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      /  Mathematical biology: Spot the difference
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 Mathematical biology: Spot the difference

Mathematical biology: Spot the difference

Jungle cats have true spots only when they are kittens. As they grow, the spots become rosettes ¡X broken rings in leopards (pictured) and polygons in jaguars. This changing pattern is the latest to be successfully described using Turing models.

Alan Turing suggested in 1952 that biological patterns could be generated by two chemicals diffusing between cells and interacting under the animal's coat. Sy-Sang Liaw of National Chung-Hsing University in Taichung, Taiwan, and his team adjusted parameters in Turing's reaction-diffusion equations to create spots. They then tweaked the parameters so that the patterns resembled the coats of middle-aged big cats. However, no one has found the chemicals, which Turing called morphogens, that might make this model work in mammals.



Source:Nature
http://www.nature.com/nature/journal/v442/n7103/full/442604a.html

http://www.nature.com/nature/journal/v442/n7103/pdf/442604a.pdf

¥x¤¤°ê¥ß¤¤¿³¤j¾Çª«²z¨tªº¹ù«äµ½±Ð±Â
http://www.nchu.edu.tw/New_nchu/know02.php?news_sn=3502

 2006-09-01 00:30
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 Re: Mathematical biology: Spot the difference

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µÛ¦WªºÒªL¤èµ{¦¡¡A¬O¥Ñª¾¦W¼Æ¾Ç®aÒªL (Alan Turing)¦b1952¦~´£¥X¡C¤¤¿³¤j¾Çª«²z¨t±Ð±Â¹ù«äµ½»¡¡A³o­Ó¼Æ¾Ç¤èµ{¦¡¥D­n¥Î¨Ó¸ÑÄÀ°Êª«´³¯¾¹Ï®×¬°¦ó§Î¦¨¡A·íªìÒªL¥u¬O´£¥X¤@­Ó·Qªk¡A¦ý¨S¯àÃÒ¹ê¡C

1970¦~¥N¡A¦³¤H§Q¥Î³o®M¤èµ{¦¡¡A§@¥X³½Ãþ©M´³°¨¨­¤Wªº¯¾¸ô¡A¦ý½ÆÂøªº¿ß¬ì°Êª«¡A¯S§O¬O¹Ï¯¾Ác½Æ¦hÅܪºªá°¡A¨ä´³¯¾ºt¤Æ¹Lµ{¹L¥h¬ì¾Ç¬É¤@ª½¨S¦³§@¥X¨Ó¡C

ÒªL·í¦~´£¥X³o­Ó¼Æ¾Ç¤èµ{¦¡®É¡A»{¬°¦³¨âºØ¥LºÙ¬°¡u¦¨§Î¯À¡v (morphogen)ªº¤Æ¾Çª«½è¡A·|¦b¤ò¥Öªí­±¤¬°Ê»s³y¥Xªá¼Ë¡C

°²³]¬Y¦¨§Î¯À·|Åý¤ò¾vÅܶ¡A¥t¤@­ÓÅý¤ò¾v«O«ù»a¥Õ¡F·í¶Â¦â¦¨§Î¯ÀÂX´²¤ñ»a¥Õ¦¨§Î¯À§Ö¡A´N§Î¦¨¬Y¨Ç¤ò¥Ö¤Wªº´³ÂI¡G¤@¶ô¶Â¦â¦¨§Î¯À¦V¥~ÂX´²¡A¦P®É±Ò°ÊÂX´²¸ûºCªº»a¥Õ¦¨§Î¯À¡A´N¥X²{¤@­Ó¶ÂÀô¡C

³o¨Ç¤Æ¾Çª«½è¦]¬°¬ï³z¤ò¥ÖªºÂX´²²v¤£¦P¡A¸g¥ÑÁc½Æ§@¥Î¡A´N§Î¦¨°Êª«¨­¤W¤£¦Pªº´³¯¾¹Ï®×¡CÒªL§â³o­Ó¤èµ{¦¡ºÙ¬°¡u¤ÏÀ³¢wÂX´²¤èµ{¦¡¡v¡C

¹ù«äµ½»¡¡Aªá°¨­¤Wªº´³¯¾¡A¦³°é¡B¦³´³ÂI¡BÁÙ¦³ª´ºÀ§Î¡A¹Ï®×«D±`Ác½Æ¦hÅÜ¡C¬ã¨s¹Î¶¤½Õ¾ã¤ÏÀ³¢wÂX´²¤è¦¡¦¡«Ü¦h°Ñ¼Æ«á¡A¦b¦¨¥§Q¥Î¹q¸£¡A¼ÒÀÀ¥X¥®°ªø¤j¬°¦¨°ªº´³¯¾¹Ï®×ÅܤơC

¡i2006/08/31 Áp¦X±ß³ø¡j¡i°OªÌÁ¿·½¬/¥x¥_³ø¾É¡j

Alan Turing:¤¤¤å²¤¶
http://home.kimo.com.tw/prometheus_chiu/home.htm

Alan Turing:­^¤å²¤¶
http://www.turing.org.uk/turing/

(§Q¥Î¼Æ¾Ç¨Ó¸Ñ¥Íª«¤WªººÃÂI,¥i¨£©Ò¦³¬ã¨s¬ì¾Ç©Î¤j¦ÛµM,¤´¥H¼Æ¾Ç¬°°ò¥»¤Jªù¬ì¥Ø,¤j®aÀ³¸Ó¦n¦n§â¼Æ¾Ç¾Ç¦n.)




