ·À µ´´³À ±´ µ²¿³À
±¸ »· À» suSm ·¿À 'KeptNh ´Á ² ½ ¶ ½ µ± ½ ´µ ½ ´¿ ½·³À ·À ½ ±´ ½ ±¸ ½ À» ½ suSm ½·³À
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56KerOiSmKetKer µ¿Á µ²³»·²µ±À¿µ µ²³»·²µ±À¿µ µ²³»·²µ±À¿µ ¿³»²´·´À´»¶ ¶³²¶µ²»¶¿µ´ ¶³»µÀ¶¶·µ²» µ´³´²»ÀÀÀ»´ suSm »¶³·¿»µÀ¸´±
56KerOiSmOitKer ´Á ¿³»²´·´À´»¶

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