 2006-09-01 00:36
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 Re: Mathematical biology: Spot the difference

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ªá°µºÄR¤S¦hÅܪº´³¯¾¬O«ç»ò§Î¦¨ªº¡H³o­Ó¬ì¾Ç¬Éªø¤[¨ÓÁÙ¨S§ä¨ìµª®×ªººÃ°Ý¡A¦b¤¤¿³¤j¾Çª«²z¨t±Ð±Â¹ù«äµ½¡B¤û¬z¤j¾Ç¼Æ¾Ç¨t±Ð±ÂPhilip Maini¡B¤¤¿³¤j¾Ç³Õ¤h¥Í¼B·ç°ó¦X§@¤U¡A²×©ó§ä¨ì¸Ñµª¡C¨Ã¦¨¬°¥@¬Éª¾¦Wªº´Á¥ZNature (¦ÛµM)ªº½u¤Wª©ÀY±ø·s»D¡C

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¸g¹L³o¶µµo²{¡A¹ù«äµ½»{¬°¡A¦ÛµM¬É³¦h¥Íª«¥]¬A¤HÃþ¡A¨ä¥~¦b§ÎºA©Î´³¯¾¤§©Ò¥H¯à°÷¥@¥N¬Û¶Ç¡A¥i¯à¬O¨Ó¦Û©ó¼Æ¾Ç©w«ß¡A¦Ó«D³æ¯Âªº°ò¦]¿ò¶Ç¡C

³o¶µ­«­nªºµo²{¡A¤£¦ý¦¨¬°°ê»Úª¾¦WªºNature Online News (Nature ªº½u¤Wª©)ÀY±ø·s»D¡A¬ü°ê¬¥§üÁF¤½¦@¹qµø¥xKCET-TV¤]©M¹ù«äµ½¬¢½Í¡A¦³·N»s§@¤@¤p®Éªº¸`¥Ø³ø¾É³o¶µ¬ã¨sµo²{¡C

¸Ó¬ã¨s¹Î¶¤´¿¦b°¸µM¶¡Åª¨ì¤@½g¥Íª«²Î­p¾Ç½×¤å¡A¸Ó½×¤å«ü¬ü¬w°ªº´³¯¾¡A¥®¦~´Á¬O²³æªº´³ÂIª¬¡A¦¨ªø«á¤~¸Hµõ¦¨Ác½Æªº¦hÃä§Î¡C³o½g½×¤åµ¹¹ù«äµ½¹Î¶¤´£¨ÑÆF·P¡A§âÒªL¤èµ{¦¡¤À¦¨¨â­Ó¶¥¬q³B²z¡A²Ä¤@¶¥¬q¥ý¼ÒÀÀ¥X¥®¦~¿ß¬ì´³ÂI¡AµM«á¦A½Õ¾ã°Ñ¼Æ¡A¦b²Ä¤G¶¥¬q¼ÒÀÀ¥X½ÆÂø¦hÅܪº¦¨°´³¯¾¡C

¹q¸£¼ÒÀÀ¦¨¥«á¡A¥L­Ì¤Sªá¤F¤@¦~ªº®É¶¡¡A§â¬ã¨sµ²ªGÂk¯Ç¥X¥¿½Tªº±Àºt¹Lµ{¡C³o¶µ½ÆÂøªº¬ì¾Ç¬ã¨s¡A¹ù«äµ½»´ÃPªº¯º»¡¡A¡u´N¬Oª±¥X¨Ó¡]¹q¸£¼ÒÀÀ¡^«á¡AÁÙ­n¦X²z¤Æµ²ªG¡A´£¥Xªá°´³¯¾¹Ï®×§Î¦¨¡Bºt¤Æªºª«²z©w«ß¡v¡C

¥L±j½Õ¡A¥Íª«¬É¦³«Ü¦h°Êª«ªº¹Ï®×¡A«D±`½ÆÂø¥B¨S¦³³W«ß©Ê¡C¹L¥hªº¬ã¨s»{¬°¥Íª«ªº¿ò¶Ç¥D­n¬O¨Ó¦Û°ò¦]¡A¦ý°ò¦]©w§Ç¥X¨Ó«á¡A³o¨Ç¥Íª«¬°¦ó¥@¥@¥N¥N³£¥X²{¬Û¦P¹Ï®×¡A¥L»{¬°À³¸Ó¬O½t©ó¬YºØ¤Æ¾Çª«½èªºÂX´²§@¥Î¡A¥Ñ©ó¤Æ¾Çª«½èÂX´²«á¿@«×¤£¦P¡A¤~¦b°Êª«¥~ªíÅã¥Ü¥X¤£¦P¹Ï®×¡C

¡i2006/08/31 Áp¦X±ß³ø¡j

 2006-09-01 00:38


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